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Subthreshold poles in electron-positron annihilation. ${\rm D}_s^+{\rm D}_s^-$ final state

Peter Lichard, Josef Juráň

TL;DR

This paper provides evidence for a subthreshold pole in the $e^+e^-$ to ${\rm D}_s^+{\rm D}_s^-$ amplitude, interpreted as an excited (2p) bound state of the ${\rm D}_s^+{\rm D}_s^-$ molecule with a binding energy around $42$ MeV. By fitting BESIII 2024 cross sections using a modified Vector Meson Dominance model, the authors show that a SP improving the low-energy cross-section region yields a mass near $3890$–$3896$ MeV and essentially zero width, compatible with a bound-state pole below threshold. The SP interpretation achieves high statistical significance ($7.4\sigma$ for SP+3R and $5.5\sigma$ for SP+4R) and aligns in mass with the G(3900) region, suggesting the G(3900) could manifest as a subthreshold pole in $e^+e^-\to {\rm D}_s^+{\rm D}_s^-$. This work highlights the role of analytic properties of hadronic amplitudes in revealing near-threshold structures and motivates further study of bound-state interpretations in the charm sector.

Abstract

We present the evidence of a subthreshold pole in the $e^+ e^-\rightarrow {\rm D}_s^+{\rm D}_s^-$ process, which can be interpreted as an excited (2p) state of the ${\rm D}_s^+{\rm D}_s^-$ molecule with a binding energy of (42$^{20}_{-13}$)~MeV. The only existing candidate on the market is the G(3900), which thus gains a new possible interpretation.

Subthreshold poles in electron-positron annihilation. ${\rm D}_s^+{\rm D}_s^-$ final state

TL;DR

This paper provides evidence for a subthreshold pole in the to amplitude, interpreted as an excited (2p) bound state of the molecule with a binding energy around MeV. By fitting BESIII 2024 cross sections using a modified Vector Meson Dominance model, the authors show that a SP improving the low-energy cross-section region yields a mass near – MeV and essentially zero width, compatible with a bound-state pole below threshold. The SP interpretation achieves high statistical significance ( for SP+3R and for SP+4R) and aligns in mass with the G(3900) region, suggesting the G(3900) could manifest as a subthreshold pole in . This work highlights the role of analytic properties of hadronic amplitudes in revealing near-threshold structures and motivates further study of bound-state interpretations in the charm sector.

Abstract

We present the evidence of a subthreshold pole in the process, which can be interpreted as an excited (2p) state of the molecule with a binding energy of (42)~MeV. The only existing candidate on the market is the G(3900), which thus gains a new possible interpretation.

Paper Structure

This paper contains 4 sections, 1 equation, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The explored data and the model
  3. The Results
  4. Conclusions

Figures (3)

  • Figure 1: The $e^+e^-\rightarrow\mathrm{D}_s^+{\mathrm D}_s^-$ cross section calculated assuming an SP and three resonances (full) is compared to the BESIII data and the pure three-resonance fit (dashed). Only a narrow region above the threshold is shown.
  • Figure 2: The $e^+e^-\rightarrow\mathrm{D}_s^+{\mathrm D}_s^-$ cross section calculated assuming an SP and four resonances (full) and its comparison to data. Also, the individual contributions from the resonance part (dashed) and SP (dotted) are shown.
  • Figure 3: Parameters of resonances in the $\Gamma-M$ plane obtained from the SP+4R fit (red) along the parameters of resonances from PDG 2024 pdg2024 (blue).