- 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 theStanford 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 theBeijing 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 theanomalous magnetic dipole moment of themuon , which is used to constrainsupersymmetry and other models of physicsbeyond 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
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