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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 22:10, 15 August 2011
, 22:10, 15 August 2011→Assembly of the full amplitude
</math>
</math>
Expressions for the angular dependence of the matrix elements of <math>U_X, U_{b1}, U_\omega, U_\rho</math> have already been written down above the unknown mass-dependent factors ''A'', ''B'', ''C'', and ''F''.
:<math>
\langle \mathbf{q} \lambda_1 \lambda_2| U | J , m \rangle =
\sum_L
\langle \Omega \lambda_1 \lambda_2| U | J , m \rangle BW(q)
Note that we leave the sum over <math>L_X</math> outside the amplitude of interest. This is convenient in partial wave analysis so that the hypothesized L-states can be listed and summed explicitly. In mass-independent fits, the Breit-Wigner for the resonance is replaced with strength factors that are parameters of the fit. An exponential dependence of ''t'' is inserted with a coefficient that can be deduced from fits in separate ''t'' bins.
Note that we leave the sum over <math>L_X</math> outside the amplitude of interest. This is convenient in partial wave analysis so that the hypothesized L-states can be listed and summed explicitly. In mass-independent fits, the Breit-Wigner for the resonance is replaced with strength factors that are parameters of the fit. An exponential dependence of ''t'' is inserted with a coefficient that can be deduced from fits in separate ''t'' bins.