Bhabha scattering

Notice that there is a relative sign difference between the two diagrams.

quare of matrix element

To calculate the unpolarized cross section, one must "average" over the spins of the incoming particles ("s"_e- and "s"_e+ possible values) and "sum" over the spins of the outgoing particles. That is,::

cattering term

Magnitude squared of M

::

Annihilation term

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::

olution

Evaluating the interference term along the same lines and adding the tree terms yields the final result::$$frac{overline

Uses

Bhabha scattering has been used as a luminosity monitor in a number of e+e- collider physics experiments. The accurate measurement of luminosity is necessary for accurate measurements of cross sections.
* 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%. [ [http://adsabs.harvard.edu/abs/1995PhDT.......160W A Study of Small Angle Radiative Bhabha Scattering and Measurement of the Luminosity at SLD] ]
* Electron-positron colliders operating in the region of the low-lying hadronic resonances (about 1 GeV to 10 GeV), such as the Beijing Electron Synchrotron (BES) and the Belle and BaBar "B-factory" experiments, use large-angle Bhabha scattering as a luminosity monitor. 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. [http://arxiv.org/abs/hep-ph/0003268] 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.

References

*cite book | author=Halzen, Francis; Martin, Alan | title=Quarks & Leptons: An Introductory Course in Modern Particle Physics | publisher=John Wiley & Sons | year=1984 | id=ISBN 0-471-88741-2
*cite book | author=Peskin, Michael E.; Schroeder, Daniel V. | title=An Introduction to Quantum Field Theory | publisher=Perseus Publishing | year=1994 | id=ISBN 0-201-50397-2