Correlations in Double Parton Distributions: Perturbative and Non-Perturbative effects

TL;DR

Double Parton Scattering (DPS) requires detailed knowledge of double parton distribution functions (dPDFs) to model backgrounds and to probe the proton’s 3D structure. The authors compute dPDFs using a Poincaré covariant Light-Front quark model at a low scale and evolve them with LO QCD, systematically testing factorized forms and GPD-based approximations. They demonstrate strong violations of simple factorization in the valence region and reveal sizeable perturbative and non-perturbative correlations, particularly in the gluon–gluon sector, which can reach about 20% at LHC scales. The results highlight a delicate interplay between non-perturbative dynamics and perturbative evolution, implying that two-parton correlations could be experimentally accessible at the LHC and offer novel insights into nucleon structure.

Abstract

The correct description of Double Parton Scattering (DPS), which represents a background in several channels for the search of new Physics at the LHC, requires the knowledge of double parton distribution functions (dPDFs). These quantities represent also a novel tool for the study of the three-dimensional nucleon structure, complementary to the possibilities offered by electromagnetic probes. In this paper we analyze dPDFs using Poincaré covariant predictions obtained by using a Light-Front constituent quark model proposed in a recent paper, and QCD evolution. We study to what extent factorized expressions for dPDFs, which neglect, at least in part, two-parton correlations, can be used. We show that they fail in reproducing the calculated dPDFs, in particular in the valence region. Actually measurable processes at existing facilities occur at low longitudinal momenta of the interacting partons; to have contact with these processes we have analyzed correlations between pairs of partons of different kind, finding that, in some cases, they are strongly suppressed at low longitudinal momenta, while for other distributions they can be sizeable. For example, the effect of gluon-gluon correlations can be as large as 20 $\%$. We have shown that these behaviors can be understood in terms of a delicate interference of non-perturbative correlations, generated by the dynamics of the model, and perturbative ones, generated by the model independent evolution procedure. Our analysis shows that at LHC kinematics two-parton correlations can be relevant in DPS, and therefore we address the possibility to study them experimentally.

Figures (20)

• Figure 1: Left panel: $x_1x_2u_Vu_V(x_1,x_2,k_\perp=0,\mu_0^2)$ as function of $x_1$ at fixed values of $x_2$. Right panel: $x_1x_2u_Vu_V(x_1,x_2=0.2,k_\perp,\mu_0^2)$ as function of $x_1$ at various values of $k_\perp$ ( $(k_0,k_1,...,k_8) \simeq (0, 0.03, 0.14, 0.32, 0.57 ,0.85 ,1.15, 1.43, 1.68) \,\,{\rm GeV}$, which are Gaussian points between 0 and 2 GeV).
• Figure 2: Left panel: $F_{u_Vu_V}(x_1,x_2,k_\perp=0,\mu_0^2)$ as function of $x_1$ at fixed values of $x_2=0.2,0.4,0.6$. The continuous lines represent the results obtained within the LF-approach ($F_{u_Vu_V} = 2 \times u_Vu_V$ of Eqs. (\ref{['eq:uVuVpol']}), (\ref{['eq:uVuVunpol']})), the dot-dashed lines the results of the approximation (\ref{['eq:HH']}). See text for discussion. Right panel: As in the left panel, in logarithmic $x$-scale to emphasized the low-$x$ behavior.
• Figure 3: Left panel: $F_{u_Vu_V}(x_1,x_2,k_\perp=0,\mu_0^2)$ as function $x_1$ at fixed $x_2=0.1$ and $k_\perp=0$. Right panel: As in the left panel, at fixed $x_2=0.3$. The continuous line ($F_{u_Vu_V} = 2 \times u_Vu_V$ of Eqs. (\ref{['eq:uVuVpol']}), (\ref{['eq:uVuVunpol']})), crosses the dashed line (approximation (\ref{['eq:HH']})) for $x_1 \approx 0.3$. See text for discussion.
• Figure 4: Left panel: $F_{u_Vu_V}(x_1,x_2,k_\perp,\mu_0^2)$ as function of $k_\perp$ at fixed $x_1=x_2=0.1$. The continuous line represents the results obtained within the LF-approach ($F_{u_Vu_V} = 2 \times u_Vu_V$ of Eqs. (\ref{['eq:uVuVpol']}), (\ref{['eq:uVuVunpol']})), the dashed lines the results of the approximation (\ref{['eq:HH']}), the dot-dashed lines neglect the corrections due to the $k_\perp^2$-term in Eq. (\ref{['eq:HH']}). See text for discussion. Right panel: As in the left panel, at fixed $x_1=x_2=0.3$.
• Figure 5: Effects of evolution on correlations according to the scheme of Ref. dkk. Upper panel: $\ln [F_{u^-u^-}(\vec{y}^2)/F_{u^-u^-}(0)]$ at $x_2=x_1=0.1$ as function of $\vec{y}^2$ [fm$^2$] at fixed values of $Q^2$ and following the assumptions of Ref. dkk. Middle panel: As in the upper panel for $\ln [F_{u^+u^+}(\vec{y}^2)/F_{u^+u^+}(0)]$. Lower panel: As previous panels, for $\ln [F_{gg}(\vec{y}^2)/ F_{gg}(0)]$.