Strange partner of $T_{cc}^+$ from lattice QCD in $D^{(*)}D_s^{(*)}$ scattering

Abstract

We report on our lattice QCD study of coupled $DD_s^* - D^*D_s$ scattering in the $J^P=1^+$ channel and elastic $DD_s$ scattering in the $J^P=0^+$ channel, aimed at investigating the possible existence of $cc\bar{u}\bar{s}$ tetraquarks near threshold. The calculation uses CLS ensembles with $m_π\approx 280$ MeV, lattice spacing $a \approx 0.09$ fm, and spatial extents $L/a=24, 32$. Finite-volume spectra are obtained from a variational analysis of two-point correlation matrices constructed from two-meson operator bases using distillation. The $l=0$ partial-wave scattering amplitudes are determined from the lattice spectra in multiple moving frames using Lüscher's formalism as well as a finite-volume implementation of the Lippmann-Schwinger equation. In both channels we observe small but nonzero shifts relative to the noninteracting spectrum, indicating weak meson interactions. The extracted physically plausible $S$-wave amplitudes show no pole structures near threshold.

Figures (5)

• Figure 1: Finite-volume energies in the center-of-momentum frame, expressed in units of the relevant thresholds and shown as a function of the spatial extent. The top (bottom) panel corresponds to irreps relevant for the scalar (axialvector) channel. Black markers denote lattice-extracted energies, while the curves indicate noninteracting two-meson levels for the channels $DD_s$ (blue dashed), $DD_s^*$ (red dot-dashed), $D^*D_s$ (green solid), and $D^*D_s^*$ (purple solid). Faded curves denote higher noninteracting shells not included in the analysis, and the gray dotted line indicates the $DD_s\pi$ threshold.
• Figure 2: Diagnostics of channel coupling in the $T_1^+(0)$ irrep. Left: spectra obtained from pruned operator bases excluding either $D^*D_s$ or $DD_s^*$ interpolators. Right: dependence of the lowest eigenenergies on the rescaling parameter $\alpha$ controlling cross-correlations between the two operator sectors.
• Figure 3: Analytical reconstruction of the finite-volume spectrum using the best-fit parameters from combined $S$–$P$ wave fits obtained with the Lippmann--Schwinger approach. Orange stars denote reconstructed energies, while circles represent the lattice eigenenergies. Energies are expressed in units of the $DD_s$ threshold.
• Figure 4: left: $k\cot{\delta_0}/E_{DD_s}$ vs. $(k/E_{DD_s})^2$ for elastic $DD_s$ scattering in $S$-wave obtained from the LSE analysis. The markers correspond to lattice eigenenergies converted to $k\cot\delta$ using Lüscher's prescription. The orange curve and band represent the fitted amplitude. The cyan and orange curves denote the unitary parabola $\pm i\sqrt{-k^2}/E_{DD_s}$, while the vertical blue dotted line marks the left-hand-cut branch point from $K^*$ exchange. The magenta line indicates the $D^*D_s^*$ threshold. right: Energy dependence of the amplitude $\rho^2|T|^2$, proportional to the elastic cross section. The inset shows the Argand trajectory $\rho T=e^{i\delta}\sin\delta$.
• Figure 5: Reconstructed spectra using the Lüscher's approach for the $DD_s^*$--$D^*D_s$ coupled-channel system in $S$-wave with $J^P=1^+$. Energies are shown in units of the $DD_s^*$ threshold. Red and green curves denote noninteracting levels. Black circles indicate levels used in the fits, while brown circles are excluded.