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Interference term in Bhabha scattering

  • Thread starter karangovil
  • Start date
  • #1
Hi guys...I am trying the problem 5.2 from Peskin to calculate cross section for Bhabha scattering. In the interference (cross) term, I'm getting a term involving trace of 8 gamma matrices and I am having some trouble in evaluating it. So can anyone help???

The term is Tr[[tex]\displaystyle{\not}p'\gamma^{\nu}\displaystyle{\not}k'\gamma^{\mu}\displaystyle{\not}k\gamma_{\nu}\displaystyle{\not}p\gamma_{\mu}[/tex]]
(here first two momenta are p' and k')
 

Answers and Replies

  • #2
25
0
Hi...
You can use some contraction identity (Peskin p. 805):
[tex]\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}\gamma_{\mu}=
-2\gamma^{\sigma}\gamma^{\rho}\gamma^{\nu} [/tex]
[tex]\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma_{\mu}=
4 g^{\nu \rho} [/tex].
Your term is:
[tex]Tr[ \gamma^{\delta}\gamma^{\nu}\gamma^{\alpha}\gamma^{\mu}\gamma^{\beta} \gamma_{\nu}\gamma^{\gamma}\gamma_{\mu}k'_{\alpha}k_{\beta}p_{\gamma}p'_{\delta}
]=-2Tr[ \gamma^{\delta}\gamma^{\beta}\gamma^{\mu}\gamma^{\alpha} \gamma^{\gamma}\gamma_{\mu}k'_{\alpha}k_{\beta}p_{\gamma}p'_{\delta}]
=[/tex]
[tex]=-8Tr[ \gamma^{\delta}\gamma^{\beta}k_{\beta}p'_{\delta}(k' \cdot p)
] =-32(k'\cdot p) (k\cdot p') [/tex]
 

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