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This document is not UTF8. It was detected as ISO-8859-1 (Latin 1) and converted to UTF8 for display.
Index: tags/opucem-00-00-00/makefile
===================================================================
--- tags/opucem-00-00-00/makefile (revision 0)
+++ tags/opucem-00-00-00/makefile (revision 7)
@@ -0,0 +1,11 @@
+CFLAGS=-Wall -I.
+CC=gcc
+
+lib: lib/opucem.o
+
+# st is an example driver code.
+all: lib st.o
+ $(CC) -o st.exe opucem.o st.o
+
+clean:
+ rm -f st.o lib/opucem.o
Index: tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.eps
===================================================================
--- tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.eps (revision 0)
+++ tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.eps (revision 7)
@@ -0,0 +1,179 @@
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+ 357 1084 357 1088 357 1092 357 1096 357 1100 357 1103 357 1107 357 1111 357 1115 357 1119 357 1123 357 1127 357 1131 357 1135 357 1139 357 1143 357 1147 357 1150 357 1154 357 1158 357 1162 357 1166 357 1170 357 1174 357 1178 357 1182 357 1186 357
+ 1190 357 1194 357 1198 357 1201 357 1205 357 1209 357 100 { m31} R 1213 357 1217 357 1221 357 1225 357 1229 357 1233 357 1237 357 1241 357 1245 357 1249 357 1252 357 1256 357 1260 357 1264 357 1268 357 1272 357 1276 357 1280 357 1284 357 1288 357
+ 1292 357 1296 357 1299 357 1303 357 1307 357 1311 357 1315 357 1319 357 1323 357 1327 357 1331 357 1335 357 1339 357 1343 357 1347 357 1350 357 1354 357 1358 357 1362 357 1366 357 1370 357 1374 357 1378 357 1382 357 1386 357 1390 357 1394 357 1398
+ 357 1401 357 1405 357 1409 357 1413 357 1417 357 1421 357 1425 357 1429 357 1433 357 1437 357 1441 357 1445 357 1449 357 1452 357 1456 357 1460 357 1464 357 1468 357 1472 357 1476 357 1480 357 1484 357 1488 357 1492 357 1496 357 1499 357 1503 357
+ 1507 357 1511 357 1515 357 1519 357 1523 357 1527 357 1531 357 1535 357 1539 357 1543 357 1547 357 1550 357 1554 357 1558 357 1562 357 1566 357 1570 357 1574 357 1578 357 1582 357 1586 357 1590 357 1594 357 1598 357 1601 357 100 { m31} R 1605 357
+ 1609 357 1613 357 1617 357 1621 357 1625 357 1629 357 1633 357 1637 357 1641 357 1645 357 1648 357 1652 357 1656 357 1660 357 1664 357 1668 357 1672 357 1676 357 1680 357 1684 357 1688 357 1692 357 1696 357 1699 357 1703 357 1707 357 1711 357 1715
+ 357 1719 357 1723 357 1727 357 1731 357 1735 357 1739 357 1743 357 1747 357 1750 357 1754 357 1758 357 1762 357 1766 357 1770 357 1774 357 1778 357 1782 357 1786 357 1790 357 1794 357 1797 357 1801 357 1805 357 1809 357 1813 357 1817 357 1821 357
+ 1825 357 1829 357 1833 357 1837 357 1841 357 1845 357 1848 357 1852 357 1856 357 1860 357 1864 357 1868 357 1872 357 1876 357 1880 357 1884 357 1888 357 1892 357 1896 357 1899 357 1903 357 1907 357 1911 357 1915 357 1919 357 1923 357 1927 357 1931
+ 357 1935 357 1939 357 1943 357 1947 357 1950 357 1954 357 1958 357 1962 357 1966 357 1970 357 1974 357 1978 357 1982 357 1986 357 1990 357 1994 357 100 { m31} R 1997 357 1 { m31} R black 0 0 1 c 429 636 433 626 437 617 441 608 445 600 449 592 453
+ 585 456 578 460 571 464 565 468 559 472 554 476 548 480 543 484 538 488 534 492 529 496 525 500 521 503 517 507 514 511 510 515 507 519 503 523 500 527 497 531 494 535 491 539 488 543 486 547 483 551 481 554 478 558 476 562 474 566 471 570 469 574
+ 467 578 465 582 463 586 461 590 460 594 458 598 456 602 454 605 453 609 451 613 450 617 448 621 447 625 445 629 444 633 442 637 441 641 440 645 439 649 437 652 436 656 435 660 434 664 433 668 432 672 430 676 429 680 428 684 427 688 426 692 425 696
+ 425 700 424 703 423 707 422 711 421 715 420 719 419 723 419 727 418 731 417 735 416 739 415 743 415 747 414 751 413 754 413 758 412 762 411 766 411 770 410 774 409 778 409 782 408 786 408 790 407 794 406 798 406 801 405 805 405 809 404 813 404 817
+ 403 100 { m31} R 821 403 825 402 829 402 833 401 837 401 841 400 845 400 849 399 852 399 856 398 860 398 864 398 868 397 872 397 876 396 880 396 884 396 888 395 892 395 896 394 900 394 903 394 907 393 911 393 915 393 919 392 923 392 927 392 931 391
+ 935 391 939 391 943 390 947 390 951 390 954 390 958 389 962 389 966 389 970 388 974 388 978 388 982 388 986 387 990 387 994 387 998 386 1001 386 1005 386 1009 386 1013 386 1017 385 1021 385 1025 385 1029 385 1033 384 1037 384 1041 384 1045 384 1049
+ 383 1052 383 1056 383 1060 383 1064 383 1068 382 1072 382 1076 382 1080 382 1084 382 1088 381 1092 381 1096 381 1100 381 1103 381 1107 380 1111 380 1115 380 1119 380 1123 380 1127 380 1131 379 1135 379 1139 379 1143 379 1147 379 1150 379 1154 378
+ 1158 378 1162 378 1166 378 1170 378 1174 378 1178 378 1182 377 1186 377 1190 377 1194 377 1198 377 1201 377 1205 377 1209 377 100 { m31} R 1213 376 1217 376 1221 376 1225 376 1229 376 1233 376 1237 376 1241 376 1245 375 1249 375 1252 375 1256 375
+ 1260 375 1264 375 1268 374 1272 374 1276 374 1280 374 1284 374 1288 374 1292 374 1296 374 1299 374 1303 374 1307 373 1311 373 1315 373 1319 373 1323 373 1327 373 1331 373 1335 373 1339 373 1343 373 1347 372 1350 372 1354 372 1358 372 1362 372 1366
+ 372 1370 372 1374 372 1378 372 1382 372 1386 371 1390 371 1394 371 1398 371 1401 371 1405 371 1409 371 1413 371 1417 371 1421 371 1425 370 1429 371 1433 370 1437 370 1441 370 1445 370 1449 370 1452 370 1456 370 1460 370 1464 370 1468 369 1472 370
+ 1476 370 1480 370 1484 370 1488 369 1492 369 1496 369 1499 369 1503 369 1507 369 1511 369 1515 368 1519 368 1523 369 1527 368 1531 369 1535 368 1539 369 1543 368 1547 368 1550 368 1554 368 1558 368 1562 368 1566 368 1570 368 1574 368 1578 368 1582
+ 368 1586 367 1590 368 1594 367 1598 368 1601 367 100 { m31} R 1605 367 1609 368 1613 369 1617 370 1621 369 1625 368 1629 368 1633 370 1637 369 1641 368 1645 369 1648 368 1652 369 1656 368 1660 368 1664 367 1668 368 1672 368 1676 369 1680 368 1684
+ 369 1688 368 1692 367 1696 367 1699 366 1703 368 1707 368 1711 367 1715 368 1719 367 1723 368 1727 367 1731 369 1735 368 1739 368 1743 367 1747 365 1750 366 1754 367 1758 368 1762 367 1766 366 1770 367 1774 368 1778 367 1782 368 1786 367 1790 368
+ 1794 365 1797 367 1801 368 1805 368 1809 368 1813 368 1817 366 1821 367 1825 366 1829 371 1833 362 1837 363 1841 362 1845 363 1848 363 1852 362 1856 364 1860 364 1864 362 1868 362 1872 365 1876 363 1880 364 1884 362 1888 367 1892 363 1896 367 1899
+ 362 1903 363 1907 362 1911 362 1915 364 1919 362 1923 363 1927 363 1931 364 1935 364 1939 365 1943 361 1947 365 1950 365 1954 362 1958 365 1962 364 1966 364 1970 359 1974 362 1978 361 1982 364 1986 361 1990 361 1994 365 100 { m31} R 1997 362 1 {
+ m31} R
+ gr gr
+showpage
+end
+%%EOF
Index: tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.sh
===================================================================
--- tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.sh (revision 0)
+++ tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.sh (revision 7)
@@ -0,0 +1,24 @@
+# This is a dirty and highly unportable way of compiling and running. To be fixed later with a proper makefile.
+# Anyway, you should see this only as an example.
+
+# Compile and link
+gcc -o kniehl_khors_fig1.exe ../../lib/opucem.o -I../.. kniehl_khors_fig1.c
+
+# remove temp files (in case they did not get cleaned at the end of last run)
+rm -f ./out?.dat drtmp.C
+
+# run the created binary and produce the inputs to ROOT graphs
+./kniehl_khors_fig1.exe | sed s/=/' '/g | awk '{for (i=0;i<4;i++) {print $2, $(i*2+4) > "./out"i".dat"}}'
+
+# create a temporary .C to draw the plot
+echo '{TGraph g0("out0.dat"); g0.Draw("alp*"); g0.SetMarkerColor(2);' > drtmp.C
+echo ' g0.GetHistogram().SetMinimum(-0.005); g0.GetHistogram().SetMaximum(0.03);' >> drtmp.C
+echo ' TGraph g1("out1.dat"); g1.Draw("*"); g1.SetMarkerColor(4);' >> drtmp.C
+echo ' TGraph g2("out2.dat"); g2.Draw("*"); g2.SetMarkerColor(2);' >> drtmp.C
+echo ' TGraph g3("out3.dat"); g3.Draw("*"); g3.SetMarkerColor(4);}' >> drtmp.C
+
+# assuming that ROOT is installed on the system, run the macro
+root -l drtmp.C
+
+# done, clean the temp files
+rm -f ./out?.dat drtmp.C
Property changes on: tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.sh
___________________________________________________________________
Added: svn:executable
\ No newline at end of property
Index: tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.c
===================================================================
--- tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.c (revision 0)
+++ tags/opucem-00-00-00/examples/prd48_pg225/kniehl_khors_fig1.c (revision 7)
@@ -0,0 +1,26 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include "inc/opucem.h"
+
+// Simple example file that reproduces the values from the fig. 1 of:
+// "Oblique radiative corrections from Majorana neutrinos", B.A. Kniehl, H.-G. Kohrs, PRD 48 (1993) 225.
+int main(int argc, char *argv[] ){
+
+ const double Z=91.1875;
+ const double S2W=0.22272;
+ const double W=sqrt(Z*Z*(1-S2W));
+
+ int i;
+ for (i=100; i<=500; i++){
+ float ksi=i*.01;
+ double m1 = ksi*50;
+ double m2 = ksi*150;
+ double mE = ksi*100;
+ double smexact = SMexact(m1, m2, mE, S2W, Z*Z);
+ printf("ksi=%f \tSa=%f\tSe=%f\tUa=%f\tUe=%f\n", ksi,
+ SM(m1, m2, mE), smexact ,
+ UMapprox(m1,m2,mE), SpUMexact(m1,m2,mE,W*W,Z*Z)-smexact);
+ }
+
+ return 0;
+}
Index: tags/opucem-00-00-00/lib/opucem.c
===================================================================
--- tags/opucem-00-00-00/lib/opucem.c (revision 0)
+++ tags/opucem-00-00-00/lib/opucem.c (revision 7)
@@ -0,0 +1,348 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include "inc/opucem.h"
+
+// **************************************************
+// Formulas from Forshaw, Ross, White, hep-ph/0107232
+// **************************************************
+
+double THSM ( double Z, double s2w, double h) {
+ return 3./(16*M_PI*(1-s2w)*s2w) * ( h*h/(Z*Z-h*h)*2*log(h/Z) - (1-s2w)*h*h/((1-s2w)*Z*Z-h*h)*log(h*h/(1-s2w)/Z/Z) );
+}
+
+double SHSM ( double Z, double h) {
+ double multiplier=0.;
+ if ( h < 2*Z) {
+ multiplier=sqrt(4*Z*Z-h*h)*atan(sqrt((4*Z*Z-h*h)/h/h));
+ } else {
+ multiplier=sqrt(h*h-4*Z*Z)*log(2*Z/(h+sqrt(h*h-4*Z*Z)));
+ }
+
+ return 1./M_PI* ( 3/8.*(h*h/Z/Z) - 1/12.*pow(h/Z,4)
+ + pow(h/Z,2)*2*log(h/Z)*((3*Z*Z-h*h)/4/Z/Z+1./24.*pow(h/Z,4)+3./4.*Z*Z/(Z*Z-h*h))
+ + (1-1/3.*h*h/Z/Z+1/12.*pow(h/Z,4))*h/Z/Z*multiplier );
+}
+
+
+// **********************************************
+// Formulas from He, Polonsky, Su, hep-ph/0102144
+// **********************************************
+
+double F ( double x1, double x2 ) {
+ // We added the equality case, using l'Hôpital's rule
+ if ( x1 == x2 ) return 0;
+ return ( (x1+x2)/2.0 - log(x1/x2)*(x1*x2)/(x1-x2));
+}
+
+double G ( double x ) {
+ return ( -4*sqrt(4*x -1)*atan(1/sqrt(4*x-1)));
+}
+
+double f ( double x1, double x2 ) {
+ double Delta = 2*(x1+x2) - (x1-x2)*(x1-x2) -1;
+
+ if (Delta == 0) return 0;
+ if (Delta < 0)
+ return ( sqrt(-Delta)*log((x1+x2-1+sqrt(-Delta))/(x1+x2-1-sqrt(-Delta)) ));
+ //if (Delta > 0)
+ return ( -2*sqrt(Delta)*(atan((x1-x2+1)/sqrt(Delta)) - atan((x1-x2-1)/sqrt(Delta)) ) );
+}
+
+double bet22 ( double qsq, double m1sq, double m2sq ) {
+ double x1=m1sq/qsq;
+ double x2=m2sq/qsq;
+
+ if (m1sq == m2sq) {
+ return ( (qsq/24)*
+ (2*log(qsq)+2*log(x1) + (16*x1 - 10./3.) + (4*x1-1)*G(x1))
+ );
+ }
+ return ( (qsq/24)*
+ (2*log(qsq)+log(x1*x2)
+ +( pow(x1-x2,3) -3*(x1*x1 -x2*x2) +3*(x1-x2))*log(x1/x2)
+ -( 2*(x1-x2)*(x1-x2) -8*(x1+x2) +10./3.)
+ -( (x1-x2)*(x1-x2) -2*(x1+x2) +1)*f(x1,x2) -6*F(x1,x2) )
+ );
+}
+
+double bet0( double qsq, double m1sq, double m2sq ) {
+ double x1=m1sq/qsq;
+ double x2=m2sq/qsq;
+ if (m1sq == m2sq) {
+ return ( 2-2*sqrt(4*x1-1)*atan(1/sqrt(4*x1-1)));
+ }
+ return ( 1+0.5*( (x1+x2)/(x1-x2) -(x1-x2))*log(x1/x2) +0.5*f(x1,x2));
+}
+
+
+double bbar0( double m1sq, double m2sq, double m3sq ) {
+ return (
+ (m1sq*log(m1sq) -m3sq*log(m3sq))/(m1sq-m3sq)
+ -(m1sq*log(m1sq) -m2sq*log(m2sq))/(m1sq-m2sq)
+ );
+}
+
+double SH_2HDM ( double Z,
+ double H, double A, double Hc, double h,
+ double b, double a ) {
+ return 1/(M_PI*Z*Z)*(
+ sin(b-a)*sin(b-a)*bet22(Z*Z, H*H, A*A) -bet22(Z*Z, Hc*Hc, Hc*Hc)
+ +cos(b-a)*cos(b-a)*( bet22(Z*Z, h*h, A*A) +bet22(Z*Z, Z*Z, H*H) -bet22(Z*Z, Z*Z, h*h)
+ -Z*Z*bet0(Z*Z,Z*Z, H*H) +Z*Z*bet0(Z*Z,Z*Z,h*h))
+ );
+}
+
+// Our modified SH. Removed all terms which have H,A,Hc. Multiplied by -1. Took cos(b-a)={1,-1}
+// Gives the same results as SHSM()
+double SH ( double Z, double h ) {
+ return -1./(M_PI*Z*Z) * ( -bet22(Z*Z, Z*Z, h*h) +Z*Z*bet0(Z*Z,Z*Z,h*h) );
+}
+
+double TH_2HDM ( double Z, double W, double s2w,
+ double H, double A, double Hc, double h,
+ double b, double a ) {
+
+ return 1/(16*M_PI*W*W*s2w)*(
+ F(Hc*Hc, A*A) + sin(b-a)*sin(b-a)*( F(Hc*Hc, H*H) - F(A*A, H*H) )
+ + cos(b-a)*cos(b-a)*( F(Hc*Hc, h*h) - F(A*A, H*H) - F(W*W, h*h)
+ - F(Z*Z, H*H) + F(Z*Z, h*h) + 4*Z*Z*bbar0(Z*Z, H*H, h*h) - 4*W*W*bbar0(W*W, H*H, h*h) )
+ );
+}
+
+// Our modified TH. Removed all terms which have H,A,Hc. Multiplied by 3. Took cos(b-a)={1,-1}
+// It gives a difference of about -0.025 when we move from mH=114 to mH=1000, in agreement with the LEPEWWG plot
+// from http://lepewwg.web.cern.ch/LEPEWWG/plots/summer2006/s06_stu_contours.eps
+// It is also in agreement with fig.1 of He, et.al.
+// Gives the same results as THSM()
+double TH ( double Z, double W, double s2w, double h) {
+ return 3./(16*M_PI*W*W*s2w)*( - F(W*W, h*h) + F(Z*Z, h*h) ) ;
+}
+
+// IMPORTANT! He et.al. define hypercharge using Q=I_z+Y. For this reason Y=1/6 (-1/2) for quarks (leptons).
+double SF ( double Y, double Nc, double m1, double m2, double Z ) {
+ double x1=(m1/Z)*(m1/Z);
+ double x2=(m2/Z)*(m2/Z);
+ return Nc/(6*M_PI)*( 2*(4*Y+3)*x1 + 2*(-4*Y+3)*x2 - 2*Y*log(x1/x2)
+ + ((1.5+2*Y)*x1+Y)*G(x1) + ((1.5-2*Y)*x2-Y)*G(x2) );
+}
+
+double TF ( double Nc, double m1, double m2, double Z, double s2w ) {
+ double x1=(m1/Z)*(m1/Z);
+ double x2=(m2/Z)*(m2/Z);
+ return Nc/(8.*M_PI*s2w*(1-s2w)) * F(x1,x2);
+}
+
+// This formula was checked against fig 2(c).
+double UF ( double Nc, double m1, double m2, double Z ) {
+ if ( m1 == m2 ) return 0; // Limiting case added manually. Oct 8, 2009, veo.
+ double x1=(m1/Z)*(m1/Z);
+ double x2=(m2/Z)*(m2/Z);
+ return Nc/(-2*M_PI)*( (x1+x2)/2 - (x1-x2)*(x1-x2)/3 + (pow(x1-x2,3)/6-0.5*(x1*x1+x2*x2)/(x1-x2))*log(x1/x2)
+ + (x1-1)/6*f(x1,x1) + (x2-1)/6*f(x2,x2) + (1/3.-(x1+x2)/6-(x1-x2)*(x1-x2)/6)*f(x1,x2) );
+}
+
+
+// ***********************************************************
+// Majorana related formulae from Gates & Terning, PRL67, 1991
+// ***********************************************************
+
+double f1 ( double m1, double m2 ) {
+ return (3*m1*m2*m2*m2 + 3*m1*m1*m1*m2 - 4*m1*m1*m2*m2) / pow((m1*m1-m2*m2),2); }
+
+double f2 ( double m1, double m2 ) {
+ return ( pow(m1,6) - 3*pow(m1,4)*m2*m2 + 6*pow(m1*m2,3) - 3*m1*m1*pow(m2,4) + pow(m2,6) ) / pow(m1*m1-m2*m2,3) ; }
+
+double SM ( double m1, double m2, double mE ) {
+ double ctsq=pow(m2/(m1+m2),1); // Power reduced to 1: Gates and Terning has an incorrect equation 10!
+ double stsq=pow(m1/(m1+m2),1);
+ return 1/(6*M_PI)*( ctsq*2*log(m1/mE) + stsq*2*log(m2/mE) + 1.5 - stsq*ctsq*(8./3.+ f1(m1,m2) - f2(m1,m2)*2*log(m1/m2)) ); }
+
+double TM ( double m1, double m2, double mE, double s2w, double W ) {
+ double ctsq=pow(m2/(m1+m2),1); // Power reduced to 1: Gates and Terning has an incorrect equation 10!
+ double stsq=pow(m1/(m1+m2),1);
+ return 1/(16*M_PI*s2w*W*W)*( ctsq*(m1*m1+mE*mE-(2*m1*m1*mE*mE)/(m1*m1-mE*mE)*2*log(m1/mE))
+ + stsq*(m2*m2+mE*mE-(2*m2*m2*mE*mE)/(m2*m2-mE*mE)*2*log(m2/mE))
+ - stsq*ctsq*(m1*m1+m2*m2-4*m1*m2 + 2*(m1*m1*m1*m2-m1*m1*m2*m2+m1*m2*m2*m2)*2*log(m1/m2)/(m1*m1-m2*m2)) ) ;
+}
+
+
+// *******************************************************************
+// Majorana related approx and exact formulae from Kniehl & Kohrs, PRD
+// *******************************************************************
+
+double A( double m1, double m2 ) {
+ // Limiting case of m1==m2 computed with Mathematica manually (Oct 5, 2009, veo)
+ if ( m1 == m2 ) return 2*m1*m1/3;
+ return m1*m1*m2*m2/pow(m1*m1-m2*m2,2)*(-3*(m1*m1+m2*m2)+4*m1*m2)
+ + m1*m2/(m1*m1-m2*m2)*(m1*m1+m2*m2+2*m1*m1*m2*m2/pow(m1*m1-m2*m2,2)*(3*m1*m2-m1*m1-m2*m2))*2*log(m1/m2) ;
+}
+
+// SMapprox() gives the same result as SM() a la Gates & Terning, but we use the modified A(), so it also works when m1==m2.
+// It gives 0.026807 as the result to inputs 100, 200, 300, in agreement with fig.1
+double SMapprox( double m1, double m2, double mE ) {
+ return 1/(6*M_PI)/(m1+m2)*(
+ 1/(m1+m2)*(1.5*(m1*m1+m2*m2)+(m1*m2/3)+A(m1,m2))
+ + m2*2*log(m1/mE) + m1*2*log(m2/mE) );
+}
+
+// UMapprox gives -0.00180571 as the result of 100,200,300, in agreement with fig.1
+double UMapprox( double m1, double m2, double mE ) {
+ return 1/(6*M_PI)/(m1+m2)*(
+ -1/(m1+m2)*(13*(m1*m1+m2*m2)/6+5*m1*m2/3+A(m1,m2))
+ +m2/pow(m1*m1-mE*mE,2)*(4*pow(m1*mE,2)+(m1*m1+mE*mE)*(pow(m1,4)+pow(mE,4)-4*pow(m1*mE,2))/(m1*m1-mE*mE)*2*log(m1/mE))
+ +m1/pow(m2*m2-mE*mE,2)*(4*pow(m2*mE,2)+(m2*m2+mE*mE)*(pow(m2,4)+pow(mE,4)-4*pow(m2*mE,2))/(m2*m2-mE*mE)*2*log(m2/mE)) );
+}
+
+// TMexact() gives the same result as TM() a la Gates & Terning
+double TMexact( double m1, double m2, double mE, double s2w, double W ) {
+ // Limiting equality cases computed with Mathematica manually (Nov 2, 2009, veo)
+ double m1mEterm = m1==mE ? -2*mE : (m2-m1*(m1*m1+mE*mE)/(m1*m1-mE*mE))*2*log(m1/mE);
+ double m2mEterm = m2==mE ? -2*mE : (m1-m2*(m2*m2+mE*mE)/(m2*m2-mE*mE))*2*log(m2/mE);
+ double m1m2term = m1==m2 ? 4*m1*m1 : 6*m1*m2+((pow(m1,4)+pow(m2,4)-2*m1*m2*(m1*m1+m2*m2))/(m1*m1-m2*m2))*2*log(m1/m2);
+ return 1/(16*M_PI*s2w*W*W)*( mE*mE
+ + m1*m2/pow(m1+m2,2) * m1m2term
+ + m1*m2/(m1+m2) * ( m1mEterm + m2mEterm ) );
+}
+
+double complex lambda( double complex x, double y, double z) {
+ return x*x + y*y + z*z - 2*(x*y+y*z+z*x);
+}
+
+long double complex B0(double s1, double m1sq, double m2sq) {
+ const double C = 0.5772156649; // Euler-Mascheroni constant
+ long double Delta = 2/little/little-C-log(M_PI); // 2/(4-n)-C-log(M_PI);
+
+ if (s1==0 && m1sq==m2sq) return Delta - logl(m1sq);
+
+ // Imaginary part of lambda(s1+I*epsilon,m1sq,m2sq) changes sign when m1sq+m2sq<s1. This causes a sign change in the
+ // imaginary part of csqrtl(lambda(...)) term, which ends up changing the real part of B0(...) itself.
+ double epssign = (m1sq+m2sq<s1) ? -1 : 1; // Accounts for lambda(...) sign issue. veo, oct 11, 2009.
+ return Delta - 0.5*logl(m1sq*m2sq) + 2
+ + 1/s1*( -0.5*(m1sq-m2sq)*logl(m1sq/m2sq)
+ + csqrtl(lambda(s1+I*epsilon*epssign,m1sq,m2sq)) * cacoshl((m1sq+m2sq-s1-I*epsilon)/(2*sqrtl(m1sq*m2sq))) );
+}
+
+long double complex PI( int vasign, double qsq, double m1, double m2 ) {
+ if ( abs(vasign)!=1 ) {
+ printf("PI function called with wrong vasign value!\n");
+ exit(1); }
+ // the first term modified to qsq from s, a la Natale-DaSilva MPLA'95. KK paper is incorrect.
+ return 1/(12*M_PI*M_PI)*(
+ ( qsq - (m1*m1+m2*m2)/2 + vasign*3*m1*m2 - pow(m1*m1-m2*m2,2)/(2*qsq) ) * B0(qsq,m1*m1,m2*m2)
+ + m1*m1*(-1+0.5*(m1*m1-m2*m2)/qsq) * B0(0,m1*m1,m1*m1)
+ + m2*m2*(-1+0.5*(m2*m2-m1*m1)/qsq) * B0(0,m2*m2,m2*m2)
+ - qsq/3 + 0.5*pow(m1*m1-m2*m2,2)/qsq ) ;
+}
+
+long double complex PI_V( double qsq, double m1, double m2 ) { return PI( 1, qsq, m1, m2 ); }
+long double complex PI_A( double qsq, double m1, double m2 ) { return PI( -1, qsq, m1, m2 ); }
+
+// Highly recommend using the wrapper SMexactWithChecks() instead of SMexact() itself. See below!
+// SMexact() can exactly reproduce fig1.
+// For ksi=1, it gives : 0.021802, and as ksi increases, it converges on to SMapprox().
+double SMexact( double m1, double m2, double mE, double s2w, double z ) {
+ long double ctsq=m2/(m1+m2);
+ long double stsq=m1/(m1+m2);
+
+ return M_PI/z*(
+ -2*ctsq*ctsq*( creall( PI_A(z,m1,m1) ) - PI_A(0+little,m1,m1) ) // creall's are actually not needed
+ -2*stsq*stsq*( creall( PI_A(z,m2,m2) ) - PI_A(0+little,m2,m2) ) // since typecasting to double takes
+ -4*ctsq*stsq*( creall( PI_V(z,m1,m2) ) - PI_V(0+little,m1,m2) ) // only the real part of complex nos
+
+ //+3* creall( PI_V(z,mE,mE) ) // the version that appears in the paper
+ +3* ( creall( PI_V(z,mE,mE) ) - PI_V(0+little,mE,mE) ) // adding PI_V(0,...) term improves the result
+ // sin2thetaW runs between q2=mZ2 down to q2=0. Take the Kappa from Ferroglia et.al., hep-ph/0307200v2 :
+ //-pow(4*s2w-1,2)* creall( PI_V(z,mE,mE) ) + pow(4*s2w*1.0317/1.0028-1,2)* PI_V(0+little,mE,mE)
+ -1* ( creall( PI_A(z,mE,mE) ) - PI_A(0+little,mE,mE) )
+ );
+}
+
+
+// S+U exact formula, checked against fig1: SpUMexact()-SMexact() replicates fig1 successfully.
+// At ksi=1, SpUMexact()-SMexact() gives 0.00623479, and it slowly converges onto UMapprox() as in fig1.
+// At ksi=5, SpUMexact()-SMexact() gives -0.00163245, in good agreement with the UMapprox() value of -0.00180571
+// SpUMexact()-SMexact() is also checked against SF() when m1=m2 and seems ok for lowish masses - at higher masses UMapprox() looks better
+double SpUMexact( double m1, double m2, double mE, double w, double z ) {
+ long double ctsq=m2/(m1+m2);
+ long double stsq=m1/(m1+m2);
+ return 2*M_PI*(
+ -1*ctsq/w* ( creall( PI_V(w,m1,mE)+PI_A(w,m1,mE) ) - (PI_V(0+little,m1,mE)+PI_A(0+little,m1,mE)) )
+ -1*stsq/w* ( creall( PI_V(w,m2,mE)+PI_A(w,m2,mE) ) - (PI_V(0+little,m2,mE)+PI_A(0+little,m2,mE)) )
+ //+2/z * ( creall( PI_V(z,mE,mE) ) )
+ +2/z * ( creall( PI_V(z,mE,mE) ) - PI_V(0+little,mE,mE) ) // adding PI_V(little,...) slightly improves agreement with UF()
+ );
+}
+
+
+// **************************************
+// Test methods for the Majorana formulae
+// **************************************
+
+long double testB0( double m ) {
+ if ( epsilon > little / 100 ) // I could also check that imag(B0(...)) << real(B0(...))
+ printf("Your B0 implementation might have a large epsilon (%Lg) compared to q^2 scale of %Lg\n", epsilon, little );
+ long double test = creall(B0(0, m*m, m*m));
+ if ( test < 0 )
+ printf("Your B0 implementation might have a very small Delta at mass scale %g (B0=%Lg)\n", m, test );
+ test = test / creall(B0(0+little, m*m, m*m)) - 1;
+ if ( fabs(test) > 5e-6 )
+ printf("Your B0 implementation is not reliable at mass scale = %g (error~=%Lg)\n", m, test );
+ return test; }
+
+// SM exact should give the same results as SF, when m1==m2, equivalent of Dirac case
+void testSMvsSF( double m, double mE, double s2w, double Z ){
+ double sf = SF(-0.5, 1, m, mE, Z);
+ double sm = SMexact(m, m, mE, s2w, Z*Z);
+ if ( fabs(sf/sm-1) > 1e-4 || fabs(sf-sm) > 1e-4 )
+ printf("Testing failed for m1=m2=%g, mE=%g, Sdirac=%g\tSmaj=%g\n", m, mE, sf, sm );
+}
+
+double SMexactWithChecks( double m1, double m2, double mE, double s2w, double Z ){
+
+ // Before we move on to the actual calculation, let's test if our epsilon and little are OK.
+ testB0(m1); testB0(m2);
+
+ // for the two neutrinos masses check that maj->dirac
+ testSMvsSF( m1, mE, s2w, Z );
+ testSMvsSF( m2, mE, s2w, Z );
+
+ // Now test against SM approx.
+ double smapprox = SMapprox(m1, m2, mE);
+ double smexact = SMexact(m1, m2, mE, s2w, Z*Z);
+ if ( fabs(smapprox/smexact-1) > 0.25 || fabs(smapprox-smexact) > 0.1 )
+ printf("Warning! Approx and exact formulas differ significantly! Sa=%g\tSe=%g\n", smapprox, smexact );
+ return smexact;
+}
+
+double UMexactWithChecks( double m1, double m2, double mE, double s2w, double Z, double smexact ) {
+ double w = Z*Z*(1-s2w);
+ // if smexact has been provided for us, we use it, otherwise we compute:
+ if ( smexact == 0 )
+ smexact = SMexactWithChecks( m1, m2, mE, s2w, Z );
+
+ // Test against UM approx.
+ double umapprox = UMapprox(m1,m2,mE);
+ double umexact = SpUMexact(m1,m2,mE,w,Z*Z) - smexact;
+ if ( fabs(umapprox-umexact) > 0.05 )
+ printf("Warning! Approx and exact formulas differ significantly! Ua=%g\tUe=%g\n", umapprox, umexact );
+ return umexact;
+}
+
+
+// ******************************
+// Other functions of convenience
+// ******************************
+
+// Contributions from the changes in the reference Higgs and top-quark masses
+double SshiftFromRef( double h, double href, double t, double tref, double Z ) {
+ double shift = SF(1/6., 3, t, 500, Z) - SF(1/6., 3, tref, 500, Z); // Sshift is independent of b-quark mass
+ shift += SH(Z,h) - SH(Z,href);
+ return shift;
+}
+
+double TshiftFromRef( double h, double href, double t, double tref, double Z, double s2w ) {
+ double shift = TF(3, t, 4.5, Z, s2w) - TF(3, tref, 4.5, Z, s2w);
+ double W = Z*sqrt(1-s2w);
+ shift += TH(Z,W,s2w,h) - TH(Z,W,s2w,href);
+ return shift;
+}
Index: tags/opucem-00-00-00/inc/opucem.h
===================================================================
--- tags/opucem-00-00-00/inc/opucem.h (revision 0)
+++ tags/opucem-00-00-00/inc/opucem.h (revision 7)
@@ -0,0 +1,80 @@
+#include <math.h>
+#include <complex.h>
+
+
+// **************************************************
+// Formulas from Forshaw, Ross, White, hep-ph/0107232
+// **************************************************
+
+double THSM ( double Z, double s2w, double h );
+double SHSM ( double Z, double h );
+
+// **********************************************
+// Formulas from He, Polonsky, Su, hep-ph/0102144
+// **********************************************
+
+double F ( double x1, double x2 );
+double G ( double x );
+double f ( double x1, double x2 );
+double bet22 ( double qsq, double m1sq, double m2sq );
+double bet0( double qsq, double m1sq, double m2sq );
+double bbar0( double m1sq, double m2sq, double m3sq );
+double SH_2HDM ( double Z,
+ double H, double A, double Hc, double h,
+ double b, double a );
+double SH ( double Z, double h );
+double TH_2HDM ( double Z, double W, double s2w,
+ double H, double A, double Hc, double h,
+ double b, double a );
+double TH ( double Z, double W, double s2w, double h );
+
+// IMPORTANT! He et.al. define hypercharge using Q=I_z+Y. For this reason Y=1/6 (-1/2) for quarks (leptons).
+double SF ( double Y, double Nc, double m1, double m2, double Z );
+double TF ( double Nc, double m1, double m2, double Z, double s2w );
+double UF ( double Nc, double m1, double m2, double Z );
+
+// ***********************************************************
+// Majorana related formulae from Gates & Terning, PRL67, 1991
+// ***********************************************************
+
+double f1 ( double m1, double m2 );
+double f2 ( double m1, double m2 );
+double SM ( double m1, double m2, double mE );
+double TM ( double m1, double m2, double mE, double s2w, double W );
+
+// *******************************************************************
+// Majorana related exact and approx formulae from Kniehl & Kohrs, PRD
+// *******************************************************************
+
+// Very small number to be used as imaginary part in complex integrals.
+static const long double epsilon = 0.00005;
+// PI() formulas have problems at q^2=0. We need a scale << m_Z^2.
+static const long double little = 91.1875*91.1875*0.00004;
+
+double A( double m1, double m2 );
+double SMapprox( double m1, double m2, double mE );
+double UMapprox( double m1, double m2, double mE );
+double TMexact( double m1, double m2, double mE, double s2w, double W );
+double complex lambda( double complex x, double y, double z );
+long double complex B0(double s1, double m1sq, double m2sq );
+long double complex PI( int vasign, double qsq, double m1, double m2 );
+long double complex PI_V( double qsq, double m1, double m2 );
+long double complex PI_A( double qsq, double m1, double m2 );
+double SMexact( double m1, double m2, double mE, double s2w, double z );
+double SpUMexact( double m1, double m2, double mE, double w, double z );
+
+// **************************************
+// Test methods for the Majorana formulae
+// **************************************
+
+long double testB0( double m );
+void testSMvsSF( double m, double mE, double s2w, double Z );
+double SMexactWithChecks( double m1, double m2, double mE, double s2w, double Z );
+double UMexactWithChecks( double m1, double m2, double mE, double s2w, double Z, double smexact );
+
+// ******************************
+// Other functions of convenience
+// ******************************
+
+double SshiftFromRef( double h, double href, double t, double tref, double Z );
+double TshiftFromRef( double h, double href, double t, double tref, double Z, double s2w );

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