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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 16:36, 12 July 2011
, 16:36, 12 July 2011no edit summary
<table>
<table>
A_{}^{J_X L_X P_X}
<td>
defining an amplitude...
</td>
</tr>
<tr>
<tr>
<td><math>
<td><math>
</math></td>
</math></td>
<td>
<td>
angular distributions two-body X and b1 decays
angular distributions two-body X and <math>b_1 (J_{b_1}^{PC}=1^{+-})</math> decays
</td>
</td>
</tr>
</tr>
<td><math>
<td><math>
\left[
\left[
(-)^{J_X+1+\epsilon} e^{2i\alpha}
P_X(-)^{J_X+1+\epsilon} e^{2i\alpha}
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
J_{b1} & L_X & J_X \\
J_{b1} & L_X & J_X \\
</math></td>
</math></td>
<td>
<td>
resonance helicity sum
resonance helicity sum: ε=0 (1) for x (y) polarization; </math>P_X</math> is the parity of the resonance
</td>
</td>
</tr>
</tr>
</math></td>
</math></td>
<td>
<td>
polarization term: ε=0 (1) for x (y) polarization; η is the polarization fraction
polarization term: η is the polarization fraction
</td>
</td>
</tr>
</tr>
<td><math>
<td><math>
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
I_{b1} & 1 & I_X \\
I_{b1} & I_\pi & I_X \\
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)
<tr>
<tr>
<td><math>
<td><math>
\sum\limits_{L_{b1}=0}^{2} \sum\limits_{m_{L_{b1}}=-L_{b1}}^{L_{b1}}
\sum\limits_{L_{b1}=0}^{2}
\sum\limits_{m_{L_{b1}}=-L_{b1}}^{L_{b1}}
\sum\limits_{m_\omega}=-J_\omega}^{J_\omega}
\sum\limits_{\lambda_\rho}=-s_\rho}^{s_\rho}
D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0)
D_{m_\omega \lambda_\rho}^{J_\omega *}(\theta_\omega,\phi_\omega,0)
Y_{m_\rho}^{s_\rho}(\theta_\rho,\phi_\rho)
Y_{\lambda_\rho}^{s_\rho}(\theta_\rho,\phi_\rho)
</math></td>
</math></td>
<td>
<td>
two-stage ω 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>
</td>
</td>
</tr>
</tr>
<td><math>
<td><math>
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
J_\omega & L_{b1} & J_{b1} \\
m_\omega & m_{L_{b1}} & m_{b1}
\end{array}\right)
\end{array}\right)
\left(\begin{array}{cc|c}
\left(\begin{array}{cc|c}
</math></td>
</math></td>
<td>
<td>
angular momentum sum Clebsch-Gordan coefficients for b1 and ω decays
angular momentum sum Clebsch-Gordan coefficients for b1 and ω decays.
</td>
</td>
</tr>
</tr>