### Four-jet DPS production in pp and pA collisions in Pythia8

In collaboration with J. Bellm, J. Gaunt, A. Kulesza, L. Lönnblad and T. Sjöstrand.

In spite of the recent progress in both theoretical and experimental studies many aspects of multiple parton interactions (MPI) still require a detail investigation. In particular, double parton scattering (DPS) processes can play a dominant role for some specific kinematic regions of multi-jet production, especially in proton-nucleus (pA) collisions where a total DPS cross section is approximately 3A times bigger as a corresponding total DPS cross section in proton-proton (pp) collisions. It is also known that DPS is sensitive to parton correlations of various types and that a combined study of DPS in pp and pA collisions at the LHC will provide us a deep insight into a protonâ€™s structure and non-perturbative dynamics of its constituents. However, a complexity of the problem leads to different models of DPS currently available in the literature. In particular there are several approaches to model so called double parton distribution functions (dPDFs) which are important ingredients for every Monte Carlo DPS simulation since dPDFs, among other effects, account for longitudinal parton correlations, flavour and momentum conservation and also for so called "1v2" splitting contribution, a situation when one initial state parton splits perturbatively into two partons which then take part in two hard interactions.

The goal of the project is to compare predictions of a model of DPS built into the Pythia event generator against predictions of other models of DPS available on the market. In particular we have studied two dif- ferent ways to model dPDFs, namely double DGLAP evolution equations and the approach of Pythia based upon dynamical modification of standard collinear PDFs. We have found that the dPDFs modelled within both frameworks obey the same set of generalized sum rules and that both approaches have rather a similar treatment of the "1v2" splitting contribution caused by a gluon splitting into quark antiquark pair at low values of Bjorken-x. We also have found that both approaches have quiet strong disagreement in description of "1v2" contributions at high values of Bjorken-x. Additionally we have studied the impact of both models of dPDFs on various DPS-sensitive differential distributions and established different regions of a phase space where existing differences may become relevant for Monte Carlo predictions.

The model of DPS being used in Pythia has inherited its main concepts from the original Pythiaâ€™s model of MPI. Which, in particular, implies that only PDFs used to generate a second hard interaction are modified in order to account for momentum and flavour conservation. This procedure, however, introduces asymmetry of the Pythiaâ€™s dPDFs and is in contradiction with the double DGLAP approach. This discrepancy was removed and, starting from Pythia version 8.240, DPS events are generated using symmetrized dPDFs.

It is know that the additional enhancement ∼ 3A of a total DPS cross section in pA collisions is due to DPS processes involving one incoming proton and two different nucleons, so called DPS II contribution. Recently a new model of pA collisions called Angantyr was implemented into the Pythia which, among others, allows to simulate some DPS processes in pA collisions. The approach being used in Angantyr differs in some aspects from the approach being used in currently available publications on DPS. In particular, Angantyr models DPS II contribution via pomeron exchange and, additionally, possesses a non-trivial collective behaviour which leads to contributions similar to those from nuclear shadowing effect. We have compared the predictions of the Angantyr model against theoretical computations currently available in the literature and found that it demonstrates a correct dependence of a total DPS cross section on a total number of nucleons. In addition to it we have studied how the enhancement of a total DPS cross section depends on different jet cuts and found a way to get an additional enhancement of a total DPS cross section in pA collisions comparing to a total DPS cross section in pp collisions evaluated for the same set of cuts.

In October 2018 some of the aforementioned results were presented at the MPI@LHC Workshop in Perugia, Italy.