% % Standard Model - unitary and t'Hooft-Feynman gauges. % option chepPDWidth=200. option chepLPWidth=850. keys gauge_fixing=Feynman. keys CKMdim=1. do_if gauge_fixing==Feynman. model 'SM+DM-CONT-VDM'/6. do_else_if gauge_fixing==unitary. model 'SM+DM-CONT-VDM(UG)'/16. do_else. write('Error: the key "gauge" should be either "Feynman" or "unitary".'). quit. end_if. option ReduceGamma5=0. let g5=gamma5. prtcformat fullname: 'Full Name ', name:' P ', aname:' aP ', pdg:' number ', spin2,mass,width, color, aux, texname: ' LaTeX(A) ', atexname:' LateX(A+) '. %%%%%%%%%%%%%% INDEPNDENT PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%% parameter pi=acos(-1), alphaSMZ=0.1184:'Srtong alpha(MZ) for running mass calculation', EE =0.31343: 'elecromagnetic constant', Q = 100: 'QCD scale'. parameter Mm = 0.1057: 'muon mass', Mtau = 1.777: 'tau-lepton mass', Ms = 0.200, McMc =1.23: 'Mc(Mc) MS-BAR', MbMb =4.25: 'Mb(Mb) MS-BAR', Mtop = 172.5: 't-quark pole mass', MH = 125: 'higgs mass', MZ = 91.188: 'Z-boson mass', MW = 80.385: 'W-boson mass', wtop = 1.59: 't-quark width (tree level 1->2x)', wZ = 2.49444: 'Z-boson width (tree level 1->2x)', wW = 2.08895: 'W-boson width (tree level 1->2x)'. parameter s12 = 0.221: 'Parameter of C-K-M matrix (PDG-94)', s23 = 0.040: 'Parameter of C-K-M matrix (PDG-94)', s13 = 0.0035 : 'Parameter of C-K-M matrix (PDG-94)'. %%%%%%%%%%%%%% DEPNDENT PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%% external_func(alphaQCD,1). parameter GG=sqrt(4*pi*alphaQCD(Q)). parameter Mcp = McMc*(1+4/3*alphaQCD(McMc)/pi):'1 loop formula like in Hdecay', Mbp = MbMb*(1+4/3*alphaQCD(MbMb)/pi):'1 loop formula like in Hdecay', alphaE0 =1/137.036:'electromagnetic constant at zero energy', CW = MW/MZ: 'on-shell cos of the Weinberg angle', SW = sqrt(1-CW**2): 'sin of the Weinberg angle', GF = EE**2/(2*SW*MW)**2/Sqrt2: 'Fermi COnstant', vv=2*MW/EE*SW. parameter c12 = sqrt(1-s12**2): 'parameter of C-K-M matrix', c23 = sqrt(1-s23**2): 'parameter of C-K-M matrix', c13 = sqrt(1-s13**2): 'parameter of C-K-M matrix'. external_func(initQCD5,4). parameter LamQCD=initQCD5(alphaSMZ,McMc,MbMb,Mtop). external_func(MbEff,1). external_func(MtEff,1). external_func(McEff,1). parameter Mb=MbEff(Q), Mt=MtEff(Q), Mc=McEff(Q). do_if CKMdim==3. parameter Vud = c12*c13 : 'C-K-M matrix element', Vus = s12*c13 : 'C-K-M matrix element', Vub = s13 : 'C-K-M matrix element', Vcd = (-s12*c23-c12*s23*s13) : 'C-K-M matrix element', Vcs = (c12*c23-s12*s23*s13) : 'C-K-M matrix element', Vcb = s23*c13 : 'C-K-M matrix element', Vtd = (s12*s23-c12*c23*s13) : 'C-K-M matrix element', Vts = (-c12*s23-s12*c23*s13) : 'C-K-M matrix element', Vtb = c23*c13 : 'C-K-M matrix element'. OrthMatrix( { {Vud,Vus,Vub}, {Vcd,Vcs,Vcb}, {Vtd,Vts,Vtb}} ). alias ckm(1,1)=Vud, ckm(2,1)=Vus, ckm(3,1)=Vub, ckm(1,2)=Vcd, ckm(2,2)=Vcs, ckm(3,2)=Vcb, ckm(1,3)=Vtd, ckm(2,3)=Vts, ckm(3,3)=Vtb. do_else_if CKMdim==2. parameter Vud = c12 : 'C-K-M matrix element', Vus = s12 : 'C-K-M matrix element', Vcs = Vud : 'C-K-M matrix element', Vcd = -Vus : 'C-K-M matrix element'. let Vub = 0, Vcb = 0, Vtd = 0, Vts = 0, Vtb = 1. OrthMatrix({{Vud,Vus}, {Vcd,Vcs}}). do_else_if CKMdim==1. let Vub=0, Vcb=0, Vtd=0, Vts=0, Vtb=1, Vud=1, Vus=0, Vcs=1, Vcd=0. end_if. do_if gauge_fixing==Feynman. vector A/A: (photon, gauge), Z/Z:('Z boson', mass MZ, width wZ, gauge), G/G: (gluon, color c8, gauge), 'W+'/'W-': ('W boson', mass MW , width wW , gauge). do_else. vector A/A: (photon, gauge), Z/Z:('Z boson', mass MZ, width wZ), G/G: (gluon, color c8, gauge), 'W+'/'W-': ('W boson', mass MW = MZ*CW, width wW). end_if. spinor n1:(neutrino,left), e1:(electron), n2:('mu-neutrino',left), e2:(muon, mass Mm), n3:('tau-neutrino',left), e3:('tau-lepton', mass Mtau). spinor u:('u-quark',color c3), d:('d-quark',color c3), c:('c-quark',color c3, mass Mcp), s:('s-quark',color c3, mass Ms), t:('t-quark',color c3, mass Mtop, width wtop), b:('b-quark',color c3, mass Mbp). scalar H/H:(Higgs, mass MH, width wH =auto, pdg 25). let l1={n1,e1}, L1={N1,E1}. let l2={n2,e2}, L2={N2,E2}. let l3={n3,e3}, L3={N3,E3}. let q1={u,d}, Q1={U,D}, q1a={u,Vud*d+Vus*s+Vub*b}, Q1a={U,Vud*D+Vus*S+Vub*B}. let q2={c,s}, Q2={C,S}, q2a={c,Vcd*d+Vcs*s+Vcb*b}, Q2a={C,Vcd*D+Vcs*S+Vcb*B}. let q3={t,b}, Q3={T,B}, q3a={t,Vtd*d+Vts*s+Vtb*b}, Q3a={T,Vtd*D+Vts*S+Vtb*B}. let B1= -SW*Z+CW*A, W3=CW*Z+SW*A, W1=('W+'+'W-')/Sqrt2, W2 = i*('W+'-'W-')/Sqrt2. do_if gauge_fixing==Feynman. let gh1 = ('W+.c'+'W-.c')/Sqrt2, gh2= i*('W+.c'-'W-.c')/Sqrt2, gh3= CW*'Z.c'+SW*'A.c', gh={gh1,gh2,gh3}. let Gh1 = ('W+.C'+'W-.C')/Sqrt2, Gh2=i*('W+.C'-'W-.C')/Sqrt2, Gh3= CW*'Z.C'+SW*'A.C', Gh={Gh1,Gh2,Gh3}. end_if. let WW1 = {W1, W2 , W3}, WW = {'W+',W3,'W-'}. let g=EE/SW, g1=EE/CW. % Self-interaction of gauge bosons lterm -F**2/4 where F=deriv^mu*B1^nu-deriv^nu*B1^mu. lterm -F**2/4 where F=deriv^mu*G^nu^a-deriv^nu*G^mu^a+i*GG*f_SU3^a^b^c*G^mu^b*G^nu^c. lterm -F**2/4 where F=deriv^mu*WW1^nu^a-deriv^nu*WW1^mu^a -g*eps^a^b^c*WW1^mu^b*WW1^nu^c. % left fermion interaction with gauge fields lterm anti(psi)*gamma*(1-g5)/2*(i*deriv-g*taupm*WW/2-Y*g1*B1)*psi where psi=l1, Y=-1/2; psi=l2, Y=-1/2; psi=l3, Y=-1/2; psi=q1a, Y= 1/6; psi=q2a, Y= 1/6; psi=q3a, Y= 1/6. % right fermion interaction with gauge fields lterm anti(psi)*gamma*(1+g5)/2*(i*deriv - Y*g1*B1)*psi where psi=e1,Y= -1; psi=e2,Y= -1; psi=e3,Y= -1; psi=u, Y= 2/3; psi=c, Y= 2/3; psi=t, Y= 2/3; psi=d, Y= -1/3; psi=s, Y= -1/3; psi=b, Y= -1/3. % quark-gluon interaction lterm GG*anti(psi)*lambda*gamma*G*psi where psi=q1; psi=q2; psi=q3. do_if gauge_fixing==Feynman. let pp = { -i*'W+.f', (vev(2*MW/EE*SW)+H+i*'Z.f')/Sqrt2 }, PP = { i*'W-.f', (vev(2*MW/EE*SW)+H-i*'Z.f')/Sqrt2 }. do_else. let pp = { 0, (vev(2*MW/EE*SW)+H)/Sqrt2 }, PP = { 0, (vev(2*MW/EE*SW)+H)/Sqrt2 }. end_if. lterm -M/MW/Sqrt2*g*(anti(pl)*(1+g5)/2*pr*pp + anti(pr)*(1-g5)/2*pl*PP ) where M=Vud*0, pl=q1a, pr=d; % 0 stands for Md M=Vus*Ms, pl=q1a, pr=s; M=Vub*Mb, pl=q1a, pr=b; M=Vcd*0, pl=q2a, pr=d; M=Vcs*Ms, pl=q2a, pr=s; M=Vcb*Mb, pl=q2a, pr=b; M=Vtd*0, pl=q3a, pr=d; M=Vts*Ms, pl=q3a, pr=s; M=Vtb*Mb, pl=q3a, pr=b. lterm -M/MW/Sqrt2*g*(anti(pl)*(1+g5)/2*i*tau2*pr*PP + anti(pr)*(1-g5)/2*i*pl*tau2*pp ) where M=0 , pl=q1a, pr=u; M=Mc, pl=q2a, pr=c; M=Mtop,pl=q3a, pr=t. lterm -M/MW/Sqrt2*g*(anti(pl)*(1+g5)/2*pr*pp + anti(pr)*(1-g5)/2*pl*PP ) where M=Mm, pl=l2, pr=e2; M=Mtau, pl=l3, pr=e3. lterm -2*lambda*(pp*PP-v**2/2)**2 where lambda=(g*MH/MW)**2/16, v=2*MW*SW/EE. let Dpp^mu^a = (deriv^mu+i*g1/2*B1^mu)*pp^a + i*g/2*taupm^a^b^c*WW^mu^c*pp^b. let DPP^mu^a = (deriv^mu-i*g1/2*B1^mu)*PP^a -i*g/2*taupm^a^b^c*{'W-'^mu,W3^mu,'W+'^mu}^c*PP^b. lterm DPP*Dpp. lterm -i*GG*f_SU3*ccghost(G)*G^mu*deriv^mu*ghost(G). lterm -1/2*(deriv*G)**2. do_if gauge_fixing==Feynman. %lterm -g*eps*gh*WW1*deriv*Gh. lterm g*eps*deriv*Gh*gh*WW1. lterm -1/2*(deriv*A)**2. lterm -1/2*(2*(deriv*'W+'+MW*'W+.f')*(deriv*'W-'+MW*'W-.f') + (deriv*Z+MW/CW*'Z.f')**2). lterm -MW*EE/2/SW*((H+i*'Z.f')*('W-.C'*'W+.c' + 'W+.C'*'W-.c') +H*'Z.C'*'Z.c'/CW**2-2*i*'Z.f'*'W+.C'*'W-.c'). lterm i*EE*MW/2/CW/SW*( 'W+.f'*('W-.C'*'Z.c'*(1-2*SW**2)+'W-.c'*'Z.C' +2*CW*SW*'W-.C'*'A.c') - 'W-.f'*('W+.C'*'Z.c'*(1-2*SW**2)+'W+.c'*'Z.C' +2*CW*SW*'W+.C'*'A.c')). end_if. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% HGG+HAA PART %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% external_func(McRun,1). external_func(MbRun,1). external_func(MtRun,1). external_func(HggF,1). external_func(HggV,1). external_func(Hgam1F,1). external_func(alphaQCD,1). parameter aQCD =alphaQCD(MH)/pi. parameter Qu=2/3, Qd=-1/3, tau2c =(MH/2/McRun(MH/2))**2, tau2b =(MH/2/MbRun(MH/2))**2, tau2t =(MH/2/MtRun(MH/2))**2, tau2l =(MH/2/Mtau)**2, tau2W =(MH/2/MW)**2. parameter Rqcd=1+149/12*aQCD+68.6482*aQCD**2-212.447*aQCD**3, Cq=1+11/4*aQCD, lnTop=2*log(Mtop/MH), Ctop=1+11/4*aQCD+ (6.1537-2.8542*lnTop)*aQCD**2 +(10.999-17.93*lnTop+5.47*lnTop**2)*aQCD**3. parameter LmbdAA= -alphaE0/(8*pi)*EE/(2*MW*SW)*cabs( 3*Qu**2*(HggF(tau2c)*(1+aQCD*Hgam1F(tau2c)) +HggF(tau2t)*(1+aQCD*Hgam1F(tau2t))) +3*Qd**2*HggF(tau2b)*(1+aQCD*Hgam1F(tau2b)) +HggF(tau2l)+HggV(tau2W)). parameter LmbdGG= -aQCD/16*sqrt(Rqcd)*EE/(2*SW*MW)*cabs( HggF((MH/2/Mcp)**2)*Cq +HggF((MH/2/Mbp)**2)*Cq +HggF((MH/2/Mtop)**2)*Ctop). lterm LmbdAA*H*F**2 where F=deriv^mu*A^nu-deriv^nu*A^mu. lterm LmbdGG*H*F**2 where F=deriv^mu*G^nu^a-deriv^nu*G^mu^a. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% EFFECTIVE Vector DM Interactions %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% from paper 1508.04466 %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vector '~vdm'/'~Vdm': (VDM, mass Mvdm=100, pdg 9000003). parameter Lam=1000. parameter gV1,gV2,gV3,gV4,gV5,gV6,gV7P,gV7M,gV8P,gV8M,gV9P,gV9M,gV10P,gV10M,gV11,gV12. let gm^m2^m3 = delta(vector)^m2^m3. let epsgam^i^j^m2^m3^m4 =-i*(gm^m2^m3*gamma^i^k^m4+gm^m3^m4*gamma^i^k^m2-gm^m2^m4*gamma^i^k^m3-gamma^i^l^m2*gamma^l^n^m3*gamma^n^k^m4)*gamma5^k^j. let epsgam2^i^k^m2^m3^m4 =-i*(gm^m2^m3*gamma^i^k^m4+gm^m3^m4*gamma^i^k^m2-gm^m2^m4*gamma^i^k^m3-gamma^i^l^m2*gamma^l^n^m3*gamma^n^k^m4). %%%%%%%%%%%%%%%%%%%%% % % %%%%%%% V1 %%%%%%% lterm gV1/Lam*anti('~vdm')*'~vdm'*(anti(q)*q) where q=u; q=d ; q=s; q=c. % % % %%%%%%% V2 %%%%%%% lterm gV2/Lam*i*anti('~vdm')*'~vdm'*(anti(q)*gamma5*q) where q=u; q=d ; q=s; q=c. % % % %%%%%%% V3 %%%%%%% lterm gV3/(2*Lam**2)*i*(anti('~vdm')^nu*deriv^mu*'~vdm'^nu - '~vdm'^nu*deriv^mu*anti('~vdm')^nu)*(anti(q)*gamma^mu*q) where q=u; q=d ; q=s; q=c. % % % %%%%%%% V4 %%%%%%% lterm gV4/(2*Lam**2)*i*(anti('~vdm')^nu*deriv^mu*'~vdm'^nu - '~vdm'^nu*deriv^mu*anti('~vdm')^nu)*(anti(q)*gamma^mu*gamma5*q) where q=u; q=d ; q=s; q=c. %%%%%%% V5 %%%%%%% lterm gV5/Lam*i*anti('~vdm')^mu*'~vdm'^nu*(anti(q)*i*(gamma^mu*gamma^nu-gamma^nu*gamma^mu)/2*q) where q=u; q=d ; q=s; q=c. % % % %%%%%%% V6 %%%%%%% lterm gV6/Lam*anti('~vdm')^mu*'~vdm'^nu*(anti(q)*i*(gamma^mu*gamma^nu-gamma^nu*gamma^mu)/2*gamma5*q) where q=u; q=d ; q=s; q=c. % % %%%%%%% V7+ %%%%%%% lterm gV7P/(2*Lam**2)*(anti('~vdm')^nu*deriv^nu*'~vdm'^mu + '~vdm'^nu*deriv^nu*anti('~vdm')^mu)*(anti(q)*gamma^mu*q) where q=u; q=d ; q=s; q=c. % % %%%%%%% V7- %%%%%%% lterm gV7M/(2*Lam**2)*i*(anti('~vdm')^nu*deriv^nu*'~vdm'^mu - '~vdm'^nu*deriv^nu*anti('~vdm')^mu)*(anti(q)*gamma^mu*q) where q=u; q=d ; q=s; q=c. % % %%%%%%% V8+ %%%%%%% lterm gV8P/(2*Lam**2)*(anti('~vdm')^nu*deriv^nu*'~vdm'^mu + '~vdm'^nu*deriv^nu*anti('~vdm')^mu)*(anti(q)*gamma^mu*gamma5*q) where q=u; q=d ; q=s; q=c. % % %%%%%%% V8- %%%%%%% lterm gV8M/(2*Lam**2)*i*(anti('~vdm')^nu*deriv^nu*'~vdm'^mu - '~vdm'^nu*deriv^nu*anti('~vdm')^mu)*(anti(q)*gamma^mu*gamma5*q) where q=u; q=d ; q=s; q=c. % %%%%%%% V9+ %%%%%%% lterm gV9P/(2*Lam**2)*(anti('~vdm')^b*deriv^c*'~vdm'^d + '~vdm'^b*deriv^c*anti('~vdm')^d)*(anti(q)*epsgam^b^c^d*q) where q=u; q=d ; q=s; q=c. % %%%%%%% V9- %%%%%%% lterm gV9M/(2*Lam**2)*i*(anti('~vdm')^b*deriv^c*'~vdm'^d - '~vdm'^b*deriv^c*anti('~vdm')^d)*(anti(q)*epsgam^b^c^d*q) where q=u; q=d ; q=s; q=c. % %%%%%%% V10+ %%%%%%% lterm gV10P/(2*Lam**2)*(anti('~vdm')^b*deriv^c*'~vdm'^d + '~vdm'^b*deriv^c*anti('~vdm')^d)*(anti(q)*epsgam2^b^c^d*q) where q=u; q=d ; q=s; q=c. % %%%%%%% V10- %%%%%%% lterm gV10M/(2*Lam**2)*i*(anti('~vdm')^b*deriv^c*'~vdm'^d - '~vdm'^b*deriv^c*anti('~vdm')^d)*(anti(q)*epsgam2^b^c^d*q) where q=u; q=d ; q=s; q=c. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% let FGG^m^n^a=deriv^m*G^n^a-deriv^n*G^m^a+i*GG*f_SU3^a^b^c*G^m^b*G^n^c. let FGGt^m^n^a=(1/2)*epsv^m^n^k^l*FGG^k^l^a. % %%%%%%% V11 %%%%%%% lterm gV11/(Lam**2)*anti('~vdm')*'~vdm'*FGG*FGG. % %%%%%%% V12 %%%%%%% lterm gV12/(Lam**2)*anti('~vdm')*'~vdm'*FGGt*FGG. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SetAngle(1-SW**2=CW**2). SetEM(A,EE). CheckHerm.