$D^\ast_{s0}(2317)$ and $DK$ scattering in $B$ decays from BaBar and LHCb data

TL;DR

This paper analyzes experimental $DK$ invariant mass spectra from B meson decays, demonstrating that the $D^ ext{*}_{s0}(2317)$ resonance is a $DK$ bound state with a significant molecular component, using unitarized chiral perturbation theory.

Contribution

It provides a detailed analysis confirming the $D^ ext{*}_{s0}(2317)$ as a $DK$ bound state and quantifies its $DK$ component using a unitarized amplitude approach.

Findings

Identifies the $D^ ext{*}_{s0}(2317)$ as a $DK$ bound state.

Determines the mass of $D^ ext{*}_{s0}(2317)$ to be approximately 2315 MeV.

Finds that about 70% of the $D^ ext{*}_{s0}(2317)$ wave function is $DK$ component.

Abstract

We study the experimental $DK$ invariant mass spectra of the reactions $B^+ \to \bar{D}^0 D^0 K^+$, $B^0 \to D^- D^0 K^+$ (measured by the BaBar Collaboration) and $B_s \to \pi^+ \bar{D}^0 K^-$ (measured by the LHCb Collaboration), where an enhancement right above the threshold is seen. We show that this enhancement is due to the presence of $D^\ast_{s0}(2317)$, which is a $DK$ bound state in the $I(J^P) = 0(0^+)$ sector. We employ a unitarized amplitude with an interaction potential fixed by heavy meson chiral perturbation theory. We obtain a mass $M_{D^\ast_{s0}} = 2315^{+12}_{-17}\ ^{+10}_{-5}\ \text{MeV}$, and we also show, by means of the Weinberg compositeness condition, that the $DK$ component in the wave function of this state is $P_{DK} = 70^{+4}_{-6}\ ^{+4}_{-8} \%$, where the first (second) error is statistical (systematic).