Title: Transverse single spin asymmetry in hadronic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>η</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math>production
Abstract: We study the transverse single spin asymmetry in ${\ensuremath{\eta}}_{c,b}$ production in polarized hadron collisions, employing the collinear twist-3 approach in combination with the color singlet model. Our main focus lies on the contribution from the twist-3 Efremov-Teryaev-Qiu-Sterman function. By extrapolating the derived spin-dependent cross section to the small transverse momentum region, consistency between the collinear twist-3 approach and the transverse-momentum-dependent factorization approach is confirmed. As a byproduct of this work, we identify a term contributing to the scale evolution of trigluon correlations in the flavor-singlet case which was originally missed, see also V. M. Braun, A. N. Manashov, and B. Pirnay [Phys. Rev. D 80, 114002 (2009); 86, 119902(E) (2012)].