Exact O(alpha) Corrections to the Single Hard Bremsstrahlung Process in Low Angle Bhabha Sc.pdf

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Exact O(alpha) Corrections to the Single Hard Bremsstrahlung Process in Low Angle Bhabha Sc.pdf

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Exact O(alpha) Corrections to the Single Hard Bremsstrahlung Process in Low Angle Bhabha Sc

a r X i v : h e p - p h / 9 6 0 3 2 4 8 v 1 7 M a r 1 9 9 6 Exact Results on O(α) Corrections to the Single Hard Bremsstrahlung Process in Low Angle Bhabha Scattering in the SLC/LEP Energy Regime? S. Jadach?, M. Melles, B.F.L. Ward, and S. A. Yost Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996-1200, USA January 1995 UTHEP-95-0101 Abstract We present the exact O(α) correction to the process e+e? → e + e ? + γ in the low angle luminosity regime at SLC/LEP energies. We give explicit formulas for the completely differential cross section. As an important application, we illustrate the size of the respective corrections of O(α2) to the SLC/LEP luminosity cross section. We show explicitly that our results have the correct infrared limit, as a cross-check. Some comments are made about the implementation of our results in the framework of a Monte Carlo event generator. This latter implementation will appear elsewhere. ?Work supported in part by the US DoE, contract DE-FG05-91ER40627, and by the Polish Government, grant KBN 2 ?Permanent address: Institute of Nuclear Physics, ul. Kawiory 26a, PL 30-059 Cracow, Poland 1 1 Introduction Recently, new luminometers at LEP[1] have made measurements of the lu- minosity process e+e? → e+e? + n(γ) at the experimental precision tags below .1%. This should be compared with the prediction by two of us (S.J. and B.F.L.W.), with E. Richter-Wa?s and Z. Wa?s, of these processes at the .25% precision tag in Ref. [2] using the YFS Monte Carlo event genera- tor BHLUMI2.00. Recently, using version 4.0 of BHLUMI, the authors in Ref. [2] have reported precision tags ～ .1% for the ALEPH SICAL detector’s asymmetric acceptance theoretical cross section prediction [3, 4] and .16% precision for the general ALEPH SICAL acceptance. The four of us, with W. P laczek, E. Richter-Wa?s, M. Skrzypek and Z. Wa?s [5], have reported the entirely equivalent conservative theoretical precision tag ～ .15% for t