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Constituent-counting rule in photoproduction of hyperon resonances

Wen-Chen Chang¹, S. Kumano^2,3, and Takayasu Sekihara⁴

¹Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
²KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1, Ooho, Tsukuba, Ibaraki 305-0801, Japan
³J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK and Theory Group, Particle and Nuclear Physics Division, J-PARC Center, 203-1, Shirakata, Tokai, Ibaraki 319-1106, Japan
⁴Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan

Phys. Rev. D 93, 034006 – Published 4 February, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.034006

Abstract

We analyze the CLAS data on the photoproduction of hyperon resonances, as well as the available data for the ground state $Λ$ and $Σ^{0}$ of the CLAS and SLAC-E84 collaborations, by considering a 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 $γ p \to K^{+} Λ$ and $K^{+} Σ^{0}$ reactions, we find that the number of elementary constituents is consistent with $n_{γ} = 1$ , $n_{p} = 3$ , $n_{K^{+}} = 2$ , and $n_{Λ} = n_{Σ^{0}} = 3$ . Then, an analysis is made for the photoproductions of the hyperon resonances $Λ (1405)$ , $Σ (1385)^{0}$ , and $Λ (1520)$ , where $Λ (1405)$ is considered to be a $\bar{K} N$ molecule, and hence its constituent number could be 5. However, we find that the current data are not enough to conclude the numbers of their constituents. It is necessary to investigate the higher-energy region at $\sqrt{s} > 2.8 GeV$ experimentally beyond the energy of the available CLAS data to count the number of constituents clearly. We also mention that our results indicate energy dependence in the constituent number, especially for $Λ (1405)$ . 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.

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