To leading order, the spin-averaged differential cross section for this process is where s,t, and u are the Mandelstam variables,
This cross section is calculated neglecting the electron mass relative to the collision energy and including only the contribution from photon exchange.
Neglecting the electron mass yields the simplified form: The process for finding the annihilation term is similar to the above.
Since the two diagrams are related by crossing symmetry, and the initial and final state particles are the same, it is sufficient to permute the momenta, yielding (This is proportional to
Three used in this article are: Using these two one finds that, for example, Bhabha scattering has been used as a luminosity monitor in a number of e+e− collider physics experiments.
Small-angle Bhabha scattering was used to measure the luminosity of the 1993 run of the Stanford Large Detector (SLD), with a relative uncertainty of less than 0.5%.
To achieve the desired precision at the 0.1% level, the experimental measurements must be compared to a theoretical calculation including next-to-leading-order radiative corrections.
[2] The high-precision measurement of the total hadronic cross section at these low energies is a crucial input into the theoretical calculation of the anomalous magnetic dipole moment of the muon, which is used to constrain supersymmetry and other models of physics beyond the Standard Model.