J/{psi}({psi}{sup '}) Production at the Tevatron and LHC at O({alpha}{sub s}{sup 4}v{sup 4}) in Nonrelativistic QCD

We present a complete evaluation for J/{psi}({psi}{sup '}) prompt production at the Tevatron and LHC at next-to-leading order in nonrelativistic QCD, including color-singlet, color-octet, and higher charmonia feeddown contributions. The short-distance coefficients of {sup 3}P{sub J}{sup [8]} at next-to-leading order are found to be larger than leading order by more than an order of magnitude but with a minus sign at high transverse momentum p{sub T}. Two new linear combinations of color-octet matrix elements are obtained from the CDF data, and used to predict J/{psi} production at the LHC, which agrees with the CMS data. The possibility of {sup 1}S{sub 0}{sup [8]} dominance and the J/{psi} polarization puzzle are also discussed.