Measurement of $$\phi $$ meson production in $$p + p$$ interactions at 40, 80 and $$158 \, \hbox {GeV}/c$$ with the NA61/SHINE spectrometer at the CERN SPS

Results on $$\phi $$ϕ meson production in inelastic $$p + p$$p+p collisions at CERN SPS energies are presented. They are derived from data collected by the NA61/SHINE fixed target experiment, by means of invariant mass spectra fits in the $$\phi \rightarrow K^+ K^- $$ϕ→K+K- decay channel. They include the first ever measured double differential spectra of $$\phi $$ϕ mesons as a function of rapidity $$y$$y and transverse momentum $$p_{\text {T}}$$pT for proton beam momenta of $$80 \, \hbox {GeV}/c$$80GeV/c and $$158 \, \hbox {GeV}/c$$158GeV/c, as well as single differential spectra of $$y$$y or $$p_{\text {T}}$$pT for beam momentum of $$40 \, \hbox {GeV}/c$$40GeV/c. The corresponding total $$\phi $$ϕ yields per inelastic $$p + p$$p+p event are obtained. These results are compared with existing data on $$\phi $$ϕ meson production in $$p + p$$p+p collisions. The comparison shows consistency but superior accuracy of the present measurements. The emission of $$\phi $$ϕ mesons in $$p + p$$p+p reactions is confronted with that occurring in $$\mathrm{Pb} + \mathrm{Pb}$$Pb+Pb collisions, and the experimental results are compared with model predictions. It appears that none of the considered models can properly describe all the experimental observations.