The one-point charge correlator in deep inelastic scattering

In this work, we propose a novel definition of the one-point charge correlator (QC) adapted to the Breit frame in deep-inelastic scattering (DIS). We demonstrate that this observable is infrared and collinear (IRC) safe, ensuring its perturbative calculability. Utilizing soft-collinear effective theory (SCET), we systematically analyze the QC in both the forward and back-to-back limits. In the forward limit, we introduce the nucleon charge correlator as a novel non-perturbative object that encodes the multi-dimensional microscopic structure of the nucleon. In the back-to-back limit, the QC establishes a direct correspondence with transverse momentum-dependent distributions (TMDs), enabling its description within the standard TMD factorization formalism. The singular distributions are derived within SCET and are verified by the full QCD calculations up to $\mathcal{O}(\alpha_s^2)$. The corresponding collinear logarithms are resummed to all orders with the accuracy of NLL (${\cal{O}}(\alpha_s^n L^{n-1})$), while the transverse momentum-dependent logarithms are resummed to all orders with the accuracy of $N^3$LL for the unpolarized distribution and N$^2$LL for the Sivers asymmetry.