Combining single and double parton scatterings in a parton shower

Abstract

Double parton scattering (DPS) processes in which there is a perturbative “1 → 2” splitting in both protons overlap with loop corrections to single parton scattering (SPS). Any fundamental theoretical treatment of DPS needs to address this double-counting issue. In this paper, we augment our Monte-Carlo simulation of DPS, dShower, to be able to generate kinematic distributions corresponding to the combination SPS+DPS without double counting. To achieve this, we formulate a fully-differential version of the subtraction scheme introduced in Diehl et al. (JHEP 06 (2017) 083). A shower is attached to the subtraction term, and this is combined with the dShower DPS shower along with the usual SPS shower. We perform a proof-of-concept study of this new algorithm in the context of Z0Z0 production. Once the subtraction term is included, we verify that the results do not depend strongly on the artificial “DPS-SPS demarcation” scale ν. As part of the development of the new algorithm, we improve the kinematics of the 1 → 2 splitting in the DPS shower (and subtraction term), allowing the daughter partons to have a relative transverse momentum. Several reasonable choices for the transverse profile in the 1 → 2 splitting are studied. We find that many kinematic distributions are not strongly affected by the choice, although we do observe some differences in the region where the transverse momenta of both bosons are small.

Improvements on dipole shower colour

“…In the case of e + e − → qq, the NLLs of some observables (i.e. thrust) do not directly depend on g → qq transitions 13 in which case our shower is accurate to NLL at full colour. Our methodology of assigning colour factors by mapping branching histories onto those of an angular-ordered shower could be generalised to assign the correct colour factors after including g → qq transitions.…”

“…12 The average sub-branch length for a multiplicity, n, of partons in the branch is n i=1 1 i ≤ ln n + 1. 13 Such transitions are restricted to secondary branchings, the remnants of which can be resummed into the CMW coupling and are otherwise rendered trivial by the angular-ordering constraint [2]. 14 Furthermore, our arguments also generalise to a hard process with more than two coloured, hard legs provided each of the dipoles found in the colour flow for the hard process is evolved in its back-to-back frame as is done in an angular ordered shower [37].…”

“…We wish to test that it correctly reproduces the terms in Table 1 and the hard-collinear physics in Eqs. (12) and (13). The relevant contributions are pictured in Fig.…”

“…By comparison, dipole showers are typically restricted to leading-colour accuracy but they can be applied across the board. In recent literature, much attention has been focused on improving the framework upon which dipole showers are constructed [4][5][6][7][8][9][10][11][12][13][14]. Substantial progress has been made demonstrating their capacity for NLL resummation [1,15] and methods for partially addressing sub-leading colour have also been proposed, by extending dipole showers beyond leading-N c colour flows [16][17][18][19].…”

Evolution and interpolation of double parton distributions using Chebyshev grids

“…[ 28 ] and further developed or adapted in subsequent work in Refs. [ 24 , 30 , 44 , 45 , 81 ]. 5 The comparison is done with the version that was used in Ref.…”