The complete study on polarization of $Υ(nS)$ hadroproduction at QCD next-to-leading order

Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Υ(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $λ_θ$, $λ_{θϕ}$, $λ_ϕ$ 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 $λ_θ$ of $Υ$ hadroproduction, our results provide a good description for the measured parameters $λ_{θϕ}$ and $λ_ϕ$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $\tildeλ$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $\tildeλ$ between available experimental data and corresponding theoretical predictions.

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