Spectrum of $[cq][\bar{s}\bar{q}]$ tetraquarks: Nature of $D^*_{s0}(2317)$, $D_{s1}(2460)$ and $T^*_{c\bar s0}(2900)$

TL;DR

This work examines open-charm exotic states by modeling them as $[cq][\bar{s}\bar{q}]$ tetraquarks in a nonrelativistic diquark–antidiquark framework. It employs universal Semay–Silvestre-Brac potentials, a regularized spin–orbit interaction, and Gaussian Expansion Method to compute the spectrum from $1S$ to $2P$, fitting key parameters to the established $D^*_{s0}(2317)$ and $D_{s1}(2460)$. The results identify the ground states with the known charmed-strange mesons and predict additional $0^+$ and $2^+$ states, including radially excited $0^+$ configurations that could explain $T^a_{c\bar{s}0}(2900)$ as two distinct interior structures; the analysis favors a softer $p=2/3$ potential for excitations and highlights the role of color screening and diquark size. The study emphasizes experimental tests of decay channels and isospin effects to distinguish interior-structure differences from isospin breaking, and provides mass-scale uncertainties of about $50$–$70$ MeV for the predicted spectra.

Abstract

Motivated by the recent observations of exotic open-charm tetraquark candidates \(T^a_{c\bar{s}0}(2900)^{++}\) and \(T^a_{c\bar{s}0}(2900)^{0}\), we systematically calculate the mass spectra of \([cq][\bar{s}\bar{q}]\) tetraquarks within a nonrelativistic constituent quark potential model. In the model, the tetraquark states are treated as diquark-antidiquark bound systems with an interior interaction similar to the quark-antiquark interaction in conventional mesons. The well established states \(D_{s0}^*(2317)\) with \(J^P=0^+\) and \(D_{s1}(2460)\) with \(J^P=1^+\) could be identified as the two ground states of the \([cq][\bar{s}\bar{q}]\) system. \(T^a_{c\bar{s}0}(2900)^{0}\) and \(T^a_{c\bar{s}0}(2900)^{++}\) could be naturally interpreted as radially excited \(0^+\) tetraquark states with different interior components. Their large mass difference may result from their different interior structure instead of an isospin symmetry breaking. Whether \(T^a_{c\bar{s}0}(2900)^{0}\) and \(T^a_{c\bar{s}0}(2900)^{++}\) belong to an isospin triplet deserves further experimental investigation. In addition, there may be another \(0^+\) \([cq][\bar{s}\bar{q}]\) tetraquark state with mass around $2450$ MeV, which is composed of a $cq$ diquark and a $\bar s\bar q$ antidiquark both with spin-0. In the energy region $2640-2700$ MeV, there may be a $J^P=2^+$ \([cq][\bar{s}\bar{q}]\) tetraquark state composed of the $cq$ diquark and the $\bar s\bar q$ antidiquark both with spin-1.