Double parton correlations and constituent quark models: a Light Front approach to the valence sector

TL;DR

The paper addresses how two partons inside a proton are correlated in the valence sector, focusing on double parton distribution functions (dPDFs). It uses a relativistic Light-Front Constituent Quark Model to compute valence dPDFs, including spin correlations via Melosh rotations and ensuring correct light-front kinematic support. The authors then evolve the results to experimental scales using LO pQCD non-singlet evolution and find that strong x1-x2 correlations persist in the valence region and spin-dependent correlations remain sizable even at low x. These findings challenge common factorization assumptions used in DPS analyses and provide guidance for interpreting DPS signals at the LHC, with future work extending to singlet evolution and DPS cross sections.

Abstract

An explicit evaluation of the double parton distribution functions (dPDFs), within a relativistic Light-Front approach to constituent quark models, is presented. dPDFs encode information on the correlations between two partons inside a target and represent the non-perturbative QCD ingredient for the description of double parton scattering in proton-proton collisions, a crucial issue in the search of new Physics at the LHC. Valence dPDFs are evaluated at the low scale of the model and the perturbative scale of the experiments is reached by means of QCD evolution. The present results show that the strong correlation effects present at the scale of the model are still sizable, in the valence region, at the experimental scale. At the low values of x presently studied at the LHC the correlations become less relevant, although they are still important for the spin-dependent contributions to unpolarized proton scattering.

Figures (11)

• Figure 1: The unpolarized dPDF, Eq. (\ref{['unp']}), as a function of $x_1$ and for three values of $x_2$, at $k_\perp =0$.
• Figure 2: The same as in Fig. 1, but for the spin-dependent dPDF Eq. (\ref{['pol']}).
• Figure 3: The ratio $r_1$, Eq. (\ref{['r1']}), at $k_\perp =0$, evaluated for three values of $x_2$, as a function of $x_1$.
• Figure 4: The ratio $r_2$, Eq. (\ref{['r2']}), at $k_\perp =0$, evaluated for three values of $x_2$, as a function of $x_1$.
• Figure 5: The ratio Eq. (\ref{['r3']}) at the hadronic scale.