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 \to 21→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 \to 21→2 splitting functions are consistent with the number and momentum sum rules for DPDs.
Highlights
Consider the integrated cross section for the production of some final state with associated hard scale Q at a hadron collider
Some of us developed a new formalism [43] that possesses several advantages over the previous approaches. This involves a description of the DPS cross section in terms of so-called position space double parton distributions (DPDs) Fa1a2(x1, x2, y), where y is the separation in transverse space between the two partons
There are two types of graph contributing to the bare partonic Double parton distributions (DPDs) at next-to-leading order (NLO): 4In practice, FORM was used in the light-cone gauge calculation, whilst FeynCalc was used for the Feynman gauge calculation
Summary
We present our results for the kernels Ps and W up to NLO and discuss some of their properties. We obtain the kernel Pq(1g),g (x1, x2, x3) from Pq(q1,)g (x1, x2, x3) if we drop the distributions terms, omitting δ(x3) and replacing 1/[x3]+ with 1/x3, and interchange x2 ↔ x3 This is symmetric in the arguments x1 and x2, as it must be. Where we have omitted the parton labels on K for brevity To obtain these relations, we used equation (B13) in [88] to bring all plus distribution terms into the form 1/[x3]+. We note that for all LO and NLO channels a0 → a1a2, there is exactly one parton combination in each type of convolution term This will no longer hold for kernels at order α3s , where for given a0, a1, and a2 there is more than one possibility for the spectator partons. The rational functions often coincide with the corresponding functions in (115), or at least they have the same denominators as these functions
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