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The Helicity Amplitude for $1/2$ and $3/2^+$ Baryon in the Pseudo-Meson Photoproduction in the Quark Model

We derive the separate helicity amplitudes involving the partial wave analysis in the process of pseudo-scalar meson photon productions with $J^P=3/2^+$, which is independent on model. According to parity, the general amplitude in the case of $J^P=1/2^-$ is given out. We prove this general amplitude is corresponding to the situation of $λ=-1$ as adopting the circular polarization. Finally, the formulas of scattering amplitudes involving the photon-meson production with $J^P=3/2^+$ are obtained from the chiral quark model.