Double parton scattering: parton correlations and their scale evolution

Abstract

Double parton scattering (DPS) describes a process in hadron-hadron scattering in which two partons are extracted from each initial hadron and then initiate hard scattering processes separated by a finite distance. After factorising the hadronic process, one obtains parton distributions functions that characterise the behaviour of partons inside the hadron at non-perturbative scales. A novel feature compared to ordinary single parton scattering (SPS) is that the two partons might be correlated in their quantum numbers. One example of such a quantum number is the colour charge under the strong force in quantum chromodynamics (QCD). This thesis focuses on the scale dependence of collinear distributions for partons correlated in their colour charge. Collinear double parton distributions (DPDs) depend on the collision energies of the partonic subprocesses and initial state rapidity. The evolution of DPDs under these variables is governed by the DGLAP and Collins-Soper (CS) equation, respectively. The corresponding coefficients, also called kernels, on which the equations depend can be calculated as a perturbation series in the strong coupling.

In the first part of the thesis, the next-to-leading order (NLO) contribution in perturbation theory to the DGLAP equation for correlated DPDs is computed. The calculation is performed for unpolarised and longitudinally polarised partons as well as transversely polarised quarks. Two independent methods with a large overlap in their produced results are combined to construct the full NLO kernels. The first method uses NLO calculations of the single parton DGLAP kernels which are already available in the literature and generalises them to correlated partons. The second one is based on the matching formula between collinear and transverse momentum dependent parton distributions. There, the results are derived from existing matrix elements of single partons with non-zero transverse momentum.

In the second part, an extension for an existing evolution library, ChiliPDF, is presented that is able to solve both the DGLAP and CS evolution equations for colour correlated DPDs. With this approach it is possible for the first time to assess the impact of colour correlated partons on DPS cross sections in a fully quantitative way. We study the effect of DGLAP evolution at different energies and interpartonic distances, the changes when taking NLO terms into account, and the contribution of correlated DPDs to the complete DPS cross-section.