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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 17:11, 15 August 2011
, 17:11, 15 August 2011→Assembly of the full amplitude
\sum_{L_X \epsilon_R} A_{L_X \epsilon_\gamma \epsilon_R}^{J_X}=
\sum_{L_X \epsilon_R} A_{L_X \epsilon_\gamma \epsilon_R}^{J_X}=
\sum_{\lambda_R,\lambda_{b_1},\lambda_\omega,\lambda_\rho}
\sum_{\lambda_R,\lambda_{b_1},\lambda_\omega,\lambda_\rho}
\langle \Omega_X 0 \lambda_{b_1} | U_X |
\langle \Omega_X \lambda_{b_1} 0| U_X |
\left\{|J_X m_X \rangle + \epsilon_\gamma \epsilon_R P_X (-1)^{J_X-m_X} |J_X\;-m_X \rangle \right\}
\left\{|J_X m_X \rangle + \epsilon_\gamma \epsilon_R P_X (-1)^{J_X-m_X} |J_X\;-m_X \rangle \right\}
</math>
</math>
::<math>
::<math>
\langle \Omega_{b_1} 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle
\langle \Omega_{b_1} \lambda_\omega 0| U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle
\langle \Omega_\omega 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle
\langle \Omega_\omega \lambda_\rho 0| U_\omega | 1 , m_\omega=\lambda_\omega \rangle
\langle \Omega_\rho 0 0 | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle C_\rho(L_\rho)
\langle \Omega_\rho 0 0 | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle C_\rho(L_\rho)
</math>
</math>