Phenomenological description of the $D^*_{s0}(2317)\to D_s\pi^0$ decay

TL;DR

This paper provides a phenomenological analysis of the decay of the $D^*_{s0}(2317)^+$ resonance into $D_s^+ o ext{pi}^0$, clarifying the decay amplitude structure and confirming unitarity and phase relations.

Contribution

It introduces a phenomenological approach to describe the $D^*_{s0}(2317)^+$ decay, including isospin violation and phase analysis, complementing existing chiral perturbation theory models.

Findings

The decay amplitude phase matches the nonresonant scattering phase, in line with Watson's theorem.

The decay width estimates are consistent with previous literature.

Unitarity is maintained through $ ext{pi}^0- ext{eta}$ mixing considerations.

Abstract

For coupled channels $D^0K^+$, $D^+K^0$, $D_s^+\eta$, and $D_s^+\pi^0$, the $S$-wave scattering amplitudes are constructed taking into account the mixing of the isoscalar resonance $D^*_{s0}(2317)^+$ with nonresonance amplitudes with isospin $I=1$. The phenomenological approach we use allows us to quite simply clear up the general structure of the $D^*_{s0}(2317)^+\to D_s^+\pi^0$ decay amplitude violating isospin. We show that the phase of this amplitude coincides with the phase of the nonresonanct $D_s^+\pi^0 $ scattering amplitude in agreement with the Watson theorem. Its modulus squared, as it should be, determines the width of the resonance peak in the $D_s^+\pi^0$ channel. Taking into account the $\pi^0-\eta$ mixing in internal lines up to the second order inclusively ensures that the unitarity condition is fulfilled. The presented analysis complements the description of the $D^*_{s0}(2317 )^+\to D_s^+\pi^0$ decay based on the coupled channel unitarized chiral perturbation theory. The numerical estimates obtained by us for the $D^*_{s0}(2317)^+\to D_s^+\pi^0$ decay width do not contradict those available in the literature.