Non-global logarithms and fiducial transverse-momentum-dependent observables in deep-inelastic scattering

Abstract

Extracting the intrinsic transverse-momentum structure of quarks from deep-inelastic scattering data requires separating nonperturbative effects from perturbative radiation, which broadens the measured transverse-momentum distributions. We address this problem in electron--proton scattering, $ep\to eX$, by introducing the fiducial imbalance $\boldsymbol{q}_T$, defined as the vector sum of the scattered electron's transverse momentum and all hadronic transverse momenta within a specified rapidity window. This construction reduces radiative recoil without requiring jet reconstruction or an explicit jet veto. We account for non-global logarithms (NGLs) arising from correlated soft emissions across the acceptance boundary. The azimuthally averaged NGL contribution is resummed to all orders at leading-logarithmic accuracy in the large-$N_c$ limit using Banfi--Marchesini--Smye evolution, while the leading NGL correction to the first azimuthal harmonic is included at $\mathcal{O}(\alpha_s^2)$. For the EIC and EicC kinematics considered, widening the rapidity window increases the cross section at low $q_T$, a region particularly sensitive to nonperturbative transverse dynamics, and reduces the dilution of spin asymmetries by azimuthally symmetric soft recoil. Both the Sivers single-spin asymmetry $A_{UT}$ and the worm-gear double-spin asymmetry $A_{LT}$ increase in magnitude, while the $\boldsymbol{q}_T$ integrated cross section remains unchanged. The unpolarized $\cos\phi$ moment generated by soft gluon radiation is sensitive to NGL effects, with its ratio definition reducing common normalization uncertainties. The absence of jet reconstruction makes this observable particularly relevant at the lower collision energies of EicC, providing a way to study nonperturbative spin--momentum correlations by varying the fiducial acceptance.