Abstract
Double hard scattering can play an important role for producing multiparticle final states in hadron-hadron collisions. The associated cross sections depend on double parton distributions, which at present are only weakly constrained by theory or measurements. A set of sum rules for these distributions has been proposed by Gaunt and Stirling some time ago. We give a proof for these sum rules at all orders in perturbation theory, including a detailed analysis of the renormalisation of ultraviolet divergences. As a by-product of our study, we obtain the form of the inhomogeneous evolution equation for double parton distributions at arbitrary perturbative order.
Highlights
In such a situation, theoretical constraints on double parton distributions (DPDs) are valuable
We have essentially shown that the parton model interpretation of the DPD sum rules is reflected in the graphs that represent single or double parton distributions in QCD, where quark number and parton momentum are conserved quantities
The sum rules proposed by Gaunt and Stirling [14] present one of the few general constraints on double parton distributions that are currently known
Summary
Theoretical constraints on double parton distributions (DPDs) are valuable. A derivation using the light-cone wave function representation is given in appendix C of [22]. The same holds for rapidity divergences that are present in light-cone wave functions (but cancel in the DPDs appearing in the sum rules). 5 to give an all-order proof of the sum rules for bare (i.e. unrenormalised) DPDs. In Sect. 7 we explore the consequences of our analysis on the evolution of DPDs: we obtain the general form of the inhomogeneous term beyond LO (confirming the NLO result given in [20]), we derive sum rules for the associated evolution kernels, and we cross check that the sum rules are preserved by evolution at any order in αs.
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