World data of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math>production consolidate nonrelativistic QCD factorization at next-to-leading order

Abstract

We calculate the cross sections of inclusive $J/\ensuremath{\psi}$ production in photoproduction and two-photon scattering, involving both direct and resolved photons, and in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, including the full relativistic corrections due to the intermediate $^{1}S_{0}^{[8]}$, $^{3}S_{1}^{[8]}$, and $^{3}P_{J}^{[8]}$ color-octet states. Exploiting also our previous results on hadroproduction, we perform a combined fit of the respective color-octet long-distance matrix elements to all available high-quality data of inclusive $J/\ensuremath{\psi}$ production, from KEKB, LEP II, RHIC, HERA, the Tevatron, and the LHC, comprising a total of 194 data points from 26 data sets.