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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 17:29, 19 August 2011
, 17:29, 19 August 2011→Photon-Reggeon-Resonance vertex
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. A consequence of this choice is that <math>m=\lambda_\gamma-\lambda_R</math>
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. A consequence of this choice is that <math>m=\lambda_\gamma-\lambda_R</math>
It is convenient to express above matrix element as
:<math>
\langle J M \epsilon|V|
\epsilon_\gamma ; J_R \lambda_R \epsilon_R ; t, s; \Omega_0 \rangle
= v\left(J,m,\epsilon;\epsilon_\gamma;J_R,\lambda_R,\epsilon_R \right) f(s,t)
</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.
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: