Transversity GPDs of the proton from lattice QCD
We present the first calculation of the x dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with nonlocal operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as 0.83, 1.25, and 1.67 GeV, and the values of the momentum transfer squared are 0.69 and 1.02 GeV 2 . These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of twisted-mass fermions with a clover term: two degenerate-mass light quarks, a strange quark, and a charm quark. The lattice results are renormalized nonperturbatively and finally matched to the light-cone GPDs using one-loop perturbation theory within the framework of large-momentum effective theory. The final GPDs are given in the $\overline{MS}$ scheme at a scale of 2 GeV. In addition to the individual GPDs, we form the combination of the transversity GPDs that is related to the transverse spin structure of the proton. Finally, we extract the lowest two moments of the GPDs and draw a number of important qualitative conclusions.