[Paper Review] Higher Twist Effects in Nuclei

Rainer J. Fries|ArXiv.org|Jan 31, 2002

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates higher twist effects in nuclear deep inelastic scattering and Drell-Yan processes, showing that multiple parton scattering in nuclei leads to nuclear-enhanced power corrections scaling as $A^{1/3}$, where $A$ is the nuclear mass number. The key contribution is a framework to isolate these dominant higher twist contributions via matrix elements that scale with nuclear size, enabling a systematic pQCD treatment of medium effects in heavy-ion collisions at RHIC and beyond.

ABSTRACT

This talk serves as an introduction to higher twist effects in nuclei. We want to discuss how perturbative QCD can be applied to processes involving heavy nuclei by taking into account multiple scattering.

Motivation & Objective

• To understand how perturbative QCD can be extended to describe scattering processes in heavy nuclei by including multiple parton scatterings.
• To identify and isolate higher twist corrections that are enhanced by nuclear size, particularly in $p+A$ and $A+A$ collisions.
• To develop a systematic twist expansion where nuclear enhancement ($A^{1/3}$) selects dominant non-perturbative matrix elements over standard power corrections.
• To provide a theoretical framework for interpreting experimental data from RHIC, especially on Drell-Yan pair production and transverse momentum broadening.
• To examine the breakdown of factorization beyond twist-4 and assess the limits of the pQCD approach in nuclear collisions.

Proposed method

• Uses twist expansion in $\lambda/Q$ with $\lambda \sim \Lambda_{QCD}$, where $Q$ is the hard scale, to separate perturbative and non-perturbative physics.
• Applies factorization theorems to express cross sections as convolutions of parton distributions and partonic cross sections, with higher twist corrections from matrix elements of higher-dimensional operators.
• Identifies nuclear-enhanced higher twist matrix elements, such as $T^{DH}_{ab} \propto A^{4/3} f_a(\xi) f_b(x)$ and $T^{SH}_{ab} \propto \lambda^2 A^{4/3} f_a(\xi)$, which scale with nuclear size.
• Models the soft-hard scattering matrix elements using parton distributions, assuming $T^{SH}_{ab}(\xi) \propto \lambda^2 A^{4/3} f_a(\xi)$, and derives predictions for Drell-Yan tensor amplitudes.
• Analyzes transverse momentum broadening via resummation of multiple scattering diagrams, leading to a shift in the $q_\perp$ spectrum proportional to $A^{1/3}\lambda^2$.
• Considers the resummation of $n$-gluon exchange diagrams, leading to a modified $q_\perp$ spectrum with a shift and smearing, derived from correlators $\langle P|\bar{q}q (FF)^n |P\rangle$.

Experimental results

Research questions

• RQ1 How do higher twist corrections in deep inelastic scattering and Drell-Yan processes on nuclei differ from those in free nucleons?
• RQ2 Which higher twist matrix elements are enhanced by the nuclear size, and how can they be isolated in a twist expansion?
• RQ3 To what extent can the Lam-Tung sum rule be violated by higher twist contributions, and what does this imply for the structure of the Drell-Yan tensor amplitudes?
• RQ4 How does transverse momentum broadening of Drell-Yan pairs arise from multiple scattering, and can it be described by a resummed higher twist formalism?
• RQ5 What are the limits of pQCD factorization in $A+A$ collisions beyond twist-4, and can nuclear enhancement preserve factorization in $p+A$?

Key findings

• Nuclear-enhanced higher twist corrections scale as $A^{1/3}$, making them dominant in heavy nuclei, while standard power corrections scale as $\lambda^2/Q^2$.
• Double hard scattering processes reproduce the leading twist Lam-Tung sum rule $2W_{\Delta\Delta} = W_L$, indicating consistency with independent binary collisions.
• Soft-hard scattering processes violate the Lam-Tung relation, with a non-zero twist-4 contribution to $W_\Delta$, signaling new physics beyond leading twist.
• The transverse momentum broadening of Drell-Yan pairs is predicted to scale as $A^{1/3}\lambda^2$, matching experimental data in the low $q_\perp$ regime.
• The ratio of second to first moments of the $q_\perp$ spectrum is $\frac{\langle q_\perp^2 \rangle}{\langle q_\perp^0 \rangle} = \frac{4\pi^2\alpha_s}{3} A^{1/3} \lambda^2$, providing a direct observable test of the model.
• Resummation of multiple scattering diagrams leads to a shift in the $q_\perp$ spectrum by $\frac{4\pi^2\alpha_s}{3} A^{1/3} \lambda^2$, consistent with observed broadening in $p+Au$ collisions at RHIC.