Dihadron correlations in small-$x$ DIS at NLO: transverse momentum dependent fragmentation

TL;DR

This paper calculates the dihadron cross-section in small-$x$ DIS at NLO, incorporating TMD fragmentation and Sudakov resummation, to improve predictions for future Electron-Ion Collider experiments.

Contribution

It introduces a NLO calculation of dihadron production in small-$x$ DIS with TMD fragmentation functions and Sudakov resummation, advancing theoretical precision.

Findings

Derived the Sudakov double logarithm coefficient for the process.

Promoted collinear fragmentation functions to TMD fragmentation functions.

Provided analytic NLO coefficient functions in the $ar{MS}$ scheme.

Abstract

We compute inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small $x$ in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is $-\frac{\alpha_s}{2\pi}\left[C_F+\frac{N_c}{2}\right]$ instead of $-\frac{\alpha_s N_c}{4\pi}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizs\"{a}cker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizs\"{a}cker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{\rm MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small $x$ at the future Electron-Ion Collider with full NLO accuracy.