Constituent-counting rule in photoproduction of hyperon resonances

TL;DR

This paper applies the constituent-counting rule from perturbative QCD to analyze hyperon photoproduction data, aiming to identify the internal quark structure of hyperons and hyperon resonances through scaling behaviors of cross sections.

Contribution

It demonstrates the use of the constituent-counting rule as a new method to determine the number of elementary constituents inside hyperons and hyperon resonances from experimental data.

Findings

Consistent constituent counts for ground state hyperons and mesons.

Current data insufficient to determine constituents of hyperon resonances.

Energy dependence observed in the scaling behavior, especially for $ ext{Lambda}(1405)$).

Abstract

We analyze the CLAS data on the photoproduction of hyperon resonances, as well as the available data for the ground state $\Lambda$ and $\Sigma ^{0}$ of the CLAS and SLAC-E84 collaborations, by considering constituent-counting rule suggested by perturbative QCD. The counting rule emerges as a scaling behavior of cross sections in hard exclusive reactions with large scattering angles, and it enables us to determine the number of elementary constituents inside hadrons. Therefore, it could be used as a new method for identifying internal constituents of exotic-hadron candidates. From the analyses of the $\gamma \, p \to K^{+} \Lambda$ and $K^{+} \Sigma ^{0}$ reactions, we find that the number of the elementary constituents is consistent with $n_{\gamma} = 1$, $n_{p} = 3$, $n_{K^{+}} = 2$, and $n_{\Lambda} = n_{\Sigma ^{0}} = 3$. Then, the analysis is made for the photoproductions of the hyperon resonances $\Lambda (1405)$, $\Sigma (1385)^{0}$, and $\Lambda (1520)$, where $\Lambda (1405)$ is considered to be a $\bar K N$ molecule and hence its constituent number could be five. However, we find that the current data are not enough to conclude the numbers of their constituent. It is necessary to investigate the higher-energy region at $\sqrt{s} > 2.8$ GeV experimentally beyond the energy of the available CLAS data for counting the number of constituents clearly. We also mention that our results indicate energy dependence in the constituent number, especially for $\Lambda (1405)$. If an excited hyperon is a mixture of three-quark and five-quark states, the energy dependence of the scaling behavior could be valuable for finding its composition and mixture.