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The STAR Collaboration reports measurements of the transverse single-spinasymmetry (TSSA) of inclusive $\pi^0$ at center-of-mass energies ($\sqrt s$) of200 GeV and 500 GeV in transversely polarized proton-proton collisions in thepseudo-rapidity region 2.7 to 4.0. The results at the two different energiesshow a continuous increase of the TSSA with Feynman-$x$, and, when compared toprevious measurements, no dependence on $\sqrt s$ from 19.4 GeV to 500 GeV isfound. To investigate the underlying physics leading to this large TSSA,different topologies have been studied. $\pi^0$ with no nearby particles tendto have a higher TSSA than inclusive $\pi^0$. The TSSA for inclusiveelectromagnetic jets, sensitive to the Sivers effect in the initial state, issubstantially smaller, but shows the same behavior as the inclusive $\pi^0$asymmetry as a function of Feynman-$x$. To investigate final-state effects, theCollins asymmetry of $\pi^0$ inside electromagnetic jets has been measured. TheCollins asymmetry is analyzed for its dependence on the $\pi^0$ momentumtransverse to the jet thrust axis and its dependence on the fraction of jetenergy carried by the $\pi^0$. The asymmetry was found to be small in each casefor both center-of-mass energies. All the measurements are compared toQCD-based theoretical calculations for transverse-momentum-dependent partondistribution functions and fragmentation functions. Some discrepancies arefound, which indicates new mechanisms might be involved.

physical review. d/physical review. d.

Measurement of transverse single-spin asymmetries of $\pi^0$ and  electromagnetic jets at forward rapidity in 200 and 500 GeV transversely  polarized proton-proton collisions