Resummation of the jet broadening in DIS

Abstract

We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS-specific procedures for matching to fixed-order calculations and compare our results to data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets from MRST and CTEQ it reveals limited discrepancies in both.

Principles of general final-state resummation and automated implementation

“…To evaluate this integral, we essentially follow the now standard method of [2], introducing a Mellin transform representation, 24) and performing the sum over m to give…”

“…The classic example is the transverse momentum of a Drell-Yan pair -since the pair transverse momentum is given by the recoil from all emissions, cancellations [53,55] in the vector sum of emitted transverse momenta imply that y can have values down to 0. Other examples of observables where y can approach zero include the e + e − oblateness [21] and the broadening (with respect to the photon axis) in DIS [24], as well as the indirectly-global hadronic dijet observables defined in [39].…”

“…The divergence is not a specificity of our semi-numerical approach to the resummation, but appears also in purely analytical resummed calculations, e.g. [24,54]. In such situations, current techniques for obtaining a full resummed answer usually require that one carry out the resummation in some appropriate transform space (e.g.…”

“…Fortunately, for most of the cases that we have examined it is only the d ℓ that have any dependence on B (modulo permutations of the indices ℓ, to be discussed shortly). 24 This means that the analysis of the observable can be carried out in full for just a single momentum configuration B ref and then for each new momentum configuration one redetermines only the d ℓ , which is a straightforward procedure.…”

Event shapes in e+e annihilation and deep inelastic scattering

“…For DIS to 1 + 1 jets the current-hemisphere observables are resummed in refs. [33,67,68] and the jet rates in [35] (though only to NLL R accuracy) while the 2 + 1 jet observables, K out and azimuthal correlations, have been resummed in [32,34]. Methods for automated resummation of arbitrary observables are currently in development for a range of processes [38], and techniques have also being developed for dealing with arbitrary processes [69].…”