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; ] :[font = input; noPageBreak; preserveAspect; ] Off[General::spell]; Off[General::spell1]; :[font = section; inactive; preserveAspect; startGroup; ] ================================ Load FeynArts: :[font = input; preserveAspect; startGroup; ] $Path :[font = output; output; inactive; preserveAspect; endGroup; ] {".", "~", "/usr/local/mathmetica/Install/Preload", "/usr/local/mathmetica/StartUp", "/usr/local/mathmetica/Packages"} ;[o] {., ~, /usr/local/mathmetica/Install/Preload, /usr/local/mathmetica/StartUp, /usr/local/mathmetica/Packages} :[font = input; inactive; preserveAspect; startGroup; ] AppendTo[$Path, "HD240:mathload:FeynArts"] :[font = output; output; inactive; preserveAspect; endGroup; ] {":Packages", ":Packages:StartUp", ":Packages:StartUp:Integrate", "HD240:mathload:FeynArts"} ;[o] {:Packages, :Packages:StartUp, :Packages:StartUp:Integrate, HD240:mathload:FeynArts} :[font = input; preserveAspect; startGroup; ] AppendTo[$Path, "/users/smuphy/olness/mathload/FeynArts/FeynArts"] :[font = output; output; inactive; preserveAspect; endGroup; ] {".", "~", "/usr/local/mathmetica/Install/Preload", "/usr/local/mathmetica/StartUp", "/usr/local/mathmetica/Packages", "/users/smuphy/olness/mathload/FeynArts/FeynArts"} ;[o] {., ~, /usr/local/mathmetica/Install/Preload, /usr/local/mathmetica/StartUp, /usr/local/mathmetica/Packages, /users/smuphy/olness/mathload/FeynArts/FeynArts} :[font = input; preserveAspect; startGroup; ] Needs["FeynArts`"] :[font = print; inactive; preserveAspect; endGroup; endGroup; ] FeynArts 1.0 for Mathematica 2.0 (October 1991) by Hagen Eck and Sepp Kueblbeck [additional packages being loaded] :[font = section; inactive; preserveAspect; startGroup; ] ================================ Create Topologies: Photon+Quark->Quark+Gluon :[font = input; preserveAspect; startGroup; ] tops= CreateTopologies[0,4 ,Tadpoles->False ,SelfEnergies->False ]; Length[tops] :[font = output; output; inactive; preserveAspect; endGroup; ] 4 ;[o] 4 :[font = input; preserveAspect; startGroup; ] ins=InsertFields[tops,{V[1],F[1]}->{V[1],F[1]} ,Model->{SM}]; :[font = print; inactive; preserveAspect; endGroup; ] ... initializing model "SM1111100" |. | |.. | |... | |.... | |.....| ... (done) 1. topology (out of 4) being inserted 1 insertions before Compare 1 insertions after Compare 2. topology (out of 4) being inserted 0 insertions before Compare 0 insertions after Compare 3. topology (out of 4) being inserted 1 insertions before Compare 1 insertions after Compare 4. topology (out of 4) being inserted 0 insertions before Compare 0 insertions after Compare Out of 4 tops. 2 have no inss. and are discarded total number of insertions: 2 :[font = input; preserveAspect; startGroup; ] ins :[font = output; output; inactive; preserveAspect; endGroup; ] TopologyList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {V[1], F[1]} -> {V[1], F[1]}][Topolo\ gy[Propagator[inc][e[1], v3[4], fi[1]], Propagator[inc][e[2], v3[1], fi[2]], Propagator[out][e[3], v3[1], fi[3]], Propagator[out][e[4], v3[4], fi[4]], Propagator[in][v3[1], v3[4], fi[5]], Insertions[Graph[1][fi[1] -> V[1], fi[2] -> F[1], fi[3] -> V[1], fi[4] -> F[-1], fi[5] -> F[1]]]], Topology[Propagator[inc][e[1], v3[1], fi[1]], Propagator[inc][e[2], v3[1], fi[2]], Propagator[out][e[3], v3[4], fi[3]], Propagator[out][e[4], v3[4], fi[4]], Propagator[in][v3[1], v3[4], fi[5]], Insertions[Graph[1][fi[1] -> V[1], fi[2] -> F[1], fi[3] -> V[1], fi[4] -> F[-1], fi[5] -> F[1]]]]] ;[o] TopologyList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {V[1], F[1]} -> {V[1], F[1]}][Topology [Propagator[inc][e[1], v3[4], fi[1]], Propagator[inc][e[2], v3[1], fi[2]], Propagator[out][e[3], v3[1], fi[3]], Propagator[out][e[4], v3[4], fi[4]], Propagator[in][v3[1], v3[4], fi[5]], Insertions[Graph[1][fi[1] -> V[1], fi[2] -> F[1], fi[3] -> V[1], fi[4] -> F[-1], fi[5] -> F[1]]]], Topology[Propagator[inc][e[1], v3[1], fi[1]], Propagator[inc][e[2], v3[1], fi[2]], Propagator[out][e[3], v3[4], fi[3]], Propagator[out][e[4], v3[4], fi[4]], Propagator[in][v3[1], v3[4], fi[5]], Insertions[Graph[1][fi[1] -> V[1], fi[2] -> F[1], fi[3] -> V[1], fi[4] -> F[-1], fi[5] -> F[1]]]]] :[font = input; preserveAspect; startGroup; ] Paint[ins ,GraphsPerRow -> 1 ,RowsPerSheet -> 2]; :[font = print; inactive; preserveAspect; ] write to file "V1F1V1F1.gra" topology: 1 insertion: 1 nr: 1 topology: 2 insertion: 1 nr: 2 :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Helvetica findfont 7 scalefont setfont % Scaling calculations 0.0204082 0.0204082 0.0204082 0.0204082 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 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.38192 .28355 L .38412 .28411 L .3861 .28493 L .38783 .28604 L .38931 .28746 L .39054 .28917 L .39154 .29116 L .39237 .29336 L .39308 .29571 L .39373 .29811 L .39441 .3005 L .39518 .30277 L .3961 .30485 L .39723 .30669 L .3986 .30824 L .40023 .30948 L .4021 .31042 L .40421 .31108 L .40651 .31152 L .40893 .3118 L .41141 .31201 L .41388 .31223 L .41627 .31255 L .41852 .31305 L .42057 .31378 L .42237 .3148 L .42393 .31613 L .42523 .31776 L .42629 .31968 L .42717 .32182 L .42791 .32413 L .42857 .32653 L s P p .00625 w .36403 .27949 m .36259 .27803 L .3614 .27627 L .36042 .27424 L .35962 .27202 L .35892 .26966 L .35827 .26725 L .35759 .26487 L .35681 .26262 L .35586 .26057 L .3547 .25877 L .3533 .25726 L .35164 .25606 L .34973 .25516 L .34759 .25453 L .34528 .25412 L .34284 .25384 L .34036 .25363 L .33789 .2534 L .33552 .25305 L .3333 .25252 L .33129 .25174 L .32952 .25067 L .328 .2493 L .32674 .24762 L .32571 .24566 L .32487 .24349 L .32415 .24116 L .3235 .23875 L .32283 .23636 L .32209 .23406 L .3212 .23195 L .32011 .23007 L .31878 .22847 L .31719 .22718 L .31535 .2262 L .31327 .22549 L .31101 .22502 L .3086 .22471 L .30612 .22449 L s P p p /Symbol findfont 7 scalefont setfont [(g)] .34835 .2983 0 0 Mshowa P P P p p .00625 w .3674 .17353 m .37006 .17131 L .37272 .16909 L .37538 .16687 L .37804 .16465 L .3807 .16243 L .38336 .16022 L .38603 .158 L .38869 .15578 L .39135 .15356 L .39401 .15134 L .39667 .14911 L .39933 .14689 L .40199 .14467 L .40465 .14245 L .4073 .14023 L .40996 .13801 L .41262 .13579 L .41528 .13356 L .41794 .13134 L .4206 .12912 L .42326 .1269 L .42591 .12467 L .42857 .12245 L s P p .00625 w .3674 .17353 m .36473 .17575 L .36207 .17797 L .35941 .18018 L .35675 .1824 L .35408 .18462 L .35142 .18683 L .34876 .18905 L .3461 .19127 L .34343 .19348 L .34077 .1957 L .3381 .19792 L .33544 .20013 L .33278 .20235 L .33011 .20456 L .32745 .20678 L .32478 .20899 L .32212 .21121 L .31945 .21342 L .31679 .21564 L .31412 .21785 L .31145 .22006 L .30879 .22228 L .30612 .22449 L s P p p /Helvetica findfont 7 scalefont setfont [(e)] .38307 .19234 0 0 Mshowa P P p .00625 w .36317 .18502 m .3674 .17353 L .35533 .17561 L s P P P p /Helvetica findfont 7 scalefont setfont [(Top.2 Ins.1)] .02449 .02449 -1 -1 Mshowa P P P p /Symbol findfont 7 scalefont setfont [(g)] -0.06122 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [( + )] .02041 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [(e)] .10204 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [( )] .18367 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [(-->)] .26531 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [( )] .34694 .96939 0 0 Mshowa P p /Symbol findfont 7 scalefont setfont [(g)] .42857 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [( + )] .5102 .96939 0 0 Mshowa P p /Helvetica findfont 7 scalefont setfont [(e)] .59184 .96939 0 0 Mshowa P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup; ] amp=CreateFeynAmp[ins]; :[font = print; inactive; preserveAspect; endGroup; ] . |(1) ..|(1) :[font = input; preserveAspect; startGroup; ] amp :[font = output; output; inactive; preserveAspect; endGroup; ] FeynAmpList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {{V[1], p1, 0}, {F[1], p2, ME}} -> {{V[1], k1, 0}, {F[1], k2, ME}}][Feyn\ Amp[GraphName[V1F1V1F1, T1, I1, N1], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li2] . (ME + DiracSlash[-k1 + p2]) . DiracMatrix[li4] . LeptonSpinor[p2, ME]*PolarizationVector[p1, li2]* PropagatorDenominator[k1 - p2, ME]], FeynAmp[GraphName[V1F1V1F1, T2, I1, N2], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li4] . (ME + DiracSlash[p1 + p2]) . DiracMatrix[li2] . LeptonSpinor[p2, ME]*PolarizationVector[p1, li2]* PropagatorDenominator[p1 + p2, ME]]] ;[o] FeynAmpList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {{V[1], p1, 0}, {F[1], p2, ME}} -> {{V[1], k1, 0}, {F[1], k2, ME}}][FeynA\ 2 mp[V1F1V1F1, T1, I1, N1][(EL ep[p1, li2] ep(*)[k1, li4] Integral[] u[k2, ME] . ga[li2] . (ME + gs[-k1 + p2]) . ga[li4] . u[p2, ME]) / 2 2 2 (-ME + (k1 - p2) )], FeynAmp[V1F1V1F1, T2, I1, N2][(EL ep[p1, li2] ep(*)[k1, li4] Integral[] u[k2, ME] . ga[li4] . (ME + gs[p1 + p2]) . ga[li2] . u[p2, ME]) / 2 2 (-ME + (p1 + p2) )]] :[font = input; preserveAspect; startGroup; ] InputForm[amp] :[font = output; output; inactive; preserveAspect; fontLeading = 0; endGroup; endGroup; ] InputForm[FeynAmpList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {{V[1], p1, 0}, {F[1], p2, ME}} -> {{V[1], k1, 0}, {F[1], k2, ME}}][FeynAmp[GraphName[V1F1V1F1, T1, I1, N1], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li2] . (ME + DiracSlash[-k1 + p2]) . DiracMatrix[li4] . LeptonSpinor[p2, ME]* PolarizationVector[p1, li2]*PropagatorDenominator[k1 - p2, ME]], FeynAmp[GraphName[V1F1V1F1, T2, I1, N2], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li4] . (ME + DiracSlash[p1 + p2]) . DiracMatrix[li2] . LeptonSpinor[p2, ME]*PolarizationVector[p1, li2]* PropagatorDenominator[p1 + p2, ME]]]] ;[o] FeynAmpList[Model -> {SM}, Generation1 -> True, Generation2 -> True, Generation3 -> True, ElectronHCoupling -> True, LightFHCoupling -> True, QuarkMixing -> False, UnitaryGauge -> False, RemoveEmptyTops -> True, ProcessName -> V1F1V1F1, Process -> {{V[1], p1, 0}, {F[1], p2, ME}} -> {{V[1], k1, 0}, {F[1], k2, ME}}][Feyn\ Amp[GraphName[V1F1V1F1, T1, I1, N1], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li2] . (ME + DiracSlash[-k1 + p2]) . DiracMatrix[li4] . LeptonSpinor[p2, ME]*PolarizationVector[p1, li2]* PropagatorDenominator[k1 - p2, ME]], FeynAmp[GraphName[V1F1V1F1, T2, I1, N2], EL^2*Conjugate[PolarizationVector[k1, li4]]* LeptonSpinor[k2, ME] . DiracMatrix[li4] . (ME + DiracSlash[p1 + p2]) . DiracMatrix[li2] . LeptonSpinor[p2, ME]*PolarizationVector[p1, li2]* PropagatorDenominator[p1 + p2, ME]]] ^*)