The topcolor-assisted technicolor (TC2) model predicts several pseudo-scalars called top-pions and at loop level they can induce the FCNC top quark decay t->cgg which is extremely suppressed in the Standard Model (SM). We find that in the allowed parameter
tttg
(a
)(b
)
t
g
(d
)tg(e)
FIG.2:Feynmandiagramsfort→cggatone-looplevelinTC2model.Thee ectivevertextc¯gin(a-c)isde nedinFig.1.Thebosonintheloopoftheboxdiagram(d)canbeaneutraltop-pion,top-Higgsorachargedtop-pion,whilethefermionintheloopcanbeatoporbottomquarkcorrespondingly.Thetwogluonsin(a,b,d,e)canbeexchanged.
These avor-changingcouplingswillinducetheFCNCcouplingtc¯g,asshowninFig.1.Wefollowtheideaofthe’e ectivevetrtex’in[4]andde neane ectivetc¯gvertextosimplifyourcalculations
tc¯gcc¯gΓeffµ(pt,pc)=Γµ(pt,pc)+Γµi(p/t+mc)
2p2c mtttgΓµ,¯(3)
qq¯gtc¯gwhereΓµ(q=c,t)istheusualQCDvertex,andΓµ,Σ(pt)andΣ(pc)arerespectivelythecontributionsfromvertexandself-energyloopsshowninFig.1,whoseexpressionsaregivenintheAppendix.Suchane ectiveveretxcanbere-shapedintheform
F1(k2)Ta(k2γµ kµk/)+mtF2(k2)Taiσµνkν,(4)
wherekdenotesthemomentumofthegluon,Ta(a=1,···,8)aretheSUc(3)generators,andF1,2(k2)areformfactorsarisingfromloopcalculations.Notethatforthetwo-bodydecayt→cg,F1doesnotcontributesincethegluonmomentumksatis esk2=0andk· =0with beingthegluonpolarizationvector(di erentfrom inEqs.(1)and(2)!).Withthee ectivevertexde nedabove,theFeynmandiagramsforthedecayt→cggareshowninFig.2,wherethediagrams(a-c)involvethee ectivevertex.Theamplitudesofthediagrams(a-c)areobviouswiththede nede ectivevertex.Inaddition,weneed