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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 23:44, 18 August 2011
, 23:44, 18 August 2011→Summing over polarizations
\frac{d^8\sigma}{d\Omega_{b1}\,d\Omega_\omega\,d\Omega_\rho\,d\Omega_\pi} \propto
\frac{d^8\sigma}{d\Omega_{b1}\,d\Omega_\omega\,d\Omega_\rho\,d\Omega_\pi} \propto
\frac{1}{2}\left\{
\frac{1}{2}\left\{
(1+g)\left| \frac{1}{\sqrt{2}}(T_{-1}e^{-i\alpha} + T_{+1}e^{i\alpha}) \right|^2
(1+g)\left| \frac{1}{\sqrt{2}}\left(T_{-1}e^{-i\alpha} + T_{+1}e^{i\alpha}\right) \right|^2
+
+
(1-g)\left| \frac{i}{\sqrt{2}}(T_{-1}e^{-i\alpha} - T_{+1}e^{i\alpha}) \right|^2 \right\}
(1-g)\left| \frac{i}{\sqrt{2}}\left(T_{-1}e^{-i\alpha} - T_{+1}e^{i\alpha}\right) \right|^2 \right\}
</math>
</math>
:::<math>
:::<math>
=\frac{1}{2}\left[
=\frac{1}{2}\left[
|T_{-1}|^2 + |T_{+1}|^2 +
|T_{-1}|^2 + |T_{+1}|^2 +
g(T_{+1}T_{-1}^*e^{2i\alpha} + T_{+1}^*T_{-1}e^{-2i\alpha}) \right]
g\left(T_{+1}T_{-1}^*e^{2i\alpha} + T_{+1}^*T_{-1}e^{-2i\alpha}\right) \right]
</math>
</math>
:::<math>
:::<math>
=\frac{|T_{-1}|^2 + |T_{+1}|^2}{2} +
=\frac{|T_{-1}|^2 + |T_{+1}|^2}{2} +
g\,\mathrm{Re}(T_{+1}T_{-1}^*)e^{2i\alpha}
g\,\mathrm{Re}\left(T_{+1}T_{-1}^* e^{2i\alpha} \right)
</math>
</math>
where ''g'' is the polarization fraction ranging from 1 (100% x-polarized) to 0 (unpolarized.)
where ''g'' is the polarization fraction ranging from 1 (100% x-polarized) to 0 (unpolarized.)