[Paper Review] Back-to-back inclusive dijets in DIS at small $x$: Complete NLO results and predictions

Paul Caucal, Farid Salazar+3 more|arXiv (Cornell University)|Jul 31, 2023

High-Energy Particle Collisions Research4 citations

TL;DR

This paper presents the first complete next-to-leading-order (NLO) calculation of back-to-back inclusive dijet production in deep inelastic scattering (DIS) at small $x$ within the Color Glass Condensate (CGC) effective field theory. It factorizes the cross-section into a convolution of the Weizsäcker-Williams (WW) gluon transverse momentum-dependent distribution (TMD), a universal soft factor with double and single Sudakov logarithms, and an NLO coefficient function, enabling the first quantitative separation of Sudakov suppression from gluon saturation effects.

ABSTRACT

We compute the back-to-back dijet cross-section in deep inelastic scattering (DIS) at small $x$ to next-to-leading order (NLO) in the Color Glass Condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse momentum dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum $P_\perp$ of the dijet pair to the dijet momentum imbalance $q_\perp$; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $x$ that is kinematically constrained to satisfy both lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Motivation & Objective

• To compute the back-to-back dijet cross-section in DIS at small $x$ to next-to-leading order (NLO) in the Color Glass Condensate (CGC) effective field theory.
• To disentangle the competing effects of Sudakov suppression and gluon saturation in dijet production at small $x$.
• To provide a framework for precision tests of QCD many-body dynamics at the Electron-Ion Collider (EIC).
• To derive exact analytical expressions for the NLO coefficient functions for both transversely and longitudinally polarized photons.

Proposed method

• The calculation employs TMD factorization in the CGC EFT framework, valid to leading power in $q_{ot}/P_{ot}$ and $Q_s/P_{ot}$, and to all orders in $Q_s/q_{ot}$.
• The cross-section is factorized into a convolution of the WW gluon TMD, a universal soft factor, and an NLO coefficient function.
• The soft factor resums double and single logarithms of $P_{ot}/q_{ot}$ via renormalization group (RG) evolution into a Sudakov factor.
• The WW TMD evolves via a nonlinear RG equation in $x$ that incorporates gluon saturation dynamics.
• Exact analytical expressions are derived for the NLO coefficient functions using light-cone gauge and dipole frame formalism.
• The derivation is validated through master integral computations involving Bessel functions and logarithmic integrals in momentum space.

Experimental results

Research questions

• RQ1 How do Sudakov double and single logarithms in $P_{ot}/q_{ot}$ affect the back-to-back dijet cross-section at NLO in small-$x$ DIS?
• RQ2 To what extent can gluon saturation effects in the WW TMD be disentangled from Sudakov suppression in dijet production?
• RQ3 What is the analytical structure of the NLO coefficient function for transversely and longitudinally polarized photons in this process?
• RQ4 Can the TMD factorization framework be consistently extended to NLO in the CGC EFT for inclusive dijet production?
• RQ5 How do the resummed soft and hard factors modify the dijet cross-section in the kinematic regime relevant for the Electron-Ion Collider (EIC)?

Key findings

• The NLO coefficient function for transversely polarized photons is derived analytically, including all logarithmic and non-logarithmic contributions in $P_{ot}$ and $Q^2$.
• The NLO coefficient function for longitudinally polarized photons is obtained with full analytical control, consistent with previous results in the literature.
• The soft factor resums both single and double logarithms of $P_{ot}/q_{ot}$ into a Sudakov factor via RG evolution, providing a precise description of the suppression mechanism.
• The WW gluon TMD evolves via a nonlinear RG equation in $x$ that captures the dynamics of gluon saturation at small $x$, with $Q_s(x)$ as the saturation scale.
• The full cross-section is factorized into a convolution of the WW TMD, the soft factor, and the NLO coefficient function, enabling a quantitative separation of Sudakov suppression and saturation effects.
• The framework is extendable to other final states, such as di-hadron production, and provides a precision tool for testing QCD many-body dynamics at the EIC.