Abstract
Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.
Highlights
The precise description of high-energy proton-proton collisions in QCD is imperative for maximising the physics potential of the LHC and of possible future hadron colliders
Our scheme is naturally formulated with double parton distributions (DPDs) that depend on the transverse distance y between the two partons, but we show in section 7 how one may instead use DPDs depending on the transverse momentum conjugate to y
double parton scattering (DPS) graphs in which such splittings occur in both protons (1v1 graphs) overlap with loop corrections to single parton scattering
Summary
The precise description of high-energy proton-proton collisions in QCD is imperative for maximising the physics potential of the LHC and of possible future hadron colliders. The two partons that take part in the two hard scatters can originate from the perturbative splitting of one parton The relevance of this splitting mechanism for the evolution equations of double parton distributions (DPDs) has been realised long ago [6, 7] and studied more recently in [8,9,10]. It was only noted in [4, 5] that the same mechanism dominates DPDs in the limit of small transverse distance between the two partons, and that the splitting contribution leads to infinities when inserted into the DPS cross section formula. Some Fourier integrals required in the main text are given in an appendix
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