Estimate of the $S$-wave $D^*K$ scattering length in the isospin-0 channel from Belle and LHCb data

TL;DR

This paper estimates the $S$-wave $D^*K$ scattering length in the isospin-0 channel using Belle and LHCb decay data, providing a precise value and discussing resonance contributions.

Contribution

It introduces a novel method to extract the $S$-wave $D^*K$ scattering length from experimental interference data, linking it to resonance effects.

Findings

Estimated $|a^{(0)}_{D^*K}|$ as 0.94±0.06 fm

Discussed the resonance contribution of $D_{s1}(2460)$

Briefly analyzed $B_{s1}(5830)$ decay

Abstract

It is shown that the Belle and LHCb data on the interference of the amplitudes of the $S$ and $D$ partial waves in the decays $D_{s1}(2536 )^+\to D^{*+}K^0_S$ and $D_{s1}(2536)^-\to\bar D^{*0}K^-$ allow us to obtain an estimate of the $S$-wave $D^*K$ scattering length in the channel with isospin $I=0$: $|a^{(0)}_{D^*K}|=(0.94\pm0.06)$ fm. The possibility of explaining the found value by the contribution of the $D_{s1}(2460)$ resonance is discussed. The decay of $B_{s1}(5830)\to B^*\bar K$ is also briefly discussed.