T-odd Wigner distributions in boost-invariant longitudinal position space and spin-momentum correlation in proton
Tanmay Maji · Nuclear Physics A · 2026
The boost invariant longitudinal position space variable σ , which is the Fourier conjugate to skewness ξ , unravels the longitudinal impact parameter information in a proton. Here, we investigate the skewness sensitivity of T-odd leading twist GTMDs within the Dokshitzer Gribov Lipatov Altarelli Parisi (DGLAP) region, considering a momentum transfer to longitudinal as well as transverse direction. The σ -space distributions of the T-odd sector show oscillatory patterns that are sensitive to the square of the total momentum transfer − t , which is analogous to the diffraction scattering of waves in Optics. An additional effect on the diffraction pattern is reported, caused by interference between transverse momentum transfer Δ ⊥ to the transverse momentum p ⊥ of quarks. We also present the correlation of proton spin to the transverse momentum of constituents through Sivers and Boer-Mulders Wigner Distributions in boost invariant longitudinal position space.