Analysis of the higher twist GTMD $F_{31}$ for proton in the light-front quark-diquark model

In the light-front quark-diquark model (LFQDM), the higher twist generalized transverse momentum dependent distribution (GTMD) $F_{31}(x,{\mathbf{p}}_{\perp },{\mathbf{\Delta }}_{\perp })$ for the proton has been analyzed. We have derived the GTMD overlap equation by the analysis of GTMD correlator, employing the light-front wave functions in both the scalar and vector diquark situations. With the relevant 2-D and 3-D figures, the behavior of GTMD $F_{31}(x,{\mathbf{p}}_{\perp },{\mathbf{\Delta }}_{\perp })$ with variations in its variables has been illustrated. Further, on applying the transverse momentum dependent distribution (TMD) limit on GTMD $F_{31}(x,{\mathbf{p}}_{\perp },{\mathbf{\Delta }}_{\perp })$, the expression of TMD $f_3(x,{\mathbf{p}}_{\perp })$ has been obtained.