Index: trunk/synchronize.sh =================================================================== --- trunk/synchronize.sh (revision 8277) +++ trunk/synchronize.sh (revision 8278) @@ -1,61 +1,61 @@ #!/bin/sh ### Consider it safer to explicitly mention all files that contain ### email addresses or copyright tags. OLD_YEAR="Copyright (C) 1999-2018"; NEW_YEAR="Copyright (C) 1999-2019"; OLD_YEAR2="Copyright (C) 2001-2018"; NEW_YEAR2="Copyright (C) 2001-2019"; OLD_YEAR3="Copyright (C) 2019-"; NEW_YEAR3="Copyright (C) 2019-2019"; # OLD_ADDRESS="Soyoung Shim " # NEW_ADDRESS="So Young Shim " OLD_ADDRESS="Soyoung Shim" NEW_ADDRESS="So Young Shim" OLD_DATE="May 31 2019" NEW_DATE="Aug 07 2019" OLD_VERSION="2.7.1" NEW_VERSION="2.8.0" #OLD_STATUS="PACKAGE_STATUS=\"alpha\"" #NEW_STATUS="PACKAGE_STATUS=\"beta\"" OLD_STATUS="PACKAGE_STATUS=\"alpha\"" #NEW_STATUS="PACKAGE_STATUS=\"rc1\"" NEW_STATUS="PACKAGE_STATUS=\"release\"" ## We should add an option to add an author here. ## share/doc/manual.tex should be changed manually ## We have to discuss the entries in gamelan/manual ## We have to discuss the entries in src/shower MAIN_FILES="AUTHORS BUGS Makefile.am.in README build_master.sh tests/Makefile.am tests/models/Makefile.am tests/models/UFO/Makefile.am tests/models/UFO/SM/Makefile.am tests/functional_tests/Makefile.am tests/ext_tests_mssm/Makefile.am tests/ext_tests_nmssm/Makefile.am tests/ext_tests_ilc/Makefile.am tests/ext_tests_nlo/Makefile.am tests/ext_tests_shower/Makefile.am tests/unit_tests/Makefile.am" CONFIGURE_FILES="configure.ac.in src/noweb-frame/whizard-prelude.nw" VERSION_FILES="NEWS circe2/src/circe2.nw" SCRIPTS_FILES="scripts/Makefile.am scripts/whizard-config.in scripts/whizard-setup.csh.in scripts/whizard-setup.sh.in" SHARE_FILES="share/Makefile.am share/doc/Makefile.am share/doc/custom.hva share/examples/NLO_eettbar_GoSam.sin share/examples/NLO_eettbar_OpenLoops.sin share/examples/HERA_DIS.sin share/examples/LEP_cc10.sin share/examples/LEP_higgs.sin share/examples/W-endpoint.sin share/examples/Z-lineshape.sin share/examples/Zprime.sin share/examples/casc_dec.sin share/examples/circe1.sin share/examples/eeww_polarized.sin share/examples/DrellYanMatchingP.sin share/examples/DrellYanMatchingW.sin share/examples/DrellYanNoMatchingP.sin share/examples/DrellYanNoMatchingW.sin share/examples/EEMatching2P.sin share/examples/EEMatching2W.sin share/examples/EEMatching3P.sin share/examples/EEMatching3W.sin share/examples/EEMatching4P.sin share/examples/EEMatching4W.sin share/examples/EEMatching5P.sin share/examples/EEMatching5W.sin share/examples/EENoMatchingP.sin share/examples/EENoMatchingW.sin share/examples/LHC_VBS_likesign.sin share/tests/Makefile.am share/interfaces/Makefile.am" SRC_FILES="src/Makefile.am src/feynmf/Makefile.am src/hepmc/Makefile.am src/hepmc/HepMCWrap_dummy.f90 src/lcio/Makefile.am src/lcio/LCIOWrap_dummy.f90 src/tauola/Makefile.am src/lhapdf/Makefile.am src/lhapdf/lhapdf.f90 src/lhapdf5/Makefile.am src/pdf_builtin/Makefile.am src/pdf_builtin/pdf_builtin.f90 src/qed_pdf/Makefile.am src/qed_pdf/qed_pdf.nw src/fastjet/Makefile.am src/fastjet/cpp_strings.f90 src/fastjet/fastjet.f90 src/fastjet/Makefile.am src/hoppet/Makefile.am src/hoppet/hoppet.f90 pythia6/Makefile.am tauola/Makefile.am mcfio/Makefile.am stdhep/Makefile.am src/noweb-frame/Makefile.am src/noweb-frame/whizard-prelude.nw src/noweb-frame/whizard-postlude.nw src/utilities/Makefile.am src/matrix_elements/Makefile.am src/matrix_elements/matrix_elements.nw src/mci/Makefile.am src/vegas/Makefile.am src/vegas/vegas.nw src/mci/mci.nw src/utilities/utilities.nw src/testing/Makefile.am src/testing/testing.nw src/system/Makefile.am src/system/system.nw src/system/system_dependencies.f90.in src/combinatorics/Makefile.am src/combinatorics/combinatorics.nw src/parsing/Makefile.am src/parsing/parsing.nw src/particles/Makefile.am src/particles/particles.nw src/phase_space/Makefile.am src/phase_space/phase_space.nw src/physics/Makefile.am src/physics/physics.nw src/beams/Makefile.am src/beams/beams.nw src/qft/Makefile.am src/qft/qft.nw src/rng/Makefile.am src/rng/rng.nw src/types/Makefile.am src/types/types.nw src/whizard-core/Makefile.am src/whizard-core/whizard.nw src/pythia8/Makefile.am src/shower/Makefile.am src/shower/shower.nw src/muli/Makefile.am src/muli/muli.nw src/user/user.nw src/user/Makefile.am src/model_features/model_features.nw src/model_features/Makefile.am src/me_methods/Makefile.am src/me_methods/me_methods.nw src/gosam/Makefile.am src/gosam/gosam.nw src/fks/Makefile.am src/fks/fks.nw src/expr_base/Makefile.am src/expr_base/expr_base.nw src/events/Makefile.am src/events/events.nw src/blha/Makefile.am src/blha/blha.nw src/variables/Makefile.am src/variables/variables.nw src/xdr/Makefile.am src/xdr/xdr_wo_stdhep.f90 src/looptools/Makefile.am src/process_integration/Makefile.am src/process_integration/process_integration.nw src/matching/Makefile.am src/matching/matching.nw src/openloops/Makefile.am src/openloops/openloops.nw src/recola/Makefile.am src/recola/recola.nw src/transforms/Makefile.am src/transforms/transforms.nw src/threshold/Makefile.am src/threshold/threshold.nw" CIRCE1_FILES="circe1/Makefile.am circe1/share/Makefile.am circe1/share/doc/Makefile.am circe1/src/Makefile.am circe1/src/circe1.nw circe1/minuit/Makefile.am circe1/src/minuit.nw circe1/tools/Makefile.am" CIRCE2_FILES="circe2/Makefile.am circe2/share/Makefile.am circe2/share/doc/Makefile.am circe2/src/Makefile.am circe2/src/Makefile.ocaml circe2/src/circe2.nw circe2/src/Makefile.sources circe2/src/postlude.nw circe2/tests/Makefile.am circe2/src/circe2_tool.ml circe2/src/commands.ml circe2/src/commands.mli circe2/src/diffmap.ml circe2/src/diffmap.mli circe2/src/diffmaps.ml circe2/src/diffmaps.mli circe2/src/division.ml circe2/src/division.mli circe2/src/events.ml circe2/src/events.mli circe2/src/filter.ml circe2/src/filter.mli circe2/src/float.ml circe2/src/float.mli circe2/src/grid.ml circe2/src/grid.mli circe2/src/histogram.mli circe2/src/histogram.ml circe2/src/syntax.ml circe2/src/syntax.mli circe2/src/thoArray.ml circe2/src/thoArray.mli circe2/src/thoMatrix.ml circe2/src/thoMatrix.mli" SRC_GAMELAN_FILES="src/gamelan/Makefile.am src/gamelan/whizard-gml.in" SRC_BASICS_FILES="src/basics/constants.f90 src/basics/iso_fortran_env_stub.f90 src/basics/io_units.f90 src/basics/Makefile.am" SRC_MODELS_FILES="src/models/threeshl_bundle/Makefile.am src/models/threeshl_bundle/threeshl_bundle.f90 src/models/threeshl_bundle/threeshl_bundle_lt.f90 src/models/external.Test.f90 src/models/external.Threeshl.f90 src/models/Makefile.am src/models/parameters.THDM.f90 src/models/parameters.GravTest.f90 src/models/parameters.Littlest.f90 src/models/parameters.Littlest_Eta.f90 src/models/parameters.Littlest_Tpar.f90 src/models/parameters.MSSM.f90 src/models/parameters.MSSM_4.f90 src/models/parameters.MSSM_CKM.f90 src/models/parameters.MSSM_Grav.f90 src/models/parameters.MSSM_Hgg.f90 src/models/parameters.NMSSM.f90 src/models/parameters.NMSSM_CKM.f90 src/models/parameters.NMSSM_Hgg.f90 src/models/parameters.PSSSM.f90 src/models/parameters.QCD.f90 src/models/parameters.QED.f90 src/models/parameters.SM.f90 src/models/parameters.SM_CKM.f90 src/models/parameters.SM_ac.f90 src/models/parameters.SM_ac_CKM.f90 src/models/parameters.SM_dim6.f90 src/models/parameters.SM_rx.f90 src/models/parameters.SM_ul.f90 src/models/parameters.NoH_rx.f90 src/models/parameters.AltH.f90 src/models/parameters.SSC.f90 src/models/parameters.SSC_2.f90 src/models/parameters.SSC_AltT.f90 src/models/parameters.SM_top.f90 src/models/parameters.SM_top_anom.f90 src/models/parameters.SM_Higgs.f90 src/models/parameters.SM_Higgs_CKM.f90 src/models/parameters.Simplest.f90 src/models/parameters.Simplest_univ.f90 src/models/parameters.Template.f90 src/models/parameters.HSExt.f90 src/models/parameters.Test.f90 src/models/parameters.Threeshl.f90 src/models/parameters.UED.f90 src/models/parameters.Xdim.f90 src/models/parameters.Zprime.f90 src/models/parameters.WZW.f90" OMEGA_FILES="omega/Makefile.am omega/share/Makefile.am omega/share/doc/Makefile.am omega/src/Makefile.am omega/src/Makefile.ocaml omega/src/Makefile.sources omega/bin/Makefile.am omega/extensions/Makefile.am omega/extensions/people/Makefile.am omega/extensions/people/jr/Makefile.am omega/extensions/people/jr/f90_SAGT.ml omega/extensions/people/jr/f90_SQED.ml omega/extensions/people/jr/f90_WZ.ml omega/extensions/people/tho/Makefile.am omega/extensions/people/tho/f90_O2.ml omega/lib/Makefile.am omega/models/Makefile.am omega/scripts/Makefile.am omega/scripts/omega-config.in omega/tools/Makefile.am omega/tests/parameters_QED.f90 omega/tests/parameters_QCD.f90 omega/tests/parameters_SM.f90 omega/tests/parameters_SM_CKM.f90 omega/tests/parameters_SM_Higgs.f90 omega/tests/parameters_SM_from_UFO.f90 omega/tests/parameters_SYM.f90 omega/tests/parameters_SM_top_anom.f90 omega/tests/parameters_HSExt.f90 omega/tests/parameters_THDM.f90 omega/tests/parameters_THDM_CKM.f90 omega/tests/parameters_Zprime.f90 omega/tests/test_openmp.f90 omega/tests/tao_random_numbers.f90 omega/tests/test_qed_eemm.f90 omega/tests/Makefile.am omega/tests/benchmark.f90 omega/tests/compare.f90 omega/tests/color_test_lib.f90 omega/tests/omega_interface.f90 omega/tests/ward_lib.f90 omega/tests/omega_unit.ml" -OMEGA_SRC_FILES="omega/src/algebra.ml omega/src/algebra.mli omega/src/bundle.ml omega/src/bundle.mli omega/src/cache.ml omega/src/cache.mli omega/src/cascade.ml omega/src/cascade.mli omega/src/cascade_lexer.mll omega/src/cascade_parser.mly omega/src/cascade_syntax.ml omega/src/cascade_syntax.mli omega/src/charges.ml omega/src/charges.mli omega/src/color.ml omega/src/color.mli omega/src/colorize.ml omega/src/colorize.mli omega/src/combinatorics.ml omega/src/combinatorics.mli omega/src/complex.ml omega/src/complex.mli omega/src/config.ml.in omega/src/config.mli omega/src/count.ml omega/src/coupling.mli omega/src/DAG.ml omega/src/DAG.mli omega/src/fusion.ml omega/src/fusion.mli omega/src/linalg.ml omega/src/linalg.mli omega/src/model.mli omega/src/modellib_BSM.ml omega/src/modellib_NoH.ml omega/src/modellib_NoH.mli omega/src/modellib_BSM.mli omega/src/modellib_MSSM.ml omega/src/modellib_MSSM.mli omega/src/modellib_NMSSM.ml omega/src/modellib_NMSSM.mli omega/src/modellib_PSSSM.ml omega/src/modellib_PSSSM.mli omega/src/modellib_SM.ml omega/src/modellib_SM.mli omega/src/modellib_Zprime.mli omega/src/modellib_Zprime.ml omega/src/modellib_WZW.mli omega/src/modellib_WZW.ml omega/src/UFO.ml omega/src/UFO.mli omega/src/UFO_syntax.ml omega/src/UFO_syntax.mli omega/src/UFOx.ml omega/src/UFOx.mli omega/src/UFO_lexer.mll omega/src/UFO_parser.mly omega/src/UFOx_syntax.ml omega/src/UFOx_syntax.mli omega/src/UFOx_lexer.mll omega/src/UFOx_parser.mly omega/src/omega_UFO.ml omega/src/modeltools.ml omega/src/modeltools.mli omega/src/momentum.ml omega/src/momentum.mli omega/src/OVM.ml omega/src/OVM.mli omega/src/ogiga.ml omega/src/omega.ml omega/src/omega.mli omega/src/omega_THDM.ml omega/src/omega_THDM_VM.ml omega/src/omega_THDM_CKM.ml omega/src/omega_THDM_CKM_VM.ml omega/src/omega_CQED.ml omega/src/omega_GravTest.ml omega/src/omega_Littlest.ml omega/src/omega_Littlest_Eta.ml omega/src/omega_Littlest_Tpar.ml omega/src/omega_Littlest_Zprime.ml omega/src/omega_MSSM.ml omega/src/omega_MSSM_CKM.ml omega/src/omega_MSSM_Grav.ml omega/src/omega_MSSM_Hgg.ml omega/src/omega_NMSSM.ml omega/src/omega_NMSSM_CKM.ml omega/src/omega_NMSSM_Hgg.ml omega/src/omega_PSSSM.ml omega/src/omega_Phi3.ml omega/src/omega_Phi3h.ml omega/src/omega_Phi4.ml omega/src/omega_Phi4h.ml omega/src/omega_QCD.ml omega/src/omega_QCD_VM.ml omega/src/omega_QED.ml omega/src/omega_QED_VM.ml omega/src/omega_SM.ml omega/src/omega_SM_VM.ml omega/src/omega_SM_CKM.ml omega/src/omega_SM_CKM_VM.ml omega/src/omega_SM_Maj.ml omega/src/ovm_SM.ml omega/src/process.ml omega/src/process.mli omega/src/thoFilename.ml omega/src/thoFilename.mli omega/src/omega_SM_Higgs.ml omega/src/omega_SM_Higgs_CKM.ml omega/src/omega_SM_Higgs_VM.ml omega/src/omega_SM_Higgs_CKM_VM.ml omega/src/omega_SM_Rxi.ml omega/src/omega_SM_ac.ml omega/src/omega_SM_ac_CKM.ml omega/src/omega_SM_clones.ml omega/src/omega_SM_rx.ml omega/src/omega_SM_ul.ml omega/src/omega_NoH_rx.ml omega/src/omega_AltH.ml omega/src/omega_SSC.ml omega/src/omega_SSC_2.ml omega/src/omega_SM_top.ml omega/src/omega_SM_top_anom.ml omega/src/omega_SMh.ml omega/src/omega_SYM.ml omega/src/omega_Simplest.ml omega/src/omega_Simplest_univ.ml omega/src/omega_Template.ml omega/src/omega_HSExt.ml omega/src/omega_HSExt_VM.ml omega/src/omega_Threeshl.ml omega/src/omega_Threeshl_nohf.ml omega/src/omega_UED.ml omega/src/omega_Xdim.ml omega/src/omega_Zprime.ml omega/src/omega_Zprime_VM.ml omega/src/omega_logo.mp omega/src/omega_parameters_tool.nw omega/src/omegalib.nw omega/src/options.ml omega/src/options.mli omega/src/partition.ml omega/src/partition.mli omega/src/phasespace.ml omega/src/phasespace.mli omega/src/pmap.ml omega/src/pmap.mli omega/src/powSet.ml omega/src/powSet.mli omega/src/product.ml omega/src/product.mli omega/src/progress.ml omega/src/progress.mli omega/src/permutation.ml omega/src/permutation.mli omega/src/target.mli omega/src/targets.ml omega/src/targets.mli omega/src/targets_Kmatrix.ml omega/src/targets_Kmatrix.mli omega/src/test_linalg.ml omega/src/thoArray.ml omega/src/thoFilename.ml omega/src/thoArray.mli omega/src/thoGButton.ml omega/src/thoGButton.mli omega/src/thoGDraw.ml omega/src/thoGDraw.mli omega/src/thoGMenu.ml omega/src/thoGMenu.mli omega/src/thoGWindow.ml omega/src/thoGWindow.mli omega/src/thoList.ml omega/src/thoList.mli omega/src/thoString.ml omega/src/thoString.mli omega/src/topology.ml omega/src/topology.mli omega/src/tree.ml omega/src/tree.mli omega/src/tree2.ml omega/src/tree2.mli omega/src/trie.ml omega/src/trie.mli omega/src/tuple.ml omega/src/tuple.mli omega/src/vertex.ml omega/src/vertex.mli omega/src/vertex_lexer.mll omega/src/vertex_parser.mly omega/src/vertex_syntax.ml omega/src/vertex_syntax.mli omega/src/whizard.ml omega/src/whizard.mli omega/src/whizard_tool.ml omega/src/constants.f90" +OMEGA_SRC_FILES="omega/src/algebra.ml omega/src/algebra.mli omega/src/bundle.ml omega/src/bundle.mli omega/src/cache.ml omega/src/cache.mli omega/src/cascade.ml omega/src/cascade.mli omega/src/cascade_lexer.mll omega/src/cascade_parser.mly omega/src/cascade_syntax.ml omega/src/cascade_syntax.mli omega/src/charges.ml omega/src/charges.mli omega/src/color.ml omega/src/color.mli omega/src/colorize.ml omega/src/colorize.mli omega/src/combinatorics.ml omega/src/combinatorics.mli omega/src/complex.ml omega/src/complex.mli omega/src/config.ml.in omega/src/config.mli omega/src/count.ml omega/src/coupling.mli omega/src/DAG.ml omega/src/DAG.mli omega/src/fusion.ml omega/src/fusion_vintage.ml omega/src/fusion.mli omega/src/fusion_vintage.mli omega/src/linalg.ml omega/src/linalg.mli omega/src/model.mli omega/src/modellib_BSM.ml omega/src/modellib_NoH.ml omega/src/modellib_NoH.mli omega/src/modellib_BSM.mli omega/src/modellib_MSSM.ml omega/src/modellib_MSSM.mli omega/src/modellib_NMSSM.ml omega/src/modellib_NMSSM.mli omega/src/modellib_PSSSM.ml omega/src/modellib_PSSSM.mli omega/src/modellib_SM.ml omega/src/modellib_SM.mli omega/src/modellib_Zprime.mli omega/src/modellib_Zprime.ml omega/src/modellib_WZW.mli omega/src/modellib_WZW.ml omega/src/UFO.ml omega/src/UFO.mli omega/src/UFO_syntax.ml omega/src/UFO_syntax.mli omega/src/UFOx.ml omega/src/UFOx.mli omega/src/UFO_lexer.mll omega/src/UFO_parser.mly omega/src/UFOx_syntax.ml omega/src/UFOx_syntax.mli omega/src/UFOx_lexer.mll omega/src/UFOx_parser.mly omega/src/omega_UFO.ml omega/src/modeltools.ml omega/src/modeltools.mli omega/src/momentum.ml omega/src/momentum.mli omega/src/OVM.ml omega/src/OVM.mli omega/src/ogiga.ml omega/src/omega.ml omega/src/omega.mli omega/src/omega_THDM.ml omega/src/omega_THDM_VM.ml omega/src/omega_THDM_CKM.ml omega/src/omega_THDM_CKM_VM.ml omega/src/omega_CQED.ml omega/src/omega_GravTest.ml omega/src/omega_Littlest.ml omega/src/omega_Littlest_Eta.ml omega/src/omega_Littlest_Tpar.ml omega/src/omega_Littlest_Zprime.ml omega/src/omega_MSSM.ml omega/src/omega_MSSM_CKM.ml omega/src/omega_MSSM_Grav.ml omega/src/omega_MSSM_Hgg.ml omega/src/omega_NMSSM.ml omega/src/omega_NMSSM_CKM.ml omega/src/omega_NMSSM_Hgg.ml omega/src/omega_PSSSM.ml omega/src/omega_Phi3.ml omega/src/omega_Phi3h.ml omega/src/omega_Phi4.ml omega/src/omega_Phi4h.ml omega/src/omega_QCD.ml omega/src/omega_QCD_VM.ml omega/src/omega_QED.ml omega/src/omega_QED_VM.ml omega/src/omega_SM.ml omega/src/omega_SM_VM.ml omega/src/omega_SM_CKM.ml omega/src/omega_SM_CKM_VM.ml omega/src/omega_SM_Maj.ml omega/src/ovm_SM.ml omega/src/process.ml omega/src/process.mli omega/src/thoFilename.ml omega/src/thoFilename.mli omega/src/omega_SM_Higgs.ml omega/src/omega_SM_Higgs_CKM.ml omega/src/omega_SM_Higgs_VM.ml omega/src/omega_SM_Higgs_CKM_VM.ml omega/src/omega_SM_Rxi.ml omega/src/omega_SM_ac.ml omega/src/omega_SM_ac_CKM.ml omega/src/omega_SM_clones.ml omega/src/omega_SM_rx.ml omega/src/omega_SM_ul.ml omega/src/omega_NoH_rx.ml omega/src/omega_AltH.ml omega/src/omega_SSC.ml omega/src/omega_SSC_2.ml omega/src/omega_SM_top.ml omega/src/omega_SM_top_anom.ml omega/src/omega_SMh.ml omega/src/omega_SYM.ml omega/src/omega_Simplest.ml omega/src/omega_Simplest_univ.ml omega/src/omega_Template.ml omega/src/omega_HSExt.ml omega/src/omega_HSExt_VM.ml omega/src/omega_Threeshl.ml omega/src/omega_Threeshl_nohf.ml omega/src/omega_UED.ml omega/src/omega_Xdim.ml omega/src/omega_Zprime.ml omega/src/omega_Zprime_VM.ml omega/src/omega_logo.mp omega/src/omega_parameters_tool.nw omega/src/omegalib.nw omega/src/options.ml omega/src/options.mli omega/src/partition.ml omega/src/partition.mli omega/src/phasespace.ml omega/src/phasespace.mli omega/src/pmap.ml omega/src/pmap.mli omega/src/powSet.ml omega/src/powSet.mli omega/src/product.ml omega/src/product.mli omega/src/progress.ml omega/src/progress.mli omega/src/permutation.ml omega/src/permutation.mli omega/src/target.mli omega/src/targets.ml omega/src/targets.mli omega/src/targets_Kmatrix.ml omega/src/targets_Kmatrix.mli omega/src/test_linalg.ml omega/src/thoArray.ml omega/src/thoFilename.ml omega/src/thoArray.mli omega/src/thoGButton.ml omega/src/thoGButton.mli omega/src/thoGDraw.ml omega/src/thoGDraw.mli omega/src/thoGMenu.ml omega/src/thoGMenu.mli omega/src/thoGWindow.ml omega/src/thoGWindow.mli omega/src/thoList.ml omega/src/thoList.mli omega/src/thoString.ml omega/src/thoString.mli omega/src/topology.ml omega/src/topology.mli omega/src/tree.ml omega/src/tree.mli omega/src/tree2.ml omega/src/tree2.mli omega/src/trie.ml omega/src/trie.mli omega/src/tuple.ml omega/src/tuple.mli omega/src/vertex.ml omega/src/vertex.mli omega/src/vertex_lexer.mll omega/src/vertex_parser.mly omega/src/vertex_syntax.ml omega/src/vertex_syntax.mli omega/src/whizard.ml omega/src/whizard.mli omega/src/whizard_tool.ml omega/src/constants.f90" SRC_PDF_BUILTIN_FILES="src/pdf_builtin/pdf_builtin.f90" VAMP_FILES="vamp/Makefile.am vamp/share/Makefile.am vamp/share/doc/Makefile.am vamp/src/Makefile.am vamp/src/iso_fortran_env_stub.f90 vamp/tests/Makefile.am" FILES="$MAIN_FILES $CONFIGURE_FILES $VERSION_FILES $SHARE_FILES $OMEGA_FILES $SCRIPTS_FILES $SRC_FILES $CIRCE1_FILES $CIRCE2_FILES $SRC_GAMELAN_FILES $SRC_PDF_BUILTIN_FILES $VAMP_FILES $SRC_BASICS_FILES $SRC_MODELS_FILES $OMEGA_SRC_FILES" for f in $FILES; do sed -e "s/$OLD_YEAR/$NEW_YEAR/g" -e "s/$OLD_YEAR2/$NEW_YEAR2/g" -e "s/$OLD_YEAR3/$NEW_YEAR3/g" -e "s/$OLD_ADDRESS/$NEW_ADDRESS/g" $f > $f.tmp; cp -f $f.tmp $f; rm -f $f.tmp; done CHANGE_FILES="$CONFIGURE_FILES $VERSION_FILES" for f in $CHANGE_FILES; do sed -e "s/$OLD_DATE/$NEW_DATE/g" -e "s/$OLD_VERSION/$NEW_VERSION/g" -e "s/$OLD_STATUS/$NEW_STATUS/g" $f > $f.tmp; cp -f $f.tmp $f; rm -f $f.tmp; done Index: trunk/omega/src/fusion_vintage.ml =================================================================== --- trunk/omega/src/fusion_vintage.ml (revision 8277) +++ trunk/omega/src/fusion_vintage.ml (revision 8278) @@ -1,2881 +1,2881 @@ -(* fusion.ml -- +(* fusion_vintage.ml -- Copyright (C) 1999-2019 by Wolfgang Kilian Thorsten Ohl Juergen Reuter with contributions from Christian Speckner Marco Sekulla WHIZARD is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. WHIZARD is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. *) module type T = sig val options : Options.t type wf val conjugate : wf -> wf type flavor type flavor_sans_color val flavor : wf -> flavor val flavor_sans_color : wf -> flavor_sans_color type p val momentum : wf -> p val momentum_list : wf -> int list val wf_tag : wf -> string option type constant type coupling type rhs type 'a children val sign : rhs -> int val coupling : rhs -> constant Coupling.t val coupling_tag : rhs -> string option type exclusions val no_exclusions : exclusions val children : rhs -> wf list type fusion val lhs : fusion -> wf val rhs : fusion -> rhs list type braket val bra : braket -> wf val ket : braket -> rhs list type amplitude type amplitude_sans_color type selectors val amplitudes : bool -> exclusions -> selectors -> flavor_sans_color list -> flavor_sans_color list -> amplitude list val amplitude_sans_color : bool -> exclusions -> selectors -> flavor_sans_color list -> flavor_sans_color list -> amplitude_sans_color val dependencies : amplitude -> wf -> (wf, coupling) Tree2.t val incoming : amplitude -> flavor list val outgoing : amplitude -> flavor list val externals : amplitude -> wf list val variables : amplitude -> wf list val fusions : amplitude -> fusion list val brakets : amplitude -> braket list val on_shell : amplitude -> (wf -> bool) val is_gauss : amplitude -> (wf -> bool) val constraints : amplitude -> string option val symmetry : amplitude -> int val allowed : amplitude -> bool val initialize_cache : string -> unit val set_cache_name : string -> unit val check_charges : unit -> flavor_sans_color list list val count_fusions : amplitude -> int val count_propagators : amplitude -> int val count_diagrams : amplitude -> int val forest : wf -> amplitude -> ((wf * coupling option, wf) Tree.t) list val poles : amplitude -> wf list list val s_channel : amplitude -> wf list val tower_to_dot : out_channel -> amplitude -> unit val amplitude_to_dot : out_channel -> amplitude -> unit val phase_space_channels : out_channel -> amplitude_sans_color -> unit val phase_space_channels_flipped : out_channel -> amplitude_sans_color -> unit end module type Maker = functor (P : Momentum.T) -> functor (M : Model.T) -> T with type p = P.t and type flavor = Colorize.It(M).flavor and type flavor_sans_color = M.flavor and type constant = M.constant and type selectors = Cascade.Make(M)(P).selectors (* \thocwmodulesection{Fermi Statistics} *) module type Stat = sig type flavor type stat exception Impossible val stat : flavor -> int -> stat val stat_fuse : stat -> stat -> flavor -> stat val stat_sign : stat -> int val stat_to_string : stat -> string end module type Stat_Maker = functor (M : Model.T) -> Stat with type flavor = M.flavor (* \thocwmodulesection{Dirac Fermions} *) module Stat_Dirac (M : Model.T) : (Stat with type flavor = M.flavor) = struct type flavor = M.flavor (* \begin{equation} \gamma_\mu\psi(1)\,G^{\mu\nu}\,\bar\psi(2)\gamma_\nu\psi(3) - \gamma_\mu\psi(3)\,G^{\mu\nu}\,\bar\psi(2)\gamma_\nu\psi(1) \end{equation} *) type stat = | Fermion of int * (int option * int option) list | AntiFermion of int * (int option * int option) list | Boson of (int option * int option) list let stat f p = let s = M.fermion f in if s = 0 then Boson [] else if s < 0 then AntiFermion (p, []) else (* [if s > 0 then] *) Fermion (p, []) let lines_to_string lines = ThoList.to_string (function | Some i, Some j -> Printf.sprintf "%d>%d" i j | Some i, None -> Printf.sprintf "%d>*" i | None, Some j -> Printf.sprintf "*>%d" j | None, None -> "*>*") lines let stat_to_string = function | Boson lines -> Printf.sprintf "Boson %s" (lines_to_string lines) | Fermion (p, lines) -> Printf.sprintf "Fermion (%d, %s)" p (lines_to_string lines) | AntiFermion (p, lines) -> Printf.sprintf "AntiFermion (%d, %s)" p (lines_to_string lines) exception Impossible let stat_fuse s1 s2 f = match s1, s2 with | Boson l1, Boson l2 -> Boson (l1 @ l2) | Boson l1, Fermion (p, l2) -> Fermion (p, l1 @ l2) | Boson l1, AntiFermion (p, l2) -> AntiFermion (p, l1 @ l2) | Fermion (p, l1), Boson l2 -> Fermion (p, l1 @ l2) | AntiFermion (p, l1), Boson l2 -> AntiFermion (p, l1 @ l2) | AntiFermion (pbar, l1), Fermion (p, l2) -> Boson ((Some pbar, Some p) :: l1 @ l2) | Fermion (p, l1), AntiFermion (pbar, l2) -> Boson ((Some pbar, Some p) :: l1 @ l2) | Fermion _, Fermion _ | AntiFermion _, AntiFermion _ -> raise Impossible (* \begin{figure} \begin{displaymath} \parbox{26\unitlength}{% \begin{fmfgraph*}(25,15) \fmfstraight \fmfleft{f} \fmfright{f1,f2,f3} \fmflabel{$\psi(1)$}{f1} \fmflabel{$\bar\psi(2)$}{f2} \fmflabel{$\psi(3)$}{f3} \fmflabel{$0$}{f} \fmf{fermion}{f1,v1,f} \fmffreeze \fmf{fermion,tension=0.5}{f3,v2,f2} \fmf{photon}{v1,v2} \fmfdot{v1,v2} \end{fmfgraph*}} \qquad\qquad-\qquad \parbox{26\unitlength}{% \begin{fmfgraph*}(25,15) \fmfstraight \fmfleft{f} \fmfright{f1,f2,f3} \fmflabel{$\psi(1)$}{f1} \fmflabel{$\bar\psi(2)$}{f2} \fmflabel{$\psi(3)$}{f3} \fmflabel{$0$}{f} \fmf{fermion}{f3,v1,f} \fmffreeze \fmf{fermion,tension=0.5}{f1,v2,f2} \fmf{photon}{v1,v2} \fmfdot{v1,v2} \end{fmfgraph*}} \end{displaymath} \caption{\label{fig:stat_fuse} Relative sign from Fermi statistics.} \end{figure} *) (* \begin{equation} \epsilon \left(\left\{ (0,1), (2,3) \right\}\right) = - \epsilon \left(\left\{ (0,3), (2,1) \right\}\right) \end{equation} *) let permutation lines = let fout, fin = List.split lines in let eps_in, _ = Combinatorics.sort_signed fin and eps_out, _ = Combinatorics.sort_signed fout in (eps_in * eps_out) (* \begin{dubious} This comparing of permutations of fermion lines is a bit tedious and takes a macroscopic fraction of time. However, it's less than 20\,\%, so we don't focus on improving on it yet. \end{dubious} *) let stat_sign = function | Boson lines -> permutation lines | Fermion (p, lines) -> permutation ((None, Some p) :: lines) | AntiFermion (pbar, lines) -> permutation ((Some pbar, None) :: lines) end (* \thocwmodulesection{Tags} *) module type Tags = sig type wf type coupling type 'a children val null_wf : wf val null_coupling : coupling val fuse : coupling -> wf children -> wf val wf_to_string : wf -> string option val coupling_to_string : coupling -> string option end module type Tagger = functor (PT : Tuple.Poly) -> Tags with type 'a children = 'a PT.t module type Tagged_Maker = functor (Tagger : Tagger) -> functor (P : Momentum.T) -> functor (M : Model.T) -> T with type p = P.t and type flavor = Colorize.It(M).flavor and type flavor_sans_color = M.flavor and type constant = M.constant (* No tags is one option for good tags \ldots *) module No_Tags (PT : Tuple.Poly) = struct type wf = unit type coupling = unit type 'a children = 'a PT.t let null_wf = () let null_coupling = () let fuse () _ = () let wf_to_string () = None let coupling_to_string () = None end (* \begin{dubious} Here's a simple additive tag that can grow into something useful for loop calculations. \end{dubious} *) module Loop_Tags (PT : Tuple.Poly) = struct type wf = int type coupling = int type 'a children = 'a PT.t let null_wf = 0 let null_coupling = 0 let fuse c wfs = PT.fold_left (+) c wfs let wf_to_string n = Some (string_of_int n) let coupling_to_string n = Some (string_of_int n) end module Order_Tags (PT : Tuple.Poly) = struct type wf = int type coupling = int type 'a children = 'a PT.t let null_wf = 0 let null_coupling = 0 let fuse c wfs = PT.fold_left (+) c wfs let wf_to_string n = Some (string_of_int n) let coupling_to_string n = Some (string_of_int n) end (* \thocwmodulesection{[Tagged], the [Fusion.Make] Functor} *) module Tagged (Tagger : Tagger) (PT : Tuple.Poly) (Stat : Stat_Maker) (T : Topology.T with type 'a children = 'a PT.t) (P : Momentum.T) (M : Model.T) = struct type cache_mode = Cache_Use | Cache_Ignore | Cache_Overwrite let cache_option = ref Cache_Ignore type qcd_order = | QCD_order of int type ew_order = | EW_order of int let qcd_order = ref (QCD_order 99) let ew_order = ref (EW_order 99) let options = Options.create [ "ignore-cache", Arg.Unit (fun () -> cache_option := Cache_Ignore), " ignore cached model tables (default)"; "use-cache", Arg.Unit (fun () -> cache_option := Cache_Use), " use cached model tables"; "overwrite-cache", Arg.Unit (fun () -> cache_option := Cache_Overwrite), " overwrite cached model tables"; "qcd", Arg.Int (fun n -> qcd_order := QCD_order n), " set QCD order n [>= 0, default = 99] (ignored)"; "ew", Arg.Int (fun n -> ew_order := EW_order n), " set QCD order n [>=0, default = 99] (ignored)"] exception Negative_QCD_order exception Negative_EW_order exception Vanishing_couplings exception Negative_QCD_EW_orders let int_orders = match !qcd_order, !ew_order with | QCD_order n, EW_order n' when n < 0 && n' >= 0 -> raise Negative_QCD_order | QCD_order n, EW_order n' when n >= 0 && n' < 0 -> raise Negative_EW_order | QCD_order n, EW_order n' when n < 0 && n' < 0 -> raise Negative_QCD_EW_orders | QCD_order n, EW_order n' -> (n, n') open Coupling module S = Stat(M) type stat = S.stat let stat = S.stat let stat_sign = S.stat_sign (* \begin{dubious} This will do \emph{something} for 4-, 6-, \ldots fermion vertices, but not necessarily the right thing \ldots \end{dubious} *) let stat_fuse s f = PT.fold_right_internal (fun s' acc -> S.stat_fuse s' acc f) s type constant = M.constant (* \thocwmodulesubsection{Wave Functions} *) (* \begin{dubious} The code below is not yet functional. Too often, we assign to [Tags.null_wf] instead of calling [Tags.fuse]. \end{dubious} *) (* We will need two types of amplitudes: with color and without color. Since we can build them using the same types with only [flavor] replaced, it pays to use a functor to set up the scaffolding. *) module Tags = Tagger(PT) (* In the future, we might want to have [Coupling] among the functor arguments. However, for the moment, [Coupling] is assumed to be comprehensive. *) module type Tagged_Coupling = sig type sign = int type t = { sign : sign; coupling : constant Coupling.t; coupling_tag : Tags.coupling } val sign : t -> sign val coupling : t -> constant Coupling.t val coupling_tag : t -> string option end module Tagged_Coupling : Tagged_Coupling = struct type sign = int type t = { sign : sign; coupling : constant Coupling.t; coupling_tag : Tags.coupling } let sign c = c.sign let coupling c = c.coupling let coupling_tag_raw c = c.coupling_tag let coupling_tag rhs = Tags.coupling_to_string (coupling_tag_raw rhs) end (* \thocwmodulesubsection{Amplitudes: Monochrome and Colored} *) module type Amplitude = sig module Tags : Tags type flavor type p type wf = { flavor : flavor; momentum : p; wf_tag : Tags.wf } val flavor : wf -> flavor val conjugate : wf -> wf val momentum : wf -> p val momentum_list : wf -> int list val wf_tag : wf -> string option val wf_tag_raw : wf -> Tags.wf val order_wf : wf -> wf -> int val external_wfs : int -> (flavor * int) list -> wf list type 'a children type coupling = Tagged_Coupling.t type rhs = coupling * wf children val sign : rhs -> int val coupling : rhs -> constant Coupling.t val coupling_tag : rhs -> string option type exclusions val no_exclusions : exclusions val children : rhs -> wf list type fusion = wf * rhs list val lhs : fusion -> wf val rhs : fusion -> rhs list type braket = wf * rhs list val bra : braket -> wf val ket : braket -> rhs list module D : DAG.T with type node = wf and type edge = coupling and type children = wf children val wavefunctions : braket list -> wf list type amplitude = { fusions : fusion list; brakets : braket list; on_shell : (wf -> bool); is_gauss : (wf -> bool); constraints : string option; incoming : flavor list; outgoing : flavor list; externals : wf list; symmetry : int; dependencies : (wf -> (wf, coupling) Tree2.t); fusion_tower : D.t; fusion_dag : D.t } val incoming : amplitude -> flavor list val outgoing : amplitude -> flavor list val externals : amplitude -> wf list val variables : amplitude -> wf list val fusions : amplitude -> fusion list val brakets : amplitude -> braket list val on_shell : amplitude -> (wf -> bool) val is_gauss : amplitude -> (wf -> bool) val constraints : amplitude -> string option val symmetry : amplitude -> int val dependencies : amplitude -> wf -> (wf, coupling) Tree2.t val fusion_dag : amplitude -> D.t end module Amplitude (PT : Tuple.Poly) (P : Momentum.T) (M : Model.T) : Amplitude with type p = P.t and type flavor = M.flavor and type 'a children = 'a PT.t and module Tags = Tags = struct type flavor = M.flavor type p = P.t module Tags = Tags type wf = { flavor : flavor; momentum : p; wf_tag : Tags.wf } let flavor wf = wf.flavor let conjugate wf = { wf with flavor = M.conjugate wf.flavor } let momentum wf = wf.momentum let momentum_list wf = P.to_ints wf.momentum let wf_tag wf = Tags.wf_to_string wf.wf_tag let wf_tag_raw wf = wf.wf_tag let external_wfs rank particles = List.map (fun (f, p) -> { flavor = f; momentum = P.singleton rank p; wf_tag = Tags.null_wf }) particles (* Order wavefunctions so that the external come first, then the pairs, etc. Also put possible Goldstone bosons \emph{before} their gauge bosons. *) let lorentz_ordering f = match M.lorentz f with | Coupling.Scalar -> 0 | Coupling.Spinor -> 1 | Coupling.ConjSpinor -> 2 | Coupling.Majorana -> 3 | Coupling.Vector -> 4 | Coupling.Massive_Vector -> 5 | Coupling.Tensor_2 -> 6 | Coupling.Tensor_1 -> 7 | Coupling.Vectorspinor -> 8 | Coupling.BRS Coupling.Scalar -> 9 | Coupling.BRS Coupling.Spinor -> 10 | Coupling.BRS Coupling.ConjSpinor -> 11 | Coupling.BRS Coupling.Majorana -> 12 | Coupling.BRS Coupling.Vector -> 13 | Coupling.BRS Coupling.Massive_Vector -> 14 | Coupling.BRS Coupling.Tensor_2 -> 15 | Coupling.BRS Coupling.Tensor_1 -> 16 | Coupling.BRS Coupling.Vectorspinor -> 17 | Coupling.BRS _ -> invalid_arg "Fusion.lorentz_ordering: not needed" | Coupling.Maj_Ghost -> 18 (*i | Coupling.Ward_Vector -> 19 i*) let order_flavor f1 f2 = let c = compare (lorentz_ordering f1) (lorentz_ordering f2) in if c <> 0 then c else compare f1 f2 (* Note that [Momentum().compare] guarantees that wavefunctions will be ordered according to \emph{increasing} [Momentum().rank] of their momenta. *) let order_wf wf1 wf2 = let c = P.compare wf1.momentum wf2.momentum in if c <> 0 then c else let c = order_flavor wf1.flavor wf2.flavor in if c <> 0 then c else compare wf1.wf_tag wf2.wf_tag (* This \emph{must} be a pair matching the [edge * node children] pairs of [DAG.Forest]! *) type coupling = Tagged_Coupling.t type 'a children = 'a PT.t type rhs = coupling * wf children let sign (c, _) = Tagged_Coupling.sign c let coupling (c, _) = Tagged_Coupling.coupling c let coupling_tag (c, _) = Tagged_Coupling.coupling_tag c type exclusions = { x_flavors : flavor list; x_couplings : coupling list } let no_exclusions = { x_flavors = []; x_couplings = [] } let children (_, wfs) = PT.to_list wfs type fusion = wf * rhs list let lhs (l, _) = l let rhs (_, r) = r type braket = wf * rhs list let bra (b, _) = b let ket (_, k) = k module D = DAG.Make (DAG.Forest(PT) (struct type t = wf let compare = order_wf end) (struct type t = coupling let compare = compare end)) module WFSet = Set.Make (struct type t = wf let compare = order_wf end) let wavefunctions brakets = WFSet.elements (List.fold_left (fun set (wf1, wf23) -> WFSet.add wf1 (List.fold_left (fun set' (_, wfs) -> PT.fold_right WFSet.add wfs set') set wf23)) WFSet.empty brakets) type amplitude = { fusions : fusion list; brakets : braket list; on_shell : (wf -> bool); is_gauss : (wf -> bool); constraints : string option; incoming : flavor list; outgoing : flavor list; externals : wf list; symmetry : int; dependencies : (wf -> (wf, coupling) Tree2.t); fusion_tower : D.t; fusion_dag : D.t } let incoming a = a.incoming let outgoing a = a.outgoing let externals a = a.externals let fusions a = a.fusions let brakets a = a.brakets let symmetry a = a.symmetry let on_shell a = a.on_shell let is_gauss a = a.is_gauss let constraints a = a.constraints let variables a = List.map lhs a.fusions let dependencies a = a.dependencies let fusion_dag a = a.fusion_dag end module A = Amplitude(PT)(P)(M) (* Operator insertions can be fused only if they are external. *) let is_source wf = match M.propagator wf.A.flavor with | Only_Insertion -> P.rank wf.A.momentum = 1 | _ -> true (* [is_goldstone_of g v] is [true] if and only if [g] is the Goldstone boson corresponding to the gauge particle [v]. *) let is_goldstone_of g v = match M.goldstone v with | None -> false | Some (g', _) -> g = g' (* \begin{dubious} In the end, [PT.to_list] should become redudant! \end{dubious} *) let fuse_rhs rhs = M.fuse (PT.to_list rhs) (* \thocwmodulesubsection{Vertices} *) (* Compute the set of all vertices in the model from the allowed fusions and the set of all flavors: \begin{dubious} One could think of using [M.vertices] instead of [M.fuse2], [M.fuse3] and [M.fuse] \ldots \end{dubious} *) module VSet = Map.Make(struct type t = A.flavor let compare = compare end) let add_vertices f rhs m = VSet.add f (try rhs :: VSet.find f m with Not_found -> [rhs]) m let collect_vertices rhs = List.fold_right (fun (f1, c) -> add_vertices (M.conjugate f1) (c, rhs)) (fuse_rhs rhs) (* The set of all vertices with common left fields factored. *) (* I used to think that constant initializers are a good idea to allow compile time optimizations. The down side turned out to be that the constant initializers will be evaluated \emph{every time} the functor is applied. \emph{Relying on the fact that the functor will be called only once is not a good idea!} *) type vertices = (A.flavor * (constant Coupling.t * A.flavor PT.t) list) list let vertices_nocache max_degree flavors : vertices = VSet.fold (fun f rhs v -> (f, rhs) :: v) (PT.power_fold collect_vertices flavors VSet.empty) [] (* Performance hack: *) type vertex_table = ((A.flavor * A.flavor * A.flavor) * constant Coupling.vertex3 * constant) list * ((A.flavor * A.flavor * A.flavor * A.flavor) * constant Coupling.vertex4 * constant) list * (A.flavor list * constant Coupling.vertexn * constant) list module VCache = Cache.Make (struct type t = vertex_table end) (struct type t = vertices end) let vertices_cache = ref None let hash () = VCache.hash (M.vertices ()) (* \begin{dubious} Can we do better than the executable name provided by [Config.cache_prefix]??? We need a better way to avoid collisions among the caches for different models in the same program. \end{dubious} *) let cache_name = ref (Config.cache_prefix ^ "." ^ Config.cache_suffix) let set_cache_name name = cache_name := name let initialize_cache dir = Printf.eprintf " >>> Initializing vertex table %s. This may take some time ... " !cache_name; flush stderr; VCache.write_dir (hash ()) dir !cache_name (vertices_nocache (M.max_degree ()) (M.flavors())); Printf.eprintf "done. <<< \n" let vertices max_degree flavors : vertices = match !vertices_cache with | None -> begin match !cache_option with | Cache_Use -> begin match VCache.maybe_read (hash ()) !cache_name with | VCache.Hit result -> result | VCache.Miss -> Printf.eprintf " >>> Initializing vertex table %s. This may take some time ... " !cache_name; flush stderr; let result = vertices_nocache max_degree flavors in VCache.write (hash ()) !cache_name (result); vertices_cache := Some result; Printf.eprintf "done. <<< \n"; flush stderr; result | VCache.Stale file -> Printf.eprintf " >>> Re-initializing stale vertex table %s in file %s. " !cache_name file; Printf.eprintf "This may take some time ... "; flush stderr; let result = vertices_nocache max_degree flavors in VCache.write (hash ()) !cache_name (result); vertices_cache := Some result; Printf.eprintf "done. <<< \n"; flush stderr; result end | Cache_Overwrite -> Printf.eprintf " >>> Overwriting vertex table %s. This may take some time ... " !cache_name; flush stderr; let result = vertices_nocache max_degree flavors in VCache.write (hash ()) !cache_name (result); vertices_cache := Some result; Printf.eprintf "done. <<< \n"; flush stderr; result | Cache_Ignore -> let result = vertices_nocache max_degree flavors in vertices_cache := Some result; result end | Some result -> result (* Note that we must perform any filtering of the vertices \emph{after} caching, because the restrictions \emph{must not} influence the cache (unless we tag the cache with model and restrictions). *) (*i let unpack_constant = function | Coupling.V3 (_, _, cs) -> cs | Coupling.V4 (_, _, cs) -> cs | Coupling.Vn (_, _, cs) -> cs let coupling_and_flavors_to_string (c, fs) = M.constant_symbol (unpack_constant c) ^ "[" ^ String.concat ", " (List.map M.flavor_to_string (PT.to_list fs)) ^ "]" let fusions_to_string (f, cfs) = M.flavor_to_string f ^ " <- { " ^ String.concat " | " (List.map coupling_and_flavors_to_string cfs) ^ " }" let vertices_to_string vertices = String.concat "; " (List.map fusions_to_string vertices) i*) let filter_vertices select_vtx vertices = List.fold_left (fun acc (f, cfs) -> let f' = M.conjugate f in let cfs = List.filter (fun (c, fs) -> select_vtx c f' (PT.to_list fs)) cfs in match cfs with | [] -> acc | cfs -> (f, cfs) :: acc) [] vertices (* \thocwmodulesubsection{Partitions} *) (* Vertices that are not crossing invariant need special treatment so that they're only generated for the correct combinations of momenta. NB: the [crossing] checks here are a bit redundant, because [CM.fuse] below will bring the killed vertices back to life and will have to filter once more. Nevertheless, we keep them here, for the unlikely case that anybody ever wants to use uncolored amplitudes directly. NB: the analogous problem does not occur for [select_wf], because this applies to momenta instead of vertices. *) (* \begin{dubious} This approach worked before the colorize, but has become \emph{futile}, because [CM.fuse] will bring the killed vertices back to life. We need to implement the same checks there again!!! \end{dubious} *) (* \begin{dubious} Using [PT.Mismatched_arity] is not really good style \ldots Tho's approach doesn't work since he does not catch charge conjugated processes or crossed processes. Another very strange thing is that O'Mega seems always to run in the q2 q3 timelike case, but not in the other two. (Property of how the DAG is built?). For the $ZZZZ$ vertex I add the same vertex again, but interchange 1 and 3 in the [crossing] vertex \end{dubious} *) let kmatrix_cuts c momenta = match c with | V4 (Vector4_K_Matrix_tho (disc, _), fusion, _) | V4 (Vector4_K_Matrix_jr (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_t0 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_t1 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_t2 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_t_rsi (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_m0 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_m1 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (Vector4_K_Matrix_cf_m7 (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F431|F342|F432) | 1, false, true, false, (F134|F143|F234|F243) | 1, false, false, true, (F314|F413|F324|F423) -> true | 2, true, false, false, (F123|F213|F124|F214) | 2, false, true, false, (F312|F321|F412|F421) | 2, false, false, true, (F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | _ -> false end | V4 (DScalar2_Vector2_K_Matrix_ms (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F432|F123|F214) | 1, false, true, false, (F134|F243|F312|F421) | 1, false, false, true, (F314|F423|F132|F241) -> true | 2, true, false, false, (F431|F342|F213|F124) | 2, false, true, false, (F143|F234|F321|F412) | 2, false, false, true, (F413|F324|F231|F142) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | 4, true, false, false, (F142|F413|F231|F324) | 4, false, true, false, (F214|F341|F123|F432) | 4, false, false, true, (F124|F431|F213|F342) -> true | 5, true, false, false, (F143|F412|F321|F234) | 5, false, true, false, (F314|F241|F132|F423) | 5, false, false, true, (F134|F421|F312|F243) -> true | 6, true, false, false, (F134|F132|F314|F312|F241|F243|F421|F423) | 6, false, true, false, (F213|F413|F231|F431|F124|F324|F142|F342) | 6, false, false, true, (F143|F123|F341|F321|F412|F214|F432|F234) -> true | 7, true, false, false, (F134|F312|F421|F243) | 7, false, true, false, (F413|F231|F142|F324) | 7, false, false, true, (F143|F321|F412|F432) -> true | 8, true, false, false, (F132|F314|F241|F423) | 8, false, true, false, (F213|F431|F124|F342) | 8, false, false, true, (F123|F341|F214|F234) -> true | _ -> false end | V4 (DScalar2_Vector2_m_0_K_Matrix_cf (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F432|F123|F214) | 1, false, true, false, (F134|F243|F312|F421) | 1, false, false, true, (F314|F423|F132|F241) -> true | 2, true, false, false, (F431|F342|F213|F124) | 2, false, true, false, (F143|F234|F321|F412) | 2, false, false, true, (F413|F324|F231|F142) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | 4, true, false, false, (F142|F413|F231|F324) | 4, false, true, false, (F214|F341|F123|F432) | 4, false, false, true, (F124|F431|F213|F342) -> true | 5, true, false, false, (F143|F412|F321|F234) | 5, false, true, false, (F314|F241|F132|F423) | 5, false, false, true, (F134|F421|F312|F243) -> true | 6, true, false, false, (F134|F132|F314|F312|F241|F243|F421|F423) | 6, false, true, false, (F213|F413|F231|F431|F124|F324|F142|F342) | 6, false, false, true, (F143|F123|F341|F321|F412|F214|F432|F234) -> true | 7, true, false, false, (F134|F312|F421|F243) | 7, false, true, false, (F413|F231|F142|F324) | 7, false, false, true, (F143|F321|F412|F432) -> true | 8, true, false, false, (F132|F314|F241|F423) | 8, false, true, false, (F213|F431|F124|F342) | 8, false, false, true, (F123|F341|F214|F234) -> true | _ -> false end | V4 (DScalar2_Vector2_m_1_K_Matrix_cf (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F432|F123|F214) | 1, false, true, false, (F134|F243|F312|F421) | 1, false, false, true, (F314|F423|F132|F241) -> true | 2, true, false, false, (F431|F342|F213|F124) | 2, false, true, false, (F143|F234|F321|F412) | 2, false, false, true, (F413|F324|F231|F142) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | 4, true, false, false, (F142|F413|F231|F324) | 4, false, true, false, (F214|F341|F123|F432) | 4, false, false, true, (F124|F431|F213|F342) -> true | 5, true, false, false, (F143|F412|F321|F234) | 5, false, true, false, (F314|F241|F132|F423) | 5, false, false, true, (F134|F421|F312|F243) -> true | 6, true, false, false, (F134|F132|F314|F312|F241|F243|F421|F423) | 6, false, true, false, (F213|F413|F231|F431|F124|F324|F142|F342) | 6, false, false, true, (F143|F123|F341|F321|F412|F214|F432|F234) -> true | 7, true, false, false, (F134|F312|F421|F243) | 7, false, true, false, (F413|F231|F142|F324) | 7, false, false, true, (F143|F321|F412|F432) -> true | 8, true, false, false, (F132|F314|F241|F423) | 8, false, true, false, (F213|F431|F124|F342) | 8, false, false, true, (F123|F341|F214|F234) -> true | _ -> false end | V4 (DScalar2_Vector2_m_7_K_Matrix_cf (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 1, true, false, false, (F341|F432|F123|F214) | 1, false, true, false, (F134|F243|F312|F421) | 1, false, false, true, (F314|F423|F132|F241) -> true | 2, true, false, false, (F431|F342|F213|F124) | 2, false, true, false, (F143|F234|F321|F412) | 2, false, false, true, (F413|F324|F231|F142) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | 4, true, false, false, (F142|F413|F231|F324) | 4, false, true, false, (F214|F341|F123|F432) | 4, false, false, true, (F124|F431|F213|F342) -> true | 5, true, false, false, (F143|F412|F321|F234) | 5, false, true, false, (F314|F241|F132|F423) | 5, false, false, true, (F134|F421|F312|F243) -> true | 6, true, false, false, (F134|F132|F314|F312|F241|F243|F421|F423) | 6, false, true, false, (F213|F413|F231|F431|F124|F324|F142|F342) | 6, false, false, true, (F143|F123|F341|F321|F412|F214|F432|F234) -> true | 7, true, false, false, (F134|F312|F421|F243) | 7, false, true, false, (F413|F231|F142|F324) | 7, false, false, true, (F143|F321|F412|F432) -> true | 8, true, false, false, (F132|F314|F241|F423) | 8, false, true, false, (F213|F431|F124|F342) | 8, false, false, true, (F123|F341|F214|F234) -> true | _ -> false end | V4 (DScalar4_K_Matrix_ms (disc, _), fusion, _) -> let s12, s23, s13 = begin match PT.to_list momenta with | [q1; q2; q3] -> (P.Scattering.timelike (P.add q1 q2), P.Scattering.timelike (P.add q2 q3), P.Scattering.timelike (P.add q1 q3)) | _ -> raise PT.Mismatched_arity end in begin match disc, s12, s23, s13, fusion with | 0, true, false, false, (F341|F431|F342|F432|F123|F213|F124|F214) | 0, false, true, false, (F134|F143|F234|F243|F312|F321|F412|F421) | 0, false, false, true, (F314|F413|F324|F423|F132|F231|F142|F241) -> true | 3, true, false, false, (F143|F413|F142|F412|F321|F231|F324|F234) | 3, false, true, false, (F314|F341|F214|F241|F132|F123|F432|F423) | 3, false, false, true, (F134|F431|F124|F421|F312|F213|F342|F243) -> true | 4, true, false, false, (F142|F413|F231|F324) | 4, false, true, false, (F214|F341|F123|F432) | 4, false, false, true, (F124|F431|F213|F342) -> true | 5, true, false, false, (F143|F412|F321|F234) | 5, false, true, false, (F314|F241|F132|F423) | 5, false, false, true, (F134|F421|F312|F243) -> true | 6, true, false, false, (F134|F132|F314|F312|F241|F243|F421|F423) | 6, false, true, false, (F213|F413|F231|F431|F124|F324|F142|F342) | 6, false, false, true, (F143|F123|F341|F321|F412|F214|F432|F234) -> true | 7, true, false, false, (F134|F312|F421|F243) | 7, false, true, false, (F413|F231|F142|F324) | 7, false, false, true, (F143|F321|F412|F432) -> true | 8, true, false, false, (F132|F314|F241|F423) | 8, false, true, false, (F213|F431|F124|F342) | 8, false, false, true, (F123|F341|F214|F234) -> true | _ -> false end | _ -> true (* Counting QCD and EW orders. *) let qcd_ew_check orders = if fst (orders) <= fst (int_orders) && snd (orders) <= snd (int_orders) then true else false (* Match a set of flavors to a set of momenta. Form the direct product for the lists of momenta two and three with the list of couplings and flavors two and three. *) let flavor_keystone select_p dim (f1, f23) (p1, p23) = ({ A.flavor = f1; A.momentum = P.of_ints dim p1; A.wf_tag = A.Tags.null_wf }, Product.fold2 (fun (c, f) p acc -> try let p' = PT.map (P.of_ints dim) p in if select_p (P.of_ints dim p1) (PT.to_list p') && kmatrix_cuts c p' then (c, PT.map2 (fun f'' p'' -> { A.flavor = f''; A.momentum = p''; A.wf_tag = A.Tags.null_wf }) f p') :: acc else acc with | PT.Mismatched_arity -> acc) f23 p23 []) (*i let cnt = ref 0 let gc_stat () = let minor, promoted, major = Gc.counters () in Printf.sprintf "(%12.0f, %12.0f, %12.0f)" minor promoted major let flavor_keystone select_p n (f1, f23) (p1, p23) = incr cnt; Gc.set { (Gc.get()) with Gc.space_overhead = 20 }; Printf.eprintf "%6d@%8.1f: %s\n" !cnt (Sys.time ()) (gc_stat ()); flush stderr; flavor_keystone select_p n (f1, f23) (p1, p23) i*) (* Produce all possible combinations of vertices (flavor keystones) and momenta by forming the direct product. The semantically equivalent [Product.list2 (flavor_keystone select_wf n) vertices keystones] with \emph{subsequent} filtering would be a \emph{very bad} idea, because a potentially huge intermediate list is built for large models. E.\,g.~for the MSSM this would lead to non-termination by thrashing for $2\to4$ processes on most PCs. *) let flavor_keystones filter select_p dim vertices keystones = Product.fold2 (fun v k acc -> filter (flavor_keystone select_p dim v k) acc) vertices keystones [] (* Flatten the nested lists of vertices into a list of attached lines. *) let flatten_keystones t = ThoList.flatmap (fun (p1, p23) -> p1 :: (ThoList.flatmap (fun (_, rhs) -> PT.to_list rhs) p23)) t (* \thocwmodulesubsection{Subtrees} *) (* Fuse a tuple of wavefunctions, keeping track of Fermi statistics. Record only the the sign \emph{relative} to the children. (The type annotation is only for documentation.) *) let fuse select_wf select_vtx wfss : (A.wf * stat * A.rhs) list = if PT.for_all (fun (wf, _) -> is_source wf) wfss then try let wfs, ss = PT.split wfss in let flavors = PT.map A.flavor wfs and momenta = PT.map A.momentum wfs and wf_tags = PT.map A.wf_tag_raw wfs in let p = PT.fold_left_internal P.add momenta in (*i let wft = PT.fold_left Tags.fuse wf_tags in i*) List.fold_left (fun acc (f, c) -> if select_wf f p (PT.to_list momenta) && select_vtx c f (PT.to_list flavors) && kmatrix_cuts c momenta then let s = stat_fuse ss f in let flip = PT.fold_left (fun acc s' -> acc * stat_sign s') (stat_sign s) ss in ({ A.flavor = f; A.momentum = p; A.wf_tag = A.Tags.null_wf }, s, ({ Tagged_Coupling.sign = flip; Tagged_Coupling.coupling = c; Tagged_Coupling.coupling_tag = A.Tags.null_coupling }, wfs)) :: acc else acc) [] (fuse_rhs flavors) with | P.Duplicate _ | S.Impossible -> [] else [] (* \begin{dubious} Eventually, the pairs of [tower] and [dag] in [fusion_tower'] below could and should be replaced by a graded [DAG]. This will look like, but currently [tower] containts statistics information that is missing from [dag]: \begin{quote} \verb+Type node = flavor * p is not compatible with type wf * stat+ \end{quote} This should be easy to fix. However, replacing [type t = wf] with [type t = wf * stat] is \emph{not} a good idea because the variable [stat] makes it impossible to test for the existance of a particular [wf] in a [DAG]. \end{dubious} \begin{dubious} In summary, it seems that [(wf * stat) list array * A.D.t] should be replaced by [(wf -> stat) * A.D.t]. \end{dubious} *) module GF = struct module Nodes = struct type t = A.wf module G = struct type t = int let compare = compare end let compare = A.order_wf let rank wf = P.rank wf.A.momentum end module Edges = struct type t = A.coupling let compare = compare end module F = DAG.Forest(PT)(Nodes)(Edges) type node = Nodes.t type edge = F.edge type children = F.children type t = F.t let compare = F.compare let for_all = F.for_all let fold = F.fold end module D' = DAG.Graded(GF) let tower_of_dag dag = let _, max_rank = D'.min_max_rank dag in Array.init max_rank (fun n -> D'.ranked n dag) (* The function [fusion_tower'] recursively builds the tower of all fusions from bottom up to a chosen level. The argument [tower] is an array of lists, where the $i$-th sublist (counting from 0) represents all off shell wave functions depending on $i+1$~momenta and their Fermistatistics. \begin{equation} \begin{aligned} \Bigl\lbrack & \{ \phi_1(p_1), \phi_2(p_2), \phi_3(p_3), \ldots \}, \\ & \{ \phi_{12}(p_1+p_2), \phi'_{12}(p_1+p_2), \ldots, \phi_{13}(p_1+p_3), \ldots, \phi_{23}(p_2+p_3), \ldots \}, \\ & \ldots \\ & \{ \phi_{1\cdots n}(p_1+\cdots+p_n), \phi'_{1\cdots n}(p_1+\cdots+p_n), \ldots \} \Bigr\rbrack \end{aligned} \end{equation} The argument [dag] is a DAG representing all the fusions calculated so far. NB: The outer array in [tower] is always very short, so we could also have accessed a list with [List.nth]. Appending of new members at the end brings no loss of performance. NB: the array is supposed to be immutable. *) (* The towers must be sorted so that the combinatorical functions can make consistent selections. \begin{dubious} Intuitively, this seems to be correct. However, one could have expected that no element appears twice and that this ordering is not necessary \ldots \end{dubious} *) let grow select_wf select_vtx tower = let rank = succ (Array.length tower) in List.sort Pervasives.compare (PT.graded_sym_power_fold rank (fun wfs acc -> fuse select_wf select_vtx wfs @ acc) tower []) let add_offspring dag (wf, _, rhs) = A.D.add_offspring wf rhs dag let filter_offspring fusions = List.map (fun (wf, s, _) -> (wf, s)) fusions let rec fusion_tower' n_max select_wf select_vtx tower dag : (A.wf * stat) list array * A.D.t = if Array.length tower >= n_max then (tower, dag) else let tower' = grow select_wf select_vtx tower in fusion_tower' n_max select_wf select_vtx (Array.append tower [|filter_offspring tower'|]) (List.fold_left add_offspring dag tower') (* Discard the tower and return a map from wave functions to Fermistatistics together with the DAG. *) let make_external_dag wfs = List.fold_left (fun m (wf, _) -> A.D.add_node wf m) A.D.empty wfs let mixed_fold_left f acc lists = Array.fold_left (List.fold_left f) acc lists module Stat_Map = Map.Make (struct type t = A.wf let compare = A.order_wf end) let fusion_tower height select_wf select_vtx wfs : (A.wf -> stat) * A.D.t = let tower, dag = fusion_tower' height select_wf select_vtx [|wfs|] (make_external_dag wfs) in let stats = mixed_fold_left (fun m (wf, s) -> Stat_Map.add wf s m) Stat_Map.empty tower in ((fun wf -> Stat_Map.find wf stats), dag) (* Calculate the minimal tower of fusions that suffices for calculating the amplitude. *) let minimal_fusion_tower n select_wf select_vtx wfs : (A.wf -> stat) * A.D.t = fusion_tower (T.max_subtree n) select_wf select_vtx wfs (* Calculate the complete tower of fusions. It is much larger than required, but it allows a complete set of gauge checks. *) let complete_fusion_tower select_wf select_vtx wfs : (A.wf -> stat) * A.D.t = fusion_tower (List.length wfs - 1) select_wf select_vtx wfs (* \begin{dubious} There is a natural product of two DAGs using [fuse]. Can this be used in a replacement for [fusion_tower]? The hard part is to avoid double counting, of course. A straight forward solution could do a diagonal sum (in order to reject flipped offspring representing the same fusion) and rely on the uniqueness in [DAG] otherwise. However, this will (probably) slow down the procedure significanty, because most fusions (including Fermi signs!) will be calculated before being rejected by [DAG().add_offspring]. \end{dubious} *) (* Add to [dag] all Goldstone bosons defined in [tower] that correspond to gauge bosons in [dag]. This is only required for checking Slavnov-Taylor identities in unitarity gauge. Currently, it is not used, because we use the complete tower for gauge checking. *) let harvest_goldstones tower dag = A.D.fold_nodes (fun wf dag' -> match M.goldstone wf.A.flavor with | Some (g, _) -> let wf' = { wf with A.flavor = g } in if A.D.is_node wf' tower then begin A.D.harvest tower wf' dag' end else begin dag' end | None -> dag') dag dag (* Calculate the sign from Fermi statistics that is not already included in the children. \begin{dubious} The use of [PT.of2_kludge] is the largest skeleton on the cupboard of unified fusions. Currently, it is just another name for [PT.of2], but the existence of the latter requires binary fusions. Of course, this is just a symptom for not fully supporting four fermion vertices \ldots \end{dubious} *) let stat_keystone stats wf1 wfs = let wf1' = stats wf1 and wfs' = PT.map stats wfs in let stat = stat_fuse (PT.of2_kludge wf1' (stat_fuse wfs' (M.conjugate (A.flavor wf1)))) (A.flavor wf1) in - Printf.eprintf "Fusion.stat_keystone: %s\n" (S.stat_to_string stat); + (*i Printf.eprintf "Fusion.stat_keystone: %s\n" (S.stat_to_string stat); i*) stat_sign stat * PT.fold_left (fun acc wf -> acc * stat_sign wf) (stat_sign wf1') wfs' (* Test all members of a list of wave functions are defined by the DAG simultaneously: *) let test_rhs dag (_, wfs) = PT.for_all (fun wf -> is_source wf && A.D.is_node wf dag) wfs (* Add the keystone [(wf1,pairs)] to [acc] only if it is present in [dag] and calculate the statistical factor depending on [stats] \emph{en passant}: *) let filter_keystone stats dag (wf1, pairs) acc = if is_source wf1 && A.D.is_node wf1 dag then match List.filter (test_rhs dag) pairs with | [] -> acc | pairs' -> (wf1, List.map (fun (c, wfs) -> ({ Tagged_Coupling.sign = stat_keystone stats wf1 wfs; Tagged_Coupling.coupling = c; Tagged_Coupling.coupling_tag = A.Tags.null_coupling }, wfs)) pairs') :: acc else acc (* \begin{figure} \begin{center} \thocwincludegraphics{width=\textwidth}{bhabha0}\\ \hfil\\ \thocwincludegraphics{width=\textwidth}{bhabha} \end{center} \caption{\label{fig:bhabha} The DAGs for Bhabha scattering before and after weeding out unused nodes. The blatant asymmetry of these DAGs is caused by our prescription for removing doubling counting for an even number of external lines.} \end{figure} \begin{figure} \begin{center} \thocwincludegraphics{width=\textwidth}{epemudbarmunumubar0}\\ \hfil\\ \thocwincludegraphics{width=\textwidth}{epemudbarmunumubar} \end{center} \caption{\label{fig:epemudbarmunumubar} The DAGs for $e^+e^-\to u\bar d \mu^-\bar\nu_\mu$ before and after weeding out unused nodes.} \end{figure} \begin{figure} \begin{center} \thocwincludegraphics{width=\textwidth}{epemudbardubar0}\\ \hfil\\ \thocwincludegraphics{width=\textwidth}{epemudbardubar} \end{center} \caption{\label{fig:epemudbardubar} The DAGs for $e^+e^-\to u\bar d d\bar u$ before and after weeding out unused nodes.} \end{figure} *) (* \thocwmodulesubsection{Amplitudes} *) module C = Cascade.Make(M)(P) type selectors = C.selectors let external_wfs n particles = List.map (fun (f, p) -> ({ A.flavor = f; A.momentum = P.singleton n p; A.wf_tag = A.Tags.null_wf }, stat f p)) particles (* \thocwmodulesubsection{Main Function} *) module WFMap = Map.Make (struct type t = A.wf let compare = compare end) (* [map_amplitude_wfs f a] applies the function [f : wf -> wf] to all wavefunctions appearing in the amplitude [a]. *) let map_amplitude_wfs f a = let map_rhs (c, wfs) = (c, PT.map f wfs) in let map_braket (wf, rhs) = (f wf, List.map map_rhs rhs) and map_fusion (lhs, rhs) = (f lhs, List.map map_rhs rhs) in let map_dag = A.D.map f (fun node rhs -> map_rhs rhs) in let tower = map_dag a.A.fusion_tower and dag = map_dag a.A.fusion_dag in let dependencies_map = A.D.fold (fun wf _ -> WFMap.add wf (A.D.dependencies dag wf)) dag WFMap.empty in { A.fusions = List.map map_fusion a.A.fusions; A.brakets = List.map map_braket a.A.brakets; A.on_shell = a.A.on_shell; A.is_gauss = a.A.is_gauss; A.constraints = a.A.constraints; A.incoming = a.A.incoming; A.outgoing = a.A.outgoing; A.externals = List.map f a.A.externals; A.symmetry = a.A.symmetry; A.dependencies = (fun wf -> WFMap.find wf dependencies_map); A.fusion_tower = tower; A.fusion_dag = dag } (*i (* \begin{dubious} Just a silly little test: \end{dubious} *) let hack_amplitude = map_amplitude_wfs (fun wf -> { wf with momentum = P.split 2 16 wf.momentum }) i*) (* This is the main function that constructs the amplitude for sets of incoming and outgoing particles and returns the results in conveniently packaged pieces. *) let amplitude goldstones selectors fin fout = (* Set up external lines and match flavors with numbered momenta. *) let f = fin @ List.map M.conjugate fout in let nin, nout = List.length fin, List.length fout in let n = nin + nout in let externals = List.combine f (ThoList.range 1 n) in let wfs = external_wfs n externals in let select_p = C.select_p selectors in let select_wf = match fin with | [_] -> C.select_wf selectors P.Decay.timelike | _ -> C.select_wf selectors P.Scattering.timelike in let select_vtx = C.select_vtx selectors in (* Build the full fusion tower (including nodes that are never needed in the amplitude). *) let stats, tower = if goldstones then complete_fusion_tower select_wf select_vtx wfs else minimal_fusion_tower n select_wf select_vtx wfs in (* Find all vertices for which \emph{all} off shell wavefunctions are defined by the tower. *) let brakets = flavor_keystones (filter_keystone stats tower) select_p n (filter_vertices select_vtx (vertices (M.max_degree ()) (M.flavors ()))) (T.keystones (ThoList.range 1 n)) in (* Remove the part of the DAG that is never needed in the amplitude. *) let dag = if goldstones then tower else A.D.harvest_list tower (A.wavefunctions brakets) in (* Remove the leaf nodes of the DAG, corresponding to external lines. *) let fusions = List.filter (function (_, []) -> false | _ -> true) (A.D.lists dag) in (* Calculate the symmetry factor for identical particles in the final state. *) let symmetry = Combinatorics.symmetry fout in let dependencies_map = A.D.fold (fun wf _ -> WFMap.add wf (A.D.dependencies dag wf)) dag WFMap.empty in (* Finally: package the results: *) { A.fusions = fusions; A.brakets = brakets; A.on_shell = (fun wf -> C.on_shell selectors (A.flavor wf) wf.A.momentum); A.is_gauss = (fun wf -> C.is_gauss selectors (A.flavor wf) wf.A.momentum); A.constraints = C.description selectors; A.incoming = fin; A.outgoing = fout; A.externals = List.map fst wfs; A.symmetry = symmetry; A.dependencies = (fun wf -> WFMap.find wf dependencies_map); A.fusion_tower = tower; A.fusion_dag = dag } (* \thocwmodulesubsection{Color} *) module CM = Colorize.It(M) module CA = Amplitude(PT)(P)(CM) let colorize_wf flavor wf = { CA.flavor = flavor; CA.momentum = wf.A.momentum; CA.wf_tag = wf.A.wf_tag } let uncolorize_wf wf = { A.flavor = CM.flavor_sans_color wf.CA.flavor; A.momentum = wf.CA.momentum; A.wf_tag = wf.CA.wf_tag } (* \begin{dubious} At the end of the day, I shall want to have some sort of \textit{fibered DAG} as abstract data type, with a projection of colored nodes to their uncolored counterparts. \end{dubious} *) module CWFBundle = Bundle.Make (struct type elt = CA.wf let compare_elt = compare type base = A.wf let compare_base = compare let pi wf = { A.flavor = CM.flavor_sans_color wf.CA.flavor; A.momentum = wf.CA.momentum; A.wf_tag = wf.CA.wf_tag } end) (* \begin{dubious} For now, we can live with simple aggregation: \end{dubious} *) type fibered_dag = { dag : CA.D.t; bundle : CWFBundle.t } (* Not yet(?) needed: [module CS = Stat (CM)] *) let colorize_sterile_nodes dag f wf fibered_dag = if A.D.is_sterile wf dag then let wf', wf_bundle' = f wf fibered_dag in { dag = CA.D.add_node wf' fibered_dag.dag; bundle = wf_bundle' } else fibered_dag let colorize_nodes f wf rhs fibered_dag = let wf_rhs_list', wf_bundle' = f wf rhs fibered_dag in let dag' = List.fold_right (fun (wf', rhs') -> CA.D.add_offspring wf' rhs') wf_rhs_list' fibered_dag.dag in { dag = dag'; bundle = wf_bundle' } (* O'Caml (correctly) infers the type [val colorize_dag : (D.node -> D.edge * D.children -> fibered_dag -> (CA.D.node * (CA.D.edge * CA.D.children)) list * CWFBundle.t) -> (D.node -> fibered_dag -> CA.D.node * CWFBundle.t) -> D.t -> CWFBundle.t -> fibered_dag]. *) let colorize_dag f_node f_ext dag wf_bundle = A.D.fold (colorize_nodes f_node) dag (A.D.fold_nodes (colorize_sterile_nodes dag f_ext) dag { dag = CA.D.empty; bundle = wf_bundle }) let colorize_external wf fibered_dag = match CWFBundle.inv_pi wf fibered_dag.bundle with | [c_wf] -> (c_wf, fibered_dag.bundle) | [] -> failwith "colorize_external: not found" | _ -> failwith "colorize_external: not unique" let fuse_c_wf rhs = let momenta = PT.map (fun wf -> wf.CA.momentum) rhs in List.filter (fun (_, c) -> kmatrix_cuts c momenta) (CM.fuse (List.map (fun wf -> wf.CA.flavor) (PT.to_list rhs))) let colorize_coupling c coupling = { coupling with Tagged_Coupling.coupling = c } let colorize_fusion wf (coupling, children) fibered_dag = let match_flavor (f, _) = (CM.flavor_sans_color f = A.flavor wf) and find_colored wf' = CWFBundle.inv_pi wf' fibered_dag.bundle in let fusions = ThoList.flatmap (fun c_children -> List.map (fun (f, c) -> (colorize_wf f wf, (colorize_coupling c coupling, c_children))) (List.filter match_flavor (fuse_c_wf c_children))) (PT.product (PT.map find_colored children)) in let bundle = List.fold_right (fun (c_wf, _) -> CWFBundle.add c_wf) fusions fibered_dag.bundle in (fusions, bundle) let colorize_braket1 (wf, (coupling, children)) fibered_dag = let find_colored wf' = CWFBundle.inv_pi wf' fibered_dag.bundle in Product.fold2 (fun bra ket acc -> List.fold_left (fun brakets (f, c) -> if CM.conjugate bra.CA.flavor = f then (bra, (colorize_coupling c coupling, ket)) :: brakets else brakets) acc (fuse_c_wf ket)) (find_colored wf) (PT.product (PT.map find_colored children)) [] module CWFMap = Map.Make (struct type t = CA.wf let compare = CA.order_wf end) module CKetSet = Set.Make (struct type t = CA.rhs let compare = compare end) (* Find a set of kets in [map] that belong to [bra]. Return the empty set, if nothing is found. *) let lookup_ketset bra map = try CWFMap.find bra map with Not_found -> CKetSet.empty (* Return the set of kets belonging to [bra] in [map], augmented by [ket]. *) let addto_ketset bra ket map = CKetSet.add ket (lookup_ketset bra map) (* Augment or update [map] with a new [(bra, ket)] relation. *) let addto_ketset_map map (bra, ket) = CWFMap.add bra (addto_ketset bra ket map) map (* Take a list of [(bra, ket)] pairs and group the [ket]s according to [bra]. This is very similar to [ThoList.factorize] on page~\pageref{ThoList.factorize}, but the latter keeps duplicate copies, while we keep only one, with equality determined by [CA.order_wf]. *) (* \begin{dubious} Isn't [Bundle]~\ref{Bundle} the correct framework for this? \end{dubious} *) let factorize_brakets brakets = CWFMap.fold (fun bra ket acc -> (bra, CKetSet.elements ket) :: acc) (List.fold_left addto_ketset_map CWFMap.empty brakets) [] let colorize_braket (wf, rhs_list) fibered_dag = factorize_brakets (ThoList.flatmap (fun rhs -> (colorize_braket1 (wf, rhs) fibered_dag)) rhs_list) let colorize_amplitude a fin fout = let f = fin @ List.map CM.conjugate fout in let nin, nout = List.length fin, List.length fout in let n = nin + nout in let externals = List.combine f (ThoList.range 1 n) in let external_wfs = CA.external_wfs n externals in let wf_bundle = CWFBundle.of_list external_wfs in let fibered_dag = colorize_dag colorize_fusion colorize_external a.A.fusion_dag wf_bundle in let brakets = ThoList.flatmap (fun braket -> colorize_braket braket fibered_dag) a.A.brakets in let dag = CA.D.harvest_list fibered_dag.dag (CA.wavefunctions brakets) in let fusions = List.filter (function (_, []) -> false | _ -> true) (CA.D.lists dag) in let dependencies_map = CA.D.fold (fun wf _ -> CWFMap.add wf (CA.D.dependencies dag wf)) dag CWFMap.empty in { CA.fusions = fusions; CA.brakets = brakets; CA.constraints = a.A.constraints; CA.incoming = fin; CA.outgoing = fout; CA.externals = external_wfs; CA.fusion_dag = dag; CA.fusion_tower = dag; CA.symmetry = a.A.symmetry; CA.on_shell = (fun wf -> a.A.on_shell (uncolorize_wf wf)); CA.is_gauss = (fun wf -> a.A.is_gauss (uncolorize_wf wf)); CA.dependencies = (fun wf -> CWFMap.find wf dependencies_map) } let allowed amplitude = match amplitude.CA.brakets with | [] -> false | _ -> true let colorize_amplitudes a = List.fold_left (fun amps (fin, fout) -> let amp = colorize_amplitude a fin fout in if allowed amp then amp :: amps else amps) [] (CM.amplitude a.A.incoming a.A.outgoing) let amplitudes goldstones exclusions selectors fin fout = colorize_amplitudes (amplitude goldstones selectors fin fout) let amplitude_sans_color goldstones exclusions selectors fin fout = amplitude goldstones selectors fin fout type flavor = CA.flavor type flavor_sans_color = A.flavor type p = A.p type wf = CA.wf let conjugate = CA.conjugate let flavor = CA.flavor let flavor_sans_color wf = CM.flavor_sans_color (CA.flavor wf) let momentum = CA.momentum let momentum_list = CA.momentum_list let wf_tag = CA.wf_tag type coupling = CA.coupling let sign = CA.sign let coupling = CA.coupling let coupling_tag = CA.coupling_tag type exclusions = CA.exclusions let no_exclusions = CA.no_exclusions type 'a children = 'a CA.children type rhs = CA.rhs let children = CA.children type fusion = CA.fusion let lhs = CA.lhs let rhs = CA.rhs type braket = CA.braket let bra = CA.bra let ket = CA.ket type amplitude = CA.amplitude type amplitude_sans_color = A.amplitude let incoming = CA.incoming let outgoing = CA.outgoing let externals = CA.externals let fusions = CA.fusions let brakets = CA.brakets let symmetry = CA.symmetry let on_shell = CA.on_shell let is_gauss = CA.is_gauss let constraints = CA.constraints let variables a = List.map lhs (fusions a) let dependencies = CA.dependencies (* \thocwmodulesubsection{Checking Conservation Laws} *) let check_charges () = let vlist3, vlist4, vlistn = M.vertices () in List.filter (fun flist -> not (M.Ch.is_null (M.Ch.sum (List.map M.charges flist)))) (List.map (fun ((f1, f2, f3), _, _) -> [f1; f2; f3]) vlist3 @ List.map (fun ((f1, f2, f3, f4), _, _) -> [f1; f2; f3; f4]) vlist4 @ List.map (fun (flist, _, _) -> flist) vlistn) (* \thocwmodulesubsection{Diagnostics} *) let count_propagators a = List.length a.CA.fusions let count_fusions a = List.fold_left (fun n (_, a) -> n + List.length a) 0 a.CA.fusions + List.fold_left (fun n (_, t) -> n + List.length t) 0 a.CA.brakets + List.length a.CA.brakets (* \begin{dubious} This brute force approach blows up for more than ten particles. Find a smarter algorithm. \end{dubious} *) let count_diagrams a = List.fold_left (fun n (wf1, wf23) -> n + CA.D.count_trees wf1 a.CA.fusion_dag * (List.fold_left (fun n' (_, wfs) -> n' + PT.fold_left (fun n'' wf -> n'' * CA.D.count_trees wf a.CA.fusion_dag) 1 wfs) 0 wf23)) 0 a.CA.brakets exception Impossible let forest' a = let below wf = CA.D.forest_memoized wf a.CA.fusion_dag in ThoList.flatmap (fun (bra, ket) -> (Product.list2 (fun bra' ket' -> bra' :: ket') (below bra) (ThoList.flatmap (fun (_, wfs) -> Product.list (fun w -> w) (PT.to_list (PT.map below wfs))) ket))) a.CA.brakets let cross wf = { CA.flavor = CM.conjugate wf.CA.flavor; CA.momentum = P.neg wf.CA.momentum; CA.wf_tag = wf.CA.wf_tag } let fuse_trees wf ts = Tree.fuse (fun (wf', e) -> (cross wf', e)) wf (fun t -> List.mem wf (Tree.leafs t)) ts let forest wf a = List.map (fuse_trees wf) (forest' a) (*i (* \begin{dubious} The following duplication should be replaced by polymorphism or a functor. \end{dubious} *) let forest_uncolored' a = let below wf = A.D.forest_memoized wf a.A.fusion_dag in ThoList.flatmap (fun (bra, ket) -> (Product.list2 (fun bra' ket' -> bra' :: ket') (below bra) (ThoList.flatmap (fun (_, wfs) -> Product.list (fun w -> w) (PT.to_list (PT.map below wfs))) ket))) a.A.brakets let cross_uncolored wf = { A.flavor = M.conjugate wf.A.flavor; A.momentum = P.neg wf.A.momentum; A.wf_tag = wf.A.wf_tag } let fuse_trees_uncolored wf ts = Tree.fuse (fun (wf', e) -> (cross_uncolored wf', e)) wf (fun t -> List.mem wf (Tree.leafs t)) ts let forest_sans_color wf a = List.map (fuse_trees_uncolored wf) (forest_uncolored' a) i*) let poles_beneath wf dag = CA.D.eval_memoized (fun wf' -> [[]]) (fun wf' _ p -> List.map (fun p' -> wf' :: p') p) (fun wf1 wf2 -> Product.fold2 (fun wf' wfs' wfs'' -> (wf' @ wfs') :: wfs'') wf1 wf2 []) (@) [[]] [[]] wf dag let poles a = ThoList.flatmap (fun (wf1, wf23) -> let poles_wf1 = poles_beneath wf1 a.CA.fusion_dag in (ThoList.flatmap (fun (_, wfs) -> Product.list List.flatten (PT.to_list (PT.map (fun wf -> poles_wf1 @ poles_beneath wf a.CA.fusion_dag) wfs))) wf23)) a.CA.brakets module WFSet = Set.Make (struct type t = CA.wf let compare = CA.order_wf end) let s_channel a = WFSet.elements (ThoList.fold_right2 (fun wf wfs -> if P.Scattering.timelike wf.CA.momentum then WFSet.add wf wfs else wfs) (poles a) WFSet.empty) (* \begin{dubious} This should be much faster! Is it correct? Is it faster indeed? \end{dubious} *) let poles' a = List.map CA.lhs a.CA.fusions let s_channel a = WFSet.elements (List.fold_right (fun wf wfs -> if P.Scattering.timelike wf.CA.momentum then WFSet.add wf wfs else wfs) (poles' a) WFSet.empty) (* \thocwmodulesubsection{Pictures} *) (* Export the DAG in the \texttt{dot(1)} file format so that we can draw pretty pictures to impress audiences \ldots *) let p2s p = if p >= 0 && p <= 9 then string_of_int p else if p <= 36 then String.make 1 (Char.chr (Char.code 'A' + p - 10)) else "_" let variable wf = CM.flavor_symbol wf.CA.flavor ^ String.concat "" (List.map p2s (P.to_ints wf.CA.momentum)) module Int = Map.Make (struct type t = int let compare = compare end) let add_to_list i n m = Int.add i (n :: try Int.find i m with Not_found -> []) m let classify_nodes dag = Int.fold (fun i n acc -> (i, n) :: acc) (CA.D.fold_nodes (fun wf -> add_to_list (P.rank wf.CA.momentum) wf) dag Int.empty) [] let dag_to_dot ch brakets dag = Printf.fprintf ch "digraph OMEGA {\n"; CA.D.iter_nodes (fun wf -> Printf.fprintf ch " \"%s\" [ label = \"%s\" ];\n" (variable wf) (variable wf)) dag; List.iter (fun (_, wfs) -> Printf.fprintf ch " { rank = same;"; List.iter (fun n -> Printf.fprintf ch " \"%s\";" (variable n)) wfs; Printf.fprintf ch " };\n") (classify_nodes dag); List.iter (fun n -> Printf.fprintf ch " \"*\" -> \"%s\";\n" (variable n)) (flatten_keystones brakets); CA.D.iter (fun n (_, ns) -> let p = variable n in PT.iter (fun n' -> Printf.fprintf ch " \"%s\" -> \"%s\";\n" p (variable n')) ns) dag; Printf.fprintf ch "}\n" let tower_to_dot ch a = dag_to_dot ch a.CA.brakets a.CA.fusion_tower let amplitude_to_dot ch a = dag_to_dot ch a.CA.brakets a.CA.fusion_dag (* \thocwmodulesubsection{Phasespace} *) let variable wf = M.flavor_to_string wf.A.flavor ^ "[" ^ String.concat "/" (List.map p2s (P.to_ints wf.A.momentum)) ^ "]" let below_to_channel transform ch dag wf = let n2s wf = variable (transform wf) and e2s c = "" in Tree2.to_channel ch n2s e2s (A.D.dependencies dag wf) let bra_to_channel transform ch dag wf = let tree = A.D.dependencies dag wf in if Tree2.is_singleton tree then let n2s wf = variable (transform wf) and e2s c = "" in Tree2.to_channel ch n2s e2s tree else failwith "Fusion.phase_space_channels: wrong topology!" let ket_to_channel transform ch dag ket = Printf.fprintf ch "("; begin match A.children ket with | [] -> () | [child] -> below_to_channel transform ch dag child | child :: children -> below_to_channel transform ch dag child; List.iter (fun child -> Printf.fprintf ch ","; below_to_channel transform ch dag child) children end; Printf.fprintf ch ")" let phase_space_braket transform ch (bra, ket) dag = bra_to_channel transform ch dag bra; Printf.fprintf ch ": {"; begin match ket with | [] -> () | [ket1] -> Printf.fprintf ch " "; ket_to_channel transform ch dag ket1 | ket1 :: kets -> Printf.fprintf ch " "; ket_to_channel transform ch dag ket1; List.iter (fun k -> Printf.fprintf ch " \\\n | "; ket_to_channel transform ch dag k) kets end; Printf.fprintf ch " }\n" (*i Food for thought: let braket_to_tree2 dag (bra, ket) = let bra' = A.D.dependencies dag bra in if Tree2.is_singleton bra' then Tree2.cons [(fst ket, bra, List.map (A.D.dependencies dag) (A.children ket))] else failwith "Fusion.phase_space_channels: wrong topology!" let phase_space_braket transform ch (bra, ket) dag = let n2s wf = variable (transform wf) and e2s c = "" in Printf.fprintf ch "%s\n" (Tree2.to_string n2s e2s (braket_to_tree2 dag (bra, ket))) i*) let phase_space_channels_transformed transform ch a = List.iter (fun braket -> phase_space_braket transform ch braket a.A.fusion_dag) a.A.brakets let phase_space_channels ch a = phase_space_channels_transformed (fun wf -> wf) ch a let exchange_momenta_list p1 p2 p = List.map (fun pi -> if pi = p1 then p2 else if pi = p2 then p1 else pi) p let exchange_momenta p1 p2 p = P.of_ints (P.dim p) (exchange_momenta_list p1 p2 (P.to_ints p)) let flip_momenta wf = { wf with A.momentum = exchange_momenta 1 2 wf.A.momentum } let phase_space_channels_flipped ch a = phase_space_channels_transformed flip_momenta ch a end module Make = Tagged(No_Tags) module Binary = Make(Tuple.Binary)(Stat_Dirac)(Topology.Binary) module Tagged_Binary (T : Tagger) = Tagged(T)(Tuple.Binary)(Stat_Dirac)(Topology.Binary) (* \thocwmodulesection{Fusions with Majorana Fermions} *) module Stat_Majorana (M : Model.T) : (Stat with type flavor = M.flavor) = struct type flavor = M.flavor type stat = | Fermion of int * int list | AntiFermion of int * int list | Boson of int list | Majorana of int * int list let stat f p = let s = M.fermion f in if s = 0 then Boson [] else if s < 0 then AntiFermion (p, []) else if s = 1 then (* [if s = 1 then] *) Fermion (p, []) else (* [if s > 1 then] *) Majorana (p, []) let lines_to_string lines = ThoList.to_string string_of_int lines let stat_to_string = function | Boson lines -> Printf.sprintf "Boson %s" (lines_to_string lines) | Fermion (p, lines) -> Printf.sprintf "Fermion (%d, %s)" p (lines_to_string lines) | AntiFermion (p, lines) -> Printf.sprintf "AntiFermion (%d, %s)" p (lines_to_string lines) | Majorana (p, lines) -> Printf.sprintf "Majorana (%d, %s)" p (lines_to_string lines) (* \begin{JR} In the formalism of~\cite{Denner:Majorana}, it does not matter to distinguish spinors and conjugate spinors, it is only important to know in which direction a fermion line is calculated. So the sign is made by the calculation together with an aditional one due to the permuation of the pairs of endpoints of fermion lines in the direction they are calculated. We propose a ``canonical'' direction from the right to the left child at a fusion point so we only have to keep in mind which external particle hangs at each side. Therefore we need not to have a list of pairs of conjugate spinors and spinors but just a list in which the pairs are right-left-right-left and so on. Unfortunately it is unavoidable to have couplings with clashing arrows in supersymmetric theories so we need transmutations from fermions in antifermions and vice versa as well. \end{JR} *) exception Impossible (*i let stat_fuse s1 s2 f = match s1, s2, M.lorentz f with | Boson l1, Boson l2, _ -> Boson (l1 @ l2) | Boson l1, Fermion (p, l2), Coupling.Majorana -> Majorana (p, l1 @ l2) | Boson l1, Fermion (p, l2), _ -> Fermion (p, l1 @ l2) | Boson l1, AntiFermion (p, l2), Coupling.Majorana -> Majorana (p, l1 @ l2) | Boson l1, AntiFermion (p, l2), _ -> AntiFermion (p, l1 @ l2) | Fermion (p, l1), Boson l2, Coupling.Majorana -> Majorana (p, l1 @ l2) | Fermion (p, l1), Boson l2, _ -> Fermion (p, l1 @ l2) | AntiFermion (p, l1), Boson l2, Coupling.Majorana -> Majorana (p, l1 @ l2) | AntiFermion (p, l1), Boson l2, _ -> AntiFermion (p, l1 @ l2) | Majorana (p, l1), Boson l2, Coupling.Spinor -> Fermion (p, l1 @ l2) | Majorana (p, l1), Boson l2, Coupling.ConjSpinor -> AntiFermion (p, l1 @ l2) | Majorana (p, l1), Boson l2, _ -> Majorana (p, l1 @ l2) | Boson l1, Majorana (p, l2), Coupling.Spinor -> Fermion (p, l1 @ l2) | Boson l1, Majorana (p, l2), Coupling.ConjSpinor -> AntiFermion (p, l1 @ l2) | Boson l1, Majorana (p, l2), _ -> Majorana (p, l1 @ l2) | AntiFermion (pbar, l1), Fermion (p, l2), _ -> Boson ([p; pbar] @ l1 @ l2) | Fermion (p, l1), AntiFermion (pbar, l2), _ -> Boson ([pbar; p] @ l1 @ l2) | Fermion (pf, l1), Majorana (pm, l2), _ -> Boson ([pm; pf] @ l1 @ l2) | Majorana (pm, l1), Fermion (pf, l2), _ -> Boson ([pf; pm] @ l1 @ l2) | AntiFermion (pa, l1), Majorana (pm, l2), _ -> Boson ([pm; pa] @ l1 @ l2) | Majorana (pm, l1), AntiFermion (pa, l2), _ -> Boson ([pa; pm] @ l1 @ l2) | Majorana (p1, l1), Majorana (p2, l2), _ -> Boson ([p2; p1] @ l1 @ l2) | Fermion _, Fermion _, _ | AntiFermion _, AntiFermion _, _ -> raise Impossible i*) let stat_fuse s1 s2 f = match s1, s2, M.lorentz f with | Boson l1, Fermion (p, l2), Coupling.Majorana | Boson l1, AntiFermion (p, l2), Coupling.Majorana | Fermion (p, l1), Boson l2, Coupling.Majorana | AntiFermion (p, l1), Boson l2, Coupling.Majorana | Majorana (p, l1), Boson l2, Coupling.Majorana | Boson l1, Majorana (p, l2), Coupling.Majorana -> Majorana (p, l1 @ l2) | Boson l1, Fermion (p, l2), Coupling.Spinor | Boson l1, AntiFermion (p, l2), Coupling.Spinor | Fermion (p, l1), Boson l2, Coupling.Spinor | AntiFermion (p, l1), Boson l2, Coupling.Spinor | Majorana (p, l1), Boson l2, Coupling.Spinor | Boson l1, Majorana (p, l2), Coupling.Spinor -> Fermion (p, l1 @ l2) | Boson l1, Fermion (p, l2), Coupling.ConjSpinor | Boson l1, AntiFermion (p, l2), Coupling.ConjSpinor | Fermion (p, l1), Boson l2, Coupling.ConjSpinor | AntiFermion (p, l1), Boson l2, Coupling.ConjSpinor | Majorana (p, l1), Boson l2, Coupling.ConjSpinor | Boson l1, Majorana (p, l2), Coupling.ConjSpinor -> AntiFermion (p, l1 @ l2) | Boson l1, Fermion (p, l2), Coupling.Vectorspinor | Boson l1, AntiFermion (p, l2), Coupling.Vectorspinor | Fermion (p, l1), Boson l2, Coupling.Vectorspinor | AntiFermion (p, l1), Boson l2, Coupling.Vectorspinor | Majorana (p, l1), Boson l2, Coupling.Vectorspinor | Boson l1, Majorana (p, l2), Coupling.Vectorspinor -> Majorana (p, l1 @ l2) | Boson l1, Boson l2, _ -> Boson (l1 @ l2) | AntiFermion (p1, l1), Fermion (p2, l2), _ | Fermion (p1, l1), AntiFermion (p2, l2), _ | Fermion (p1, l1), Fermion (p2, l2), _ | AntiFermion (p1, l1), AntiFermion (p2, l2), _ | Fermion (p1, l1), Majorana (p2, l2), _ | Majorana (p1, l1), Fermion (p2, l2), _ | AntiFermion (p1, l1), Majorana (p2, l2), _ | Majorana (p1, l1), AntiFermion (p2, l2), _ | Majorana (p1, l1), Majorana (p2, l2), _ -> Boson ([p2; p1] @ l1 @ l2) | Boson l1, Majorana (p, l2), _ -> Majorana (p, l1 @ l2) | Boson l1, Fermion (p, l2), _ -> Fermion (p, l1 @ l2) | Boson l1, AntiFermion (p, l2), _ -> AntiFermion (p, l1 @ l2) | Fermion (p, l1), Boson l2, _ -> Fermion (p, l1 @ l2) | AntiFermion (p, l1), Boson l2, _ -> AntiFermion (p, l1 @ l2) | Majorana (p, l1), Boson l2, _ -> Majorana (p, l1 @ l2) let stat_fuse s1 s2 f = let stat = stat_fuse s1 s2 f in - Printf.eprintf - "Fusion.Stat_Majorana.stat_fuse_legacy: %s <- %s -> %s\n" - (M.flavor_to_string f) - (ThoList.to_string stat_to_string [s1; s2]) - (stat_to_string stat); + (*i Printf.eprintf + "Fusion.Stat_Majorana.stat_fuse_legacy: %s <- %s -> %s\n" + (M.flavor_to_string f) + (ThoList.to_string stat_to_string [s1; s2]) + (stat_to_string stat); i*) stat (*i These are the old Impossible raising rules. We keep them to ask Ohl what the generalized topologies do and if our stat_fuse does the right for 4-vertices with | Boson l1, AntiFermion (p, l2), _ | Fermion (p, l1), Boson l2, _ | AntiFermion (p, l1), Boson l2, _ | Majorana (p, l1), Boson l2, _ | Boson l1, Majorana (p, l2), _ -> raise Impossible i*) let permutation lines = fst (Combinatorics.sort_signed lines) let stat_sign = function | Boson lines -> permutation lines | Fermion (p, lines) -> permutation (p :: lines) | AntiFermion (pbar, lines) -> permutation (pbar :: lines) | Majorana (pm, lines) -> permutation (pm :: lines) end module Binary_Majorana = Make(Tuple.Binary)(Stat_Majorana)(Topology.Binary) module Nary (B: Tuple.Bound) = Make(Tuple.Nary(B))(Stat_Dirac)(Topology.Nary(B)) module Nary_Majorana (B: Tuple.Bound) = Make(Tuple.Nary(B))(Stat_Majorana)(Topology.Nary(B)) module Mixed23 = Make(Tuple.Mixed23)(Stat_Dirac)(Topology.Mixed23) module Mixed23_Majorana = Make(Tuple.Mixed23)(Stat_Majorana)(Topology.Mixed23) module Helac (B: Tuple.Bound) = Make(Tuple.Nary(B))(Stat_Dirac)(Topology.Helac(B)) module Helac_Majorana (B: Tuple.Bound) = Make(Tuple.Nary(B))(Stat_Majorana)(Topology.Helac(B)) (* \thocwmodulesection{Multiple Amplitudes} *) module type Multi = sig exception Mismatch val options : Options.t type flavor type process = flavor list * flavor list type amplitude type fusion type wf type exclusions val no_exclusions : exclusions type selectors type amplitudes val amplitudes : bool -> int option -> exclusions -> selectors -> process list -> amplitudes val empty : amplitudes val initialize_cache : string -> unit val set_cache_name : string -> unit val flavors : amplitudes -> process list val vanishing_flavors : amplitudes -> process list val color_flows : amplitudes -> Color.Flow.t list val helicities : amplitudes -> (int list * int list) list val processes : amplitudes -> amplitude list val process_table : amplitudes -> amplitude option array array val fusions : amplitudes -> (fusion * amplitude) list val multiplicity : amplitudes -> wf -> int val dictionary : amplitudes -> amplitude -> wf -> int val color_factors : amplitudes -> Color.Flow.factor array array val constraints : amplitudes -> string option end module type Multi_Maker = functor (Fusion_Maker : Maker) -> functor (P : Momentum.T) -> functor (M : Model.T) -> Multi with type flavor = M.flavor and type amplitude = Fusion_Maker(P)(M).amplitude and type fusion = Fusion_Maker(P)(M).fusion and type wf = Fusion_Maker(P)(M).wf and type selectors = Fusion_Maker(P)(M).selectors module Multi (Fusion_Maker : Maker) (P : Momentum.T) (M : Model.T) = struct exception Mismatch type progress_mode = | Quiet | Channel of out_channel | File of string let progress_option = ref Quiet module CM = Colorize.It(M) module F = Fusion_Maker(P)(M) module C = Cascade.Make(M)(P) (* \begin{dubious} A kludge, at best \ldots \end{dubious} *) let options = Options.extend F.options [ "progress", Arg.Unit (fun () -> progress_option := Channel stderr), "report progress to the standard error stream"; "progress_file", Arg.String (fun s -> progress_option := File s), "report progress to a file" ] type flavor = M.flavor type p = F.p type process = flavor list * flavor list type amplitude = F.amplitude type fusion = F.fusion type wf = F.wf type exclusions = F.exclusions let no_exclusions = F.no_exclusions type selectors = F.selectors type flavors = flavor list array type helicities = int list array type colors = Color.Flow.t array type amplitudes' = amplitude array array array type amplitudes = { flavors : process list; vanishing_flavors : process list; color_flows : Color.Flow.t list; helicities : (int list * int list) list; processes : amplitude list; process_table : amplitude option array array; fusions : (fusion * amplitude) list; multiplicity : (wf -> int); dictionary : (amplitude -> wf -> int); color_factors : Color.Flow.factor array array; constraints : string option } let flavors a = a.flavors let vanishing_flavors a = a.vanishing_flavors let color_flows a = a.color_flows let helicities a = a.helicities let processes a = a.processes let process_table a = a.process_table let fusions a = a.fusions let multiplicity a = a.multiplicity let dictionary a = a.dictionary let color_factors a = a.color_factors let constraints a = a.constraints let sans_colors f = List.map CM.flavor_sans_color f let colors (fin, fout) = List.map M.color (fin @ fout) let process_sans_color a = (sans_colors (F.incoming a), sans_colors (F.outgoing a)) let color_flow a = CM.flow (F.incoming a) (F.outgoing a) let process_to_string fin fout = String.concat " " (List.map M.flavor_to_string fin) ^ " -> " ^ String.concat " " (List.map M.flavor_to_string fout) let count_processes colored_processes = List.length colored_processes module FMap = Map.Make (struct type t = process let compare = compare end) module CMap = Map.Make (struct type t = Color.Flow.t let compare = compare end) (* Recently [Product.list] began to guarantee lexicographic order for sorted arguments. Anyway, we still force a lexicographic order. *) let rec order_spin_table1 s1 s2 = match s1, s2 with | h1 :: t1, h2 :: t2 -> let c = compare h1 h2 in if c <> 0 then c else order_spin_table1 t1 t2 | [], [] -> 0 | _ -> invalid_arg "order_spin_table: inconsistent lengths" let order_spin_table (s1_in, s1_out) (s2_in, s2_out) = let c = compare s1_in s2_in in if c <> 0 then c else order_spin_table1 s1_out s2_out let sort_spin_table table = List.sort order_spin_table table let id x = x let pair x y = (x, y) (* \begin{dubious} Improve support for on shell Ward identities: [Coupling.Vector -> [4]] for one and only one external vector. \end{dubious} *) let rec hs_of_lorentz = function | Coupling.Scalar -> [0] | Coupling.Spinor | Coupling.ConjSpinor | Coupling.Majorana | Coupling.Maj_Ghost -> [-1; 1] | Coupling.Vector -> [-1; 1] | Coupling.Massive_Vector -> [-1; 0; 1] | Coupling.Tensor_1 -> [-1; 0; 1] | Coupling.Vectorspinor -> [-2; -1; 1; 2] | Coupling.Tensor_2 -> [-2; -1; 0; 1; 2] | Coupling.BRS f -> hs_of_lorentz f let hs_of_flavor f = hs_of_lorentz (M.lorentz f) let hs_of_flavors (fin, fout) = (List.map hs_of_flavor fin, List.map hs_of_flavor fout) let rec unphysical_of_lorentz = function | Coupling.Vector -> [4] | Coupling.Massive_Vector -> [4] | _ -> invalid_arg "unphysical_of_lorentz: not a vector particle" let unphysical_of_flavor f = unphysical_of_lorentz (M.lorentz f) let unphysical_of_flavors1 n f_list = ThoList.mapi (fun i f -> if i = n then unphysical_of_flavor f else hs_of_flavor f) 1 f_list let unphysical_of_flavors n (fin, fout) = (unphysical_of_flavors1 n fin, unphysical_of_flavors1 (n - List.length fin) fout) let helicity_table unphysical flavors = let hs = begin match unphysical with | None -> List.map hs_of_flavors flavors | Some n -> List.map (unphysical_of_flavors n) flavors end in if not (ThoList.homogeneous hs) then invalid_arg "Fusion.helicity_table: not all flavors have the same helicity states!" else match hs with | [] -> [] | (hs_in, hs_out) :: _ -> sort_spin_table (Product.list2 pair (Product.list id hs_in) (Product.list id hs_out)) module Proc = Process.Make(M) module WFMap = Map.Make (struct type t = F.wf let compare = compare end) module WFSet2 = Set.Make (struct type t = F.wf * (F.wf, F.coupling) Tree2.t let compare = compare end) module WFMap2 = Map.Make (struct type t = F.wf * (F.wf, F.coupling) Tree2.t let compare = compare end) module WFTSet = Set.Make (struct type t = (F.wf, F.coupling) Tree2.t let compare = compare end) (* All wavefunctions are unique per amplitude. So we can use per-amplitude dependency trees without additional \emph{internal} tags to identify identical wave functions. *) (* \textbf{NB:} we miss potential optimizations, because we assume all coupling to be different, while in fact we have horizontal/family symmetries and non abelian gauge couplings are universal anyway. *) let disambiguate_fusions amplitudes = let fusions = ThoList.flatmap (fun amplitude -> List.map (fun fusion -> (fusion, F.dependencies amplitude (F.lhs fusion))) (F.fusions amplitude)) amplitudes in let duplicates = List.fold_left (fun map (fusion, dependencies) -> let wf = F.lhs fusion in let set = try WFMap.find wf map with Not_found -> WFTSet.empty in WFMap.add wf (WFTSet.add dependencies set) map) WFMap.empty fusions in let multiplicity_map = WFMap.fold (fun wf dependencies acc -> let cardinal = WFTSet.cardinal dependencies in if cardinal <= 1 then acc else WFMap.add wf cardinal acc) duplicates WFMap.empty and dictionary_map = WFMap.fold (fun wf dependencies acc -> let cardinal = WFTSet.cardinal dependencies in if cardinal <= 1 then acc else snd (WFTSet.fold (fun dependency (i', acc') -> (succ i', WFMap2.add (wf, dependency) i' acc')) dependencies (1, acc))) duplicates WFMap2.empty in let multiplicity wf = WFMap.find wf multiplicity_map and dictionary amplitude wf = WFMap2.find (wf, F.dependencies amplitude wf) dictionary_map in (multiplicity, dictionary) let eliminate_common_fusions1 seen_wfs amplitude = List.fold_left (fun (seen, acc) f -> let wf = F.lhs f in let dependencies = F.dependencies amplitude wf in if WFSet2.mem (wf, dependencies) seen then (seen, acc) else (WFSet2.add (wf, dependencies) seen, (f, amplitude) :: acc)) seen_wfs (F.fusions amplitude) let eliminate_common_fusions processes = let _, rev_fusions = List.fold_left eliminate_common_fusions1 (WFSet2.empty, []) processes in List.rev rev_fusions (*i let eliminate_common_fusions processes = ThoList.flatmap (fun amplitude -> (List.map (fun f -> (f, amplitude)) (F.fusions amplitude))) processes i*) (* \thocwmodulesubsection{Calculate All The Amplitudes} *) let amplitudes goldstones unphysical exclusions select_wf processes = (* \begin{dubious} Eventually, we might want to support inhomogeneous helicities. However, this makes little physics sense for external particles on the mass shell, unless we have a model with degenerate massive fermions and bosons. \end{dubious} *) if not (ThoList.homogeneous (List.map hs_of_flavors processes)) then invalid_arg "Fusion.Multi.amplitudes: incompatible helicities"; let unique_uncolored_processes = Proc.remove_duplicate_final_states (C.partition select_wf) processes in let progress = match !progress_option with | Quiet -> Progress.dummy | Channel oc -> Progress.channel oc (count_processes unique_uncolored_processes) | File name -> Progress.file name (count_processes unique_uncolored_processes) in let allowed = ThoList.flatmap (fun (fi, fo) -> Progress.begin_step progress (process_to_string fi fo); let amps = F.amplitudes goldstones exclusions select_wf fi fo in begin match amps with | [] -> Progress.end_step progress "forbidden" | _ -> Progress.end_step progress "allowed" end; amps) unique_uncolored_processes in Progress.summary progress "all processes done"; let color_flows = ThoList.uniq (List.sort compare (List.map color_flow allowed)) and flavors = ThoList.uniq (List.sort compare (List.map process_sans_color allowed)) in let vanishing_flavors = Proc.diff processes flavors in let helicities = helicity_table unphysical flavors in let f_index = fst (List.fold_left (fun (m, i) f -> (FMap.add f i m, succ i)) (FMap.empty, 0) flavors) and c_index = fst (List.fold_left (fun (m, i) c -> (CMap.add c i m, succ i)) (CMap.empty, 0) color_flows) in let table = Array.make_matrix (List.length flavors) (List.length color_flows) None in List.iter (fun a -> let f = FMap.find (process_sans_color a) f_index and c = CMap.find (color_flow a) c_index in table.(f).(c) <- Some (a)) allowed; let cf_array = Array.of_list color_flows in let ncf = Array.length cf_array in let color_factor_table = Array.make_matrix ncf ncf Color.Flow.zero in for i = 0 to pred ncf do for j = 0 to i do color_factor_table.(i).(j) <- Color.Flow.factor cf_array.(i) cf_array.(j); color_factor_table.(j).(i) <- color_factor_table.(i).(j) done done; let fusions = eliminate_common_fusions allowed and multiplicity, dictionary = disambiguate_fusions allowed in { flavors = flavors; vanishing_flavors = vanishing_flavors; color_flows = color_flows; helicities = helicities; processes = allowed; process_table = table; fusions = fusions; multiplicity = multiplicity; dictionary = dictionary; color_factors = color_factor_table; constraints = C.description select_wf } let initialize_cache = F.initialize_cache let set_cache_name = F.set_cache_name let empty = { flavors = []; vanishing_flavors = []; color_flows = []; helicities = []; processes = []; process_table = Array.make_matrix 0 0 None; fusions = []; multiplicity = (fun _ -> 1); dictionary = (fun _ _ -> 1); color_factors = Array.make_matrix 0 0 Color.Flow.zero; constraints = None } end