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

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of $φ$(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 $σ_φ=[2.28 \pm 0.09\,{\rm (stat)} \pm 0.14\,{\rm (syst)} \pm 0.27\, {\rm (norm)}] \times 10^{-2}$~mb. The energy dependence of $σ_φ$ ($1.2<|y|<2.2, \; 2<p_T<5$ 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}).