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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 19:33, 13 August 2011
, 19:33, 13 August 2011→Production
Acting with the reflectivity operator on initial and final state brings out the reflectivity eigenvalues of the
Acting with the reflectivity operator on initial and final state brings out the reflectivity eigenvalues of the
resonance, photon and reggeon. This result leads to a constraint
resonance, photon and Reggeon. This result leads to a constraint
<math>\displaystyle\epsilon = \epsilon_\gamma \epsilon_R</math> that embodies parity conservation in this decay.
<math>\displaystyle\epsilon = \epsilon_\gamma \epsilon_R</math> that embodies parity conservation in this decay.
It is convenient to adopt the Gottfried Jackson frame. In particular, we boost into the reference frame of the produced resonance and orient the coordinate system such that the photon is in the +z direction and the x-axis is co-planar to the recoiling proton, thus defining xz as the production plane. To project the photon polarization state onto the production plane, we relate the linear polarization bases in the laboratory and production coordinate systems:
:<math>\left(\begin{array}{c}x \\ y\end{array}\right)=
\left(\begin{array}{cc}
\cos\alpha & -\sin\alpha \\
\sin\alpha & \cos\alpha
\end{array}\right)
\left(\begin{array}{c}x_\mathrm{lab} \\ y_\mathrm{lab}\end{array}\right)=
\left(\begin{array}{cc}
e^{-i\alpha} & e^{i\alpha} \\
ie^{-i\alpha} & -ie^{i\alpha}
\end{array}\right)
\left(\begin{array}{c}|1,-1\rangle \\ |1,+1\rangle\end{array}\right)
</math>
== Decay of t-channel resonance X==
== Decay of t-channel resonance X==