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

Results on $$\phi $$ meson production in inelastic $$p + p$$ 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 $$\phi \rightarrow K^+ K^- $$ decay channel. They include the first ever measured double differential spectra of $$\phi $$ mesons as a function of rapidity $$y$$ and transverse momentum $$p_{\text {T}}$$ for proton beam momenta of $$80 \, \hbox {GeV}/c$$ and $$158 \, \hbox {GeV}/c$$, as well as single differential spectra of $$y$$ or $$p_{\text {T}}$$ for beam momentum of $$40 \, \hbox {GeV}/c$$. The corresponding total $$\phi $$ yields per inelastic $$p + p$$ event are obtained. These results are compared with existing data on $$\phi $$ meson production in $$p + p$$ collisions. The comparison shows consistency but superior accuracy of the present measurements. The emission of $$\phi $$ mesons in $$p + p$$ reactions is confronted with that occurring in $$\mathrm{Pb} + \mathrm{Pb}$$ 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.