Two-loop splitting in double parton distributions

Abstract

Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 → 2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 → 2 splitting functions are consistent with the number and momentum sum rules for DPDs.

Evidence in favor of single parton scattering mechanism in ϒ and D associated production at the LHC

“…In total and taking into account the uncertainties, our hybrid PRA+NRQCD+fragmentation model can account more than a half of experimentally observed cross-section for ΥD pair production. The shapes of all differential distributions in our SPS model also turn out to reproduce experimental data rather well, except for the shape of ∆ϕ-spectrum which has a puzzling "upside-down" behavior, un-explainable even by the DPS model (1). Therefore, we show that radiative corrections to the SPS crosssection of the process under consideration are large and mimicking the behavior of DPS, thus weakening the case for DPS-dominance in this process.…”

“…Double Parton Scattering (DPS) mechanism attracts a lot of attention, both theoretically and experimentally. Recent advances in theory of DPS include computation [1] of NLO corrections to 1 → 2 splitting functions, contributing to the scale-evolution of two-parton collinear Parton Diastrbution Functions (PDFs) and filling remaining gaps in the proof of TMD-factorization theorem for double Drell-Yan process [2].…”

“…where σ DPS is the DPS contribution to the production cross-section of the pair of objects, σ (1,2) SPS is the Single Parton Scattering (SPS) cross-section of the production of one final-state object and σ eff is the non-perturbative "effective cross-section" which is typically assumed to be universal, energy-independent parameter. Eq.…”

Sum rule improved double parton distributions in position space

“…in D = 4−2 dimensions, where f a 0 is the PDF for parton a 0 . The function P a 1 a 2 ,a 0 (v, ) is equal to the ordinary DGLAP splitting function P a 1 a 0 (v) for = 0, and its form for nonzero may be found in [82]. Instead of the DPDs F(x 1 , x 2 , y; μ) in transverse-position space, one may also consider distributions depending on the transverse momentum Δ that is Fourier conjugate to y.…”

A Monte-Carlo simulation of double parton scattering

“…Unfortunately, no set of mPDFs is available for the moment. However, the case n = 2, referred to as double parton scattering (DPS), has been widely studied [26][27][28][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Despite the lack of experimental data, several groups managed to produce sets of double parton distribution functions (dPDFs) that represent an improvement over the simple product ansatz.…”