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

Starting from an earlier benchmark analytical calculation of the luminosity process $e^{+}{e}^{-}\to e^{+}{e}^{-}+\left(\gamma \right)$ at the SLAC Linear Collider (SLC) and the CERN $e^{+}{e}^{-}$ 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 $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ theory in complete analogy with the famous high-precision $Z^0$ line-shape formulas for the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ process discussed by Berends et al., for example.