Small Angle Bhabha Scattering for LEP.pdf

a r X i v : h e p - p h / 9 5 0 6 3 2 3 v 1 1 4 J u n 1 9 9 5 Small Angle Bhabha Scattering for LEP ?? A. Arbuzov a V. Fadin b E. Kuraev a L. Lipatov c N. Merenkov d L. Trentadue e a Joint Institute for Nuclear Research, Head Post Office, P.O. Box 79, Dubna 141980, Moscow region, Russia b Budker Institute for Nuclear Physics and Novosibirsk State University, 630090, Novosibirsk, Russia c St.-Petersburg Institute of Nuclear Physics, 188350 Gatchina, Leningrad region, Russia d Physical-Technical Institute, 310108 Kharkov, Ukraine e Dipartimento di Fisica, Universita? di Parma, 43100 Parma INFN Sezione di Roma II, via della Ricerca Scientifica, 1, 00133 Roma, Italy present address: CERN, TH-Division, Geneva, Switzerland Abstract We present the results of our calculations to a one, two, and three loop approx- imation of the e+e?→e+e? Bhabha scattering cross-section at small angles. All terms contributing to the radiatively corrected cross-section, within an accuracy of δσ/σ = 0.1%, are explicitely evaluated and presented in an analytic form. O(α) and O(α2) contributions are kept up to next-to-leading logarithmic accuracy, and O(α3) terms are taken into account to the leading logarithmic approximation. We define an experimentally measurable cross-section by integrating the calculated distribu- tions over a given range of final-state energies and angles. The cross-sections for exclusive channels as well as for the totally integrated distributions are also given. ?Work supported by the Istituto Nazionale di F isica Nucleare (INFN). INTAS grant 93-1867. ?Appeared as a contribution to the ”Reports of the Working Group on Precision Calculations for the Z Resonance” CERN 95-03, March 1995. 1 1 Introduction An accurate verification of the Standard Model is one of the primary aims of LEP [1]. While electroweak radiative corrections to the s-channel annihilation process and to large angle Bhabha scattering allow a direct extraction of the Standard Model parameters, small ang