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 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 q pentaquark mass of all configurations, where the Cornell-like potential is employed.

The optical Talbot effect has been used to explore the topological charges of optical vortices. We recorded the self-imaging of a diffraction grating in the near-field regime with the optical vortex of several topological charges. Our twisted light was generated by a spatial light modulator (SLM). Previous studies showed that interferometric methods can determine the particular orbital angular momentum (OAM) states, but a large number of OAM eigenvalues are difficult to distinguish from the interference patterns. Here, we show that the Talbot patterns can distinguish the charges as well as the OAM of the vortices with high orders. Owing to the high sensitivity and self-imaging of the Talbot effect, several OAM eigenvalues can be distinguished by direct measurement. We check the experimental results with our theory. The present results are useful for classical and quantum metrology as well as future implementations of quantum communications.

We study pentaquark states of both light q 4q and hidden heavy q 3 QQ (q = u,d,s quark in SU(3) flavor symmetry; Q = c, b quark) systems with a general group theory approach in the constituent quark model, and the spectrum of light baryon resonances in the ansatz that the l = 1 baryon states may consist of the q 3 as well as q 4q pentaquark component. The model is fitted to ground state baryons and light baryon resonances which are believed to be normal three-quark states. The work reveals that the N (1535)1/2 − and N (1520)3/2 − may consist of a large q 4q component while the N (1895)1/2 − and N (1875)3/2 − are respectively their partners, and the N + (1685) might be a q 4q state. By the way, a new set of color-spin-flavor-spatial wave function for q 3 QQ systems in the compact pentaquark picture are constructed systematically for studying hidden charm pentaquark states. *

The pentaquark component uudss is included in the proton wave functions to study φ meson production proton-antiproton annihilation reactions. With all possible configurations of the uuds subsystem proposed for describing the strangeness spin and magnetic moment of the proton, we estimate the branching ratios of the annihilation reactions at rest pp → φX (X = π 0 , η, ρ 0 , ω) from atomic pp S-and P -wave states by using effective quark line diagrams incorporating the 3 P0 model. The best agreement of theoretical prediction with the experimental data is found when the pentaquark configuration of the proton wave function takes the flavor-spin symmetry [4]F S [22]F [22]S . a Corresponding author: yupeng@sut.ac.th

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