Changes

</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''.

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, in terms of the unknown mass-dependent factors ''a'', ''b'', ''c'', and ''f''.  The mass dependence of the ''a'' factor can be written in terms of a standard relativistic Breit-Wigner resonance lineshape as follows, although often its mass dependence is determined empirically by binning in the mass of ''X'', and fitting each bin independently.

:<math>

:<math>

\langle \mathbf{q} \lambda_1 \lambda_2| U | J , m \rangle =

\langle \mathbf{q} \lambda_1 \lambda_2| U | J , m \rangle =

\sum_L

\sum_L

\langle \Omega \lambda_1 \lambda_2| U | J , m \rangle BW(q)

\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.