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
functions’dependencegivenby
0)D1=D1(p2,p1, pt,mt,mt,mπt(A11)
(A12)
(A13)D2=D2(p2,p1, pt,mt,mt,mh0)t+)D3=D3(p2,p1, pt,mb,mb,mπt
Theamplitudesofthetop-quarktriangleloopdigramsinFig.2(e)aregivenby
M1=1
16π2
22agsT2ii(p1+p2)2 m2π0t 2+8pαCg 4pgC 4p·pgC+4ppC¯t ν(p2) 12µν01ν2µ0u1αµν1µν0µ(p1)
bawithT2=TnmTmlandtheloopfunctions’dependencegivenby
22B=B(p22,mt,mt),C=C( p1, p2,mt,mt,mt).u¯cPLmt 4gµνB0 16p1νCµ+16Cµν(A15) (A16)
IntheaboveexpressionstheloopfunctionsB,CandDwithLorentzindicescanbeexpandedintoscalarfunctions[12],whichcanbecalculatedbyusingLoopTools[13].
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A.Cordero-Cid,etal.,Phys.Rev.D73,094005(2006);G.Eilam,M.FrankandI.Turan,Phys.Rev.D73,053011(2006).
[3]Forrecentreviews,see,e.g.,http://www.77cn.com.cnrios,R.Martinez,M.A.Perez,Int.J.Mod.Phys.A21,3473(2006);J.M.Yang,AnnalsPhys.316,529(2005).
[4]ForthelatestresultsofMSSMpredictionsforFCNCtopdecaysandproductionsatLHC,see,J.Cao,et.al.,Phys.Rev.D75,075021(2007);Phys.Rev.D74,031701(2006).