diff --git a/src/Wjets.cc b/src/Wjets.cc index 609290c..c471e6a 100644 --- a/src/Wjets.cc +++ b/src/Wjets.cc @@ -1,648 +1,593 @@ /** * \authors The HEJ collaboration (see AUTHORS for details) * \date 2020 * \copyright GPLv2 or later */ #include "HEJ/Wjets.hh" #include #include #include #include #include #include "HEJ/Constants.hh" #include "HEJ/EWConstants.hh" #include "HEJ/LorentzVector.hh" #include "HEJ/exceptions.hh" #include "HEJ/jets.hh" // generated headers #include "HEJ/currents/jV_j.hh" #include "HEJ/currents/jV_juno.hh" #include "HEJ/currents/jVuno_j.hh" #include "HEJ/currents/jW_jqqbar.hh" #include "HEJ/currents/jW_qqbar_j.hh" #include "HEJ/currents/jWqqbar_j.hh" #include "HEJ/currents/j_Wqqbar_j.hh" namespace HEJ { namespace currents { namespace { using COM = std::complex; // --- Helper Functions --- // FKL W Helper Functions double WProp(const HLV & plbar, const HLV & pl, ParticleProperties const & wprop ){ COM propW = COM(0.,-1.)/( (pl+plbar).m2() - wprop.mass*wprop.mass + COM(0.,1.)*wprop.mass*wprop.width); double PropFactor=(propW*conj(propW)).real(); return PropFactor; } /** * @brief Contraction of W + unordered jet current with FKL current * * See eq:wunocurrent in the developer manual for the definition * of the W + unordered jet current */ template double jM2Wuno( HLV const & pg, HLV const & p1, HLV const & plbar, HLV const & pl, HLV const & pa, HLV const & p2, HLV const & pb, ParticleProperties const & wprop ){ using helicity::minus; const COM u1 = U1(p1, p2, pa, pb, pg, pl, plbar); const COM u2 = U2(p1, p2, pa, pb, pg, pl, plbar); const COM l = L(p1, p2, pa, pb, pg, pl, plbar); const COM x = u1 - l; const COM y = u2 + l; double amp = C_A*C_F*C_F/2.*(norm(x)+norm(y)) - C_F/2.*(x*conj(y)).real(); amp *= WProp(plbar, pl, wprop); const HLV q1g = pa-pl-plbar-p1-pg; const HLV q2 = p2-pb; const double t1 = q1g.m2(); const double t2 = q2.m2(); amp /= (t1*t2); return amp; } /** * @brief Contraction of W + extremal qqbar current with FKL current * * See eq:crossed in the developer manual for the definition * of the W + extremal qqbar current. * */ template double jM2_W_extremal_qqbar( HLV const & pg, HLV const & pq, HLV const & plbar, HLV const & pl, HLV const & pqbar, HLV const & p3, HLV const & pb, ParticleProperties const & wprop ){ const COM u1Xcontr = U1X(pg, pq, plbar, pl, pqbar, p3, pb); const COM u2Xcontr = U2X(pg, pq, plbar, pl, pqbar, p3, pb); const COM lXcontr = LX(pg, pq, plbar, pl, pqbar, p3, pb); const COM x = u1Xcontr - lXcontr; const COM y = u2Xcontr + lXcontr; double amp = C_A*C_F*C_F/2.*(norm(x)+norm(y)) - C_F/2.*(x*conj(y)).real(); amp *= WProp(plbar, pl, wprop); const HLV q1 = pg-pl-plbar-pq-pqbar; const HLV q2 = p3-pb; const double t1 = q1.m2(); const double t2 = q2.m2(); amp /= (t1*t2); return amp; } } // Anonymous Namespace //! W+Jets FKL Contributions double ME_W_qQ( HLV const & p1out, HLV const & plbar, HLV const & pl, HLV const & p1in, HLV const & p2out, HLV const & p2in, ParticleProperties const & wprop ){ using helicity::minus; using helicity::plus; const COM ampm = jV_j(p1in,p1out,p2in,p2out,pl,plbar); const COM ampp = jV_j(p1in,p1out,p2in,p2out,pl,plbar); const double Msqr = std::norm(ampm) + std::norm(ampp); return WProp(plbar, pl, wprop) * Msqr; } namespace { // helicity amplitude squares for contraction of W current with unordered // current template double ampsq_jW_juno( HLV const & pa, HLV const & p1, HLV const & pb, HLV const & p2, HLV const & pg, HLV const & pl, HLV const & plbar ){ using helicity::minus; const COM u1 = U1_jV(pa,p1,pb,p2,pg,pl,plbar); const COM u2 = U2_jV(pa,p1,pb,p2,pg,pl,plbar); const COM l = L_jV(pa,p1,pb,p2,pg,pl,plbar); return 2.*C_F*std::real((l-u1)*std::conj(l+u2)) + 2.*C_F*C_F/3.*std::norm(u1+u2) ; } - - /** - * @brief W+Jets Unordered Contributions, function to handle all incoming types. - * @param p1out Outgoing Particle 1. (W emission) - * @param plbar Outgoing election momenta - * @param pl Outgoing neutrino momenta - * @param p1in Incoming Particle 1. (W emission) - * @param p2out Outgoing Particle 2 (Quark, unordered emission this side.) - * @param p2in Incoming Particle 2 (Quark, unordered emission this side.) - * @param pg Unordered Gluon momenta - * @param aqlineb Bool. Is Backwards quark line an anti-quark line? - * @param aqlinef Bool. Is Forwards quark line an anti-quark line? - * - * Calculates j_W ^\mu j_{uno}_\mu. Ie, unordered with W emission - * opposite side. Handles all possible incoming states. - * - * @TODO use const & for pl plbar - */ - double jW_juno( - HLV const & p1out, HLV plbar, HLV pl, HLV const & p1in, - HLV const & p2out, HLV const & p2in, HLV const & pg, - bool /* aqlineb */, bool /* aqlinef */, - ParticleProperties const & wprop - ){ - using helicity::minus; - using helicity::plus; - - // helicity assignments assume quarks - // in the end, this is irrelevant since we sum over all helicities - const double ampsq = - + ampsq_jW_juno(p1in,p1out,p2in,p2out,pg,pl,plbar) - + ampsq_jW_juno(p1in,p1out,p2in,p2out,pg,pl,plbar) - + ampsq_jW_juno(p1in,p1out,p2in,p2out,pg,pl,plbar) - + ampsq_jW_juno(p1in,p1out,p2in,p2out,pg,pl,plbar) - ; - - const HLV q1=p1in-p1out-plbar-pl; - const HLV q2=-(p2in-p2out-pg); - - //! @TODO explain magic 16 - return WProp(plbar, pl, wprop)*ampsq/(16.*q2.m2()*q1.m2()); - } } // Anonymous Namespace double ME_W_unob_qQ( HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in, HLV const & pg, HLV const & plbar, HLV const & pl, ParticleProperties const & wprop ){ - return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, false, wprop); + using helicity::minus; + using helicity::plus; + + // helicity assignments assume quarks + // in the end, this is irrelevant since we sum over all helicities + const double ampsq = + + ampsq_jW_juno(p2in,p2out,p1in,p1out,pg,pl,plbar) + + ampsq_jW_juno (p2in,p2out,p1in,p1out,pg,pl,plbar) + + ampsq_jW_juno (p2in,p2out,p1in,p1out,pg,pl,plbar) + + ampsq_jW_juno (p2in,p2out,p1in,p1out,pg,pl,plbar) + ; + + const double t1 = (p1in - p1out - pg).m2(); + const double tn = (p2in - p2out - plbar - pl).m2(); + + //! @TODO explain magic 16 + return WProp(plbar, pl, wprop)*ampsq/(16.*t1*tn); } namespace { // helicity sum helper for jWuno_j(...) template double jWuno_j_helsum( HLV const & pg, HLV const & p1, HLV const & plbar, HLV const & pl, HLV const & pa, HLV const & p2, HLV const & pb, ParticleProperties const & wprop ){ using helicity::minus; using helicity::plus; const double ME2h1pp = jM2Wuno( pg, p1, plbar, pl, pa, p2, pb, wprop ); const double ME2h1pm = jM2Wuno( pg, p1, plbar, pl, pa, p2, pb, wprop ); const double ME2h1mp = jM2Wuno( pg, p1, plbar, pl, pa, p2, pb, wprop ); const double ME2h1mm = jM2Wuno( pg, p1, plbar, pl, pa, p2, pb, wprop ); return ME2h1pp + ME2h1pm + ME2h1mp + ME2h1mm; } - /** - * @brief W+Jets Unordered Contributions, function to handle all incoming - * @types. - * @param pg Unordered Gluon momenta - * @param p1out Outgoing Particle 1. (Quark - W and Uno emission) - * @param plbar Outgoing election momenta - * @param pl Outgoing neutrino momenta - * @param p1in Incoming Particle 1. (Quark - W and Uno emission) - * @param p2out Outgoing Particle 2 - * @param p2in Incoming Particle 2 - * @param aqlineb Bool. Is Backwards quark line an anti-quark line? - * - * Calculates j_W_{uno} ^\mu j_\mu. Ie, unordered with W emission same - * side. Handles all possible incoming states. Note this handles both forward - * and back- -ward Wuno emission. For forward, ensure p1out is the uno and W - * emission parton. - * @TODO: Include separate wrapper functions for forward and backward to clean -up * ME_W_unof_current in `MatrixElement.cc`. - */ - double jWuno_j( - HLV const & pg, HLV const & p1out, HLV const & plbar, HLV const & pl, - HLV const & p1in, HLV const & p2out, HLV const & p2in, bool aqlineb, - ParticleProperties const & wprop - ){ - const auto helsum = aqlineb? - jWuno_j_helsum: - jWuno_j_helsum; - - //Helicity sum and average over initial states - return helsum(pg, p1out,plbar,pl,p1in,p2out,p2in, wprop)/(4.*C_A*C_A); - } } // Anonymous Namespace double ME_Wuno_qQ( HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in, HLV const & pg, HLV const & plbar, HLV const & pl, ParticleProperties const & wprop ){ - return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop); + return jWuno_j_helsum( + pg, p1out, plbar, pl, p1in, p2out, p2in, wprop + )/(4.*C_A*C_A); } // helicity sum helper for jWqqbar_j(...) template double jWqqbar_j_helsum( HLV const & pg, HLV const & pq, HLV const & plbar, HLV const & pl, HLV const & pqbar, HLV const & p3, HLV const & pb, ParticleProperties const & wprop ){ using helicity::minus; using helicity::plus; const double amp_h1pp = jM2_W_extremal_qqbar( pg, pq, plbar, pl, pqbar, p3, pb, wprop ); const double amp_h1pm = jM2_W_extremal_qqbar( pg, pq, plbar, pl, pqbar, p3, pb, wprop ); const double amp_h1mp = jM2_W_extremal_qqbar( pg, pq, plbar, pl, pqbar, p3, pb, wprop ); const double amp_h1mm = jM2_W_extremal_qqbar( pg, pq, plbar, pl, pqbar, p3, pb, wprop ); return amp_h1pp + amp_h1pm + amp_h1mp + amp_h1mm; } /** * @brief W+Jets Extremal qqbar Contributions, function to handle all incoming * @types. * @param pgin Incoming gluon which will split into qqbar. * @param pqout Quark of extremal qqbar outgoing (W-Emission). * @param plbar Outgoing anti-lepton momenta * @param pl Outgoing lepton momenta * @param pqbarout Anti-quark of extremal qqbar pair. (W-Emission) * @param pout Outgoing Particle 2 (end of FKL chain) * @param p2in Incoming Particle 2 * @param aqlinef Bool. Is Forwards quark line an anti-quark line? * * Calculates j_W_{qqbar} ^\mu j_\mu. Ie, Ex-QQbar with W emission same side. * Handles all possible incoming states. Calculated via crossing symmetry from * jWuno_j. */ double jWqqbar_j( HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl, HLV const & pqbarout, HLV const & p2out, HLV const & p2in, bool aqlinef, ParticleProperties const & wprop ){ const auto helsum = aqlinef? jWqqbar_j_helsum: jWqqbar_j_helsum; //Helicity sum and average over initial states. double ME2 = helsum(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, wprop)/ (4.*C_A*C_A); //Correct colour averaging after crossing: ME2*=(3.0/8.0); return ME2; } double ME_WExqqbar_qbarqQ( HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl, HLV const & pqbarout, HLV const & p2out, HLV const & p2in, ParticleProperties const & wprop ){ return jWqqbar_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop); } double ME_WExqqbar_qqbarQ( HLV const & pgin, HLV const & pqbarout, HLV const & plbar, HLV const & pl, HLV const & pqout, HLV const & p2out, HLV const & p2in, ParticleProperties const & wprop ){ return jWqqbar_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop); } double ME_WExqqbar_qbarqg( HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl, HLV const & pqbarout, HLV const & p2out, HLV const & p2in, ParticleProperties const & wprop ){ return jWqqbar_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop) *K_g(p2out,p2in)/C_F; } double ME_WExqqbar_qqbarg( HLV const & pgin, HLV const & pqbarout, HLV const & plbar, HLV const & pl, HLV const & pqout, HLV const & p2out, HLV const & p2in, ParticleProperties const & wprop ){ return jWqqbar_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop) *K_g(p2out,p2in)/C_F; } namespace { template double jW_jqqbar( HLV const & pb, HLV const & p2, HLV const & p3, HLV const & pa, HLV const & p1, HLV const & pl, HLV const & plbar ){ using std::norm; static constexpr double cm1m1 = 8./3.; static constexpr double cm2m2 = 8./3.; static constexpr double cm3m3 = 6.; static constexpr double cm1m2 =-1./3.; static constexpr COM cm1m3 = COM{0.,-3.}; static constexpr COM cm2m3 = COM{0.,3.}; const COM m1 = jW_qggm1(pb,p2,p3,pa,p1,pl,plbar); const COM m2 = jW_qggm2(pb,p2,p3,pa,p1,pl,plbar); const COM m3 = jW_qggm3(pb,p2,p3,pa,p1,pl,plbar); return + cm1m1*norm(m1) + cm2m2*norm(m2) + cm3m3*norm(m3) + 2.*real(cm1m2*m1*conj(m2)) + 2.*real(cm1m3*m1*conj(m3)) + 2.*real(cm2m3*m2*conj(m3)) ; } } // Anonymous Namespace // contraction of W current with extremal qqbar on the other side double ME_W_Exqqbar_QQq( HLV const & pa, HLV const & pb, HLV const & p1, HLV const & p2, HLV const & p3, HLV const & plbar, HLV const & pl, bool aqlinepa, ParticleProperties const & wprop ){ using helicity::minus; using helicity::plus; const double wPropfact = WProp(plbar, pl, wprop); const double prefactor = 2.*wPropfact /24./4./((pa-p1-pl-plbar).m2()*(p2+p3-pb).m2()); if(aqlinepa) { return prefactor*( jW_jqqbar(pb,p2,p3,pa,p1,pl,plbar) + jW_jqqbar(pb,p2,p3,pa,p1,pl,plbar) ); } return prefactor*( jW_jqqbar(pb,p2,p3,pa,p1,pl,plbar) + jW_jqqbar(pb,p2,p3,pa,p1,pl,plbar) ); } namespace { // helper function for matrix element for W + Jets with central qqbar template double amp_WCenqqbar_qq( HLV const & pa, HLV const & p1, HLV const & pb, HLV const & p4, HLV const & pq, HLV const & pqbar, HLV const & pl, HLV const & plbar, HLV const & q11, HLV const & q12 ){ using std::norm; const COM sym = M_sym_W( pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12 ); const COM cross = M_cross_W( pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12 ); const COM uncross = M_uncross_W( pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12 ); // Colour factors static constexpr double cmsms = 3.; static constexpr double cmumu = 4./3.; static constexpr double cmcmc = 4./3.; static constexpr COM cmsmu = COM{0., 3./2.}; static constexpr COM cmsmc = COM{0.,-3./2.}; static constexpr double cmumc = -1./6.; return +cmsms*norm(sym) +cmumu*norm(uncross) +cmcmc*norm(cross) +2.*real(cmsmu*sym*conj(uncross)) +2.*real(cmsmc*sym*conj(cross)) +2.*real(cmumc*uncross*conj(cross)) ; } } // Anonymous Namespace // matrix element for W + Jets with W emission off central qqbar double ME_WCenqqbar_qq( HLV const & pa, HLV const & pb, HLV const & pl, HLV const & plbar, std::vector const & partons, bool /* aqlinepa */, bool /* aqlinepb */, bool qqbar_marker, int nabove, ParticleProperties const & wprop ){ using helicity::plus; using helicity::minus; CLHEP::HepLorentzVector q1 = pa; for(int i = 0; i <= nabove; ++i){ q1 -= partons[i]; } const auto qq = split_into_lightlike(q1); // since q1.m2() < 0 the following assertion is always true // see documentation for split_into_lightlike assert(qq.second.e() < 0); HLV pq; HLV pqbar; if (qqbar_marker){ pqbar = partons[nabove+1]; pq = partons[nabove+2];} else{ pq = partons[nabove+1]; pqbar = partons[nabove+2]; } const HLV p1 = partons.front(); const HLV p4 = partons.back(); // 4 Different Helicity Choices (Differs from Pure Jet Case, where there is // also the choice in qqbar helicity. // the first helicity label is for aqlinepa == true, // the second one for aqlinepb == true // In principle the corresponding helicity should be flipped // if either of them is false, but we sum up all helicities, // so this has no effect in the end. const double amp_mm = amp_WCenqqbar_qq( pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_mp = amp_WCenqqbar_qq( pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_pm = amp_WCenqqbar_qq( pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_pp = amp_WCenqqbar_qq( pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second ); // Divide by t channels, extremal + adjacent central vertex const double ta = (pa-p1).m2(); const double t1 = q1.m2(); const double t3 = (q1-pl-plbar-pq-pqbar).m2(); const double tb = (p4-pb).m2(); const double amp = WProp(plbar, pl, wprop)*( amp_mm+amp_mp+amp_pm+amp_pp )/(9.*4.*ta*t1*t3*tb); return amp; } // helper function for matrix element for W + Jets with central qqbar // W emitted off extremal parton // @TODO: code duplication with amp_WCenqqbar_qq template double amp_W_Cenqqbar_qq( HLV const & pa, HLV const & p1, HLV const & pb, HLV const & pn, HLV const & pq, HLV const & pqbar, HLV const & pl, HLV const & plbar, HLV const & q11, HLV const & q12 ){ using std::norm; const COM crossed = M_cross( pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12 ); const COM uncrossed = M_qbar( pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12 ); const COM sym = M_sym( pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12 ); //Colour factors: static constexpr double cmsms = 3.; static constexpr double cmumu = 4./3.; static constexpr double cmcmc = 4./3.; static constexpr COM cmsmu = COM{0.,3./2.}; static constexpr COM cmsmc = COM{0.,-3./2.}; static constexpr double cmumc = -1./6.; return +cmsms*norm(sym) +cmumu*norm(uncrossed) +cmcmc*norm(crossed) +2.*real(cmsmu*sym*conj(uncrossed)) +2.*real(cmsmc*sym*conj(crossed)) +2.*real(cmumc*uncrossed*conj(crossed)) ; } // matrix element for W + Jets with W emission *not* off central qqbar double ME_W_Cenqqbar_qq( HLV pa, HLV pb, HLV pl,HLV plbar, std::vector partons, bool aqlinepa, bool aqlinepb, bool qqbar_marker, int nabove, int nbelow, bool forwards, ParticleProperties const & wprop ){ using helicity::minus; using helicity::plus; if (!forwards){ //If Emission from Leg a instead, flip process. std::swap(pa, pb); std::reverse(partons.begin(),partons.end()); std::swap(aqlinepa, aqlinepb); qqbar_marker = !qqbar_marker; std::swap(nabove,nbelow); } HLV q1=pa; for(int i=0;i( pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_mp = amp_W_Cenqqbar_qq( pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_pm = amp_W_Cenqqbar_qq( pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second ); const double amp_pp = amp_W_Cenqqbar_qq( pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second ); // Divide by t channels, extremal + adjacent central vertex const double ta = (pa-p1).m2(); const double t1 = q1.m2(); const double t3 = (q1 - pq - pqbar).m2(); const double tb = (pn+pl+plbar-pb).m2(); const double amp= WProp(plbar, pl, wprop)*( amp_mm+amp_mp+amp_pm+amp_pp )/(9.*4.*ta*t1*t3*tb); return amp; } } // namespace currents } // namespace HEJ