Energy dependence of $\phi $ meson production at forward rapidity in pp collisions at the LHC

The production of $\phi $ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $2.5< y < 4$. Measurements of the differential cross section $\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$ are presented as a function of the transverse momentum ($p_{\mathrm {T}}$) at the center-of-mass energies $\sqrt{s}=5.02$, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $\sqrt{s}=5.02$ and 13 TeV are also studied in several rapidity intervals as a function of $p_{\mathrm {T}}$, and as a function of rapidity in three $p_{\mathrm {T}}$ intervals. A hardening of the $p_{\mathrm {T}}$-differential cross section with the collision energy is observed, while, for a given energy, $p_{\mathrm {T}}$ spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $p_{\mathrm {T}}$. The new results, complementing the published measurements at $\sqrt{s}=2.76$ and 7 TeV, allow one to establish the energy dependence of $\phi $ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $p_{\mathrm {T}}$ and rapidity at all the energies.