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

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 Weizsäcker-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 Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{\mathrm{MS}}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small $x$ at the future Electron-Ion Collider with full NLO accuracy.

Comments: 42 pages, 1 figure