Exact differentialO(α2)results for hard bremsstrahlung ine+

Abstract

We present the exact O(α) correction to the process e + e − → ff + γ, f = e, for ISR⊕FSR at and beyond LEP2 energies. We give explicit formulas for the completely differential cross section. As an important application, we compute the size of the respective sub-leading corrections of O(αL) to the ff cross section, where L is the respective big logarithm in the renormalization group sense so that it is identifiable as L = ln |s|/m e 2 when s is the squared e + e − cms energy. Comparisons are made with the available literature. 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 the Monte Carlo event generator KK MC.

Comparisons of exact results for the virtual photon contribution to single hard bremsstrahlung in radiative return fore+e−annihilation

“…Therefore, although the expressions for f 0 , f 1 , f 2 are analytically equivalent to those of Ref. [3], they are more stable when evaluated numerically. The functions R 1 and R 2 are related to the function R used in Ref.…”

“…[3], we have previously presented comparisons of the results in Refs. [1][2][3], and in general a very good agreement was found. However, it is clear from the comparisons in Ref.…”

“…In Ref. [3], the matrix element was evaluated using helicity amplitude techniques of CALKUL [20], Xu et al [21], and KleissStirling [22], together with algebraic simplification using FORM [23]. The mass corrections were then added following the methods in Ref.…”

“…Exact results for the virtual corrections to single hard bremsstrahlung have been studied by a number of groups [1][2][3][4]. Comparisons of these results are important to be certain of their correctness at a high level of precision.…”

“…Both Ref. [3] (JMWY) and Ref. [1] include mass corrections, but the former is fully differential, while the latter averages over the photon angle.…”