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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 16:16, 15 August 2011
, 16:16, 15 August 2011→Photon-Reggeon-Resonance vertex
To express the initial photon linear polarization state in the reflectivity basis, we relate the linear polarization bases in the laboratory and Gottfried-Jackson coordinate systems:
To express the initial photon linear polarization state in the reflectivity basis, we relate the linear polarization bases in the laboratory and Gottfried-Jackson coordinate systems:
:<math>\left(\begin{array}{c}x_\mathrm{lab} \\ y_\mathrm{lab}\end{array}\right)=
:<math>\left(\begin{array}{c} \epsilon_\gamma=-1\\ \epsilon_\gamma=+1\end{array}\right)=
\left(\begin{array}{cc}
\left(\begin{array}{cc}
\cos\alpha & -\sin\alpha \\
\cos\alpha & -\sin\alpha \\
\sin\alpha & \cos\alpha
\sin\alpha & \cos\alpha
\end{array}\right)
\end{array}\right)
\left(\begin{array}{c}x \\ y\end{array}\right)=
\left(\begin{array}{c}x_\mathrm{lab} \\ y_\mathrm{lab}\end{array}\right)=
\left(\begin{array}{cc}
\left(\begin{array}{cc}
e^{-i\alpha} & e^{i\alpha} \\
e^{-i\alpha} & e^{i\alpha} \\
</math>
</math>
where <math>\alpha=-\phi</math>: the rotation angle to return from production plane to lab xz plane. Thus, the production amplitude becomes:
where <math>\alpha=\phi</math>: the rotation angle to return from production plane to lab xz plane. Thus, the production amplitude becomes:
:<math>
:<math>