High-precision improved-analytic-exponentiation results for multiple-photon effects in low-angle Bhabha scattering at the SLAC Linear Collider and the CERN e+e- collider LEP.

Abstract

Starting from an earlier benchmark analytical calculation of the luminosity process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}+(\ensuremath{\gamma})$ at the SLAC Linear Collider (SLC) and the CERN ${e}^{+}{e}^{\ensuremath{-}}$ collider LEP, we use the methods of Yennie, Frautschi, and Suura to develop an analytical improved naive exponentiated formula for this process. The formula is compared to our multiple-photon Monte Carlo event generator bhlumi (1.13) for the same process. We find agreement on the overall cross-section normalization between the exponentiated formula and bhlumi below the 0.2% level. In this way, we obtain an important cross-check on the normalization of our higher-order results in bhlumi and we arrive at formulas which represent the LEP/SLC luminosity process in the below 1% ${Z}^{0}$ physics tests of the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theory in complete analogy with the famous high-precision ${Z}^{0}$ line-shape formulas for the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ process discussed by Berends et al., for example.