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

Zhi-Yuan Chen, Zhe-Hao Cao+3 more|arXiv (Cornell University)|Feb 12, 2026

Quantum Chromodynamics and Particle Interactions0 citations

TL;DR

The paper computes the mass spectrum of open-charm [cq][\bar{s}\bar{q}] tetraquarks using a nonrelativistic diquark–antidiquark potential model, identifying D^{*}_{s0}(2317) and D_{s1}(2460) as ground states and interpreting T^{a}_{c\bar{s}0}(2900) as radially excited states with distinct internal structures.

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.

Motivation & Objective

• Motivate and explain the observed open-charm exotic candidates T^{a}_{c\bar{s}0}(2900)^{++/0} and their relation to D^{*}_{s0}(2317) and D_{s1}(2460).
• Construct a nonrelativistic diquark–antidiquark potential model for [cq][\bar{s}\bar{q}] tetraquarks and solve for the mass spectrum.
• Fit interaction parameters to the well-established D^{*}_{s0}(2317) and D_{s1}(2460) states and predict higher excitations.
• Explore how interior diquark/antidiquark structures affect mass splittings and the possible existence of additional states near 2640–2700 MeV and around 2900 MeV.

Proposed method

• Treat tetraquarks as bound diquark–antidiquark systems with V_{qq}=1/2 V_{q\bar{q}} for the interaction.
• Use Semay–Silvestre-Brac nonrelativistic potentials with parameters (AL1, AL2, AP1, AP2) to model confinement and Coulomb-like terms.
• Incorporate spin–orbit and tensor spin-dependent terms with a regularization factor (1-e^{-r/r_0}) in V_{sl}.
• Compute diquark/antidiquark masses for cq and \bar{s}\bar{q} with spins 0/1, then solve a generalized eigenvalue problem from the Gaussian Expansion Method (GEM).
• Ground states are fixed by D^{*}_{s0}(2317) and D_{s1}(2460); four parameter sets (α, λ) are obtained and used to predict the [cq][\bar{s}\bar{q}] spectrum from 1S to 2P.

Experimental results

Research questions

• RQ1 Can D^{*}_{s0}(2317) and D_{s1}(2460) be interpreted as ground-state [cq][\bar{s}\bar{q}] tetraquarks within the diquark–antidiquark picture?
• RQ2 Do the observed T^{a}_{c\bar{s}0}(2900)^{0,++} arise as radially excited [cq][\bar{s}\bar{q}] tetraquark states with different internal structures?
• RQ3 What are the predicted masses and quantum numbers of other [cq][\bar{s}\bar{q}] states (including 2P excitations) and do they lie near experimental thresholds?
• RQ4 How do color configurations, spin couplings, and interior diquark sizes influence mass splittings among S- and P-wave tetraquarks?

Key findings

• D^{*}_{s0}(2317) and D_{s1}(2460) are compatible with the 1S states 1|[1,1]_{0},0>_{0} and 1|[1,1]_{1},0>_{1} cq\bar{s}\bar{q} tetraquarks across all four potentials.
• The 2900 MeV states T^{a}_{c\bar{s}0}(2900)^{0,++} can be interpreted as radially excited 0^{+} tetraquarks with configurations 2|[0,0]_{0},0> and 2|[1,1]_{0},0>, respectively, with their ~30 MeV mass difference attributed to interior structure rather than isospin breaking.
• A possible 2^{+} ground state around 2640–2700 MeV and additional J^{P} states near 2900 MeV are predicted for the [cq][\bar{s}\bar{q}] system.
• Two low-lying 0^{+} states around 2318–2688 MeV exist in S-wave; mass splittings within the S-wave multiplet are large (140–370 MeV) compared to conventional mesons.
• A softer power-law potential with p=2/3 (AP-type) better describes radially excited tetraquarks, due to color screening and diquark finite-size effects.
• Uncertainties: shifting the assumed ground states by +50 MeV yields ~50–70 MeV shifts in predicted masses, preserving hierarchy and splittings.