Amplitudes for the Exotic b1π Decay

A_{}^{J_X L_X P_X}

defining an amplitude...
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum\limits_{m_X=-L_X}^{L_X} \sum\limits_{m_{b1}=-J_{b1}}^{J_{b1}} Y_{m_X}^{L_X}(\theta_X,\phi_X) D_{m_{b1} n_{b1}}^{J_{b1}*}(\theta_{b1},\phi_{b1},0) }	angular distributions two-body X and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_1 (J_{b_1}^{PC}=1^{+-})} decays
$\left[P_{X}(-)^{J_{X}+1+\epsilon }e^{2i\alpha }\left({\begin{array}{cc|c}J_{b1}&L_{X}&J_{X}\\m_{b1}&m_{X}&-1\end{array}}\right)+\left({\begin{array}{cc|c}J_{b1}&L_{X}&J_{X}\\m_{b1}&m_{X}&+1\end{array}}\right)\right]$	resonance helicity sum: ε=0 (1) for x (y) polarization; </math>P_X</math> is the parity of the resonance
$\left({\frac {1+(-)^{\epsilon }\eta }{4}}\right)$	polarization term: η is the polarization fraction
$k^{L_{X}}q^{J_{b1}}$	k, q are breakup momenta for the resonance and isobar, respectively
$\left({\begin{array}{cc|c}I_{b1}&I_{\pi }&I_{X}\\I_{z\pi ^{+}}&I_{z\pi ^{-}}&I_{z\pi ^{+}}+I_{z\pi ^{-}}\end{array}}\right)$	Clebsch-Gordan coefficients for isospin sum $b_{1}\oplus \pi ^{-}\rightarrow X$
Failed to parse (syntax error): {\displaystyle \sum\limits_{L_{b1}=0}^{2} \sum\limits_{m_{L_{b1}}=-L_{b1}}^{L_{b1}} \sum\limits_{m_\omega}=-J_\omega}^{J_\omega} \sum\limits_{\lambda_\rho}=-s_\rho}^{s_\rho} D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0) Y_{\lambda_\rho}^{s_\rho}(\theta_\rho,\phi_\rho) }	two-stage $\omega (J_{\omega }^{PC}=1^{--})$ breakup angular distributions, currently modeled as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L_{\omega\rightarrow\pi^0-\rho}=0; L_{\rho\rightarrow\pi^++\pi^-}=1=s_\rho}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\begin{array}{cc|c} J_\omega & L_{b1} & J_{b1} \\ m_\omega & m_{L_{b1}} & m_{b1} \end{array}\right) \left(\begin{array}{cc|c} 1 & s_\rho & J_\omega \\ 0 & \lambda_\rho & m_\omega \end{array}\right) }	angular momentum sum Clebsch-Gordan coefficients for b1 and ω decays.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum\limits_{I_\rho=0}^{1} \sum\limits_{I_{z\rho}=-I_\rho}^{I_\rho} \left(\begin{array}{cc|c} 1 & I_\rho & 0 \\ 0 & I_{z\rho} & 0 \end{array}\right) \left(\begin{array}{cc|c} I_{\pi} & I_{\pi} & I_\rho \\ +1 & -1 & I_{z\rho} \end{array}\right) }	Clebsch-Gordan coefficients for isospin sums: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi^0 \oplus (\pi^+ \oplus \pi^-) \rightarrow \omega}