Impact of the interference between the resonance and continuum amplitudes on vector quarkonia decay branching fraction measurements

TL;DR

This paper examines how interference between resonance and continuum amplitudes affects the measurement of heavy quarkonium decay branching fractions at electron-positron colliders, emphasizing the importance of accounting for these effects in high-precision experiments.

Contribution

It introduces ratios to estimate interference effects and highlights their significance for accurate branching fraction measurements, especially for broad resonances.

Findings

Interference effects can reach a few percent for narrow resonances.

Both interference ratios can be large for broad resonances.

Proper estimation of interference is crucial for percent-level precision measurements.

Abstract

The measurement of the branching fraction of a heavy quarkonium decaying into light hadronic final state at $e^+e^-$ colliders is revisited. In $e^+e^-$ annihilation experiments, background contributions from the continuum amplitude and its interference with the resonance amplitude are irreducible. These effects become more and more significant as the precision of experimental measurements improves. While the former can be easily subtracted with data taken off the resonance peak, the latter depends on the relative size and phase between the resonance and continuum amplitudes. Two ratios are defined to estimate the size of these effects, $r_{R}^{f}$ for the ratio of the contribution of the interference term to the resonance term and $r_{c}^{f}$ for that to the continuum term. We find that $r_{R}^{f}$ could be as large as a few percent for narrow resonances, and both $r_{R}^{f}$ and $r_{c}^{f}$ could be large for broad resonances. This indicates that the interference effect is crucial for the measurements of the branching fractions aiming at the percent level or better precision and needs to be measured or estimated properly.