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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 20:19, 15 August 2011
, 20:19, 15 August 2011→Assembly of the full amplitude
T_{fi} = \sum_{R,\lambda_R\lambda_{b_1},\lambda_\omega,\lambda_\rho}
T_{fi} = \sum_{R,\lambda_R\lambda_{b_1},\lambda_\omega,\lambda_\rho}
\langle \mathbf{q}_\pi 0 0; \mathbf{q}_\rho \lambda_\rho 0; \mathbf{q}_\omega \lambda_\omega 0; \mathbf{q}_{b1}\lambda_{b1} 0
\langle \mathbf{q}_\pi 0 0; \mathbf{q}_\rho \lambda_\rho 0; \mathbf{q}_\omega \lambda_\omega 0; \mathbf{q}_{b1}\lambda_{b1} 0
| U | \epsilon_\gamma; J_R \lambda_R \epsilon_R \rangle
| U | \epsilon_\gamma; J_R \lambda_R \epsilon_R;s,t \rangle
\langle J_R \lambda_R \epsilon_R; \mathbf{p_f}, \lambda_f | W | \mathbf{p_i}, \lambda_i\rangle
\langle J_R \lambda_R \epsilon_R; \mathbf{p_f}, \lambda_f | W | \mathbf{p_i}, \lambda_i\rangle
</math>
</math>
:<math>
:<math>
\langle \mathbf{q}_\pi 0 0; \mathbf{q}_\rho \lambda_\rho 0; \mathbf{q}_\omega \lambda_\omega 0; \mathbf{q}_{b1}\lambda_{b1} 0
\langle \mathbf{q}_\pi 0 0; \mathbf{q}_\rho \lambda_\rho 0; \mathbf{q}_\omega \lambda_\omega 0; \mathbf{q}_{b1}\lambda_{b1} 0
| U | \epsilon_\gamma; J_R \lambda_R \epsilon_R,s,t \rangle
| U | \epsilon_\gamma; J_R \lambda_R \epsilon_R; s,t \rangle
</math>
</math>
::<math>=\sum_{\lambda_R,\lambda_{b_1},\lambda_\omega,\lambda_\rho,m_X}
::<math>=\sum_{\lambda_R,\lambda_{b_1},\lambda_\omega,\lambda_\rho,m_X}
\langle \mathbf{q}_{b1} \lambda_{b_1} 0| U_X | J_X m_X \epsilon_X\rangle
\langle \mathbf{q}_{b1} \lambda_{b_1} 0| U_X | J_X m_X \epsilon_X\rangle
\langle J_X m_X \epsilon_X | V |
\langle J_X m_X \epsilon_X | V |
\epsilon_\gamma; J_R \lambda_R \epsilon_R,s,t \rangle
\epsilon_\gamma; J_R \lambda_R \epsilon_R; s,t \rangle
</math>
</math>
:::::::<math>
:::::::<math>