$J/��$ and $��(2S)$ production at forward rapidity in $p$+$p$ collisions at $\sqrt{s}=510$ 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 $J/��$ and cross-section ratio of $��(2S)$ to $J/��$ at forward rapidity in \pp collisions at \sqrts = 510 GeV via the dimuon decay channel. Comparison is made to inclusive $J/��$ cross sections measured at \sqrts = 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 $\approx3$ GeV/$c$, the calculations are systematically below the data. The total cross section times the branching ratio is BR $d��^{J/��}_{pp}/dy (1.2
361 authors from 71 institutions, 13 pages, 4 tables, 11 figures, 2013 data. v2 is version accepted for publication in Physical Review D. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html