[Paper Review] Semi-inclusive Diffractive Deep Inelastic Scattering at Small-$x$

Yoshitaka Hatta, Bo-Wen Xiao+1 more|arXiv (Cornell University)|May 17, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes semi-inclusive diffractive deep inelastic scattering (SIDDIS) as a novel probe of gluon tomography at small-$x$, using diffractive parton distribution functions (DPDFs) derived from color dipole S-matrices in the fundamental (quark) and adjoint (gluon) representations. The key contribution is a systematic QCD factorization framework that connects SIDDIS observables to the gluon Wigner distribution and saturation effects via the CGC formalism, with DPDFs calculable from dipole amplitudes and consistent with both CGC and GPD approaches.

ABSTRACT

Inspired by a recent study of Iancu, Mueller and Triantafyllopoulos [1] and earlier papers by Golec-Biernat and Wusthoff [2,3], we propose semi-inclusive diffractive deep inelastic scattering (SIDDIS) to investigate the gluon tomography in the nucleon and nuclei at small-$x$. The relevant diffractive quark and gluon parton distribution functions (DPDF) can be computed in terms of the color dipole S-matrices in the fundamental and adjoint representations, respectively. Novel correlations from the gluon tomography in the dipole S-matrix can be experimentally studied through the DPDFs in these processes at the future electron-ion collider (EIC).

Motivation & Objective

• To develop a systematic QCD factorization framework for semi-inclusive diffractive DIS (SIDDIS) at small-$x$ to probe gluon tomography in nucleons and nuclei.
• To connect diffractive parton distribution functions (DPDFs) for quarks and gluons to the color dipole S-matrix in the CGC formalism, enabling systematic computation of saturation effects.
• To demonstrate consistency between the CGC/dipole formalism and the collinear DPDF formalism, extending previous consistency results from DVCS to SIDDIS.
• To provide a unified theoretical framework linking TMD, GPD, and CGC approaches via SIDDIS, with applications to future electron-ion collider (EIC) experiments.

Proposed method

• Uses QCD factorization for SIDDIS, extending methods from SIDIS and hard diffractive processes, with factorization valid in the small-$x$ regime.
• Derives quark and gluon DPDFs from the operator definitions of the color dipole S-matrix in the fundamental and adjoint representations, respectively.
• Applies the dipole formalism to compute DPDFs, ensuring consistency with gluon saturation effects in the CGC framework.
• Integrates over transverse momentum to obtain collinear factorization, where soft factors decouple, enabling extraction of DPDFs from experimental data.
• Performs $k_T$-factorization and collinear limit analysis to connect the results to standard DPDFs and validate consistency with existing calculations.
• Identifies ambiguities in prior work (e.g., Golec-Biernat et al.) due to inconsistent normalization of quark and gluon saturation scales, and corrects them via proper dipole amplitude matching.

Experimental results

Research questions

• RQ1 How can semi-inclusive diffractive DIS (SIDDIS) be used to probe the gluon Wigner distribution and saturation effects at small-$x$?
• RQ2 What is the precise relation between the diffractive parton distribution functions (DPDFs) for quarks and gluons and the color dipole S-matrix in the CGC formalism?
• RQ3 How does the QCD factorization of SIDDIS connect with the generalized parton distribution (GPD) and dipole formalism approaches in the small-$x$ regime?
• RQ4 What corrections arise from semi-hard gluon radiation (e.g., trijet production) in diffractive processes, and how do they affect the DPDF extraction?
• RQ5 Why do prior calculations of the integrated gluon DPDF differ by a factor of 2, and how can this ambiguity be resolved?

Key findings

• The quark and gluon DPDFs in SIDDIS are systematically calculable from the color dipole S-matrix in the fundamental and adjoint representations, respectively, ensuring consistency with gluon saturation effects.
• The $k_T$-factorized cross section for SIDDIS matches the structure of the diffractive structure function in Golec-Biernat et al., with the $q\bar{q}$ contribution directly linked to the quark DPDF.
• The $q\bar{q}g$ contribution to the transverse structure function is shown to be related to the gluon DPDF via a $g\to q$ DGLAP evolution kernel, confirming its role in probing gluon dynamics.
• A correction to the normalization of the gluon distribution in prior work (Golec-Biernat et al.) is identified: using $Q_{as} = Q_s$ for both quark and gluon distributions violates dipole S-matrix unitarity, leading to a factor-of-2 discrepancy in the integrated gluon DPDF.
• The corrected normalization ensures consistency with the dipole formalism and restores unitarity, resolving prior ambiguities in the extraction of the gluon DPDF.
• The framework unifies the CGC/dipole, GPD, and TMD approaches for diffractive processes at small-$x$, providing a consistent path for EIC measurements of the gluon Wigner distribution.