Order-αs2 corrections to one-particle inclusive processes in DIS

Two-loop splitting in double parton distributions

“…For example, in our results P (1) qq,g is symmetric under x 1 ↔ x 2 , which is due to the equivalent status of partons a 1 and a 2 together with charge conjugation invariance. By contrast, the same is not true for the corresponding function in [112,113].…”

“…In [114] it was proposed that the NLO 1 → 2 splitting functions in the evolution of fracture functions are actually equal to the evolution kernels P (1) s for DPDs, after a simple transformation of the momentum fraction arguments to take into account the fact that one of the momentum fraction arguments in the splitting functions of [112,113] is not the light-cone momentum of the final parton over that of the initial parton, but that of the final parton over that of the other final parton. We find that this equality does not hold, and that in general the transformed splitting functions of [112,113] do not have the symmetry that our kernels P (1) s have (and must have) under the interchange of partons 1 and 2. For example, in our results P (1) qq,g is symmetric under x 1 ↔ x 2 , which is due to the equivalent status of partons a 1 and a 2 together with charge conjugation invariance.…”

“…We now turn to the case in which both momentum fractions x 1 and x 2 are small; this is a typical situation at high collision energy when two systems of moderately large invariant mass are produced. In the limit x 1 + x 2 → 0 the convolution integral (112) includes the region z → 0 in the kernel K(zu, zū), where u is defined in terms of the external momentum fractions x 1 and x 2 by (113). Let us first recall the analogous situation for the one-dimensional Mellin convolution of an LO DGLAP kernel and a PDF,…”

Erratum to: “Inclusive production of single hadrons with finite transverse momenta in deep-inelastic scattering at next-to-leading order” [Nucl. Phys. B 711 (2005) 345]

“…[12], the phase-space slicing method was applied to handle the IR singularities. Another related work, focusing on fracture functions of the proton, was published in two parts, related to incoming gluons [14] and quarks [15]. This paper is organized as follows.…”

NLO QCD corrections to inclusive jet and hadron production in DIS

“…From a more formal point of view, the analytic computation of higher order QCD corrections to one particle inclusive cross sections has always lagged behind that of more inclusive observables, and the reason is the much more involved singularity structure [16,17]. As usual in these corrections, diagrams are plagued with collinear singularities that have to be identified, prescribed, and canceled to get the physical cross section, but at variance with the inclusive case, here one has to deal typically with overlapping singularities in several variables, which is a real technical challenge.…”