Measurement of $\varphi$-meson production at forward rapidity in p0p collisions at $\sqrt{s}$=510 GeV and energy dependence of ${\sigma }_{\varphi }$ from $\sqrt{s}$=200 GeV to 7 TeV

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of $\varphi$(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 $1.2<\mathrm{\mid }y\mathrm{\mid }<2.2$ 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\mathrm{.}Theenergydependenceof$\sigma_\phi$($1.2<|y|<2.2, ; 2<p_T<5$GeV\mathrm{/}$c$) 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}).