The STAR Collaboration reports measurements of the transverse single-spin asymmetry (TSSA) of inclusive neutral pions at center-of-mass energies 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 center-of-mass energies show a continuous increase of the TSSA with Feynman-$x$, and comparing with previous measurements, no dependence on the center-of-mass energy from 19.4 GeV to 500 GeV is found. To investigate the underlying physics leading to this large TSSA, different topologies have been studied. Pions with no nearby particles tend to have a higher TSSA than inclusive pions. The TSSA for inclusive electromagnetic jets, sensitive to the Sivers effect in the initial state, is lower, but shows the same behavior as the inclusive $\pi^0$ asymmetry as function of Feynman-$x$. To investigate final state effects, the Collins asymmetry of neutral pions inside electromagnetic jets has been measured.  It was found to be small for both center-of-mass energies as function of the transverse momentum and the energy fraction of the $\pi^0$ with respect to the jet axis and energy, respectively. All of the measurements are compared to state of the art theoretical calculations for transverse momentum-dependent parton distribution functions and fragmentation functions.

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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