  There have been numerous attempts, in the last decades, to understand the
origin of the unexpectedly large transverse single-spin asymmetry ($A_{N}$)
observed in inclusive hadron productions at forward rapidities in transversely
polarized $p^{\uparrow}$+$p$ collisions at different center-of-mass energies
($\sqrt{s}$). The current theoretical frameworks aimed at explaining this
puzzle include the twist-3 contributions in the collinear factorization
framework, as well as the transverse-momentum-dependent contributions from the
initial-state quark and gluon Sivers functions, and/or final-state Collins
fragmentation functions. Besides, there are indications that the diffractive
processes may contribute to the large $A_{N}$. We present the detailed
investigations into the $A_{N}$ for electromagnetic jets (EM-jets) produced in
inclusive processes using the Forward Meson Spectrometer with transversely
polarized $p^{\uparrow}$+ $p$ data at $\sqrt{s} =$ 200 GeV collected in 2015 at
STAR. We observe a negative value for the $A_{N}$ of EM-jets in diffractive
processes. This finding shows a different sign for $A_{N}$ in inclusive
processes and needs further theoretical input in order to be understood.
Finally, we present the statistical projections of the $A_{N}$ for inclusive
and diffractive EM-jets utilizing $p^{\uparrow}$+ $p$ data at $\sqrt{s} =$ 510
GeV collected in 2017 at STAR. This dataset allows for a substantial
enhancement in statistical precision.

Nuclear Experiment