\[\begin{split}\begin{array}{rcl}
A^{1}_{- \frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1}^{1}{- \frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{1,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}^{*}(892)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}^{*}(892)^{0}, 0, 0} d^{1}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{- \frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(1430)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(1430)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{- \frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(700)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(700)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=-2}^{2}{- \frac{\sqrt{6} \delta_{- \frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{1,0,\frac{3}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},\lambda_{R} + \frac{1}{2}}_{2,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{2}^{*}(1980)^{0}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{2}^{*}(1980)^{0}, 0, 0} d^{2}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} \\
A^{2}_{- \frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1232)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1232)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1600)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1600)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1700)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1700)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{- \frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1405), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1405), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1600), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1600), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1670), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1670), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(2000), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(2000), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1520), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1520), - \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1690), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1690), - \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{1}_{- \frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1}^{1}{\frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{1,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}^{*}(892)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}^{*}(892)^{0}, 0, 0} d^{1}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{\frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(1430)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(1430)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{\frac{\sqrt{2} \delta_{- \frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(700)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(700)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=-2}^{2}{\frac{\sqrt{6} \delta_{- \frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{1,0,\frac{3}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},\lambda_{R} - \frac{1}{2}}_{2,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{2}^{*}(1980)^{0}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{2}^{*}(1980)^{0}, 0, 0} d^{2}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} \\
A^{2}_{- \frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1232)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1232)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1600)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1600)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1700)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1700)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{- \frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1405), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1405), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1600), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1600), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1670), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1670), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(2000), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(2000), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1520), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1520), \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{- \frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1690), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1690), \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{1}_{\frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1}^{1}{- \frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{1,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}^{*}(892)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}^{*}(892)^{0}, 0, 0} d^{1}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{- \frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(1430)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(1430)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{- \frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(700)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(700)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=-2}^{2}{- \frac{\sqrt{6} \delta_{\frac{1}{2}, \lambda_{R} + \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} + \frac{1}{2}}_{1,0,\frac{3}{2},\lambda_{R} + \frac{1}{2}} C^{\frac{3}{2},\lambda_{R} + \frac{1}{2}}_{2,\lambda_{R},\frac{1}{2},\frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{2}^{*}(1980)^{0}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{2}^{*}(1980)^{0}, 0, 0} d^{2}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} \\
A^{2}_{\frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1232)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1232)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1600)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1600)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{- \frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1700)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1700)^{++}, 0, - \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{\frac{1}{2}, - \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1405), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1405), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1600), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1600), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1670), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1670), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(2000), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(2000), - \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1520), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1520), - \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1690), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1690), - \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
A^{1}_{\frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1}^{1}{\frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{1,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}^{*}(892)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}^{*}(892)^{0}, 0, 0} d^{1}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{\frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(1430)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(1430)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=0}{\frac{\sqrt{2} \delta_{\frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,0,\frac{1}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{0,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{0}^{*}(700)^{0}, 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{0}^{*}(700)^{0}, 0, 0} d^{0}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} + \sum_{\lambda_{R}=-2}^{2}{\frac{\sqrt{6} \delta_{\frac{1}{2}, \lambda_{R} - \frac{1}{2}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{1}\right) C^{\frac{1}{2},\lambda_{R} - \frac{1}{2}}_{1,0,\frac{3}{2},\lambda_{R} - \frac{1}{2}} C^{\frac{3}{2},\lambda_{R} - \frac{1}{2}}_{2,\lambda_{R},\frac{1}{2},- \frac{1}{2}} \mathcal{H}^\mathrm{LS,production}_{\overline{K}_{2}^{*}(1980)^{0}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\overline{K}_{2}^{*}(1980)^{0}, 0, 0} d^{2}_{\lambda_{R},0}\left(\theta_{23}\right)}{2}} \\
A^{2}_{\frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1232)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1232)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1600)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1600)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{2}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Delta(1700)^{++}, 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Delta(1700)^{++}, 0, \frac{1}{2}} d^{\frac{3}{2}}_{\lambda_{R},- \frac{1}{2}}\left(\theta_{31}\right)}{2}} \\
A^{3}_{\frac{1}{2}, \frac{1}{2}, 0, 0} &=& \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1405), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1405), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{1,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1600), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1600), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1670), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1670), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-1/2}^{1/2}{\frac{\sqrt{2} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{0,0}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{0,0,\frac{1}{2},\lambda_{R}} C^{\frac{1}{2},\lambda_{R}}_{\frac{1}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(2000), 0, \frac{1}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(2000), \frac{1}{2}, 0} d^{\frac{1}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1520), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1520), \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} + \sum_{\lambda_{R}=-3/2}^{3/2}{\frac{\sqrt{6} \delta_{\frac{1}{2} \lambda_{R}} \mathcal{R}^\mathrm{BW}_{2,1}\left(\sigma_{3}\right) C^{\frac{1}{2},\lambda_{R}}_{1,0,\frac{3}{2},\lambda_{R}} C^{\frac{3}{2},\lambda_{R}}_{\frac{3}{2},\lambda_{R},0,0} \mathcal{H}^\mathrm{LS,production}_{\Lambda(1690), 1, \frac{3}{2}} \mathcal{H}^\mathrm{decay}_{\Lambda(1690), \frac{1}{2}, 0} d^{\frac{3}{2}}_{\lambda_{R},\frac{1}{2}}\left(\theta_{12}\right)}{2}} \\
\end{array}\end{split}\]