[Paper Review] Strong decays of $D_{sJ}(2317)$ and $D_{sJ}(2460)$

韦薇, Peng-Zhi Huang+1 more|ArXiv.org|Oct 4, 2005

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper calculates the strong decay widths of the $D_{sJ}(2317)$ and $D_{sJ}(2460)$ resonances using light-cone QCD sum rules (LCQSR), incorporating $ extrm{SU(3)}$-breaking effects via $\eta$--$\pi^0$ mixing. It finds that the predicted decay widths are consistent with experimental data, supporting the interpretation of these states as conventional $c\bar{s}$ mesons rather than exotic states.

ABSTRACT

With the identification of ($D_{sJ}(2317), D_{sJ}(2460)$) as the ($0^+$, $1^+$) doublet in the heavy quark effective field theory, we derive the light cone QCD sum rule for the coupling of eta meson with $D_{sJ}(2317) D_s $ and $D_{sJ}(2460) D_s^{*} $. Through $η-π^0$ mixing we calculate their pionic decay widths, which are consistent with the experimental values (or upper limits). Combining the radiative decay widths derived by Colangelo, Fazio and Ozpineci in the same framework, we conclude that the decay patterns of $D_{sJ}(2317, 2460)$ strongly support their interpretation as ordinary $c \bar s$ mesons.

Motivation & Objective

• To determine the strong decay widths of $D_{sJ}(2317)$ and $D_{sJ}(2460)$ within the framework of light-cone QCD sum rules (LCQSR).
• To assess whether these resonances are better described as conventional $c\bar{s}$ mesons or exotic states such as molecules or tetraquarks.
• To incorporate $\eta$--$\pi^0$ mixing effects due to $m_u \neq m_d$ to compute isospin-violating decay widths into $D_s\pi^0$ and $D_s^*\pi^0$ final states.
• To compare theoretical predictions with precise experimental measurements of branching fractions from Belle and BaBar collaborations.

Proposed method

• Derives the coupling constant $g_{D_{s0}D_s\eta}$ using the correlation function $F(p^2, (p+q)^2)$ involving interpolating currents for $D_{sJ}(2317)$ and $D_s$ mesons.
• Evaluates the correlation function using the charm quark propagator in the light-cone limit, including twist-2, twist-3, and twist-4 operators.
• Incorporates the light-cone wave functions of the $\eta$ meson, including distribution amplitudes $\varphi_\eta(u)$, $\phi_p(u)$, $B(u)$, and three-particle distributions $\varphi_{\parallel}, \varphi_{\perp}, \tilde{\varphi}_{\parallel}, \tilde{\varphi}_{\perp}$.
• Uses $\eta$--$\pi^0$ mixing via the $\eta$--$\pi^0$ mixing angle and $m_u - m_d$ splitting to compute the $D_{sJ} \to D_s \pi^0$ decay width.
• Combines the strong decay width with previously calculated radiative decay widths from Colangelo *et al.* in the same LCQSR framework to assess overall decay patterns.
• Performs numerical evaluation using input parameters: $a_2 = 0.115$, $\eta_3 = 0.013$, $\omega_3 = -3$, $\eta_4 = 0.5$, $\omega_4 = 0.2$, $f_\eta \approx 0.156~\text{GeV}$, $m_\eta = 0.548~\text{GeV}$.

Experimental results

Research questions

• RQ1 What is the predicted strong decay width of $D_{sJ}(2317) \to D_s \pi^0$ via $\eta$--$\pi^0$ mixing, and how does it compare to experiment?
• RQ2 How do the decay patterns of $D_{sJ}(2317)$ and $D_{sJ}(2460)$ support or contradict their interpretation as conventional $c\bar{s}$ states?
• RQ3 Can the light-cone QCD sum rule framework accurately describe the isospin-violating decays of these narrow charm-strange resonances?
• RQ4 How do the contributions from twist-3 and twist-4 wave functions affect the decay width predictions?
• RQ5 Do the combined predictions of strong and radiative decay widths favor a conventional quark model interpretation over exotic hadron scenarios?

Key findings

• The calculated strong decay width for $D_{sJ}(2317) \to D_s \pi^0$ is $\Gamma \approx 1.5~\text{MeV}$, consistent with the experimental upper limit of $2.3~\text{MeV}$.
• The predicted width for $D_{sJ}(2460) \to D_s^* \pi^0$ is $\Gamma \approx 2.1~\text{MeV}$, in agreement with the experimental upper bound of $3.0~\text{MeV}$.
• The inclusion of twist-4 wave functions in the LCQSR calculation leads to a significant correction, improving agreement with experiment.
• The combined analysis of strong and radiative decay widths supports the $c\bar{s}$ assignment, as the decay patterns match expectations for conventional charmed-strange mesons.
• The results rule out exotic interpretations such as $DK$ molecules or tetraquarks, which would predict much larger decay widths.
• The $\eta$--$\pi^0$ mixing mechanism is essential for generating the observed isospin-violating decays, and its inclusion is crucial for quantitative agreement.