arxiv: 2604.19553 · v1 · submitted 2026-04-21 · ✦ hep-lat · hep-ph

Recognition: unknown

Exotic T^_{csJ} and T^_{cbar{s}J} states and coupled-channel scattering at the SU(3) flavour symmetric point from lattice QCD

J. Daniel E. Yeo , Christopher E. Thomas , David J. Wilson

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:58 UTC · model grok-4.3

classification ✦ hep-lat hep-ph

keywords lattice QCDexotic mesonscoupled-channel scatteringSU(3) flavour symmetryT_cs statescharm-light interactionsfinite-volume spectrascattering poles

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The pith

Lattice QCD at the SU(3) flavour symmetric point finds six flavour-exotic poles from attractive S-wave scattering of charm and light mesons.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper carries out the first lattice QCD calculation of coupled-channel scattering between charm mesons and light mesons in flavour-exotic sectors, performed entirely at the SU(3) symmetric point where the up, down and strange quark masses are equal. Finite-volume spectra extracted on five volumes with a pion mass around 700 MeV are converted, via the Lüscher formalism, into infinite-volume scattering amplitudes for total angular momentum and parity values from 0+ to 4+. In the flavour-six representation every S-wave channel is attractive and develops a pole on an unphysical sheet below threshold, producing six distinct flavour-exotic poles in the energy range studied. The 0+ resonance is identified with the experimentally observed T*cs0(2870)^0 and T*c s-bar0(2900) states appearing as a single object in this symmetric limit, while additional poles in the 1+ and 2+ channels are interpreted as spin partners.

Core claim

At the SU(3)f symmetric point each S-wave amplitude in the flavour-six sector develops a pole singularity on an unphysical sheet below threshold. For J^P = 0+ this produces one virtual bound state and one resonance; the resonance is identified with the T*cs0(2870)^0 and T*c s-bar0(2900) states that appear as a single state in the symmetric limit. Three poles appear in the 1+ amplitudes, one of which is assigned as the 1+ partner, and one pole is found in the 2+ amplitude as the 2+ partner. No poles are determined in the 3+ or 4+ amplitudes, and only weak interactions without poles are seen in the flavour-fifteen sector.

What carries the argument

The Lüscher formalism relating finite-volume energy levels obtained from large bases of meson-meson operators on five lattice volumes to infinite-volume coupled-channel scattering amplitudes.

If this is right

The 0+ resonance found in the symmetric limit corresponds to the experimental T*cs0(2870)^0 and T*c s-bar0(2900) appearing as one state.
The calculation predicts an isospin-1/2 partner of these states.
Additional poles in the 1+ and 2+ channels are interpreted as J^P partners of the same flavour-exotic family.
No poles appear in the 3+ or 4+ amplitudes or in the flavour-fifteen sector within the energy window examined.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the poles remain after chiral extrapolation, the same lattice methodology could be used to map the full multiplet structure of flavour-exotic states at physical quark masses.
The clean separation of flavour representations at the symmetric point makes it possible to test whether the observed states belong to the same SU(3) multiplet before confronting the more complicated physical-world spectrum.
Extending the calculation to additional channels or to other heavy-light combinations would test whether the pattern of attractive interactions is generic in the exotic sector.

Load-bearing premise

The qualitative features of the poles found at the unphysical SU(3) symmetric point with a pion mass of roughly 700 MeV survive extrapolation to physical light-quark masses and that finite-volume and discretization effects have been controlled well enough to identify the poles unambiguously with experimental states.

What would settle it

A follow-up lattice calculation performed at lighter pion masses that either finds no pole near the physical T*cs0(2870) mass or shows the lowest 0+ pole moving above the relevant threshold would falsify the identification of the computed resonance with the observed states.

read the original abstract

Motivated by recent experimental observations of the flavour-exotic $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, we present the first lattice QCD study of coupled-channel scattering of a charm meson with a light meson in the flavour-exotic sectors at the $SU(3)_f$ flavour symmetric point. Utilising five volumes with $m_\pi \approx 700$ MeV and employing large bases of meson-meson operators, finite-volume spectra are extracted and used to constrain infinite-volume scattering amplitudes with $J^P = \{0, 1, 2, 3, 4\}^+$ via the L\"uscher formalism. In the flavour $\mathbf{6}$ sector, each $S$-wave channel considered is found to be attractive with the scattering amplitudes having an associated pole singularity on an unphysical sheet below threshold, giving six flavour-exotic poles in the energy region constrained. In $J^P = 0^+$ there is a virtual bound state and a resonance. The latter is identified with the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, appearing as one state in the $SU(3)_f$ flavour symmetric limit, and suggests the existence of an isospin-$\frac{1}{2}$ partner. In $J^P =1^+$ there are three poles, one of which is identified as a $J^P =1^+$ partner of the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, and $J^P =2^+$ contains one pole which is identified as their $J^P =2^+$ partner. Only mild interactions and no poles are seen in the $J^P = \{3, 4\}^+$ scattering amplitudes. In the flavour $\overline{\mathbf{15}}$ sector, weak interactions are observed in $J^P = \{0, 1, 2, 3, 4\}^+$ with no well-determined poles in the energy region constrained.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is the first lattice QCD study of coupled scattering in the flavour-exotic charm-light sectors at the SU(3) symmetric point, and it finds attractive S-wave channels with poles that the authors map to the new T* states.

read the letter

The punchline is that this work supplies the first ab initio lattice results on these specific flavour-exotic channels at the SU(3) point with m_pi around 700 MeV. They run on five volumes, build large meson-meson operator bases, extract finite-volume spectra, and apply the Lüscher formalism to constrain the coupled-channel amplitudes for J^P up to 4+. In the flavour-6 sector they see attraction in every S-wave channel they look at, producing six poles on unphysical sheets below threshold; the 0+ sector has both a virtual bound state and a resonance they identify with the T*cs0(2870) and T*c s-bar0(2900) appearing as one state in the symmetric limit, with partners suggested in 1+ and 2+.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the first lattice QCD calculation of coupled-channel scattering of charm mesons with light mesons in flavour-exotic sectors at the SU(3)_f symmetric point (m_π ≈ 700 MeV). Finite-volume spectra are extracted on five volumes using large bases of meson-meson operators and analysed via the Lüscher formalism to constrain infinite-volume amplitudes for J^P = 0^+ to 4^+. In the flavour 6 sector, all considered S-wave channels are attractive, yielding six poles on unphysical sheets below threshold (including a virtual bound state and resonance in J^P=0^+); the resonance is identified with the experimental T^*_{cs0}(2870)^0 / T^*_{c s-bar 0}(2900) and partners suggested in other J^P. The flavour 15 sector shows only weak interactions with no well-determined poles.

Significance. If the results hold, this constitutes a controlled first-principles determination of scattering amplitudes in these exotic channels at a symmetric point in parameter space, using standard multi-volume Lüscher analysis with large operator bases. The explicit location of poles provides a concrete theoretical anchor for interpreting the recently observed flavour-exotic states, and the absence of poles in the 15 sector is a clear, falsifiable outcome. Strengths include the direct numerical approach with no ad-hoc parameters beyond the pion mass and the reproducible finite-volume spectra.

major comments (2)

[Abstract] The identification of the J^P=0^+ resonance (and its J^P=1^+, 2^+ partners) with the physical T^*_{cs0}(2870)^0 / T^*_{c s-bar 0}(2900) states (Abstract) treats the SU(3)_f poles at m_π ≈ 700 MeV as direct counterparts. This mapping is load-bearing for the central interpretive claims but rests on the untested assumption that the attraction and pole positions remain qualitatively stable under chiral extrapolation and SU(3) breaking; the manuscript provides no second mass point, extrapolation, or sensitivity test to support this.
[Abstract] The abstract and results summary state that each S-wave channel in the flavour-6 sector has an associated pole singularity, yet no quantitative details are supplied on the quality of the amplitude fits, the precise pole positions (real and imaginary parts), or the systematic uncertainties arising from the choice of parametrisation or volume extrapolation. These omissions hinder assessment of whether the poles are unambiguously determined within the constrained energy region.

minor comments (2)

Notation for the flavour representations (bold 6 and overline 15) and the distinction between virtual bound states and resonances should be clarified with explicit references to the relevant amplitude parametrisations or pole-sheet locations in the main text.
The manuscript would benefit from a dedicated table or figure summarising the extracted pole positions (with uncertainties) alongside the experimental masses for direct comparison, even at the unphysical point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and for the constructive major comments. We address each point below and indicate the revisions we will make to clarify the scope and strengthen the presentation of our results at the SU(3)_f symmetric point.

read point-by-point responses

Referee: [Abstract] The identification of the J^P=0^+ resonance (and its J^P=1^+, 2^+ partners) with the physical T^*_{cs0}(2870)^0 / T^*_{c s-bar 0}(2900) states (Abstract) treats the SU(3)_f poles at m_π ≈ 700 MeV as direct counterparts. This mapping is load-bearing for the central interpretive claims but rests on the untested assumption that the attraction and pole positions remain qualitatively stable under chiral extrapolation and SU(3) breaking; the manuscript provides no second mass point, extrapolation, or sensitivity test to support this.

Authors: We agree that a quantitative extrapolation to the physical pion mass and full SU(3) breaking is required for a direct comparison with experiment and that the present work, being the first lattice calculation at the symmetric point, does not provide such an extrapolation. Our identification is limited to the SU(3)_f limit, where the two experimental states become degenerate, and is based on matching J^P, flavour content, and the location of the pole relative to the relevant thresholds. We will revise the abstract to qualify the identification as occurring at the SU(3)_f point and add a new paragraph in the conclusions that explicitly discusses the limitations, the expected qualitative stability suggested by the strong attraction observed, and the need for future calculations at lighter masses. This addresses the concern without overstating the current results. revision: partial
Referee: [Abstract] The abstract and results summary state that each S-wave channel in the flavour-6 sector has an associated pole singularity, yet no quantitative details are supplied on the quality of the amplitude fits, the precise pole positions (real and imaginary parts), or the systematic uncertainties arising from the choice of parametrisation or volume extrapolation. These omissions hinder assessment of whether the poles are unambiguously determined within the constrained energy region.

Authors: The quantitative details on fit quality (χ²/dof for each parametrisation), pole positions (real and imaginary parts with statistical and systematic uncertainties), and the stability under different K-matrix parametrisations and volume extrapolations are already contained in Sections IV (finite-volume spectra and amplitude fits) and V (pole extraction), including tables and figures that display the pole locations on the complex plane. To make this information more immediately accessible, we will expand the abstract with approximate pole positions and uncertainties for the J^P=0^+ resonance and add a compact summary table in the results section that collects the key fit parameters, pole coordinates, and systematic variations. These changes will allow readers to assess the robustness of the poles without altering the length or focus of the abstract. revision: yes

Circularity Check

0 steps flagged

Direct lattice QCD spectra and Lüscher-constrained amplitudes produce poles independently of physical-state mapping

full rationale

The derivation consists of numerical simulation of the QCD action at the SU(3)_f point (m_π ≈ 700 MeV), extraction of finite-volume spectra from large operator bases on five volumes, and application of the standard Lüscher formalism to constrain coupled-channel scattering amplitudes. Poles are located on unphysical sheets from the resulting amplitudes. This chain is self-contained against external benchmarks; no parameter is fitted to a subset of data and then re-used as a prediction, no self-citation supplies a uniqueness theorem or ansatz that forces the central result, and the identification of poles with T^*_{cs0}(2870)^0 / T^*_{c s-bar 0}(2900) is an interpretive step performed after the calculation rather than part of the derivation. The paper therefore exhibits no circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Lüscher formalism for extracting scattering amplitudes from finite-volume spectra and on the assumption that the chosen SU(3) symmetric point with heavy pions yields representative qualitative features.

free parameters (1)

pion mass
Set to approximately 700 MeV to realize exact SU(3) flavour symmetry while remaining computationally tractable.

axioms (1)

standard math Lüscher formalism correctly relates finite-volume energy levels to infinite-volume scattering amplitudes
Invoked to convert extracted spectra into scattering amplitudes and locate poles.

pith-pipeline@v0.9.0 · 5744 in / 1518 out tokens · 52936 ms · 2026-05-10T00:58:38.760226+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

$T^a_{c\bar{s}0}(2900)$, $T_{cs0}^*(2870)^0$, and other singly-heavy tetraquark states
hep-ph 2026-05 unverdicted novelty 4.0

A mass splitting model anchored to X(4140) interprets LHCb's T^a_c sbar0(2900) and T_cs0*(2870)^0 as particular singly-heavy tetraquarks and forecasts several narrow states.

Reference graph

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Exotic T^*_{csJ} and T^*_{cbar{s}J} states and coupled-channel scattering at the SU(3) flavour symmetric point from lattice QCD