[Paper Review] Origins of parton correlations in nucleon and multi-parton collisions

B. Blok, Yuri L. Dokshitzer+2 more|arXiv (Cornell University)|Jun 25, 2012

High-Energy Particle Collisions Research12 citations

TL;DR

This paper demonstrates that perturbative QCD generates positive 3D parton-parton correlations within the nucleon, explaining the observed ~2× enhancement in multi-parton interaction (MPI) cross sections at Tevatron energies compared to the independent parton approximation. It identifies both perturbative and nonperturbative mechanisms as sources of these correlations, with the latter dominating at low $x < 10^{-3}$, and shows that the combined effect yields a factor-of-two enhancement in MPI rates, consistent with experimental data.

ABSTRACT

We demonstrate that perturbative QCD leads to positive 3D parton--parton correlations inside nucleon explaining a factor two enhancement of the cross section of multi-parton interactions observed at Tevatron at $x_i\ge 0.01$ as compared to the predictions of the independent parton approximation. We also find that though perturbative correlations decrease with $x$ decreasing, the nonperturbative mechanism kicks in and should generate correlation which, at $x$ below $10^{-3}$, is comparable in magnitude with the perturbative one for $x\sim 0.01$.

Motivation & Objective

• To resolve the longstanding discrepancy between the independent parton approximation and Tevatron MPI data, which shows a factor-of-two larger cross section.
• To identify the origin of parton correlations in nucleons, distinguishing between perturbative and nonperturbative mechanisms.
• To quantify how these correlations affect multi-parton interaction rates at high energies, particularly at low parton momentum fractions $x$.
• To provide a theoretical framework for incorporating realistic parton correlations into Monte Carlo event generators for $pp$ collisions at the LHC.

Proposed method

• Introduce a two-particle generalized parton distribution (2 GPD) to describe non-perturbative two-parton correlations in the nucleon wave function.
• Separate the 2 GPD into two components: one from two partons originating from the non-perturbative hadron wave function (${}_{[2]}D$), and one from perturbative splitting of a single parton (${}_{[1]}D$).
• Use QCD factorization and Regge field theory to model the soft Pomeron exchange as a two-Pomeron diagram, linking diffractive processes at HERA to parton correlations.
• Extract the correlation strength $\omega = 0.25 \pm 0.05$ from HERA data on vector meson electroproduction, using the ratio of inelastic to elastic cross sections.
• Calculate the total MPI enhancement factor $\eta$ using the $t$-dependence of elastic and inelastic vertices, with $B_{\text{el}} = 5\div6\,\text{GeV}^2$ and $B_{\text{inel}} = 1.4\div1.7\,\text{GeV}^2$, yielding $\eta = 2$ for $\omega = 0.25$.
• Establish a smooth matching between soft and hard QCD regimes at $Q_0^2 \sim 1\,\text{GeV}^2$, validating the use of soft Pomeron exchange at low $x$.

Experimental results

Research questions

• RQ1 What causes the observed factor-of-two enhancement in multi-parton interaction cross sections at Tevatron energies compared to the independent parton model?
• RQ2 How do perturbative and nonperturbative QCD mechanisms contribute to parton correlations in the nucleon at different values of the parton momentum fraction $x$?
• RQ3 Can the correlation strength extracted from HERA diffractive data be reliably extrapolated to describe MPI at LHC energies?
• RQ4 What is the quantitative impact of parton correlations on the total $4\to4$ MPI cross section in $pp$ collisions?
• RQ5 How can Monte Carlo event generators be improved to incorporate realistic parton-parton correlations and transverse spatial distributions?

Key findings

• Perturbative QCD generates positive 3D parton-parton correlations inside the nucleon, which account for the observed ~2× enhancement in MPI cross sections at $x \geq 0.01$.
• The enhancement factor $\eta = 2$ is obtained from the combined effect of perturbative and nonperturbative correlations, with $\omega = 0.25$ and $B_{\text{el}}/B_{\text{inel}}$ ratios from HERA data.
• Nonperturbative correlations dominate at low $x < 10^{-3}$, where perturbative correlations diminish, and are comparable in magnitude to perturbative ones at $x \sim 0.01$.
• The ratio $\omega = 0.25 \pm 0.05$ extracted from HERA data on vector meson production quantifies the strength of longitudinal parton correlations.
• The $t$-dependence of the inelastic vertex in the two-Pomeron exchange diagram is consistent with a slope $B_{\text{inel}} \approx 1.4\div1.7\,\text{GeV}^2$, supporting a smooth transition between soft and hard QCD regimes.
• The model predicts that MPI enhancement persists even at $x < 10^{-3}$, where nonperturbative mechanisms dominate, ensuring the observed cross-section enhancement remains significant.