Measurement of $\phi$-meson production at forward rapidity in $p$$+$$p$ collisions at $\sqrt{s}$=510 GeV and energy dependence of $\sigma_\phi$ from $\sqrt{s}$=200 GeV to 7 TeV

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of $\phi$(1020)-meson production at forward rapidity in $p$$+$$p$ collisions at $\sqrt{s}=$510 GeV via the dimuon decay channel. The partial cross section in the rapidity and $p_T$ ranges $1.2<|y|<2.2$ and $2<p_T<7$ GeV/$c$ is $\sigma_\phi=[2.28 \pm 0.09\,{\rm (stat)} \pm 0.14\,{\rm (syst)} \pm 0.27\, {\rm (norm)}] \times 10^{-2}$~mb. The energy dependence of $\sigma_\phi$ ($1.2<|y|<2.2, \; 2<p_T<5$ GeV/$c$) is studied using the PHENIX measurements at $\sqrt{s}=$200 and 510 GeV and the Large-Hadron-Collider measurements at $\sqrt{s}=$2.76 and 7 TeV. The experimental results are compared to various event generator predictions ({\sc pythia6, pythia8, phojet, ampt, epos3,} and {\sc epos-lhc}).
Comment: 363 authors, 13 pages, 9 figures, 3 tables, 2013 data. v2 is the version accepted for publication by Phys. Rev. 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