Large-x resummation in semi-inclusive e^+ e^- annihilation

Abstract

Recently methods have been developed to extend the resummation of large-x double logarithms in inclusive deep-inelastic scattering (DIS) to terms not addressed by the soft-gluon exponentiation. Here we briefly outline our approach based on fixed-order results, the general large-x structure in dimensional regularization and the all-order factorization of mass singularities, which is directly applicable also to semi-inclusive e + e − annihilation (SIA). We then present some main results for the corresponding timelike splitting functions and transverse and longitudinal fragmentation functions. The close relation between DIS and SIA facilitates the determination of additional third-order results for the latter function which is fully known only at the next-to-leading order. Therefore all above quantities can be resummed at next-to-next-to-leading logarithmic accuracy. * Speaker.

Recent higher-order results in perturbative QCD

“…Corresponding results for P S gq , their timelike counterparts with, e.g., C −1 F P T gq = n −1 f P S qg at LL accuracy, and the related coefficient functions will be presented in Ref. [32]. These results explain the vanishing LL coefficients at order α 4 s as the start of an all-order pattern due to B 2n+1 = 0 for n ≥ 1.…”

“…In the remainder of this contribution we briefly summarize results derived for all other cases in Refs. [23][24][25][26][27][28][29][30][31][32][33] with some emphasis on the phenomenologically directly relevant cases of r = 0 at large x in DIS and r = −1 at small x in SIA. This relevance is illustrated in Fig.…”

“…Still, the iteration of unfactorized observables might offer access to resummations of quantities outside the scope of Refs. [28][29][30][31][32][33].…”

“…Most of the results in Refs. [23][24][25][26][27][28][29][30][31][32][33] will not have a direct phenomenological impact, but will hopefully prove useful in conjunction with future developments such as, e.g., a computation of fourth-order moments of structure functions analogous to Refs. [57].…”

Why Precision ?

“…The threshold resummation of the total hadronic tt cross section at NNLL was carried out in [104,105], resumming also the Coulomb singularity [104]. The resummation of large x terms in semi-inclusive e + e −annihilation was performed in [106]. Amplitude-based resummation in Quantum Field Theories was discussed in [107].…”