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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 22:18, 19 August 2011
, 22:18, 19 August 2011→Photon-Reggeon-Resonance vertex
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; t, s; \Omega_0 \rangle =
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; t, s; \Omega_0 \rangle =
\epsilon \epsilon_\gamma \epsilon_R \langle J M \epsilon|V|
\epsilon \epsilon_\gamma \epsilon_R \langle J M \epsilon|V|
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; t, s; \Omega_0 \rangle
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; \Omega_0 \rangle
</math>
</math>
:<math>
:<math>
\langle J M \epsilon|V|
\langle J M \epsilon|V|
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; t, s; \Omega_0 \rangle
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; \Omega_0 \rangle
= v\left(J,m,\epsilon;\epsilon_\gamma;J_R,\lambda_R,\epsilon_R \right) f_R(s,t)
= v\left(J,m,\epsilon;\epsilon_\gamma;J_R,\lambda_R,\epsilon_R \right)
</math>
</math>
so that the indexed coefficient ''v'' specifies the couplings and the function f(s,t) encapsulates the ''s'', and ''t'' dependence of the production amplitude.
so that the indexed coefficient ''v'' specifies the couplings together with the consequences of angular momentum and parity conservation. The function ''v'' is implicitly dependent upon the kinematical variables ''s'' and ''t''. This dependence will be made explicit in a following section, after the matrix element for the baryon vertex has been studied.
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: