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The PHENIX experiment at the Relativistic Heavy Ion Collider has measured thedifferential cross section of $\phi$(1020)-meson production at forward rapidityin $p$$+$$p$ collisions at $\sqrt{s}=$510 GeV via the dimuon decay channel. Thepartial 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 PHENIXmeasurements at $\sqrt{s}=$200 and 510 GeV and the Large-Hadron-Collidermeasurements at $\sqrt{s}=$2.76 and 7 TeV. The experimental results arecompared to various event generator predictions ({\sc pythia6, pythia8, phojet,ampt, epos3,} and {\sc epos-lhc}).

physical review. d/physical review. d.

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