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Line 13:
Line 13: − Y_{m_X}^{L_X}(\theta_X,\phi_X)+ Line 59:
Line 59: − + Line 70:
Line 70: − + − + − + + + + + + + − + Line 86:
Line 92: − 1 & s_\rho & J_\omega \\+ − + Line 96:
Line 102: − \sum\limits_{I_\rho=0}^{1} − \sum\limits_{I_{z\rho}=-I_\rho}^{I_\rho} − 1 & I_\rho & 0 \\+ − 0 & I_{z\rho} & 0+ − + − +
Amplitudes for the Exotic b1π Decay (view source)
Revision as of 20:20, 14 July 2011
, 20:20, 14 July 2011no edit summary
\sum\limits_{m_{b1}=-J_{b_1}}^{J_{b_1}}
\sum\limits_{m_{b1}=-J_{b_1}}^{J_{b_1}}
\sum\limits_{m_\omega=-J_\omega}^{J_\omega}
\sum\limits_{m_\omega=-J_\omega}^{J_\omega}
D_{m_X m_{b_1}}^{L_X *}(\theta_X,\phi_X,0)
D_{m_{b_1} m_\omega}^{J_{b_1}*}(\theta_{b_1},\phi_{b_1},0)
D_{m_{b_1} m_\omega}^{J_{b_1}*}(\theta_{b_1},\phi_{b_1},0)
</math></td>
</math></td>
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
I_{b_1} & I_\pi & I_X \\
I_{b_1} & I_\pi & I_X \\
I_{z\pi^+} & I_{z\pi^-} & I_{z\pi^+}+I_{z\pi^-}
I_{zb_1^+} & I_{z\pi^-} & I_{zb_1^+}+I_{z\pi^-}
\end{array}\right)
\end{array}\right)
</math></td>
</math></td>
\sum\limits_{L_{b_1}=0}^{2}
\sum\limits_{L_{b_1}=0}^{2}
\sum\limits_{m_{L_{b_1}}=-L_{b_1}}^{L_{b_1}}
\sum\limits_{m_{L_{b_1}}=-L_{b_1}}^{L_{b_1}}
\sum\limits_{\lambda_\rho=-s_\rho}^{s_\rho}
\sum\limits_{L_{\pi^+\pi^-},L_\omega=1,3}
D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0)
\sum\limits_{m_{\pi^+\pi^-}=-L_{\pi^+\pi^-}}^{L_{\pi^+\pi^-}}
Y_{\lambda_\rho}^{s_\rho}(\theta_\rho,\phi_\rho)
u^{L_\omega} v^{L_{\pi^+\pi^-}}
</math></td>
</tr>
<tr>
<td><math>
D_{m_\omega m_{\pi^+\pi^-}}^{J_\omega *}(\theta_\omega,\phi_\omega,0)
Y_{m_{\pi^+\pi^-}}^{L_{\pi^+\pi^-}}(\theta_\rho,\phi_\rho)
</math></td>
</math></td>
<td>
<td>
two-stage <math>\omega (J_\omega^{PC}=1^{--})</math> breakup angular distributions,
two-stage <math>\omega (J_\omega^{PC}=1^{--})</math> breakup angular distributions,
currently modeled as <math>L_{\omega\rightarrow\pi^0+\rho}=0; L_{\rho\rightarrow\pi^++\pi^-}=1=s_\rho</math>
currently modeled as <math>L_{\omega\rightarrow\pi^0+\rho}=0; L_{\rho\rightarrow\pi^++\pi^-}=1=L_{\pi^+\pi^-}</math>
</td>
</td>
</tr>
</tr>
\end{array}\right)
\end{array}\right)
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
L_\omega & L_{\pi^+\pi^-} & J_\omega \\
0 & \lambda_\rho & m_\omega
0 & m_{\pi^+\pi^-} & m_\omega
\end{array}\right)
\end{array}\right)
</math></td>
</math></td>
<tr>
<tr>
<td><math>
<td><math>
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
I_\pi & 1 & 0 \\
I_{\pi^0} & 0 & 0
\end{array}\right)
\end{array}\right)
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
I_{\pi} & I_{\pi} & I_\rho \\
I_{\pi} & I_{\pi} & 1 \\
+1 & -1 & I_{z\rho}
I_{z\pi^+} & I_{z\pi^-} & 0
\end{array}\right)
\end{array}\right)
</math></td>
</math></td>