Difference between revisions of "Amplitudes for the Exotic b1π Decay"

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(Created page with '<math> \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) \left[ (-)^{J_X+1…')
 
Line 17: Line 17:
 
\end{array}\right)
 
\end{array}\right)
 
\right]
 
\right]
 +
\left(\frac{1+(-)^\epsilon \eta}{4}\right)
 
k^{L_X} q^{J_{b1}}
 
k^{L_X} q^{J_{b1}}
 
\left(\begin{array}{cc|c}
 
\left(\begin{array}{cc|c}
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I_{z\pi^+} & I_{z\pi^-} & I_{z\pi^+}+I_{z\pi^-}
 
I_{z\pi^+} & I_{z\pi^-} & I_{z\pi^+}+I_{z\pi^-}
 
\end{array}\right)
 
\end{array}\right)
 +
 +
\sum\limits_{L_{b1}=0}^{2} \sum\limits_{m_{L_{b1}}=-L_{b1}}^{L_{b1}}
 +
\left(\begin{array}{cc|c}
 +
s_\omega & L_{b1} & J_{b1} \\
 +
0        & m_{L_{b1}} & m_{b1}
 +
\end{array}\right)
 +
D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0)
 +
Y_{m_\rho}^{s_\rho}(\theta_\rho,\phi_\rho)
 +
\left(\begin{array}{cc|c}
 +
1 & s_\rho      & J_\omega \\
 +
0 & \lambda_\rho & m_\omega
 +
\end{array}\right)
 +
 +
\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)
 +
  
  
  
 
</math>
 
</math>

Revision as of 03:46, 12 July 2011

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) \left[ (-)^{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] \left(\frac{1+(-)^\epsilon \eta}{4}\right) k^{L_X} q^{J_{b1}} \left(\begin{array}{cc|c} I_{b1} & 1 & I_X \\ I_{z\pi^+} & I_{z\pi^-} & I_{z\pi^+}+I_{z\pi^-} \end{array}\right) \sum\limits_{L_{b1}=0}^{2} \sum\limits_{m_{L_{b1}}=-L_{b1}}^{L_{b1}} \left(\begin{array}{cc|c} s_\omega & L_{b1} & J_{b1} \\ 0 & m_{L_{b1}} & m_{b1} \end{array}\right) D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0) Y_{m_\rho}^{s_\rho}(\theta_\rho,\phi_\rho) \left(\begin{array}{cc|c} 1 & s_\rho & J_\omega \\ 0 & \lambda_\rho & m_\omega \end{array}\right) \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) }