J/psi and psi(2S) production at forward rapidity in p plus p collisions at root s=510 GeV

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section, mean transverse momentum, mean transverse momentum squared of inclusive J/psi, and cross section ratio of psi(2S) to J/psi at forward rapidity in p + p collisions at root s = 510 GeV via the dimuon decay channel. Comparison is made to inclusive J/psi cross sections measured at root s = 200 GeV and 2.76-13 TeV. The result is also compared to leading-order nonrelativistic QCD calculations coupled to a color-glass-condensate description of the low-x gluons in the proton at low transverse momentum (p(T)) and to next-to-leading order nonrelativistic QCD calculations for the rest of the p(T) range. These calculations overestimate the data at low p(T). While consistent with the data within uncertainties above approximate to 3 GeV/c, the calculations are systematically below the data. The total cross section times the branching ratio is BR d sigma(J/)(psi)(pp) / dy(1.2 < vertical bar y vertical bar < 2.2,0 < p(T) < 10 GeV/c) = 54.3 +/- 0.5(stat) +/- 5.5(syst) nb.