Twisting Small-$x$ Gluon Tomography with Orbital Angular Momentum

Abstract: We propose an orbital-angular-momentum-resolved extension of small-$x$ gluon tomography in hard diffractive dijet deep inelastic scattering. In the standard plane-wave setup, the elliptic correlation between the dijet relative momentum and the target recoil probes the elliptic component of the small-$x$ gluon Wigner distribution through a fixed transverse readout. We show that replacing the plane-wave lepton current by a twisted wave-packet current promotes this readout into a tunable OAM--Bessel projection kernel. The exchanged virtual photon is not treated as an asymptotic vortex particle; the OAM dependence enters through the transverse structure of the lepton electromagnetic current. The resulting observable is a family of $M$-resolved elliptic correlations $A_2^{(M)}(q_T,R_γ)$, where $q_T$ denotes the transverse Bessel scale of the projection kernel, not the transverse momentum of the exchanged photon. We derive the normalized linear response and show that it contains a subtraction from the deformation of the total diffractive rate. Consequently, the elliptic response can vanish while the diffractive rate remains finite. This finite-rate null is a normalized projection zero of the response to the target elliptic gluon component, not a disappearance of diffraction. It is not available as a tunable mode zero in the standard single plane-wave readout, and provides an external projection basis in which the response to the same small-$x$ elliptic geometry can be probed with either sign or tuned to zero.