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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 04:28, 28 July 2011
, 04:28, 28 July 2011no edit summary
== General Relations ==
=== Angular Distribution of Two-Body Decay ===
=== Angular Distribution of Two-Body Decay ===
== Application ==
<math>
\langle \Omega_X 0 \lambda_{b_1} | U | J_X m_X \rangle
=\sum_{L_X}
\left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_X,0) \right]
\left[ \sqrt{\frac{2L_X+1}{2J_X+1}}
\left(\begin{array}{cc|c}
L_X & 1 & J \\
0 & \lambda_{b_1} & \lambda_{b_1}
\end{array}\right)
\right]
a_{L_X}^{J_X}
</math>
<math>
\langle \Omega_{b_1} 0 \lambda_\omega | U | 1 , m_{b_1}=\lambda_{b_1} \rangle
=\sum_{L_{b_1}}
\left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1}=\lambda_{b_1} \lambda_\omega}^{1 *}(\Omega_{b_1},0) \right]
\left[ \sqrt{\frac{2L_{b_1}+1}{2J_{b_1}+1}}
\left(\begin{array}{cc|c}
L_{b_1} & 1 & 1 \\
0 & \lambda_\omega & \lambda_\omega
\end{array}\right)
\right]
b_{L_{b_1}}
</math>
<math>
\langle \Omega_\omega 0 \lambda_\rho | U | 1 , m_\omega=\lambda_\omega \rangle
=\sum_{L_\omega J_\rho}
\left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega=\lambda_\omega \lambda_\rho}^{1 *}(\Omega_\omega,0) \right]
\left[ \sqrt{\frac{2L_\omega+1}{2J_\omega+1}}
\left(\begin{array}{cc|c}
L_\omega & 1 & 1 \\
0 & \lambda_\rho & \lambda_\rho
\end{array}\right)
\right]
c_{L_\omega J_\rho}
</math>
<math>
\langle \Omega_\rho 0 \lambda_\rho | U | J_\rho , m_\rho=\lambda_\rho \rangle
=\sum_{L_\rho}
\left[ \sqrt{\frac{2J_\rho+1}{4\pi}} D_{m_\rho 0}^{J_\rho *}(\Omega_\rho,0) \right]
\left[ \sqrt{\frac{2L_\rho+1}{2J_\rho+1}}
\left(\begin{array}{cc|c}
L_\rho & 0 & J_\rho \\
0 & 0 & 0
\end{array}\right)
\right]
d_{L_\rho}
=\sum_{L_\rho}
\sqrt{\frac{2L_\rho+1}{2J_\rho+1}}
Y_{m_\rho}^{J_\rho *}(\Omega_\rho)
d_{L_\rho}
</math>