The STAR Collaboration reports measurements of the transverse single-spin asymmetry (TSSA) of inclusive $\pi^0$ at center-of-mass energies ($\sqrt s$) of 200~GeV and 500~GeV in transversely polarized proton-proton collisions in the pseudo-rapidity region 2.7 to 4.0. The results at the two different energies show a continuous increase of the TSSA with Feynman-$x$, and, when compared to previous measurements, no dependence on $\sqrt s$ from 19.4~GeV to 500~GeV is found. To investigate the underlying physics leading to this large TSSA, different topologies have been studied. $\pi^0$ with no nearby particles tend to have a higher TSSA than inclusive $\pi^0$. The TSSA for inclusive electromagnetic jets, sensitive to the Sivers effect in the initial state, is substantially smaller, but shows the same behavior as the inclusive $\pi^0$ asymmetry as a function of Feynman-$x$. To investigate final-state effects, the Collins asymmetry of $\pi^0$ inside electromagnetic jets has been measured. The Collins asymmetry is analyzed for its dependence on the $\pi^0$ momentum transverse to the jet thrust axis and its dependence on the fraction of jet energy carried by the $\pi^0$. The asymmetry was found to be small in each case for both center-of-mass energies. All the measurements are compared to QCD-based theoretical calculations for transverse-momentum-dependent parton distribution functions and fragmentation functions. Some discrepancies are found, which indicates new mechanisms might be involved.

We report the measurements of transverse single-spin asymmetries for $\pi^0$s in the forward rapidity region in proton-proton collisions at 500 GeV using the FMS at STAR. The same measurement at 200 GeV is done with the highest statistics so far. The asymmetries increase with Feynman-$x$. No energy dependence was found comparing the current results with data previously measured at RHIC and FNAL with center-of mass energies as low as 19.4 GeV. 

 

The transverse single-spin asymmetries for isolated and non-isolated $\pi^0$ at both 200 GeV and 500 GeV are presented. The asymmetries of isolated $\pi^0$s are significantly larger than those of non-isolated $\pi^0$s. 

 

The transverse single-spin asymmetries for electromagnetic jets are measured with the FMS in transversely polarized proton-proton collisions at both 200 GeV and 500 GeV. The 500 GeV result with a minimum photon multiplicity requirement is consistent with zero, which coincides with the full jet measurement from the $A_NDY$ experiment. The 200 GeV results are small but clearly non-zero within uncertainties. 

 

Collins asymmetries for $\pi^0$s within an electromagnetic jet were measured in proton-proton collisions at both 200 GeV and 500 GeV. The asymmetries are small across the $z_{em}$ bins and might exhibit a $j_T$ dependence at 200 GeV. 

 

These new data provide important information for understanding the underlying physics mechanism for the transverse single-spin asymmetry. In particular, the observed small TSSA for non-isolated $\pi^0$s and also small Collins asymmetries with EM jets suggest that the Collins effect itself can not account for the observed $\pi^0$ TSSA.

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