"Rosenbluth" separation of the $J/ψ$ near-threshold photoproduction -- an access to the gluon Gravitational Form Factors at high $t$

We perform analysis of the near-threshold $J/\psi $ photoproduction data off the proton based on the high skewness expansion ( $\xi \to 1$) of the cross-section in Ref. [1]. This expansion allows to separate the corresponding gluonic form factors, in much the same way as this is done in the electro-magnetic case with the Rosenbluth separation. We examine the independence of the extracted form factors with the photon beam energy. In Ref. [1] these form factors, in the leading-moment approximation, are related to the proton's gluon Gravitational Form Factors (gGFF). Using this approximation, we compare the extracted data points with lattice calculations in the region of momentum transfer squared of $1<|t|<2$ GeV$^{2}$, where the data and lattice results overlap. Such analysis demonstrates the possibility of extracting some combinations of the gGFFs from the data at high $t$, complementary to the lattice calculations available in the low $t$ region. However, higher statistics is needed to more accurately check the predicted $\xi$-scaling behavior of the data and compare with the lattice results, thus testing the theoretical assumptions used in Ref. [1].