\[\begin{split}\begin{array}{rcl}
A^{2}_{-1, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{-1, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{-1, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{-1, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{-1, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{-1, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{-1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{-1, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{-1, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{-1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{0, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{0, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{0, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{0, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{0, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{0, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{0, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{0, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{0, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{0, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{1, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{1, 0, - \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{1, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,0,\lambda_{R} + \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{- \frac{\sqrt{30} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,2,\lambda_{R} + \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} + \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{1, 0, - \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{1, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{1,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\frac{1}{2}}_{0,0,\frac{1}{2},\frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},\frac{1}{2}}_{2,0,\frac{1}{2},\frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{1, 0, \frac{1}{2}, - \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{- \frac{\sqrt{2} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{0,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{5} \delta_{1, \lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{1,0,1,\lambda_{R} + \frac{1}{2}} C^{1,\lambda_{R} + \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},\frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{2}_{1, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} \left(C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}}\right)^{2} C^{0,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,0,\lambda_{R} - \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1750)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{0}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1750)^{-}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1750)^{-}, 1, 0} \mathcal{R}_{0}\left(\sigma_{2}, m_{\overline{\Sigma}(1750)^{-}}, \Gamma_{\overline{\Sigma}(1750)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{\overline{\Sigma}(1660)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{1}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1660)^{-}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1660)^{-}, 0, 1} \mathcal{R}_{1}\left(\sigma_{2}, m_{\overline{\Sigma}(1660)^{-}}, \Gamma_{\overline{\Sigma}(1660)^{-}}\right) d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-5/2}^{5/2}{\frac{\sqrt{30} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,2,\lambda_{R} - \frac{1}{2}} C^{\frac{5}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} C^{2,\lambda_{R} - \frac{1}{2}}_{\frac{5}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1775)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1775)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1775)^{-}, 1, 2} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1775)^{-}}, \Gamma_{\overline{\Sigma}(1775)^{-}}\right) d^{\frac{5}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{6}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1670)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1670)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1670)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1670)^{-}}, \Gamma_{\overline{\Sigma}(1670)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{\overline{\Sigma}(1940)^{-}}, m_{\Sigma^{+}}\right) \mathcal{F}_{2}\left(\sigma_{2}^{2}, m_{K^{0}}, m_{\overline{p}}\right) \mathcal{H}^\mathrm{LS,decay}_{\overline{\Sigma}(1940)^{-}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{\Sigma}(1940)^{-}, 1, 1} \mathcal{R}_{2}\left(\sigma_{2}, m_{\overline{\Sigma}(1940)^{-}}, \Gamma_{\overline{\Sigma}(1940)^{-}}\right) d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{1, 0, \frac{1}{2}, \frac{1}{2}} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1720)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1720)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1720)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1720)^{+}}, \Gamma_{N(1720)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{0,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{1}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{1,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{0}\left(m_{0}^{2}, m_{N(1710)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{1}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1710)^{+}, 1, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1710)^{+}, 0, 1} \mathcal{R}_{1}\left(\sigma_{3}, m_{N(1710)^{+}}, \Gamma_{N(1710)^{+}}\right) d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{5} \delta_{1, \lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},- \frac{1}{2}}_{0,0,\frac{1}{2},- \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{1,0,1,\lambda_{R} - \frac{1}{2}} C^{1,\lambda_{R} - \frac{1}{2}}_{\frac{3}{2},\lambda_{R},\frac{1}{2},- \frac{1}{2}} C^{\frac{3}{2},- \frac{1}{2}}_{2,0,\frac{1}{2},- \frac{1}{2}} \mathcal{F}_{1}\left(m_{0}^{2}, m_{N(1700)^{+}}, m_{\overline{p}}\right) \mathcal{F}_{2}\left(\sigma_{3}^{2}, m_{K^{0}}, m_{\Sigma^{+}}\right) \mathcal{H}^\mathrm{LS,decay}_{N(1700)^{+}, 2, \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{N(1700)^{+}, 1, 1} \mathcal{R}_{2}\left(\sigma_{3}, m_{N(1700)^{+}}, \Gamma_{N(1700)^{+}}\right) d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
\end{array}\end{split}\]