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We consider the recent RHIC data on the transverse single spin asymmetry(SSA) A_N, measured in p(transv. polarized) p -> pi^0 X processes atmid-rapidity by the PHENIX collaboration. The measurement is consistent with avanishing SSA. We analyze this experimental information within a hardscattering approach based on a generalized QCD factorization scheme, withunintegrated, transverse momentum dependent (TMD), parton distribution andfragmentation functions. It turns out that, in the kinematical region of thedata, only the gluon Sivers effect could give a large contribution to A_N; itsvanishing value is thus an indication about the possible size of the gluonSivers function (GSF). Approximate upper limits on its magnitude are derived.Additional constraints obtained combining available parameterizations of thequark Sivers function and the Burkardt sum rule (BSR) for the Siversdistributions are also discussed

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Constraints on the gluon Sivers distribution via transverse single spin asymmetries at midrapidity in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>p</mml:mi><mml:mo>↑</mml:mo></mml:msup><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mi>X</mml:mi></mml:math>processes at BNL RHIC

Constraints on the gluon Sivers distribution via transverse single spin asymmetries at midrapidity inp↑p→π0Xprocesses at BNL RHIC