[Paper Review] Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$

Bo Wang, Kan Chen+2 more|arXiv (Cornell University)|Sep 5, 2023

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper proposes an effective field theory model based on light-quark exchange to describe low-energy S-wave interactions between heavy hadrons, identifying the recently observed $T_{cs0}(2900)$ and $T_{car{s}0}^{a}(2900)$ as molecular states in the $\bar{D}^{(*)}K^{*}$ and $D^{(*)}K^{*}$ systems. It predicts numerous molecular partners across charmed and charmed-strange sectors, with consistent line-shapes in $D_s\pi$ invariant mass spectra matching experimental data.

ABSTRACT

We relate the interactions of the $\bar{D}^{(\ast)} K^\ast$ and $D^{(\ast)} K^\ast$ systems to those of $D^{(\ast)}D^{(\ast)}$ and $D^{(\ast)}\bar{D}^{(\ast)}$ respectively, considering the residual strong interactions at the near-threshold energy is too weak to excite the strange quarks inside the hadrons. We propose an effective model to describe the low-energy S-wave interactions that are undertaken by the light $u$, $d$ quarks between two separated heavy hadrons. We find that the existence of molecules in the heavy-(anti)heavy sectors will naturally lead to the emergence of molecular states in $\bar{D}^{(\ast)} K^\ast$ and $D^{(\ast)} K^\ast$ systems. The recently observed $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$ can be well identified as the $0(0^+)$ and $1(0^+)$ partners of $T_{cc}(3875)$ and $Z_c(3900)$ in the charmed strange sector, respectively. We also predict their members under the {\it heavy} ($c$ and $s$) quark symmetry and SU(2) flavor symmetry. Most of them are very good molecule candidates, for example, (i) the $0(1^+)$ states in $D^\ast D^\ast$, $\bar{D}K^\ast$, $\bar{D}^\ast K^\ast$; (ii) the $0^{(+)}(2^{+(+)})$ states in $D^\ast \bar{D}^\ast$, $\bar{D}^\ast K^\ast$, $D^\ast K^\ast$; (iii) the $1^-(0^{++})$ state in $D^\ast\bar{D}^\ast$ and $1(1^+)$ state in $D^\ast K^\ast$. The $0^+(0^{++})$ state in $D\bar{D}$ and the $0(1^+)$ state in $DK^\ast$ might also exist as virtual states, and the $0(1^+)$ $DK^\ast$ can serve as a key to infer the existence of $0^+(0^{++})$ $D\bar{D}$. The $D_sπ$ invariant mass spectrum of $T_{c\bar{s}0}^a(2900)$ is also studied within the coupled-channel approach, and the molecular interpretation of $T_{c\bar{s}0}^a(2900)$ is consistent with the experimental data. Searching for the predicted states in experiments is crucial to discriminate the different pictures for interpreting these near-threshold exotica.

Motivation & Objective

• To explain the recently observed $T_{cs0}(2900)$ and $T_{c\bar{s}0}^{a}(2900)$ as molecular states in the $\bar{D}^{(*)}K^{*}$ and $D^{(*)}K^{*}$ systems.
• To establish a connection between $\bar{D}^{(*)}K^{*}$ and $D^{(*)}K^{*}$ systems and the $D^{(*)}D^{(*)}$ and $D^{(*)}\bar{D}^{(*)}$ systems via light-quark exchange interactions.
• To predict new molecular states in the charmed and charmed-strange sectors under heavy quark and SU(2) flavor symmetries.
• To test the molecular interpretation of $T_{c\bar{s}0}^{a}(2900)$ against experimental $D_s\pi$ invariant mass spectra using a coupled-channel framework.
• To identify key experimental signatures for verifying the molecular nature of these exotic states through line-shape analysis.

Proposed method

• Constructs an effective potential model based on residual strong interactions between light $u$ and $d$ quarks in two separated heavy hadrons.
• Applies heavy quark symmetry and SU(2) flavor symmetry to relate $\bar{D}^{(*)}K^{*}$ and $D^{(*)}K^{*}$ systems to $D^{(*)}D^{(*)}$ and $D^{(*)}\bar{D}^{(*)}$ systems.
• Uses the $T_{cc}(3875)$, $X(3872)$, and $Z_{c}(3900)$ as reference states to determine low-energy constants (LECs) in the effective Lagrangian.
• Performs coupled-channel calculations including $D_s\pi$ and $D^*K^*$ channels to model the $D_s\pi$ invariant mass spectrum of $T_{c\bar{s}0}^{a}(2900)$.
• Treats the $K^*$ meson with finite width (25–50 MeV) to simulate realistic experimental conditions.
• Analyzes pole structures and virtual state behavior in the complex energy plane to assess molecular stability and resonance features.

Figure 1: The isospin triplet (left column) and singlet (right column) of the di-meson systems that contain a light $q\bar{q}$ (first row) or $qq$ (second row) pair in the SU(2) flavor symmetry, respectively.

Experimental results

Research questions

• RQ1 Can the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^{a}(2900)$ be interpreted as molecular states in the $\bar{D}^{(*)}K^{*}$ and $D^{(*)}K^{*}$ systems?
• RQ2 What are the predicted molecular partners of $T_{cs0}(2900)$ and $T_{c\bar{s}0}^{a}(2900)$ under heavy quark and SU(2) flavor symmetries?
• RQ3 How does the finite width of the $K^*$ meson affect the $D_s\pi$ invariant mass spectrum of $T_{c\bar{s}0}^{a}(2900)$?
• RQ4 Can the $0(1^{+})$ $DK^*$ state serve as a key probe for the existence of the $0^{+}(0^{++})$ $D\bar{D}$ molecular state?
• RQ5 Are the observed line-shapes in the $D_s\pi$ channel consistent with a molecular (virtual state) interpretation of $T_{c\bar{s}0}^{a}(2900)$?

Key findings

• The $T_{cs0}(2900)$ and $T_{c\bar{s}0}^{a}(2900)$ are identified as the $0^{+}$ and $1^{-}$ partners of $T_{cc}(3875)$ and $Z_{c}(3900)$ in the charmed strange sector.
• The $0(1^{+})$ states in $D^*D^*$, $\bar{D}K^*$, and $\bar{D}^*K^*$ are predicted as good molecular candidates with strong binding or virtual state features.
• The $0^{+}(2^{+})$ states in $D^*\bar{D}^*$, $\bar{D}^*K^*$, and $D^*K^*$ are also predicted as viable molecular states.
• The $1^{-}(0^{++})$ state in $D^*\bar{D}^*$ and the $1(1^{+})$ state in $D^*K^*$ are identified as strong molecular candidates.
• The $0^{+}(0^{++})$ $D\bar{D}$ and $0(1^{+})$ $DK^*$ states may exist as virtual states, with the latter serving as a key probe for the former.
• The coupled-channel analysis of $T_{c\bar{s}0}^{a}(2900)$ shows that the molecular interpretation is consistent with the $D_s\pi$ invariant mass spectrum, especially when the $K^*$ width is taken as 25–50 MeV.

Figure 2: The schematic diagrams for the near-threshold interactions that are undertaken by the light quark interplays. The thick, thin and dashed lines denote the heavy quarks ( $c$ and $s$ ), light quarks ( $u$ and $d$ ) and the exchanged mesons (isospin triplet plus the singlet), respectively.