Abstract
Permutation groups are applied to analyze the symmetries of pentaquark states. All possible quark configurations of the color, flavor, spin and spatial degrees of freedom are worked out in the language of permutation groups, and the corresponding wave functions are constructed systematically in the form of a Yamanouchi basis. The pentaquark spatial wave functions of various symmetries, which are derived in the harmonic-oscillator interaction, are applied as complete bases to evaluate the low-lying light $q^4\overline q$ pentaquark mass of all configurations, where the Cornell-like potential is employed.
Highlights
In recent decades, hadron physicists have expended great effort hunting for evidence of the multiquark states
Though we have been dealing with a system where the quark-quark potential is the harmonic oscillator interaction, the spatial wave functions grouped in this work according to the permutation symmetry can be employed as complete bases to study a system with other interactions
In the work we have worked out all the spatial-spinflavor as well as spin-flavor configurations of pentaquark systems, and derived explicitly the spatial-spin-flavor as well as spin-flavor wave functions
Summary
Hadron physicists have expended great effort hunting for evidence of the multiquark states. A group theory approach has been applied to construct the pentaquark wave functions and study the role of pentaquark components in baryons [4,5,6,7,8,9,10,11]. The construction of high-order spatial wave functions of pentaquark states in various permutation symmetries has been a challenge. In this work we systematically construct in the group theory approach the pentaquark wave function in the form of a Yamanouchi basis, including high-order spatial excitations.
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