\,q^i_T \,\Delta^j_T}{M^2} \,\,
 F_{1,4} \,\right] \,u(p, \lambda). \hspace{10mm}\end{aligned}$$ The GTMD defined by the 2nd line of the above equation generally contains 4 pieces of invariant functions $F_{1,i} (x, \xi, \bm{q}_T^2, \bm{\Delta}_T^2, \eta)$ with $i = 1, \cdots, 4$, which are functions of the Bjorken variable $x$, the skewedness parameter $\xi$, the transverse-momentum square $\bm{q}_T^2$, the transverse-momentum-transfer square $\bm{\Delta}_T^2$, and the parameter $\eta$ characterizing the nature of the functions under time-reversal. In the forward limit, the first and the second pieces respectively reduce to the usual spin-independent TMD and the naively-time-reversal-odd Sivers function. On the other hand, the last two terms disappear in the forward limit, $\bm{\Delta}_\perp \rightarrow 0$. Nonetheless, within the framework of a quark model, which does not pay much attention to the gauge-invariance issue, Lorce and Pasquini showed [@LP11] that a weighted integral of this 4th function is related to the nucleon matrix element of the canonical OAM given as $$\begin{aligned}
 L_{can}
 \ = \ - \,\int \, dx \,d^2 q_T \,\,
 \frac{\bm{q}^2_T}{M^2} \,\,\,F^q_{1,4}
 (x, 0, q^2_T,0,0) .\end{aligned}$$ This is just the sum rule, to which Hatta gave a gauge-invariant meaning, i.e. the meaning within the framework of QCD as a color gauge theory. In this sense, Hatta’s 