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

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 -ₛ2F+Nc2 instead of -ₛ Nc4 when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizs\"acker-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\"acker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the 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.