(or [*mechanical*]{}) OAM not [*canonical*]{} OAM. This conclusion is nothing different from Ji’s finding [@Ji97PRL].

Also for the gluon part, we find that the difference between the 2nd moment of gluon GPD $H + E$ and the 1st moment of polarized gluon distribution coincides with the proton matrix element of our gluon OAM operator given as follows. $$\begin{aligned}
 \hspace{10mm} L_g &\equiv& 
 \langle p \uparrow \,| \, M^{012}_{g-OAM} \,| \,
 p \uparrow \rangle \nonumber \\
 &=& \frac{1}{2} \,\int_{-1}^1 \,x \,[\,
 H^g (x,0,0) \ + \ E^g (x,0,0) \,] \,dx \ - \ 
 \int_0^1 \,\Delta g(x) \,dx , \end{aligned}$$ with $$\begin{aligned}
 \hspace{10mm} M^{012}_{g-OAM} &=& 
 2 \,\mbox{\rm Tr} \,[\,E^j \,(\mbox{\boldmath $x$} \times 
 \mbox{\boldmath $D$}_{pure})^3 \,A^{phys}_j \,] 
 \hspace{10mm} : \ \ \ 
 \mbox{\rm canonical OAM}
 \nonumber \\
 &+& 2 \,\mbox{\rm Tr} \,[\,\rho \,(\mbox{\boldmath $x$} \times
 \mbox{\boldmath $A$}_{phys})^3 \,]
 \hspace{22mm} : \ \ \ 
 \mbox{\rm potential OAM term} .\end{aligned}$$ Namely, the gluon OAM extracted from the combined analysis of GPD and polarized PDF contains [*potential*]{} OAM term, in addition to [*canonical*]{} OAM. (Notice that this also clarifies the reason why the sum of the gluon spin and OAM in the Jaffe-Manohar decomposition does not coincide with the total gluon angular momentum in the Ji decompostion.) 