Forest Bhabha Scattering

Bhabha (electron -positron) Scattering

Bhabha scattering identifies the scatterng of an electron and positron (particle and anti-particle). There are two processes that can occur

1.) scattering via the exchange of a virtual photon

2.) annihilation in which the e+ and e- spend some time as a photon which then reconverts back to an e+e- pair

variables

Let:

[math]p_1 \equiv[/math] initial electron 4-momentum

u_1 \equiv initial electron spinor

p_2 \equiv final electron 4-momentum

u_2 \equiv final electron spinor

p_3 \equiv initial positron 4-momentum

\bar{u}_3 \equiv initial positron spinor

p_4 \equiv finial positron 4-momentum

[math]\bar{u}_4 \equiv[/math] finial positron spinor

Matrix element for scaqttering

[math]\mathcal{M_s} = \,[/math] [math]e^2 \left( \bar{u}_{s} \gamma^\nu u_1 \right) \frac{1}{(p_1+p_2)^2} \left( \bar{u}_{2} \gamma_\nu u_{4} \right) [/math]

Matrix element for annihilation

[math]\mathcal{M} = \,[/math] [math]-e^2 \left( \bar{v}_{k} \gamma^\mu v_{k'} \right) \frac{1}{(k-k')^2} \left( \bar{u}_{p'} \gamma_\mu u_p \right) [/math] [math]+e^2 \left( \bar{v}_{k} \gamma^\nu u_p \right) \frac{1}{(k+p)^2} \left( \bar{u}_{p'} \gamma_\nu v_{k'} \right) [/math]

Forest_QMII