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New spectrum of charm-strange meson with constituent quark model $c\bar{s}$ contributions

Liu-Lin Wang, Xing-Meng Zhao, Xiao-Hai Liu, Mao-Jun Yan

TL;DR

This paper tackles the charm–strange meson spectrum by modeling S-wave Nambu–Goldstone boson scattering off charm mesons in the $(S,I)=(1,0)$ sector within a chiral unitary framework. It combines Weinberg–Tomozawa contact interactions with s-/u-channel exchanges of bare $c\bar{s}$ states predicted by a constituent-quark model and unitarizes the amplitudes to locate poles on the complex energy plane. The analysis reproduces the established $D_{s0}^*(2317)$ as a DK molecular state, identifies the $D_{s1}(2460)$ as a WT-driven pole, and predicts additional higher-mass poles across $J^P=0^+,1^+,1^-,2^-$ sectors, some interpreted as hadronic molecules such as $D_1K$ for $D_{s1}(2860)$. Regularization effects, including a Gaussian regulator for the WT term, reveal significant sensitivity of higher poles’ widths to short-distance dynamics, underscoring the mixed molecular–quark-model nature of charm–strange resonances and guiding future experimental exploration.

Abstract

We systematically investigate the $S$-wave interactions between Nambu-Goldstone bosons (NGBs) and charmed mesons in the $(S,I)=(1,0)$ sector using the chiral unitary approach. The scattering amplitudes incorporate both the Weinberg-Tomozawa term and additional contributions from $s$- and $u$-channel exchanges of $c\bar{s}$ states predicted by the constituent quark model (CQM). Through analytic continuation of the unitarized amplitudes to the complex energy plane, we identify multiple poles corresponding to bound states and resonances. Our analysis reveals a rich spectrum of $D_{sJ}$ states across $J^P = 0^+, 1^+, 1^-$, and $2^-$ sectors, providing new insights into the nature of established resonances like $D_{s0}^*(2317)$ and $D_{s1}(2460)$, while predicting several new states that could be observed in future experiments.

New spectrum of charm-strange meson with constituent quark model $c\bar{s}$ contributions

TL;DR

This paper tackles the charm–strange meson spectrum by modeling S-wave Nambu–Goldstone boson scattering off charm mesons in the sector within a chiral unitary framework. It combines Weinberg–Tomozawa contact interactions with s-/u-channel exchanges of bare states predicted by a constituent-quark model and unitarizes the amplitudes to locate poles on the complex energy plane. The analysis reproduces the established as a DK molecular state, identifies the as a WT-driven pole, and predicts additional higher-mass poles across sectors, some interpreted as hadronic molecules such as for . Regularization effects, including a Gaussian regulator for the WT term, reveal significant sensitivity of higher poles’ widths to short-distance dynamics, underscoring the mixed molecular–quark-model nature of charm–strange resonances and guiding future experimental exploration.

Abstract

We systematically investigate the -wave interactions between Nambu-Goldstone bosons (NGBs) and charmed mesons in the sector using the chiral unitary approach. The scattering amplitudes incorporate both the Weinberg-Tomozawa term and additional contributions from - and -channel exchanges of states predicted by the constituent quark model (CQM). Through analytic continuation of the unitarized amplitudes to the complex energy plane, we identify multiple poles corresponding to bound states and resonances. Our analysis reveals a rich spectrum of states across , and sectors, providing new insights into the nature of established resonances like and , while predicting several new states that could be observed in future experiments.

Paper Structure

This paper contains 11 sections, 31 equations, 2 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Chiral potentials
  4. Bare state exchange potentials
  5. Unitarized amplitude
  6. Numeric result
  7. Model parameters
  8. $D_{sJ}$ spectrum with $J^P=0^+$ and $1^+$
  9. $D_{sJ}$ spectrum with $J^P=1^-$ and $2^-$
  10. Summary
  11. Chiral quark model

Figures (2)

  • Figure 1: Distinct interaction channels for NGB--charmed meson scattering: (a) Weinberg-Tomozawa term, (b) $s$-channel pole from a bare $c\bar{s}$ state, and (c) $u$-channel exchange.
  • Figure 2: Upper panel: width of the higher pole as a function of the regulator $\Lambda$. Lower panel: corresponding pole mass variation. The subtraction constant is fixed at $a(\mu) = -1.549$.