Energy-Flow Moments for Elliptic Gluon Wigner Tomography

Abstract

The elliptic small-$x$ gluon Wigner distribution correlates transverse momentum with impact parameter, but it is usually accessed through exclusive diffractive dijets whose recoil is sensitive to soft radiation. We propose instead an azimuthal energy-flow moment in DIS dijet production. Within leading-power small-$x$ dijet factorization, its normalized $\cos2ϕ$ moment is a linear projection of the elliptic Wigner harmonic after a calculable kinematic subtraction, while the final-state energy weighting is infrared and collinear safe. In conjugate recoil space a rotationally scalar Sudakov factor evolves the isotropic and elliptic channels through a fixed $J_0/J_2$ Hankel pair without $W_0\to W_1$ leakage. A proof-of-principle calculation gives a per-mille Sudakov-level moment in an unoptimized conservative window, while auxiliary perturbative-window scans reach several per mille. The observable therefore formulates elliptic Wigner tomography as a moment-level energy-flow measurement whose statistical reach can be assessed by simple angular-moment counting.