Double Parton Correlations in the Bag Model

TL;DR

This work investigates double parton distributions within a proton using a bag model to estimate correlations relevant for double parton scattering. By computing both single PDFs and dPDFs at a low scale, including detailed spin-flavor structures, the authors quantify correlations in momentum fractions and flavor-spin, while finding only weak dependence on transverse separation. They show that x1-x2 and flavor-spin correlations are sizeable and cannot be captured by simple factorized ansatzes, whereas the k_perp dependence is largely uncorrelated with x. These results provide benchmark guidance for interpreting DPS measurements at the LHC and for initializing QCD evolution of dPDFs to higher scales.

Abstract

Double parton scattering is sensitive to correlations between the two partons in the hadron, including correlations in flavor, spin, color, momentum fractions and transverse separation. We obtain a first estimate of the size of these correlations by calculating the corresponding double parton distribution functions in a bag model of the proton. We find significant correlations between momentum fractions, spin and flavor, but negligible correlations with transverse separation. The model estimates of the relative importance of these correlations will help experimental studies disentangle them.

Figures (7)

• Figure 1: The proton PDFs ${u}$ (solid red), ${\Delta u}$ (dashed blue) and ${\delta u}$ (dotted green).
• Figure 2: Plot of the PY factors which enter the calculation of the single PDF (dotted blue) and double PDF (solid red). They suppress the PDFs in the unphysical regions $x>1$ and $x<0$.
• Figure 3: Plot of the bag model proton PDF ${u}(x)$ with (solid red) and without (dotted blue) PY factors.
• Figure 4: The double PDF ${uu}(x_1, x_2,{\bf k_\perp})$ as a function of $x_1$ and $|\bf k_\perp|$ for fixed $x_2=0.4$. The right panel tests the ansatz in Eq. \ref{['eq:zfact']} that $x_i$ and ${\bf k_\perp}$ are uncorrelated. This holds reasonably well, since the different $|\bf k_\perp|$ curves are nearly identical.
• Figure 5: The double PDF ${uu}(x_1, x_2,{\bf k_\perp})$ as a function of $x_1$ and $x_2$ for fixed ${\bf k_\perp=0}$. In the right panel, we divide by ${u}(x_2)$ to test the often-used assumption in Eq. \ref{['eq:xfact']} that the $x_i$ are uncorrelated. This clearly fails, since the ratio depends strongly on $x_2$.