The complete study on polarization of ${\rm Y}(nS)$ hadroproduction at QCD next-to-leading order

Abstract

Applying the nonrelativistic quantum chromodynamics factorization formalism to the ${\rm Y}(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters ${\lambda }_{\theta }$, ${\lambda }_{\theta \varphi }$, ${\lambda }_{\varphi }$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter ${\lambda }_{\theta }$ of ${\rm Y}$ hadroproduction, our results provide a good description for the measured parameters ${\lambda }_{\theta \varphi }$ and ${\lambda }_{\varphi }$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $\tilde{\lambda }$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $\tilde{\lambda }$ between available experimental data and corresponding theoretical predictions.

Comments: 9 pages, 8 figures