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Radiative Corrections to Moller Scattering of Polarized Particles
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Radiative Corrections to Moller Scattering of
Polarized Particles
N. M. Shumeiko, J.G. Suarez
National Scientific and Education Center of Particle and
High Energy Physics attached to Byelorussian State University
February 1, 2008
Abstract
Principal contributions to QED radiative effects for Moller scat-
tering of polarized particles are investigated both on the Born level
and taking into account radiative corrections (RC). Scattering on
the case of longitudinal and transversal polarized targets is also
considered. In a general way the expressions for differential cross
section and polarization asymmetry (PA) have been defined, and re-
spective graphics for longitudinal and transversal polarization asym-
metries and also for radiative corrections to asymmetry are pre-
sented. All quantities are presented in terms of covariant variables.
The ultrarelativistic approximation was applied for calculations.
The results of a computer run are presented.
1 Introduction
For a wide serie of experiments in SLAC (E-142,E-143,E-154,E-155),
it is neccesary to know the polarization of electron beam. For this aim
a single arm Moller polarimeter is utilized. In order to extract (with de-
sirable accuracy) beam polarization pb we need to calculate theoretically,
taking into account the experimental conditions, the quantities σth and
Ath - theoretical meaning of cross section (CS) and polarization asym-
metry. If the experimental data for polarization asymmetry (Ameas) and
target polarization (pt) are known, the ratio
Ameas = pbptA
th, (1)
allows to find the polarization of electron beam.
1
2 Method of Calculation
The Moller (e? + e? → e? + e?) scattering CS of order O(α3) can be
written in the form (within the QED treatment)
σ = σo + σV + σR, (2)
where each σo,V,R
def
= dσo,V,R/dy, and y
def
= 1 ? E ′/E, where E(E’) is the
energy of the initial (scattered) electron. σo is the Born (non radiative)
contribution of order O
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