Radiative decays of the $Ω(2012)$ as a hadronic molecule

Qing-Hua Shen, Jun-Xu Lu, Li-Sheng Geng, Xiang Liu, Ju-Jun Xie

TL;DR

The paper investigates the Ω(2012) resonance as a hadronic molecule generated by coupled-channel dynamics among $ar{K}ar{X}_{1530}$, $ar{K}ar{X}$, and $ar{ ext{?}}ar{ ext{?}}$ channels, within a chiral unitary framework. It computes the radiative decay width for Ω(2012) → γΩ via a triangle-loop mechanism where the state couples to $ar{K}ar{X}_{1530}$ and transitions to γΩ through $ ext{Ξ}$ exchange, extracting a width of $\Gamma_{\Omega(2012)\to\gamma\Omega} = 13.2^{+4.5}_{-3.9}$ keV and a branching ratio of $BR[\Omega(2012)\to\gamma\Omega] = 3.88^{+1.32}_{-1.15} \times 10^{-3}$ (using $\Gamma_R = 3.4$ MeV). The result shows sensitivity to the cutoff parameter $\Lambda$ but remains stable for $\Lambda \approx 1$ GeV, supporting the molecular interpretation and offering a testable prediction for future experiments such as Belle II and BESIII. The work complements prior quark-model analyses by providing a distinct radiative decay signature tied to the hadronic molecular structure of Ω(2012).

Abstract

We present a theoretical investigation of the radiative decay process $Ω(2012) \to γΩ$, where the $Ω(2012)$ resonance with spin-parity $J^P=\frac{3}{2}^-$, is treated as a dynamically generated state from $\bar{K}Ξ(1530)$ and $ηΩ$ in $s$-wave and $\bar{K}Ξ$ in $d$-wave. The radiative decay width of the $Ω(2012)$ is calculated using a triangular loop mechanism, where the $Ω(2012)$ couples to the $\bar{K} Ξ(1530)$ channel. Subsequently, the final state interactions between $Ξ(1530)$ and $\bar{K}$ transition to a photon and $Ω$ through the exchange of a $Ξ$ baryon. Our calculations yield a radiative decay width of $13.2 ^{+4.5}_{-3.9}$ KeV, with uncertainties arising from the model parameters. This result provides valuable insights into the nature of the $Ω(2012)$ resonance and its decay dynamics. It is expected that the calculations presented here could be verified by future experiments, which would open a new door for studying the still elusive nature of the $Ω(2012)$.

Radiative decays of the $Ω(2012)$ as a hadronic molecule

TL;DR

The paper investigates the Ω(2012) resonance as a hadronic molecule generated by coupled-channel dynamics among

,

, and

channels, within a chiral unitary framework. It computes the radiative decay width for Ω(2012) → γΩ via a triangle-loop mechanism where the state couples to

and transitions to γΩ through

exchange, extracting a width of

keV and a branching ratio of

(using

MeV). The result shows sensitivity to the cutoff parameter

but remains stable for

GeV, supporting the molecular interpretation and offering a testable prediction for future experiments such as Belle II and BESIII. The work complements prior quark-model analyses by providing a distinct radiative decay signature tied to the hadronic molecular structure of Ω(2012).

Abstract

We present a theoretical investigation of the radiative decay process

, where the

resonance with spin-parity

, is treated as a dynamically generated state from

and

in

-wave and

in

-wave. The radiative decay width of the

is calculated using a triangular loop mechanism, where the

couples to the

channel. Subsequently, the final state interactions between

and

transition to a photon and

through the exchange of a

baryon. Our calculations yield a radiative decay width of

KeV, with uncertainties arising from the model parameters. This result provides valuable insights into the nature of the

resonance and its decay dynamics. It is expected that the calculations presented here could be verified by future experiments, which would open a new door for studying the still elusive nature of the

.

Paper Structure (7 sections, 23 equations, 4 figures, 2 tables)

This paper contains 7 sections, 23 equations, 4 figures, 2 tables.

Table of Contents

Introduction
Formalism and ingredients
The molecular nature of $\Omega(2012)$ and its coupling to $\bar{K} \Xi(1530)$
The effective Lagrangians for the $\Xi(1530)\Xi\gamma$ and $\Omega \bar{K} \Xi$ interaction
The radiative decay $\Omega(2012) \to \gamma \Omega$
Numerical results
Summary

Figures (4)

Figure 1: The current status of ground $\Omega$ and excited $\Omega^*$(-like) states. Data are taken from the RPP ParticleDataGroup:2024cfk.
Figure 2: The interaction of (a) $\bar{K} \Xi(1530) \to \bar{K} \Xi(1530)$ and (b) $\eta\Omega \to \eta\Omega$ at the one-loop order.
Figure 3: The radiative decay of $\Omega(2012) \to \gamma\Omega$ through triangle loop mechanism with the strong coupling of the $\Omega(2012)$ to the $\bar{K}\Xi(1530)$ channel.
Figure 4: The obtained partial decay width of $\Omega(2012)$$\to \gamma \Omega$ as a function of the parameter $\Lambda$.