Production mechanism of doubly charmed exotic mesons $T_{cc}$

Hee-Jin Kim; Hyun-Chul Kim

REVIEW 4 major objections 6 minor 2 cited by

Production mechanism of doubly charmed exotic mesons $T_{cc}$

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper reports that, with no fit to Tcc data, the coupled DD/DD*/D*D* system yields Tcc(3875)+ as an isovector DD* bound state at 3875.677 MeV, 0.0328 MeV below threshold, plus three partner tetraquark states.

desk verdict A serious coupled-channel calculation whose Tcc identification rests on an isospin-averaged pole sitting ~0.6 MeV above the physical D0D*+ threshold; the three companion predictions stand, but the central claim needs three-body treatment and a numerical cleanup. read the letter →

arxiv 2507.09191 v2 pith:GHLJ7F6P submitted 2025-07-12 hep-ph hep-ex

Hee-Jin Kim , Hyun-Chul Kim This is my paper

classification hep-phhep-ex

keywords Tcc(3875)+doublycharmedtetraquarkDD*molecularstatecoupled-channelformalismBlankenbecler-SugarreductionheavyquarksymmetryhiddenlocaleffectiveLagrangian

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to show that the observed doubly charmed tetraquark $T_{cc}(3875)^+$ can be produced dynamically, without any fit to its data, as a loosely bound $DD^*$ state in the isovector axial-vector channel. Solving the coupled $DD$, $DD^*$, and $D^*D^*$ scattering equations with interactions fixed by heavy-quark, chiral, SU(3) flavor, and hidden local symmetries, the authors find a pole at $3875.677$ MeV, just $0.0328$ MeV below the $DD^*$ threshold. They also obtain three partner tetraquark states: an isoscalar $1^+$ bound state near $3823$ MeV, an isoscalar $1^+$ resonance near $4102$ MeV, and an isoscalar $1^-$ resonance near $4090$ MeV. If the identification is right, one no-fit production mechanism accounts for all four states and explains why $T_{cc}(3875)^+$ sits almost exactly at threshold.

What carries the argument

The load-bearing machinery is the coupled-channel Blankenbecler–Sugar reduction of the Bethe–Salpeter equation for the three two-body channels $DD$, $DD^*$, and $D^*D^*$. The two-body Feynman kernels are built from effective Lagrangians respecting heavy-quark spin-flavor symmetry, chiral symmetry, SU(3) flavor symmetry, and hidden local symmetry, with the pion coupling fixed by the $D^*$ width, the vector couplings by vector meson dominance, and the $\sigma$ and $\rho$ couplings by dispersion relations. A single reduced cutoff $\Lambda_0 = \Lambda - m_{\rm ex} = 600$ MeV, chosen from the idea that heavier hadrons are more compact, regulates the vertices with no fit to $T_{cc}$ data. The $S$-wave axial-vector kernel amplitudes provide the strong attraction that produces the two positive-parity bound states, while the negative-parity state arises from a mix of $^1P_1$ and $^3P_1$ waves once all channels are coupled.

What would settle it

A decisive check is to include the open $D^0D^0\pi^+$ three-body channel and the $D^0$–$D^+$ mass splitting in the same coupled equations: if the $3875.677$ MeV pole disappears, moves into the complex plane with a width far from the observed roughly $410$ keV, or becomes a cusp, the central identification fails. A second, purely experimental check is a measurement of the isospin of $T_{cc}(3875)^+$: if it is confirmed to be $I = 0$, the isovector assignment at the heart of the paper is excluded.

Watch

Extended reading notes

Core claim

The central claim is that the coupled $DD/DD^*/D^*D^*$ system, with all couplings fixed from independent sources rather than fitted to $T_{cc}$ data, dynamically generates $T_{cc}(3875)^+$ as an isovector $J^P = 1^+$ $DD^*$ bound state. The pole sits at $3875.677$ MeV, with binding energy $\delta m = 0.0328$ MeV relative to the $DD^*$ threshold, and its dominant coupling is to the $DD^*$ channel, so the state qualifies as a hadronic molecule. The same calculation yields an isoscalar $1^+$ bound state at $3823.058$ MeV, an isoscalar $1^+$ resonance at $(4102.326 - i\,83.044)$ MeV, and a negative-parity isoscalar resonance at $(4089.67 - i\,41.88)$ MeV, the last emerging as a $P$-wave mixture rather than a molecule. The authors note that although experiment has tentatively assigned $I = 0$ to $T_{cc}(3875)^+$, they regard the isovector assignment as favorable because their isovector $DD^*$ pole lands essentially on top of the observed state.

Load-bearing premise

The calculation assumes that two-body channels with isospin-averaged masses — $DD$, $DD^*$, and $D^*D^*$ — are enough to fix the position of a pole whose binding energy is only $0.03$ MeV, even though the open $D^0D^0\pi^+$ channel and the $D^0$/$D^+$ mass difference are the same size as that binding.

Editorial extensions

If this is right

If the calculation is right, $T_{cc}(3875)^+$ is predominantly a $DD^*$ molecule in the isovector channel, with a dominant coupling to $DD^*$ and a negligible coupling to $D^*D^*$.
The same dynamics predicts an isoscalar $1^+$ bound state near $3823$ MeV that couples most strongly to $D^*D^*$, and an isoscalar $1^+$ resonance near $4102$ MeV with a width of about $166$ MeV.
A negative-parity isoscalar tetraquark resonance near $4090$ MeV is predicted, formed from $P$-wave mixing rather than as a two-meson molecule.
The $T_{cc}(3875)^+$ pole remains a bound state for the reduced cutoff $\Lambda_0$ between $600$ and $700$ MeV; at the softer value of $500$ MeV it degenerates into a cusp, so the prediction carries a definite parameter window.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the predicted binding energy is only $0.033$ MeV, comparable to the $D^0$–$D^+$ mass difference, including the open $D^0D^0\pi^+$ channel and isospin breaking could move the pole into the complex plane or turn it into a cusp; the paper itself remarks that adding a $DD\pi$ channel would move the bound state into the complex plane.
If future data assign $T_{cc}(3875)^+$ to $I = 0$, the isovector identification fails, and the most natural alternative in this framework, the $3823$ MeV isoscalar state, is too deeply bound to match the observed narrow near-threshold state, putting the model's association in tension.
The fixed-coupling strategy suggests a testable extension: apply the same no-fit machinery to other near-threshold doubly heavy candidates and check whether their predicted poles and partner states appear in $D^{(*)}D^{(*)}$ invariant-mass spectra.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, this is a serious, internally coherent coupled-channel calculation: the Bonn-Jülich BbS formalism is applied to the DD/DD*/D*D* system with couplings fixed from external data and a universal reduced cutoff, not fitted to the Tcc. The three additional J=1 states — the isoscalar bound state near 3823 MeV, the isoscalar D*D* resonance near 4102 MeV, and the negative-parity isoscalar resonance near 4090 MeV — are genuinely new predictions from this framework, and the Λ0 dependence is honestly reported. Second, the central claim is fragile: the Tcc(3875)+ identification rests on a pole at 3875.677 MeV, quoted as 0.0328 MeV below the isospin-averaged DD* threshold. With physical meson masses, the D0D*+ threshold is 3875.10 MeV, so the pole sits 0.58 MeV above the open channel. That is more than an order of magnitude on the wrong side of the threshold that defines the experimental state. In S-wave, a state 0.6 MeV above threshold gets a width of order an MeV — far above the measured (410±164) keV. So the supposed bound state is, in the physical channel, a resonance with the wrong width. The authors acknowledge in Sec. III.B that adding a DDπ three-body channel would move the bound state into the complex plane; but the two-body mass splitting already does that. This is not a small correction for a state bound by a tenth of an MeV.

The paper does what it does honestly: the parameters are not tuned to Tcc, the pole is not circular, and the uncertainty study is useful. But the title promises a production mechanism, and the calculation delivers pole positions and couplings, not cross sections or yields. There are also internal inconsistencies: the text quotes the 4102 state width as 93.044 MeV and the negative-parity width as 93.85 MeV, while Table III gives the corresponding imaginary parts as 83.044 and 41.88 MeV (the latter implying 83.76 MeV width). These are exactly the kind of errors a careful referee should catch. The isovector assignment also conflicts with the tentative experimental I=0, and the paper only notes this in passing.

Verdict: the model is a plausible addition to the molecular-Tcc literature, and the three extra states are searchable predictions. But the headline identification does not survive a physical-threshold sanity check. With mass splittings and a three-body width estimate, the paper could be made convincing. As it stands, it deserves a serious referee but not acceptance without revision. A hadron spectroscopist would get value from the formalism and the predictions; I would not cite the Tcc claim as is.

Referee Report

4 major / 6 minor

Summary. The paper presents a coupled-channel Blankenbecler-Sugar (BbS) calculation of S- and P-wave DD, DD*, and D*D* scattering with kernels built from effective Lagrangians respecting heavy-quark, chiral, SU(3), and hidden local symmetries. The authors report four J=1 tetraquark poles: an isoscalar axial-vector bound state at 3823 MeV, an isoscalar axial-vector resonance near 4102 MeV, an isovector axial-vector state at 3875.677 MeV, and an isoscalar negative-parity resonance near 4089.67 - i41.88 MeV. They identify the isovector state with the LHCb Tcc(3875)+ and analyze its coupling strengths and the dependence on the reduced cutoff Lambda0.

Significance. If the central identification were robust, the paper would provide a parameter-non-fitted dynamical origin for the Tcc and would predict several additional doubly charmed states, which is of clear interest for the hadron-exotics community. The calculation is internally coherent, and it is commendable that the Tcc pole mass is not an input: the couplings are fixed by external data or by the authors' earlier dispersion-relation analysis, and the universal reduced cutoff Lambda0=600 MeV is not tuned to the Tcc. The framework has also been applied successfully to other hadronic systems by this group. However, the near-threshold isovector state lies only 0.033 MeV below the isospin-averaged DD* threshold, and the paper's approximations of exact isospin and isospin-averaged masses are not controlled at this scale; the physical D0D*+ threshold is actually 0.58 MeV above the pole. This issue, together with internal inconsistencies in the reported pole positions, calls into question the main quantitative claims.

major comments (4)

[Sec. III.C, Table III] The identification of the I=1, 1+ pole at sqrt(s_R)=3875.677 MeV with Tcc(3875)+ is not supported by the quoted threshold. The paper states a binding energy of 0.0328 MeV relative to the isospin-averaged DD* threshold at 3875.81 MeV, but the physical D0D*+ threshold is 3875.10 MeV using PDG masses, so the pole is 0.58 MeV above the only open two-body channel. This excess is 18 times the quoted binding energy and lies on the wrong side of the threshold that defines the experimental state. With S-wave phase space at this excess, k ~ 34 MeV, and the large residue g_DD* = 3.276 GeV in Table III, the resulting two-body width is of order several MeV, far above the measured (410 +/- 164) keV. The paper's own comment in Sec. III.B that adding a DDpi three-body channel would move a bound state into the complex plane applies already to the two-body isospin mass splitting, which is neglected here. The real-axis bound-state identification therefore rests on an uncontrolled approximation.
[Title and Abstract; Sec. I and Sec. IV] The paper advertises a 'production mechanism' for doubly charmed tetraquark mesons, but it does not compute any production observable: there are no cross sections, yields, or event distributions, and no production process is specified. The content is a pole-position and coupling-strength analysis of the scattering amplitudes. The title and abstract should be revised to state that the paper studies the dynamical generation and pole content of Tcc states, or the authors should add production observables such as invariant-mass distributions in a concrete production reaction.
[Sec. III.C and Table III] There are internal inconsistencies in the central numerical output. In Sec. III.C the positive-parity isoscalar resonance is quoted as sqrt(s_R)=(4102.326 - i93.044) MeV, whereas Table III lists (4102.326 - i83.044) MeV; the corresponding full widths differ by 20 MeV. For the negative-parity state, the text gives a total width of 93.85 MeV, while Table III's pole at 4089.67 - i41.88 MeV corresponds to a width of 83.76 MeV. These discrepancies show that the pole positions need to be re-derived and reported consistently before the quantitative claims can be trusted.
[Sec. III.C] The assignment of the near-threshold state to the isovector channel conflicts with the tentative experimental quantum numbers: the LHCb analysis favors I(J^P)=0(1+) for Tcc(3875)+, while the present calculation places the isoscalar axial-vector states at 3823 MeV and 4102 MeV, neither of which is near the observed mass. The paper should explain why the tentative I=0 assignment is disfavored, or present the isovector identification as a testable prediction rather than a direct identification with the observed state.

minor comments (6)

[Table II] The caption of Table II states 'isoscalar (I = 0)', but the table lists isospin factors appropriate to the isovector channel; the caption should read 'isovector (I = 1)'.
[Sec. III.C, text before Table III] The text says the pole positions and couplings are 'listed in Table I', but the relevant table is Table III; this cross-reference should be corrected.
[Eq. (9)] Equation (9) is difficult to read because the logarithmic subtraction term and the absolute-value structure are garbled; please rewrite this expression with a clear notation for the principal value and the on-shell subtraction.
[Sec. II and elsewhere] The spelling 'Blanckenbecler-Sugar' appears in Sec. II; the correct spelling is 'Blankenbecler-Sugar' as used in the references.
[Fig. 1] Figure 1 would be more informative if the DD, DD*, and D*D* thresholds were drawn as horizontal lines, since the near-threshold character of the Tcc candidate is central to the paper.
[Abstract and Sec. IV] The phrase 'remains stable' for the Tcc(3875) state is ambiguous because the pole is on the real axis only within the isospin-averaged truncation; 'remains bound' or 'remains robust in the chosen truncation' would be more precise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Tcc pole is dynamically generated from externally fixed couplings and a non-fitted cutoff, not from its own input.

full rationale

The derivation chain does not reduce to its inputs. The paper explicitly states that no fitting to Tcc data is performed: 'we do not fit the experimental data by adjusting parameters such as coupling constants and reduced cutoff masses' (Sec. III) and 'this value is not fitted to the existing data on Tcc(3875)' (Sec. II). The coupling constants are fixed by external decay or form-factor data (g=0.59 from D*+→D0π+, beta=0.9 from vector-meson dominance, lambda=0.56 GeV^-1 from B→K* form factors) or inherited from the authors' earlier dispersion-relation analysis [88], which predates the Tcc observation and therefore cannot have the Tcc pole as an input. The reduced cutoff Λ0=600 MeV is a universal hadron-size parameter rather than a fit to the target state. The central I=1(1+) pole at 3875.677 MeV emerges from solving the coupled BbS equations, and nothing in the kernel is parametrized by the pole position. The acknowledged limitations—the omitted DDπ three-body channel and the use of isospin-averaged masses (Sec. III.B: 'Had we considered three-body channels such as the DDπ channel, the bound state would have moved to the complex plane')—are correctness and robustness concerns, not circularity. Likewise, the internal inconsistency between Table III and the text for the 4102 state width is a correctness issue, not a circular step. Self-citations to previous applications of the formalism are validations, not definitional inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model rests on a large set of phenomenological inputs: the universal reduced cutoff, coupling constants from external data and from the authors' previous dispersion analysis, and symmetry assumptions. The Tcc mass itself is not among the inputs, but all parameters were partly shaped by the same group's earlier applications to near-threshold states such as D_s0*(2317).

free parameters (6)

Reduced cutoff mass Lambda0 = 600 MeV central; 500-700 MeV scanned
Controls the hadronic form factor scale; the central Tcc pole becomes a cusp at 500 MeV, so the result depends sensitively on this parameter.
D*Dpi coupling g = 0.59
Fixed from the partial width of D*+ -> D0 pi+, Eq. (22).
Vector coupling beta = 0.9
Fixed by vector meson dominance.
Tensor coupling lambda = 0.56 GeV^-1
Fixed phenomenologically by the B -> K* transition form factor at high q^2.
Scalar and vector charmed-meson couplings = g_sigmaDD=1.50, g_sigmaD*D*=5.21, g_rhoDD=1.65, g_rhoD*D*=6.47, g_rhoDD*=5.8
Adopted from the authors' earlier dispersion-relation analysis in Ref. [88] and from the KSRF relation.
Form factor power n = 2
Chosen by hand; the authors state the results are not sensitive to this choice.

assumptions (5)

domain assumption Heavy quark limit m_Q -> infinity with superfield normalization
Underlies the effective vertices in Eqs. (11)-(14); corrections of order Lambda_QCD/m_c are not estimated.
domain assumption Blankenbecler-Sugar reduction replaces the four-dimensional two-body propagator by the three-dimensional form in Eqs. (4)-(6)
This is a standard but uncontrolled approximation for near-threshold poles; no comparison with the full Bethe-Salpeter solution is given.
ad hoc to paper The coupled-channel space {DD, DD*, D*D*} with exact isospin and isospin-averaged masses is complete
The open three-body D0D0pi+ channel and D0/D+ mass splitting are omitted; the paper itself notes that adding DDpi would move the isoscalar bound state into the complex plane.
ad hoc to paper A universal reduced cutoff mass Lambda0 = Lambda - m_ex = 600 MeV applies to every vertex
The choice is motivated by compactness of heavier hadrons and prior phenomenological success, not derived independently; the central Tcc pole becomes a cusp at 500 MeV.
domain assumption s-channel pole diagrams are excluded
The authors state this in Section II; it is necessary for their dynamical-generation interpretation but is a modeling choice.

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Cite this review

Pith. "Pith review of Production mechanism of doubly charmed exotic mesons $T_{cc}$." pith.science (2026). https://pith.science/paper/GHLJ7F6P

@misc{pith2026250709191,
  author       = {Pith},
  title        = {Pith review of: Production mechanism of doubly charmed exotic mesons $T_cc$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GHLJ7F6P}},
  note         = {Machine review of arXiv:2507.09191}
}

abstract

We investigate the production mechanism for doubly charmed tetraquark mesons within a coupled-channel formalism. The two-body Feynman kernel amplitudes are constructed using effective Lagrangians that respect heavy quark symmetry, chiral symmetry, SU(3) flavor symmetry, and hidden local symmetry. The fully off-shell coupled scattering equations are solved within the Blankenbecler-Sugar (BbS) reduction scheme. We find three positive-parity and one negative-parity tetraquark states with total spin $J=1$. Among them, two positive-parity states appear as bound states in the isoscalar and isovector $DD^*$ channels, while another appears as a resonance in the $D^*D^*$ channel. A negative-parity resonance is also predicted in the isoscalar channel. We analyze the coupling strengths of these tetraquark states to various channels. The dependence of the results on the reduced cutoff mass $\Lambda_0$ is examined. The most significant tetraquark state remains stable within the range of $\Lambda_0=(600-700)$ MeV.

Figures

Figures reproduced from arXiv: 2507.09191 by the authors.

**Figure 2.** FIG. 2. Graphical representation of the coupled Bethe-Salpeter integral scattering equation. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: FIG. 4. Scalar kernel amplitudes as functions of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. Axial-vector kernel amplitudes as functions of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. Pseudoscalar kernel amplitudes as functions of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7. Vector kernel amplitudes as functions of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8. Single-channel transition amplitudes for elastic [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: FIG. 9. Single-channel transition amplitudes for elastic [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: FIG. 10. Transition amplitudes for the elastic [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

**Figure 11.** Figure 11: FIG. 11. Transition amplitudes for the elastic [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

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Reference graph

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4, we present the numerical results for the partial-wave kernel amplitudes V J ij for the isoscalar-scalar channel (I = 0, J = 0)

Positive parity In Fig. 4, we present the numerical results for the partial-wave kernel amplitudes V J ij for the isoscalar-scalar channel (I = 0, J = 0). Since the contributions from partial-wave amplitudes higher than the P -wave turn out to be negligible, we focus on the scalar (S-wave) kernel amplitudes for the positive-parity channels. Note that the ...
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Negative parity 3600 3700 3800 3900 4000 4100 4200√s [MeV] −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 Vi→j[I(JP ) = 0(0−)](3P0) ×103 DD → DD DD∗ → DD∗ D∗D∗ → D∗D∗ DD → DD∗ DD → D∗D∗ DD∗ → D∗D∗ 3600 3700 3800 3900 4000 4100 4200√s [MeV] −10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 Vi→j[I(JP ) = 1(0−)](3P0) ×102 DD→DD DD∗→DD∗ D∗D∗→D∗D∗ DD→DD∗ DD→D∗D∗ DD∗→D∗D∗ FIG. 6. Pseudoscal...
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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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4, we present the numerical results for the partial-wave kernel amplitudes V J ij for the isoscalar-scalar channel (I = 0, J = 0)

Positive parity In Fig. 4, we present the numerical results for the partial-wave kernel amplitudes V J ij for the isoscalar-scalar channel (I = 0, J = 0). Since the contributions from partial-wave amplitudes higher than the P -wave turn out to be negligible, we focus on the scalar (S-wave) kernel amplitudes for the positive-parity channels. Note that the ...

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Negative parity 3600 3700 3800 3900 4000 4100 4200√s [MeV] −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 Vi→j[I(JP ) = 0(0−)](3P0) ×103 DD → DD DD∗ → DD∗ D∗D∗ → D∗D∗ DD → DD∗ DD → D∗D∗ DD∗ → D∗D∗ 3600 3700 3800 3900 4000 4100 4200√s [MeV] −10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 Vi→j[I(JP ) = 1(0−)](3P0) ×102 DD→DD DD∗→DD∗ D∗D∗→D∗D∗ DD→DD∗ DD→D∗D∗ DD∗→D∗D∗ FIG. 6. Pseudoscal...

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Positive parity 3860 3865 3870 3875 3880 3885 3890√s [MeV] −6 −4 −2 0 2 4 6 Ti→j[I(JP ) = 0(1+)](3S1) ×104 ReTDD∗ ImTDD∗ 3860 3865 3870 3875 3880 3885√s [MeV] −6 −4 −2 0 2 4 6 Ti→j[I(JP ) = 1(1+)](3S1) ×104 ReTDD∗ ImTDD∗ FIG. 8. Single-channel transition amplitudes for elastic DD∗ scattering in the 3S1 channels with isospin I = 0 (left panel) and I = 1 (r...

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7, the kernel amplitudes for the 1P1 channels are mostly attractive

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