Relativistic effects in model calculations of double parton distribution functions

Abstract

In this paper we consider double parton distribution functions (dPDFs) which are the main non perturbative ingredients appearing in the double parton scattering cross section formula in hadronic collisions. By using recent calculation of dPDFs by means of constituent quark models within the so called Light-Front approach, we investigate the role of relativistic effects on dPDFs. We find, in particular, that the so called Melosh operators, which allow to properly convert the LF spin into the canonical one and incorporate a proper treatment of boosts, produce sizeable effects on dPDFs. We discuss specific partonic correlations induced by these operators in transverse plane which are relevant to the proton structure and study under which conditions these results are stable against variations in the choice of the proton wave function.

Hadronic structure from double parton scattering

“…It is worth mentioning that dPDF calculations within hadronic models show, in general, a breaking of the factorized ansatz, Eq. (6), in a specific region of phase space, where sizable longitudinal and mixed longitudinal-transverse partonic correlations do appear [5][6][7][8][9]. Nevertheless, in this paper we still the use the approximation in Eq.…”

“…However, our result does depend weakly on the details of fðk ⊥ Þ, since just the general conditions in Eq. (9) and its limiting asymptotics at large k ⊥ are assumed, leaving the detailed shape fðk ⊥ Þ largely unconstrained.…”

“…In this scenario, calculations of dPDFs via hadronic models have been used to obtain basic information and to gauge the impact of longitudinal and transverse correlations [5][6][7][8][9]. Despite this wealth of information possibly encoded in dPDFs, the experimental knowledge on DPS cross section has been accumulated, up to now, into the socalled effective cross section, σ eff .…”

Double parton scattering and the proton transverse structure at the LHC

“…In the last part of the paper, we focus on relativistic effects in dPDF model calculations, in the relevant kinematic conditions of collider experiments, and already addressed in Ref. [12] for valence quarks at the hadronic scale. The aim of this part of the analysis is to offer insight to unfactorized ansatz for dPDFs as induced by the implementation of relativistic effects in dPDFs calculation via Melosh operators.…”

Transverse Momentum Dependence in Double Parton Scattering

“…The two partons can be correlated either kinematically or through their quantum numbers, for recent reviews we refer to [36,37] and references therein. Model calculations of DPDFs suggest that such correlations can be large, at least at large values of x [38][39][40][41][42][43][44][45]; however, evolution to large scales tends to decrease their importance, especially at low x [26,46]. It was recently demonstrated that spin correlations can have a measurable impact on differential distributions in at least one process (same-sign W W production) at the LHC [47].…”