Λ_c⁺ → p π⁺ K⁻

Contents

Λ_c⁺ → p π⁺ K⁻#

Decay definition#

_images/2ca90648340bc196f3c9bf227c679323be3e4e0c81215af0b2361f2dbdc00449.svg

index	name	LaTeX	$J^{P}$	mass (MeV)	width (MeV)
0	`Lambda(c)+`	$Λ_{c}^{+}$	${\frac{1}{2}}^{+}$	2,286	0
1	`p`	$p$	${\frac{1}{2}}^{+}$	938	0
2	`K-`	$K^{-}$	$0^{-}$	493	0
3	`pi+`	$π^{+}$	$0^{-}$	139	0

name	LaTeX	$J^{P}$	mass (MeV)	width (MeV)
`Delta(1232)++`	$Δ (1232)^{+ +}$	${\frac{3}{2}}^{+}$	1,232	117
`Delta(1600)++`	$Δ (1600)^{+ +}$	${\frac{3}{2}}^{+}$	1,570	250
`Delta(1700)++`	$Δ (1700)^{+ +}$	${\frac{3}{2}}^{-}$	1,710	300
`K(0)*(700)~0`	${\overset{―}{K}}_{0}^{*} (700)^{0}$	$0^{+}$	845	468
`K*(892)~0`	${\overset{―}{K}}^{*} (892)^{0}$	$1^{-}$	895	47
`K(0)*(1430)~0`	${\overset{―}{K}}_{0}^{*} (1430)^{0}$	$0^{+}$	1,430	270
`K(2)*(1980)~0`	${\overset{―}{K}}_{2}^{*} (1980)^{0}$	$2^{+}$	1,990	348
`Lambda(1405)`	$Λ (1405)$	${\frac{1}{2}}^{-}$	1,405	50
`Lambda(1520)`	$Λ (1520)$	${\frac{3}{2}}^{-}$	1,519	16
`Lambda(1600)`	$Λ (1600)$	${\frac{1}{2}}^{+}$	1,600	200
`Lambda(1670)`	$Λ (1670)$	${\frac{1}{2}}^{-}$	1,674	30
`Lambda(1690)`	$Λ (1690)$	${\frac{3}{2}}^{-}$	1,690	70
`Lambda(2000)`	$Λ (2000)$	${\frac{1}{2}}^{-}$	2,000	210

\begin{array}{r} \begin{array}{c} Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} (Δ (1232)^{+ +} [{\frac{3}{2}}^{+}] \to_{S = 1 / 2}^{L = 1} p [{\frac{1}{2}}^{+}] π^{+} [0^{-}]) K^{-} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} (Δ (1600)^{+ +} [{\frac{3}{2}}^{+}] \to_{S = 1 / 2}^{L = 1} p [{\frac{1}{2}}^{+}] π^{+} [0^{-}]) K^{-} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} (Δ (1700)^{+ +} [{\frac{3}{2}}^{-}] \to_{S = 1 / 2}^{L = 2} p [{\frac{1}{2}}^{+}] π^{+} [0^{-}]) K^{-} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} ({\overset{―}{K}}_{0}^{*} (1430)^{0} [0^{+}] \to_{S = 0}^{L = 0} K^{-} [0^{-}] π^{+} [0^{-}]) p [{\frac{1}{2}}^{+}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} ({\overset{―}{K}}_{0}^{*} (700)^{0} [0^{+}] \to_{S = 0}^{L = 0} K^{-} [0^{-}] π^{+} [0^{-}]) p [{\frac{1}{2}}^{+}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} ({\overset{―}{K}}_{2}^{*} (1980)^{0} [2^{+}] \to_{S = 0}^{L = 2} K^{-} [0^{-}] π^{+} [0^{-}]) p [{\frac{1}{2}}^{+}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} ({\overset{―}{K}}^{*} (892)^{0} [1^{-}] \to_{S = 0}^{L = 1} K^{-} [0^{-}] π^{+} [0^{-}]) p [{\frac{1}{2}}^{+}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} (Λ (1405) [{\frac{1}{2}}^{-}] \to_{S = 1 / 2}^{L = 0} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} (Λ (1520) [{\frac{3}{2}}^{-}] \to_{S = 1 / 2}^{L = 2} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} (Λ (1600) [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 1} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} (Λ (1670) [{\frac{1}{2}}^{-}] \to_{S = 1 / 2}^{L = 0} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 3 / 2}^{L = 1} (Λ (1690) [{\frac{3}{2}}^{-}] \to_{S = 1 / 2}^{L = 2} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \\ Λ_{c}^{+} [{\frac{1}{2}}^{+}] \to_{S = 1 / 2}^{L = 0} (Λ (2000) [{\frac{1}{2}}^{-}] \to_{S = 1 / 2}^{L = 0} p [{\frac{1}{2}}^{+}] K^{-} [0^{-}]) π^{+} [0^{-}] \end{array} \end{array}

Lineshapes for dynamics#

\begin{array}{r} \begin{array}{rcl} R_{l_{R}, l_{Λ_{c}}}^{BW} (s) & = & \frac{\frac{F_{l_{R}} (R_{res} p_{_{m_{1}, m_{2}}} (s))}{F_{l_{R}} (R_{res} p_{_{m_{1}, m_{2}}} (m_{0}^{2}))} \frac{F_{l_{Λ_{c}}} (R_{Λ_{c}} q_{_{m_{top}, m_{spectator}}} (s))}{F_{l_{Λ_{c}}} (R_{Λ_{c}} q_{_{m_{top}, m_{spectator}}} (m_{0}^{2}))} {(\frac{p_{_{m_{1}, m_{2}}} (s)}{p_{_{m_{1}, m_{2}}} (m_{0}^{2})})}^{l_{R}} {(\frac{q_{_{m_{top}, m_{spectator}}} (s)}{q_{_{m_{top}, m_{spectator}}} (m_{0}^{2})})}^{l_{Λ_{c}}}}{m_{0}^{2} - i m_{0} Γ_{l_{R}} (s) - s} \end{array} \end{array}

Model formulation#

model_builder = DalitzPlotDecompositionBuilder(DECAY, min_ls=(False, True))
for chain in model_builder.decay.chains:
    model_builder.dynamics_choices.register_builder(chain, formulate_breit_wigner)
model = model_builder.formulate(reference_subsystem=1)
model.intensity

\sum_{λ_{0} = - 1 / 2}^{1 / 2} \sum_{λ_{1} = - 1 / 2}^{1 / 2} \sum_{λ_{2} = 0} \sum_{λ_{3} = 0} {| \sum_{λ_{0}^{'} = - 1 / 2}^{1 / 2} \sum_{λ_{1}^{'} = - 1 / 2}^{1 / 2} \sum_{λ_{2}^{'} = 0} \sum_{λ_{3}^{'} = 0} A_{λ_{0}^{'}, λ_{1}^{'}, λ_{2}^{'}, λ_{3}^{'}}^{1} d_{λ_{1}^{'}, λ_{1}}^{\frac{1}{2}} (ζ_{1 (1)}^{1}) d_{λ_{0}, λ_{0}^{'}}^{\frac{1}{2}} (ζ_{1 (1)}^{0}) + A_{λ_{0}^{'}, λ_{1}^{'}, λ_{2}^{'}, λ_{3}^{'}}^{2} d_{λ_{1}^{'}, λ_{1}}^{\frac{1}{2}} (ζ_{2 (1)}^{1}) d_{λ_{0}, λ_{0}^{'}}^{\frac{1}{2}} (ζ_{2 (1)}^{0}) + A_{λ_{0}^{'}, λ_{1}^{'}, λ_{2}^{'}, λ_{3}^{'}}^{3} d_{λ_{1}^{'}, λ_{1}}^{\frac{1}{2}} (ζ_{3 (1)}^{1}) d_{λ_{0}, λ_{0}^{'}}^{\frac{1}{2}} (ζ_{3 (1)}^{0}) |}^{2}

Show code cell output Hide code cell output

\begin{array}{r} \begin{array}{rcl} A_{- \frac{1}{2}, - \frac{1}{2}, 0, 0}^{1} & = & \sum_{λ_{R} = - 1}^{1} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{1, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{1, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{1} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = - 2}^{2} - \frac{\sqrt{6} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{2, 1}^{BW} (σ_{1}) C_{1, 0, \frac{3}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{2, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{3}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 1, \frac{3}{2}}^{LS, production} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{2} (θ_{23})}{2} \\ A_{- \frac{1}{2}, - \frac{1}{2}, 0, 0}^{2} & = & \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1232)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1232)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1600)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1600)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1700)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1700)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} \\ A_{- \frac{1}{2}, - \frac{1}{2}, 0, 0}^{3} & = & \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1405), 0, \frac{1}{2}}^{LS, production} H_{Λ (1405), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{1, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1600), 0, \frac{1}{2}}^{LS, production} H_{Λ (1600), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1670), 0, \frac{1}{2}}^{LS, production} H_{Λ (1670), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (2000), 0, \frac{1}{2}}^{LS, production} H_{Λ (2000), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1520), 1, \frac{3}{2}}^{LS, production} H_{Λ (1520), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1690), 1, \frac{3}{2}}^{LS, production} H_{Λ (1690), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} \\ A_{- \frac{1}{2}, \frac{1}{2}, 0, 0}^{1} & = & \sum_{λ_{R} = - 1}^{1} \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} - \frac{1}{2}} R_{1, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{1, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{1} (θ_{23})}{2} + \sum_{λ_{R} = 0} \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} - \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = 0} \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} - \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = - 2}^{2} \frac{\sqrt{6} δ_{- \frac{1}{2}, λ_{R} - \frac{1}{2}} R_{2, 1}^{BW} (σ_{1}) C_{1, 0, \frac{3}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{2, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{3}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 1, \frac{3}{2}}^{LS, production} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{2} (θ_{23})}{2} \\ A_{- \frac{1}{2}, \frac{1}{2}, 0, 0}^{2} & = & \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1232)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1232)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1600)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1600)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1700)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1700)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} \\ A_{- \frac{1}{2}, \frac{1}{2}, 0, 0}^{3} & = & \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1405), 0, \frac{1}{2}}^{LS, production} H_{Λ (1405), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{1, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1600), 0, \frac{1}{2}}^{LS, production} H_{Λ (1600), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1670), 0, \frac{1}{2}}^{LS, production} H_{Λ (1670), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{- \frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (2000), 0, \frac{1}{2}}^{LS, production} H_{Λ (2000), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1520), 1, \frac{3}{2}}^{LS, production} H_{Λ (1520), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{- \frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1690), 1, \frac{3}{2}}^{LS, production} H_{Λ (1690), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} \\ A_{\frac{1}{2}, - \frac{1}{2}, 0, 0}^{1} & = & \sum_{λ_{R} = - 1}^{1} - \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} + \frac{1}{2}} R_{1, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{1, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{1} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = - 2}^{2} - \frac{\sqrt{6} δ_{\frac{1}{2}, λ_{R} + \frac{1}{2}} R_{2, 1}^{BW} (σ_{1}) C_{1, 0, \frac{3}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{2, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{3}{2}, λ_{R} + \frac{1}{2}} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 1, \frac{3}{2}}^{LS, production} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{2} (θ_{23})}{2} \\ A_{\frac{1}{2}, - \frac{1}{2}, 0, 0}^{2} & = & \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1232)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1232)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1600)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1600)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} - \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1700)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1700)^{+ +}, 0, - \frac{1}{2}}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} \\ A_{\frac{1}{2}, - \frac{1}{2}, 0, 0}^{3} & = & \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1405), 0, \frac{1}{2}}^{LS, production} H_{Λ (1405), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{1, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1600), 0, \frac{1}{2}}^{LS, production} H_{Λ (1600), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1670), 0, \frac{1}{2}}^{LS, production} H_{Λ (1670), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (2000), 0, \frac{1}{2}}^{LS, production} H_{Λ (2000), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1520), 1, \frac{3}{2}}^{LS, production} H_{Λ (1520), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1690), 1, \frac{3}{2}}^{LS, production} H_{Λ (1690), - \frac{1}{2}, 0}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} \\ A_{\frac{1}{2}, \frac{1}{2}, 0, 0}^{1} & = & \sum_{λ_{R} = - 1}^{1} \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} - \frac{1}{2}} R_{1, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{1, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}^{*} (892)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{1} (θ_{23})}{2} + \sum_{λ_{R} = 0} \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} - \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (1430)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = 0} \frac{\sqrt{2} δ_{\frac{1}{2}, λ_{R} - \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, \frac{1}{2}}^{LS, production} H_{{\overset{―}{K}}_{0}^{*} (700)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = - 2}^{2} \frac{\sqrt{6} δ_{\frac{1}{2}, λ_{R} - \frac{1}{2}} R_{2, 1}^{BW} (σ_{1}) C_{1, 0, \frac{3}{2}, λ_{R} - \frac{1}{2}}^{\frac{1}{2}, λ_{R} - \frac{1}{2}} C_{2, λ_{R}, \frac{1}{2}, - \frac{1}{2}}^{\frac{3}{2}, λ_{R} - \frac{1}{2}} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 1, \frac{3}{2}}^{LS, production} H_{{\overset{―}{K}}_{2}^{*} (1980)^{0}, 0, 0}^{decay} d_{λ_{R}, 0}^{2} (θ_{23})}{2} \\ A_{\frac{1}{2}, \frac{1}{2}, 0, 0}^{2} & = & \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1232)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1232)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{1, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1600)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1600)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{2}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Δ (1700)^{+ +}, 1, \frac{3}{2}}^{LS, production} H_{Δ (1700)^{+ +}, 0, \frac{1}{2}}^{decay} d_{λ_{R}, - \frac{1}{2}}^{\frac{3}{2}} (θ_{31})}{2} \\ A_{\frac{1}{2}, \frac{1}{2}, 0, 0}^{3} & = & \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1405), 0, \frac{1}{2}}^{LS, production} H_{Λ (1405), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{1, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1600), 0, \frac{1}{2}}^{LS, production} H_{Λ (1600), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (1670), 0, \frac{1}{2}}^{LS, production} H_{Λ (1670), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 1 / 2}^{1 / 2} \frac{\sqrt{2} δ_{\frac{1}{2} λ_{R}} R_{0, 0}^{BW} (σ_{3}) C_{0, 0, \frac{1}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{1}{2}, λ_{R}, 0, 0}^{\frac{1}{2}, λ_{R}} H_{Λ (2000), 0, \frac{1}{2}}^{LS, production} H_{Λ (2000), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{1}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1520), 1, \frac{3}{2}}^{LS, production} H_{Λ (1520), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} + \sum_{λ_{R} = - 3 / 2}^{3 / 2} \frac{\sqrt{6} δ_{\frac{1}{2} λ_{R}} R_{2, 1}^{BW} (σ_{3}) C_{1, 0, \frac{3}{2}, λ_{R}}^{\frac{1}{2}, λ_{R}} C_{\frac{3}{2}, λ_{R}, 0, 0}^{\frac{3}{2}, λ_{R}} H_{Λ (1690), 1, \frac{3}{2}}^{LS, production} H_{Λ (1690), \frac{1}{2}, 0}^{decay} d_{λ_{R}, \frac{1}{2}}^{\frac{3}{2}} (θ_{12})}{2} \end{array} \end{array}

By default, the aligned amplitudes are built up of Wigner- $d$ functions, Clebsch–Gordan coefficients ( $C$ ), a resonance parametrization ( $R (σ)$ ), and two coupling symbols $Missing open brace for subscript$ . In some cases, you want to combine the couplings into one scaling factor. That can be done with the use_coefficients flag:

model = model_builder.formulate(reference_subsystem=1, use_coefficients=True)
(symbol, expr), *_ = model.amplitudes.items()
Latex(aslatex({symbol: expr}).replace(R"\sum_", R"\sum\limits_"))

\begin{array}{r} \begin{array}{rcl} A_{- \frac{1}{2}, - \frac{1}{2}, 0, 0}^{1} & = & \sum_{λ_{R} = - 1}^{1} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{1, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{1, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{0, \frac{1}{2}, 0, 0}^{λ, LS, {\overset{―}{K}}^{*} (892)^{0}} d_{λ_{R}, 0}^{1} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{0, \frac{1}{2}, 0, 0}^{λ, LS, {\overset{―}{K}}_{0}^{*} (1430)^{0}} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = 0} - \frac{\sqrt{2} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{0, 0}^{BW} (σ_{1}) C_{0, 0, \frac{1}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{0, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} H_{0, \frac{1}{2}, 0, 0}^{λ, LS, {\overset{―}{K}}_{0}^{*} (700)^{0}} d_{λ_{R}, 0}^{0} (θ_{23})}{2} + \sum_{λ_{R} = - 2}^{2} - \frac{\sqrt{6} δ_{- \frac{1}{2}, λ_{R} + \frac{1}{2}} R_{2, 1}^{BW} (σ_{1}) C_{1, 0, \frac{3}{2}, λ_{R} + \frac{1}{2}}^{\frac{1}{2}, λ_{R} + \frac{1}{2}} C_{2, λ_{R}, \frac{1}{2}, \frac{1}{2}}^{\frac{3}{2}, λ_{R} + \frac{1}{2}} H_{1, \frac{3}{2}, 0, 0}^{λ, LS, {\overset{―}{K}}_{2}^{*} (1980)^{0}} d_{λ_{R}, 0}^{2} (θ_{23})}{2} \end{array} \end{array}