An essential part of any factorisation proof is the demonstration that the exchange of Glauber gluons cancels for the considered observable. We show this cancellation at all orders for double Drell-Yan production (the double parton scattering process in which a pair of electroweak gauge bosons is produced) both for the integrated cross section and for the cross section differential in the transverse boson momenta. In the process of constructing this proof, we also revisit and clarify some issues regarding the Glauber cancellation argument and its relation to the rest of the factorisation proof for the single Drell-Yan process.

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 → 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 → 2 splitting functions are consistent with the number and momentum sum rules for DPDs.

We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form D[ψ, ψ * ]e iR[ψ,ψ * ] with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space.As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.

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.

Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.