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The structure of the lightest positive-parity charmed mesons from LQCD

Eric B. Gregory, Feng-Kun Guo, Christoph Hanhart, Stefan Krieg, Thomas Luu

Abstract

The nature of low-lying scalar and axial-vector charmed mesons has long been debated, specifically whether they are best explained as hadronic molecules or compact tetraquark systems. These two scenarios exhibit quite different features for the accessible $SU(3)$ multiplets in the scalar and axial-vector sectors. To resolve this debate, we performed $N_f=3+1$ lattice simulations and calculated the energy levels of the $SU(3)$ $[6]$ and $[\overline{15}]$ multiplets for both the scalar and axial-vector mesons in an $SU(3)$ flavor-symmetric setting. In both sectors we find attractive states for the [6] and repulsive interactions for the $[\overline{15}]$. This is consistent with the hadronic molecule picture, but not the compact tetraquark picture which predicts a low-lying $[\overline{15}]$ states in the axial-vector sector but not in the scalar sector.

The structure of the lightest positive-parity charmed mesons from LQCD

Abstract

The nature of low-lying scalar and axial-vector charmed mesons has long been debated, specifically whether they are best explained as hadronic molecules or compact tetraquark systems. These two scenarios exhibit quite different features for the accessible multiplets in the scalar and axial-vector sectors. To resolve this debate, we performed lattice simulations and calculated the energy levels of the and multiplets for both the scalar and axial-vector mesons in an flavor-symmetric setting. In both sectors we find attractive states for the [6] and repulsive interactions for the . This is consistent with the hadronic molecule picture, but not the compact tetraquark picture which predicts a low-lying states in the axial-vector sector but not in the scalar sector.

Paper Structure

This paper contains 10 sections, 13 equations, 4 figures, 1 table.

Table of Contents

  1. Motivation
  2. Model predictions
  3. Hadronic molecules
  4. Tetraquark model
  5. Lattice calculation
  6. Contractions
  7. Correlators and fits
  8. Analysis
  9. Results and interpretation
  10. Acknowledgements

Figures (4)

  • Figure 1: Plot from Guo_2025, illustrating predicted axial-vector textraquark spectrum. Added arrow annotations show the calculated bad diquark costs. Blue (red) symbols refer to states containing spin-zero (spin-one) light diquarks. Added green arrows show the added cost of a bad $cq$ diquark from \ref{['eq:cqdiquark']}, while the yellow arrows denote the cost of adding a bad $qq$ diquark from \ref{['eq:qqantidiquark']}.
  • Figure 2: Tuning process for $SU(3)_f$ ensembles. First $m_c$ is tuned to give correct value of hyperfine splitting ratio (left). Hyperfine splitting ratio is used to calibrate lattice spacing $a$ (middle). Light quark is tuned to give $600 \text{ MeV } < M_{\pi}< 700$ MeV (right).)
  • Figure 3: Representative correlators for the $\pi$, $D^*$, $[\overline{15}]_{\rm axvec}$ and $[6]_{\rm axvec}$.
  • Figure 4: Fit results for the ground-state mass shifts for $[\overline{15}]$ (red) and $[6]$ (blue) for the scalar sector (left) and the axial-vector (right). Circles, squares and triangles represent $N=2,3,4$-state fits, respectively. Shaded bands represent the results of the fit model-averaging procedure and jackknife determination of statistical uncertainty. The green dashed line is the $\pi +D$ or $\pi + D^*$ threshold.