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Line 243:
Line 243: + − An exponential dependence of ''t'' is inserted with a coefficient that can be deduced from fits in separate ''t'' bins.+ + + + + + Line 251:
Line 257: −
Amplitudes for the Exotic b1π Decay (view source)
Revision as of 23:32, 15 August 2011
, 23:32, 15 August 2011no edit summary
</math>
</math>
===Describing s and t dependence===
It is doubtful that this is needed, because the range in ''s'' covered by GlueX is very small, and one expects to carry out independent fits for different ranges in t. However, it might be useful at some point to do a global fit to all s,t values. In such a case, it is useful to recall the expected behavior in high-energy peripheral production given by Regge theory.
:<math>
\sigma ~ s^{\alpha_R-1} e^bt
</math>
where <math>\alpha_R</math> is the intercept of the Regge trajectory for exchange particle ''R'', and b is the forward t-slope parameter for exchange trajectory ''R'' at this value of ''s''.
=== Summing over polarizations ===
The intensity would then require an incoherent summation of amplitudes with laboratory x and y polarization.
The intensity would then require an incoherent summation of amplitudes with laboratory x and y polarization.
:<math>I=
:<math>I=
\frac{1-f}{2}\left|\sum_{L_X \epsilon_R} A_{L_X\;+1\;\epsilon_R}^{J_X}\right|^2
\frac{1-f}{2}\left|\sum_{L_X \epsilon_R} A_{L_X\;+1\;\epsilon_R}^{J_X}\right|^2
</math>
</math>
where f is the polarization fraction varying from 1, 100% x-polarized, to 0, unpolarized.
where f is the polarization fraction varying from 1, 100% x-polarized, to 0, unpolarized.
\sum_{L_X \epsilon_R} A_{L_X \epsilon_\gamma \epsilon_R}^{J_X}=
\sum_{L_X \epsilon_R} A_{L_X \epsilon_\gamma \epsilon_R}^{J_X}=