Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation

Abstract

Abstract:We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e + e − annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are small for the splitting functions but large for the coefficient functions. In both cases more terms in the threshold expansion need to be determined in order to arrive at quantitatively reliable results.

The soft quark Sudakov

“…2 Although we do not here solve the problem of endpoint divergences in QCD, based on our fixed order calculations, combined with intuition from the case of N = 1 QCD, we conjecture a form for the leading logarithmic "soft quark Sudakov" in QCD. Our result takes a simple, but interesting form with similarities to structures observed in the large-x resummation of off-diagonal splitting functions [54][55][56][57]66]. We also show that this soft quark Sudakov seems to have some degree of universality.…”

“…This is not at all apparent before integration. Intriguingly, identical color structures have appeared in the x → 1 resummation of the off diagonal splitting functions [54][55][56][57]. We believe that this is not a coincidence, and we believe that it provides some non-trivial evidence for our conjecture.…”

“…Alternatively, if one can argue for the color structure eq. (4.3), as was done in [54][55][56][57] for the off-diagonal splitting functions, then one can extend the result in N = 1, where it can be proven to the case of QCD by adding terms proportional to (C A − C F ) n .…”

Perturbative evolution: a different approach at small x

“…Although fixed-order perturbative QCD is widely applied to data for the proton structure function F 2 (x, Q 2 ), it is well known [1][2][3][4][5][6] that there are theoretical problems at small x. In this paper, we refine our previous approach [7] to overcoming this problem, which combines the DGLAP evolution equation with Regge theory.…”

Universal structure of the Drell-Yan process beyond threshold

“…The literature about the resummation of the leading terms, which are plus-distributions in momentum space, is extensive [1][2][3] and relies largely on the eikonal approximation. Preliminary studies on the structure of the subleading terms have been performed in [4][5][6][7][8][9][10][11]. They typically require a generalization of standard techniques to a subleading degree of approximation (known in the literature as "next-to-soft" or "next-to-eikonal").…”