Resonances are uniquely characterized by their complex pole locations and the
corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching fractions of resonances determined as ratios of count rates. To make contact between these quantities it is necessary to connect line shapes and resonance parameters.
In this work we propose such a connection and illustrate the formalism
with detailed studies of the $\rho(770)$ and $f_0(500)$ resonances.
Based on the line shapes inferred from the resonance parameters along these lines, expressions for partial widths and branching ratios are derived
and compared to other approaches
in the literature.