A quantitative study of two-loop splitting in double parton distributions

Abstract

Double parton distributions at small distances between the two partons are dominated by a mechanism in which the two observed partons originate from the splitting of a single parton. This contribution can be computed in terms of single-parton distributions and perturbative splitting kernels. We demonstrate that two-loop corrections to these kernels can have a substantial quantitative impact and considerably improve the stability of predictions for double parton scattering. We also consider the impact of heavy quark masses in the two-loop splitting kernels in an approximate manner.

Figures (26)

• Figure 1: Graph corresponding to the factorisation formula for double parton scattering, given by \ref{['dps-Xsect']} and \ref{['dpd-lumi-def']}. Pairs of parton lines have their colour indices coupled to irreducible representations $R_i$ of SU(3). The final-state cut would be a vertical line through the centre of the graph and is omitted for clarity. The horizontal lines at the very left and the very right represent the incoming protons.
• Figure 2: (a): Box graph for the production of two electroweak gauge bosons via SPS. All loop momenta are routed such that they flow towards the gauge boson vertex. (b): The same graph, interpreted as a contribution to DPS with two splitting DPDs. The final state cut would be a vertical line through the centre of the graph and is omitted for clarity.
• Figure 3: Splitting DPDs for $g g$ and $u g$ at $x_1 = x_2 \approx 5.7 \times 10^{-3}$, evolved to scales $\mu_1 = \mu_2 = 80 \operatorname{GeV}$. The first specification of "LO" or "NLO" in the plots refers to the DPD splitting kernels, and the second one refers to the order of DGLAP evolution of the DPDs and of the PDFs in the splitting formula.
• Figure 4: As figure \ref{['fig:dpds-g']}, but for $u \bar{d}$ and $u \bar{u}$.
• Figure 5: As the bottom row of figure \ref{['fig:dpds-q']}, but for asymmetric momentum fractions $x_1 \approx 0.31$ and $x_2 \approx 10^{-4}$.