Amplitude Analysis of the Invariant-Mass Spectra of Centrally Exclusively Produced $π^+π^-$ and $K^+K^-$ Pairs in $pp$ Collisions at $\sqrt{s}=510$ GeV

Abstract

We present an amplitude analysis of the $π^{+}π^{-}$ and $K^{+}K^{-}$ invariant-mass spectra from central exclusive $pp$ collisions at $\sqrt{s}=510~\mathrm{GeV}$, measured by the STAR experiment with forward-scattered protons tagged in the Roman Pot detectors. The $π^{+}π^{-}$ channel is described with $f_{0}(500)$, $ρ^{0}(770)$, $f_{0}(980)$, $f_{2}(1270)$, $f_{0}(1500)$ and $f_{0}(1710)$ resonances with $χ^{2}/\mathrm{ndf}=121.712/57$. The fit also yields $m_{f_{0}(980)}=0.989$ GeV and $Γ=0.091$ GeV. The $K^{+}K^{-}$ channel is described with $f_{0}(980)$, $f_{2}(1270)$, $f_{2}^{\prime}(1525)$ and $f_{0}(1710)$ resonances with $χ^{2}/\mathrm{ndf}=14.662/15$. The fiducial cross sections for the individual resonances and interference terms were calculated, together with their ratios relative to the total fitted cross section. These ratios were compared across decay channels and qualitatively with previous measurements. A consistent flavor dependence of $f_{0}(1500)$ and $f_{0}(1710)$ has been derived for the highest RHIC collision energies, which is in agreement with low energy data.