Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering

Abstract

We present the first lattice QCD determination of coupled $D{D}_s^{\ast }$ and $D^{\ast }{D}_s$ scattering amplitudes in the $J^P=1^{+}$ channel and elastic $D{D}_s$ scattering amplitude in the $J^P=0^{+}$ channel. The aim is to investigate whether tetraquarks with flavor $cc\bar{u}\bar{s}$ exist in the region near threshold. Lattice QCD ensembles from the CLS consortium with $m_{\pi }\sim 280$ MeV, $a\sim 0.09$ fm and $L/a=24,32$ are utilized. Finite-volume spectra are determined via variational analysis of two-point correlation matrices, computed using large bases of operators resembling bilocal two-meson structures within the distillation framework. The scattering matrix for partial wave $l=0$ is determined using lattice eigenenergies from multiple inertial frames following Lüscher's formalism as well as following the solutions of Lippmann-Schwinger Equation in the finite-volume on a plane-wave basis. We observe small nonzero energy shifts in the simulated spectra from the noninteracting scenario in both the channels studied, which points to rather weak nontrivial interactions between the mesons involved. Despite the nonzero energy shifts, the lattice-extracted $S$-wave amplitudes do not carry signatures of any hadron pole features in the physical amplitudes in the energy region near the threshold.

Comments: 30 pages, 17 figures, 10 tables, published version