######################################################################## # Standard Model with trivial CKM matrix (CompHEP: Feynman gauge) # Independent parameters parameter GF 1.16639E-5 # Fermi constant parameter mZ 91.1882 # Z-boson mass parameter mW 80.419 # W-boson mass parameter mH 200 # Higgs mass parameter alphas 0.1178 # Strong coupling constant (Z point) parameter me 0.000511 # electron mass parameter mmu 0.1057 # muon mass parameter mtau 1.777 # tau-lepton mass parameter ms 0.12 # s-quark mass parameter mc 1.25 # c-quark mass parameter mb 4.2 # b-quark mass parameter mtop 174 # t-quark mass parameter wtop 1.523 # t-quark width parameter wZ 2.443 # Z-boson width parameter wW 2.049 # W-boson width parameter wH 1.419 # Higgs width # Here are the values from PDG 2006 parameter vckm11 0.97383 # Vud parameter vckm12 0.2272 # Vus parameter vckm13 0.00396 # Vub parameter vckm21 -0.2271 # Vcd parameter vckm22 0.97296 # Vcs parameter vckm23 0.04221 # Vcb parameter vckm31 0.00814 # Vtd parameter vckm32 -0.04161 # Vts parameter vckm33 0.99910 # Vtb parameter khgaz 1.000 # anomaly Higgs couplings K factors parameter khgaga 1.000 # anomaly Higgs couplings K factors parameter khgg 1.000 # anomaly Higgs couplings K factors # Dependent parameters derived v 1/Sqrt(Sqrt2*GF) # v (Higgs vev) derived cw mW/mZ # cos(theta-W) derived sw Sqrt(1-cw**2) # sin(theta-W) derived ee 2*sw*mW*Sqrt(Sqrt2*GF) # em-coupling (GF scheme) derived ez ee/(sw*cw) derived ey ee*(sw/cw) derived aQED ee**2/(4*3.1415926536) # alpha_QED derived aQEDi 1/aQED # alpha_QED inverse derived sw2 sw*sw # sin^2(theta-W) ######################################################################## # Particle content # The quarks particle D_QUARK 1 parton spin 1/2, isospin -1/2, charge -1/3, color 3 name d, down anti chep:D, omega:dbar, mad:d~, tex:"\bar{d}" particle U_QUARK 2 parton spin 1/2, isospin 1/2, charge 2/3, color 3 name u, up anti chep:U, omega:ubar, mad:u~, tex:"\bar{u}" particle S_QUARK 3 like D_QUARK name s, strange anti chep:S, omega:sbar, mad:s~, tex:"\bar{s}" mass ms particle C_QUARK 4 like U_QUARK name c, charm anti chep:C, omega:cbar, mad:c~, tex:"\bar{c}" mass mc particle B_QUARK 5 like D_QUARK name b, bottom anti chep:B, omega:bbar, mad:b~, tex:"\bar{b}" mass mb particle T_QUARK 6 like U_QUARK name t, top anti chep:T, omega:tbar, mad:t~, tex:"\bar{t}" mass mtop, width wtop # The leptons particle E_LEPTON 11 spin 1/2, isospin -1/2, charge -1 name e, mad:omega:e-, chep:e1, electron, tex:e^- anti mad:omega:e+, chep:E1, positron, tex:e^+ mass me particle E_NEUTRINO 12 left spin 1/2, isospin 1/2 name nu_e, omega:nue, chep:n1, mad:ve, e-neutrino, tex:\nu_e anti omega:nuebar, chep:N1, mad:ve~, tex:\bar\nu_e particle MU_LEPTON 13 like E_LEPTON name mu, mad:omega:mu-, chep:e2, muon, tex:\mu^- anti mad:omega:mu+, chep:E2, tex:\mu^+ mass mmu particle MU_NEUTRINO 14 like E_NEUTRINO name nu_mu, omega:numu, chep:n2, mad:vm, mu-neutrino, tex:\nu_\mu anti omega:numubar, chep:N2, mad:vm~, tex:\bar\nu_\mu particle TAU_LEPTON 15 like E_LEPTON name tau, omega:tau-, chep:e3, mad:ta-, tauon, tex:\tau^- anti omega:tau+, chep:E3, mad:ta+, tex:\tau^+ mass mtau particle TAU_NEUTRINO 16 like E_NEUTRINO name nu_tau, omega:nutau, chep:n3, mad:vt, tau_neutrino, tex:\nu_\tau anti omega:nutaubar, chep:N3, mad:vt~, tex:\bar\nu_\tau # The vector bosons particle GLUON 21 parton gauge spin 1, color 8 name g, omega: gl, chep:G, gluon particle PHOTON 22 gauge spin 1 name gamma, omega:chep:mad:A, photon, tex:\gamma particle Z_BOSON 23 gauge spin 1 name Z mass mZ, width wZ particle W_BOSON 24 gauge spin 1, charge 1 name W+, tex:W^+ anti omega:chep:mad:W-, tex:W^- mass mW, width wW # The Higgs particle HIGGS 25 spin 0 name H, h, Higgs mass mH, width wH ######################################################################## # Vertices of the Standard model # In graphs with identical structure, the first vertex is kept for phase space, # therefore, lighter particles come before heavier ones. # QED vertex D d A chep: { (-1/3)*ee | G(m3) } mad: { ee/3 | QED } vertex U u A chep: { (2/3)*ee | G(m3) } mad: { -ee*2/3 | QED } vertex S s A chep: { (-1/3)*ee | G(m3) } mad: { ee/3 | QED } vertex C c A chep: { (2/3)*ee | G(m3) } mad: { -ee*2/3 | QED } vertex B b A chep: { (-1/3)*ee | G(m3) } mad: { ee/3 | QED } vertex T t A chep: { (2/3)*ee | G(m3) } mad: { -ee*2/3 | QED } vertex E1 e1 A chep: { -ee | G(m3) } mad: { ee | QED } vertex E2 e2 A chep: { -ee | G(m3) } mad: { ee | QED } vertex E3 e3 A chep: { -ee | G(m3) } mad: { ee | QED } # QCD vertex G G G chep: { gg | m1.m2*(p1-p2).m3+m2.m3*(p2-p3).m1+m3.m1*(p3-p1).m2 } mad: { gg | QCD } vertex G G G G mad: { gg | QCD } vertex G G G.t chep: { gg/Sqrt2 | m1.M3*m2.m3-m1.m3*m2.M3 } vertex G.C G.c G chep: { -gg | p1.m3 } vertex D d G chep: { gg | G(m3) } mad: { -gg | QCD } vertex U u G chep: { gg | G(m3) } mad: { -gg | QCD } vertex S s G chep: { gg | G(m3) } mad: { -gg | QCD } vertex C c G chep: { gg | G(m3) } mad: { -gg | QCD } vertex B b G chep: { gg | G(m3) } mad: { -gg | QCD } vertex T t G chep: { gg | G(m3) } mad: { -gg | QCD } # Neutral currents vertex D d Z chep: { -ee/(12*sw*cw) | +3*G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2/3)/2, -ey/3 /) | QFD } vertex U u Z chep: { -ee/(12*sw*cw) | -3*G(m3)*(1-G5)+8*(sw^ 2)*G(m3) } mad: { (/ -ez*( 1-4*sw2/3)/2, ey*2/3 /) | QFD } vertex S s Z chep: { -ee/(12*sw*cw) | +3*G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2/3)/2, -ey/3 /) | QFD } vertex C c Z chep: { -ee/(12*sw*cw) | -3*G(m3)*(1-G5)+8*(sw^ 2)*G(m3) } mad: { (/ -ez*( 1-4*sw2/3)/2, ey*2/3 /) | QFD } vertex B b Z chep: { -ee/(12*sw*cw) | +3*G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2/3)/2, -ey/3 /) | QFD } vertex T t Z chep: { -ee/(12*sw*cw) | -3*G(m3)*(1-G5)+8*(sw^ 2)*G(m3) } mad: { (/ -ez*( 1-4*sw2/3)/2, ey*2/3 /) | QFD } vertex E1 e1 Z chep: { -ee/(4*sw*cw) | G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2)/2, -ey /) | QFD } vertex E2 e2 Z chep: { -ee/(4*sw*cw) | G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2)/2, -ey /) | QFD } vertex E3 e3 Z chep: { -ee/(4*sw*cw) | G(m3)*(1-G5)-4*(sw^ 2)*G(m3) } mad: { (/ -ez*(-1+2*sw2)/2, -ey /) | QFD } vertex N1 n1 Z chep: { ee/(4*sw*cw) | G(m3)*(1-G5) } mad: { (/ -ez/2, zero /) | QFD } vertex N2 n2 Z chep: { ee/(4*sw*cw) | G(m3)*(1-G5) } mad: { (/ -ez/2, zero /) | QFD } vertex N3 n3 Z chep: { ee/(4*sw*cw) | G(m3)*(1-G5) } mad: { (/ -ez/2, zero /) | QFD } # Charged currents # For Comphep and Madgraph things do not work with this model!!! vertex U d W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex C s W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex T b W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex D u W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex S c W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex B t W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex N1 e1 W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex N2 e2 W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex N3 e3 W+ chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex E1 n1 W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex E2 n2 W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex E3 n3 W- chep: { ee/(2*Sqrt2*sw) | G(m3)*(1-G5) } mad: { (/ -ee/sqrt(2*sw2), zero /) | QFD } vertex U s W+ vertex U b W+ vertex C d W+ vertex C b W+ vertex T d W+ vertex T s W+ vertex S u W- vertex B u W- vertex D c W- vertex B c W- vertex D t W- vertex S t W- # Yukawa (neutral) vertex S s H chep: { -ee*ms/(2*mW*sw) } mad: { -ms/v | QFD } vertex C c H chep: { -ee*mc/(2*mW*sw) } mad: { -mc/v | QFD } vertex B b H chep: { -ee*mb/(2*mW*sw) } mad: { -mb/v | QFD } vertex T t H chep: { -ee*mtop/(2*mW*sw) } mad: { -mtop/v | QFD } vertex E2 e2 H chep: { -ee*mmu/(2*mW*sw) } mad: { -mmu/v | QFD } vertex E3 e3 H chep: { -ee*mtau/(2*mW*sw) } mad: { -mtau/v | QFD } vertex S s Z.f chep: { i*ee*ms/(2*mW*sw) | G5 } vertex C c Z.f chep: { -i*ee*mc/(2*mW*sw) | G5 } vertex B b Z.f chep: { i*ee*mb/(2*mW*sw) | G5 } vertex T t Z.f chep: { -i*ee*mtop/(2*mW*sw) | G5 } vertex E2 e2 Z.f chep: { i*ee*mmu/(2*mW*sw) | G5 } vertex E3 e3 Z.f chep: { i*ee*mtau/(2*mW*sw) | G5 } # Yukawa (charged) # No CKM mixing included for Goldstone boson vertices !!! vertex C s W+.f chep: { -i*ee/(2*Sqrt2*mW*sw) | ms*(1+G5)-mc*(1-G5) } vertex T b W+.f chep: { -i*ee/(2*Sqrt2*mW*sw) | mb*(1+G5)-mtop*(1-G5) } vertex S c W-.f chep: { -i*ee/(2*Sqrt2*mW*sw) | mc*(1+G5)-ms*(1-G5) } vertex B t W-.f chep: { -i*ee/(2*Sqrt2*mW*sw) | mtop*(1+G5)-mb*(1-G5) } vertex E2 n2 W-.f chep: { -i*ee*mmu/(2*Sqrt2*mW*sw) | -(1-G5) } vertex E3 n3 W-.f chep: { -i*ee*mtau/(2*Sqrt2*mW*sw) | -(1-G5) } vertex N2 e2 W+.f chep: { -i*ee*mmu/(2*Sqrt2*mW*sw) | (1+G5) } vertex N3 e3 W+.f chep: { -i*ee*mtau/(2*Sqrt2*mW*sw) | (1+G5) } # Vector-boson self-interactions vertex W+ W- A chep: { -ee | m1.m2*(p1-p2).m3+m2.m3*(p2-p3).m1+m3.m1*(p3-p1).m2 } mad: { ee | QFD } vertex W+ W- Z chep: { -ee*cw/sw | m1.m2*(p1-p2).m3+m2.m3*(p2-p3).m1+m3.m1*(p3-p1).m2 } mad: { ee*cw/sw | QFD } vertex W+ W- Z Z chep: { -(ee*cw/sw)**2 | 2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3 } mad: { (ee*cw/sw)**2 | QFD } vertex W+ W+ W- W- chep: { (ee/sw)**2 | 2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3 } mad: { (ee/sw)**2 | QFD } vertex W+ W- Z A chep: { -ee**2*cw/sw | 2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3 } mad: { ee**2*cw/sw | QFD } vertex W+ W- A A chep: { -ee**2 | 2*m1.m2*m3.m4-m1.m3*m2.m4-m1.m4*m2.m3 } mad: { ee**2 | QFD } vertex W-.C Z.c W+ chep: { ee*cw/sw | p1.m3 } vertex W+.C Z.c W- chep: { -ee*cw/sw | p1.m3 } vertex Z.C W-.c W+ chep: { -ee*cw/sw | p1.m3 } vertex Z.C W+.c W- chep: { ee*cw/sw | p1.m3 } vertex W-.C W+.c Z chep: { -ee*cw/sw | p1.m3 } vertex W+.C W-.c Z chep: { ee*cw/sw | p1.m3 } vertex W-.C W+.c A chep: { -ee | p1.m3 } vertex W+.C W-.c A chep: { ee | p1.m3 } # Higgs - vector boson vertex H Z A vertex H A A vertex H g g vertex H W+ W- chep: { ee*mW/sw | m2.m3 } mad: { (ee/sw)**2*v/2 | QFD } vertex H Z Z chep: { ee/(sw*cw**2)*mW | m2.m3 } mad: { (ee/sw/cw)**2*v/2 | QFD } vertex H H W+ W- chep: { (1/2)*(ee/sw)**2 | m3.m4 } mad: { (ee/sw)**2/2 | QFD } vertex H H Z Z chep: { (1/2)*(ee/(sw*cw))**2 | m3.m4 } mad: { (ee/sw/cw)**2/2 | QFD } vertex H Z.f Z chep: { i*ee/(2*cw*sw) | (p2-p1).m3 } vertex H W-.f W+ chep: { i*ee/(2*sw) | (p2-p1).m3 } vertex H W+.f W- chep: { i*ee/(2*sw) | (p2-p1).m3 } vertex Z.f W+.f W- chep: { ee/(2*sw) | -(p2-p1).m3 } vertex Z.f W-.f W+ chep: { ee/(2*sw) | (p2-p1).m3 } vertex W-.f W+.f Z chep: { ee/(2*cw*sw) | (1-2*sw^ 2)* (p2-p1).m3 } vertex W-.f W+.f A chep: { ee | (p2-p1).m3 } vertex W-.f W+ A chep: { -i*ee*mW | m2.m3 } vertex W+.f W- A chep: { -i*ee*mW | -m2.m3 } vertex W-.f W+ Z chep: { -i*ee*mW*sw/cw | -m2.m3 } vertex W+.f W- Z chep: { -i*ee*mW*sw/cw | m2.m3 } vertex W-.f W+.f A A chep: { 2*ee**2 | m3.m4 } vertex W-.f W+.f Z Z chep: { (ee/(cw*sw))**2/2 | (1-2*sw^ 2)^ 2*m3.m4 } vertex W-.f W+.f W- W+ chep: { ee**2/(2*sw*sw) | m3.m4 } vertex W-.f W+.f Z A chep: { ee**2/(sw*cw) | (1-2*sw^ 2)*m3.m4 } vertex Z.f Z.f Z Z chep: { (ee/(sw*cw))**2/2 | m3.m4 } vertex Z.f Z.f W- W+ chep: { ee**2/(2*sw*sw) | m3.m4 } vertex W-.f Z.f W+ A chep: { -ee**2/(2*sw) | m3.m4 } vertex W+.f Z.f W- A chep: { -ee**2/(2*sw) | m3.m4 } vertex W-.f Z.f W+ Z chep: { ee**2/(2*cw) | m3.m4 } vertex W+.f Z.f W- Z chep: { ee**2/(2*cw) | m3.m4 } vertex W-.f H W+ A chep: { -i*ee**2/(2*sw) | m3.m4 } vertex W+.f H W- A chep: { i*ee**2/(2*sw) | m3.m4 } vertex W-.f H W+ Z chep: { i*ee**2/(2*cw) | m3.m4 } vertex W+.f H W- Z chep: { -i*ee**2/(2*cw) | m3.m4 } vertex Z.C Z.c H chep: { -ee*mW/(2*sw*cw*cw) } vertex W-.C W+.c H chep: { -ee*mW/(2*sw) } vertex W+.C W-.c H chep: { -ee*mW/(2*sw) } vertex W-.C W+.c Z.f chep: { i*ee*mW/(2*sw) } vertex W+.C W-.c Z.f chep: { -i*ee*mW/(2*sw) } vertex W-.C Z.c W+.f chep: { -i*ee*mW/(2*cw*sw) | 1-2*sw^ 2 } vertex W+.C Z.c W-.f chep: { i*ee*mW/(2*cw*sw) | 1-2*sw^ 2 } vertex Z.C W-.c W+.f chep: { i*ee*mW/(2*cw*sw) } vertex Z.C W+.c W-.f chep: { -i*ee*mW/(2*cw*sw) } vertex W-.C A.c W+ chep: { ee | p1.m3 } vertex W+.C A.c W- chep: { -ee | p1.m3 } vertex A.C W-.c W+ chep: { -ee | p1.m3 } vertex A.C W+.c W- chep: { ee | p1.m3 } vertex W-.C A.c W+.f chep: { -i*ee*mW } vertex W+.C A.c W-.f chep: { i*ee*mW } # Higgs self-interactions vertex H H H chep: { -(3/2)*ee*mH**2/(mW*sw) } mad: { -3*mh**2/v | QFD } vertex W+.f W-.f H chep: { -ee*mH**2/(2*mW*sw) } vertex Z.f Z.f H chep: { -ee*mH**2/(2*mW*sw) } vertex H H H H chep: { (-3/4)*(ee*mH/(mW*sw))**2 } # mad: not implemented vertex Z.f Z.f Z.f Z.f chep: { -3*(ee*mH/(2*mW*sw))**2 } vertex Z.f Z.f W-.f W+.f chep: { -(ee*mH/(2*mW*sw))**2 } vertex W-.f W-.f W+.f W+.f chep: { - (ee*mH/(mW*sw))**2/2 } vertex Z.f Z.f H H chep: { -(ee*mH/(2*mW*sw))**2 } vertex W+.f W-.f H H chep: { -(ee*mH/(2*mW*sw))**2 }