Summing up subleading Sudakov logarithms

Abstract

We apply the strategy of regions within dimensional regularization to find functions involved in evolution equations which govern the asymptotic dynamics of the Abelian form factor and four-fermion amplitude in the SU (N ) gauge theory in the Sudakov limit up to the next-to-leading logarithmic approximation. The results are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in the e + e − annihilation at high energy.

High energy behavior ofγγ→ff¯processes in the standard model and minimal supersymmetric standard model

“…Explicit analytic expressions are given in Appendix A and B, and turn out to be rather simple, and reflecting in a remarkable way the theoretical properties of the SM charged gauge, neutral gauge and Higgs sectors and of the MSSM gaugino and Higgsino sectors. These results satisfy the known general properties of leading electroweak logarithms at one loop [7,10,11]. They also match with the complete one loop computations performed around 1 TeV in [14,15].…”

“…In fact, since many years, it was known that, in certain circumstances, large logarithmic terms, in particular quadratic logarithms can appear [5,6]. The general features of the asymptotic one loop electroweak corrections have been studied, a classification of the linear and quadratic logarithms have been established, some two loop effects have been computed and the possibility of resumming certain classes of contributions have been discussed [7][8][9][10][11].…”

Electroweak corrections to W-boson pair production at the LHC

“…However, this approach is only justified for energies of order M W or M Z . As is well known from earlier investigations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], EW corrections increase with the squared logarithm of the energy, and may reach several tens of percent for energies accessible at the LHC. In view of their strong dependence both on energy and scattering angle, they will induce significant distortions in transverse-momentum and rapidity distributions and consequently may well mimic "New Physics" and hence must be carefully taken into account.…”

“…This line of research was motivated by the necessity of including at least the dominant two-loop terms, once one-loop corrections exceed the 20 − 30% level. Using evolution equations, originally derived in the context of QED [20][21][22][23] and QCD, fourfermion processes have been studied up to N 4 LL [7,[13][14][15][16], W-pair production in electronpositron and quark-antiquark annihilation up to N 3 LL [24,25]. Employing diagrammatic methods or the framework of soft-collinear effective field theory most of these results were confirmed in the NLL and NNLL approximation [10,12,18,26].…”

An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy

“…On the one hand, resummation prescriptions have been proposed [8][9][10][11][12], which predict the leading logarithms (LLs) and next-to-leading logarithms (NLLs), i.e. terms with j = 2L and 2L − 1 in (1), for arbitrary processes and also the next-to-next-to-leading logarithms (NNLLs), with j = 2L−2, for 2 → 2 massless fermionic processes [13].…”