Measurement of the $\eta$ -$\eta'$ mixing angle in $\pi^{-}$ and $K^{-}$ beams with GAMS-$4\pi$ Setup

TL;DR

This paper measures the $ heta$ mixing angle of $ ext{eta}$ and $ ext{eta'}$ mesons using charge exchange reactions with $ ext{pi}^{-}$ and $ ext{K}^{-}$ beams, providing insights into meson wave functions and gluonium content.

Contribution

It presents a novel measurement of the $ ext{eta}$-$ ext{eta'}$ mixing angle and gluonium content using the GAMS-4$ ext{ extpi}$ setup with charge exchange reactions.

Findings

Mixing angle $ heta_P = (36.8 extpm 1)^ ext{o}$ from $ ext{pi}^{-}$ beam data.

Gluonium content in $ ext{eta'}$ is $ ext{sin}^2 extpsi_G = 0.15 extpm 0.06$.

Cross section ratios differ between $ ext{pi}^{-}$ and $ ext{K}^{-}$ beams.

Abstract

The results of mixing angle measurement for $\eta'$, $\eta$ mesons generated in charge exchange reactions with $\pi^{-}$ and $K^{-}$ beams are preseneted. When the $\eta'$, $\eta$ mesons are described in nonstrange(NS)--strange(S) quark basis the $\pi^{-}$ and $K^{-}$ beams allow to study $|\eta_{q}>$ and $|\eta_{s}>$ parts of the meson wave function. The cross section ratio at $t'=0$ (GeV/c)$^{2}$ in the $\pi^{-}$ beam is $R_{\pi}(\eta'/\eta)= 0.56 \pm 0.04$, results in mixing angle $\phi_{P} = (36.8 \pm 1.)^{o} $. For $K^{-}$ beam the ratio is $R_{K}(\eta'/\eta)= 1.30 \pm 0.16$. It was found that gluonium content in $\eta'$ is $\sin^{2}\psi_{G}= 0.15 \pm 0.06$. The experiment was carried out with GAMS-4$\pi$ Setup.