Near-threshold resonances in $e^+e^-$ annihilation

A.E. Bondar; A.I. Milstein; S.G. Salnikov

REVIEW 5 major objections 7 minor 179 references

Near-threshold resonances in $e^+e^-$ annihilation

T0 review · 5 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Final-state interactions between slow hadrons, not new exotic particles, explain the near-threshold peaks and dips seen in $e^+e^-$ pair-production cross sections.

desk verdict A readable review of the Novosibirsk FSI program, but the 'no new particles' conclusion is stronger than the fits can support. read the letter →

arxiv 2608.08769 v1 pith:XHENVMRQ submitted 2026-08-09 hep-ph hep-ex

S.G. Salnikov , A.E. Bondar , A.I. Milstein This is my paper · ORCID

classification hep-phhep-ex

keywords final-stateinteractionsnear-thresholdresonancese+e-annihilationhadronpairproductionSchrödingerequationcoupledchannelselectromagneticformfactorsexoticcandidates

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

This review argues that the nontrivial energy dependence of $e^+e^-$ annihilation into hadron pairs near threshold—sharp rises, resonance-like peaks, dips, and form-factor anomalies—is, in the vast majority of cases, produced by the strong interaction between the slow final-state hadrons rather than by new particles. The paper shows that one Schrödinger-equation treatment, with the production amplitude factored into an energy-independent short-distance part and a final-state enhancement factor, fits measured cross sections and form-factor ratios for $p\bar p$, $n\bar n$, $\Lambda\bar\Lambda$, $\Lambda_c\bar\Lambda_c$, $D^{(*)}\bar D^{(*)}$, and $B^{(*)}\bar B^{(*)}$ production with $\chi^2/N_{\rm df}$ between 1.2 and 1.6. It also predicts bound states of $\Lambda\bar\Lambda$ and $\Lambda_c\bar\Lambda_c$ below their thresholds. If this is right, many claimed exotic resonances near hadron-pair thresholds are reinterpreted as kinematic manifestations of hadron-hadron forces.

What carries the argument

The carrying object is the final-state enhancement factor $F_L = \frac{(2L+1)!!}{k^L L!}\,\frac{\partial^L \psi_L^{(R)}(0)}{\partial r^L}$, which multiplies the bare production amplitude for a pair in partial wave $L$; the measured cross section is proportional to $k^{2L+1}|F_L|^2$. Here $\psi_L^{(R)}(r)$ is the regular radial wave function of the nonrelativistic hadron pair obtained by solving the Schrödinger equation in a potential describing their interaction, and its value or derivative at $r=0$ captures the probability that the interacting pair is at short distances where it was formed. The paper computes this factor for single channels, optical potentials, coupled channels with nearby thresholds, tensor-force mixing of $S$ and $D$ waves, and Coulomb corrections, and uses it to convert fitted potential parameters into cross sections and form-factor ratios.

What would settle it

A high-statistics measurement in a channel where the predicted FSI cross section from the fitted potentials is smooth, such as a narrowly peaked structure in $e^+e^-\to \Lambda\bar\Lambda$ or $e^+e^-\to B\bar B$ that would require an energy-dependent short-distance amplitude or an additional pole, would refute the claim that all near-threshold features are final-state effects. Concretely, the model predicts $\Lambda\bar\Lambda$ and $\Lambda_c\bar\Lambda_c$ bound states near $-30$ MeV and $-40$ MeV below their thresholds; if high-precision data exclude narrow structures at those energies, the bound-state predictions fail.

Watch

Extended reading notes

Core claim

The central claim is that the observed near-threshold structures in $e^+e^-$ annihilation into hadron pairs—including the rapid rise of $\sigma(e^+e^-\to p\bar p)$ and $n\bar n$, the $\Lambda\bar\Lambda$ and $\Lambda_c\bar\Lambda_c$ cross-section enhancements, the dips in $D^{(*)}\bar D^{(*)}$ and $B^{(*)}\bar B^{(*)}$ production, and the deviations of $|G_E/G_M|$ from unity—are all consequences of final-state interactions calculable from the Schrödinger equation. The paper exhibits a single framework in which the hadron pair's wave function at the origin, or its $L$-th derivative, multiplies an energy-independent bare amplitude, and with simple rectangular-well potentials, optical potentials for annihilation, Coulomb forces, tensor forces, and multichannel coupling it reproduces the data with $\chi^2/N_{\rm df}$ from 1.19 to 1.57. Consequently the paper concludes that it is not necessary to assume unknown intermediate particles to explain these features.

Load-bearing premise

The short-distance quark-production amplitude is treated as a constant, apart from an empirical dipole form factor, in the final-state integral, so all near-threshold energy dependence is attributed to the hadronic wave function at the origin; if the bare amplitude carries additional energy dependence, for example from charmonium or bottomonium poles, the fitted potentials would absorb it and the explanation would become curve fitting.

Editorial extensions

If this is right

Near-threshold peaks in $e^+e^-$ cross sections, including the $\psi(3770)$ and $\Upsilon(4S)$ bumps, can arise from virtual levels in the interacting meson pairs, without treating them purely as $c\bar c$ or $b\bar b$ quarkonium states.
The model predicts a $\Lambda\bar\Lambda$ bound state near $E_0\approx -30$ MeV and a $\Lambda_c\bar\Lambda_c$ bound state about 40 MeV below threshold; both should show up as sharp energy dependences in other production and decay processes.
Isospin-violating final-state interactions in $B^{(*)}\bar B^{(*)}$ production can shift the measured $B^+$-$B^0$ mass difference by up to $\delta M\sim 0.4$ MeV, so FSI must be included in precision mass measurements.
Inelastic channels such as $e^+e^-\to 6\pi$ and $K^+K^-\pi^+\pi^-$ inherit a sharp drop at the $N\bar N$ threshold from virtual $N\bar N$ pairs in the intermediate state, and the fitted probability for an $I=1$ $N\bar N$ pair to annihilate into six pions (62%) is close to the known annihilation fraction (56%).

Reading between the lines

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

If the FSI explanation is universal, many resonances currently classified as exotic hadron candidates near two-body thresholds should be re-examined as threshold cusps or virtual-level enhancements; the burden of proof shifts to finding a peak whose shape cannot be produced by any reasonable hadronic potential.
The same $F_L$ enhancement applies to any production process with a short-distance source and slow outgoing hadrons, so the framework could be transferred to heavy-meson decays, two-photon collisions, and antiproton-proton annihilation, where similar threshold anomalies are observed.
A decisive test would be measuring the exclusive charged-to-neutral $B^{(*)}\bar B^{(*)}$ ratios above $\Upsilon(4S)$; the three parameter sets in the paper give different predictions for those ratios, so future data could select one set and rule out the others.
The fitted well parameters could be compared with first-principles strong-interaction calculations for the same channels; since the framework claims insensitivity to potential details, agreement would support the mechanism, while large discrepancies would indicate missing energy-dependent short-distance physics.

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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

Let me give you the short version: this is a review of the authors' own final-state-interaction program, not a new research result. The useful part is the collection: the framework is coherent, the fits cover a lot of channels, and the chi2 values are decent. The soft part is the punchline. They claim FSI explains virtually all cases and that no new particles are needed, but the model is not identifiable against the alternative of energy dependence in the production vertex. The stress-test note is right. The dipole form factor in Eq. (28) with s0 = 1 GeV2 is already strongly energy-dependent in the fitted region, so the bare amplitude is not smooth. With potentials fitted to the same data, a virtual level can mimic a resonance pole, and the predicted bound states below threshold are inferred from potentials fitted to the same cross sections, so they are not independent checks.

Credit where due: the Schrodinger-equation approach with rectangular wells is transparent; the treatment of the Lambda_c Lambda_c process with Coulomb and tensor forces is genuinely nontrivial and describes the cross section and GE/GM ratio reasonably well; and the paper does not hide the fact that some data are excluded (Belle Lambda_c, older pbarp data). As a review it is well organized and will be useful for students coming into the area.

The soft spots are real but not fatal. No parameter uncertainties or theory bands are given, so you cannot judge how rigid the predictions are. The data exclusions are mentioned but not analyzed in detail. Reinterpreting psi(3770) and Upsilon(4S) as virtual levels in D and B meson channels is a provocative position, but it is not a disproof of quarkonium poles; it is a choice of how to distribute the energy dependence between the production vertex and the final-state interaction. The conclusion goes beyond what the current fits can establish.

Who is this for? Experimentalists and students working on near-threshold hadroproduction who want a compact summary of the Novosibirsk approach. It is not a neutral review; it is an advocacy piece for their own program. Still, it is competent and the fits are worth seeing.

Recommendation: send it to peer review. The identifiability issue should be a major referee concern, and the claim about no new particles should be substantially softened, but the paper deserves a serious referee rather than a desk rejection.

Referee Report

5 major / 7 minor

Summary. The paper presents a phenomenological framework for final-state interactions (FSI) in hadronic pair production near threshold, based on solving the Schrödinger equation with simple potential wells and expressing production amplitudes through the wave function at the origin. The framework is applied to e+e- -> Lambda Lambda, Lambda_c Lambda_c, pbar p, nbar n, to multimeson processes via NbarN intermediate states, and to D(*)Dbar(*) and B(*)Bbar(*). The authors report good chi2/Ndf values (1.18-1.57) and claim that FSI can explain the observed near-threshold structures without invoking new particles. They also predict bound states of Lambda-Lambda_bar and Lambda_c-Lambda_c_bar and reproduce the psi(3770) and Upsilon(4S) bumps as virtual levels in meson-meson systems.

Significance. The paper is valuable as a coherent, broad phenomenological synthesis. Its strengths include a unified treatment of Coulomb, tensor, isospin-breaking, and multichannel effects; simultaneous fits to cross sections and form-factor ratios; and explicit, falsifiable predictions such as the exclusive charged/neutral B(*)Bbar(*) ratios R_ij. If the central 'no new particles' claim is to be sustained, however, the statistical identifiability of the production vertex versus the FSI wave function must be established; the present manuscript does not yet do so. The reported chi2 values are encouraging but not conclusive.

major comments (5)

[Sec. II A and IV, Eqs. (4), (27), (28)] The load-bearing assumption is that the bare production amplitude is energy-independent up to a fixed dipole form factor FD(s)=1/(1-s/s0)^2 with s0=1 GeV^2. This assumption forces all energy dependence near threshold into the FSI enhancement factor. Since the potential parameters are fitted to the same cross sections, the good chi2/Ndf values (e.g., 376/29 in Sec. IV) only show that the model is flexible enough to absorb the data; they do not discriminate FSI from energy dependence in the production vertex. The manuscript needs a sensitivity study in s0 and, ideally, a test in which an explicit resonance pole is added to the bare amplitude (e.g., a charmonium pole in the D(*)Dbar(*) channel) and compared with the FSI-only fit using a model-selection criterion.
[Sec. VIII and IX, virtual-level description of psi(3770) and Upsilon(4S)] The claim that these resonances arise as virtual levels in the D- and B-meson potentials is presented as support for the no-new-particles conclusion. However, the potentials are fitted to the cross-section data containing those very resonances, so the 'reproduction' is not independent evidence against a quarkonium pole. An identifiability check is required: for instance, compare the FSI-only model with a model containing an explicit charmonium/bottomonium pole and an energy-independent (or weakly energy-dependent) production vertex, using an information criterion or a chi2 difference test. Without such a test, the central conclusion overreaches.
[Sec. V and VI, data selection] The Belle Lambda_c Lambda_c data are excluded because they 'contradict' BESIII data, and 'some results from older experiments' are excluded in the NbarN fits because they 'clearly contradict' newer data. The exclusion criteria are not quantified, and no fit including the excluded points is shown. Since the central claim rests on the quality of the quoted chi2 values, the selection must be documented transparently: list the excluded data sets, give the quantitative conflict criterion, and show the effect on the fit parameters and chi2.
[Throughout Secs. IV-IX, parameter uncertainties and theory bands] No parameter uncertainties or theory bands are reported for any fit; only chi2/Ndf values are quoted (e.g., 376/29, 105.6/89, 397/338, 50.2/32). Without uncertainties on V0, a, Uij, g, etc., it is impossible to judge whether the predicted bound states (e.g., Lambda-Lambda_bar at E0 about -30 MeV and Lambda_c-Lambda_c_bar at sqrt(s) about 4530 MeV) are robust or dominated by the arbitrary choice of rectangular-well parametrization. The authors should provide at least a profile-likelihood or bootstrap estimate for the key parameters and show representative theory bands in the figures.
[Sec. IV after Eq. (17) and Sec. V after Eq. (40), bound-state predictions] The bound states are presented as 'predictions' although they are computed from potentials fitted to the same data that the model is said to explain. This is not circular in the logical sense, but it is a model extrapolation below threshold rather than an independent prediction. The wording should distinguish parameter-derived consequences from independent predictions, and the claims should be tested against observables not used in the fit, such as pbar p -> Lambda Lambda_bar scattering or line shapes in other final states.

minor comments (7)

[Eq. (28)] There is a typo in the text: 'We fixed the parameters 0 equal to 1 GeV2' should be 'We fixed the parameter s0 equal to 1 GeV^2'.
[Figs. 4 and 5 captions] In both captions, sigma(1) and sigma(2) are both described as dashed lines, which makes the plots impossible to read; the line styles in the caption should match those in the figure.
[Sec. II C] Internal references such as 'Fig. II C' should be replaced with the actual figure numbers.
[Sec. VI] The section refers to Ref. [147] for all details of the NbarN potential and fit; for a self-contained review, at least the potential parametrization and the fitted parameter values should be summarized in a table or in an appendix.
[Sec. V, after Eq. (43)] The regularization parameter b=10 fm^-1 is said to give results 'practically independent' of b, but no supporting test is shown; a brief scan over b or a statement of the resulting variation would justify this claim.
[Fig. 16 and reference list] The caption cites 'Dong2020' without a corresponding entry in the reference list; the intended reference appears to be [168], which should be cited explicitly.
[Sec. VII] The text contains typographical errors such as 'multi-mezonic states' and 'mison'; these should be corrected in a final proofreading pass.

Circularity Check

3 steps flagged · score 6.0 of 10

Fitted potentials are re-labeled as predictions: bound states, ψ(3770)/Υ(4S) virtual levels, and Nijmegen partial cross sections are all outcomes of the same fitted parameters.

fitted input called prediction [Sec. IV (e+e−→ΛΛbar), paragraph after Eq. (31); analogous passage in Sec. V]
"As a result, the following parameter values were found: V0 = 584 MeV, a = 0.45 fm, g = 237 (these results were presented in our paper [125]). The corresponding value is χ2/Ndf = 376/29 = 1.3 ... Our model predicts the existence of a bound state of Λ and ¯Λ with a binding energy of E0 ≈ −30 MeV. ... Our model predicts the existence of a bound state of Λc and ¯Λc at an energy of approximately 40 MeV below the threshold, which corresponds to √s≈4530 MeV."

The parameters V0 and a are free parameters obtained by minimizing χ2 against the same e+e−→ΛΛbar cross-section data that the model is said to explain (σ in Eq. (31) uses F0 from Eq. (17)). For the square-well potential, the bound-state energy is a single-valued function of (V0,a), so 'predicts a bound state' is a restatement of the fitted potential in pole language, not a test against new data. The same structure repeats in Sec. V: the Table I well depths/radii are fitted to the BESIII σ(e+e−→ΛcΛcbar) and |GE/GM| data, and the 'predicted' bound state about 40 MeV below threshold is the bound pole of that fitted potential. Since the supporting 'no new particles' conclusion is a universal negative, this fit-derived pole cannot independently rule out other interpretations.
fitted input called prediction [Sec. VIII, paragraph after Fig. 15; Sec. IX, paragraph after Fig. 16]
"In addition, raw measurement results for the cross section of the e+e−→D¯D process at BESIII in the region of the ψ(3770) resonance were presented in the dissertation paper [155]... All of the above measurements were used by us to determine the parameters of the interaction potentials in the D(∗) meson system (see Ref. [154] and Ref. [156]). ... The ψ(3770) resonance in the D¯D production cross section in our approach arises due to the presence of a virtual level in the system of interacting D-mesons in our multichannel problem."

The ψ(3770) bump is part of the fitted dataset: the raw BESIII ψ(3770)-region data are explicitly included among 'all of the above measurements' used to fix the potential parameters. Therefore 'the resonance arises due to a virtual level' is a re-description of the same fitted bump in FSI language, not an independent explanation; the fit would equally well absorb the bump into the potential parameters. The same holds for Υ(4S) in Sec. IX, which is also fitted and then declared to arise from a virtual level in the B-meson potential. Both passages are offered as support for the conclusion that no new particles are needed, but they only show that a flexible fitted potential can mimic a resonance.

1 more flagged steps

fitted input called prediction [Sec. VI, comparison with Nijmegen partial cross sections, around Fig. 9]
"We select the parameters of our model to best describe the available experimental data obtained in the study of nucleon-antinucleon scattering and the production of nucleon-antinucleon pairs in e+e− annihilation. First, we use the results of the analysis of nucleon-antinucleon scattering data performed by the Nijmegen group [14], which determined the partial cross sections... The optimal parameters of our model, obtained by minimizing χ2, are given in Ref.[147]..."

The Nijmegen partial-wave cross sections were among the inputs used to fix the model parameters ('First, we use the results of the analysis...'), so Fig. 9's agreement is a check that the fitted model reproduces the fitted input, not a prediction. The paper even notes that the Nijmegen partial cross sections are derived from the experimental scattering data and that other models fitting the same data give different partial cross sections, so the comparison has no independent falsifying power for the central claim. This is a mild form of fitted-input-called-prediction, but it is how Sec. VI supports the model's ability to describe NbarN scattering.

full rationale

The core Watson-Migdal factorization (Eqs. (4) and (27)) is a standard, self-contained derivation: the energy-independent production constant g plus a fixed dipole form factor FD(s) make the model assign all near-threshold energy dependence to the FSI wave function at the origin. That is a legitimate modeling assumption, not by itself circular, and the reported χ2/Ndf values show genuine descriptive quality against external data. The numerous self-citations (Refs. [125,140,141,145-147,149-151,154,156,166,167]) are mostly normal references to the authors' own earlier calculations; they do not invoke a uniqueness theorem and are not the main circularity. The circularity is concentrated in the paper's advertised 'predictions': the ΛΛbar and ΛcΛcbar bound states are poles of potentials fitted to the very cross sections whose features the model claims to explain; ψ(3770) and Υ(4S) are fitted resonance bumps re-described as virtual levels of the fitted D- and B-meson potentials; and the agreement with Nijmegen partial cross sections is a comparison against data used in the parameter selection. In each case, the 'prediction' is statistically forced by construction, so the universal conclusion that 'it is not necessary to assume the existence of any new, unknown particles' is not independently established by these steps. The deeper question of whether the production vertex could carry energy dependence (e.g., charmonium poles) is an identifiability/correctness risk rather than a circularity, so it is not scored higher than 6.

Assumptions & free parameters 17 free parameters · 9 assumptions · 3 invented entities

The central examples require roughly 15 to 20 fitted parameters (potential depths and radii, production constants, inelastic coefficients). The paper's headline 'explanations' are fits to the same data, and the bound-state predictions are outputs of those fits. No fitted parameter carries an uncertainty, and several parameter sets live only in earlier papers.

free parameters (17)

Lambda-Lambda potential depth V0 = 584 MeV
Fitted to e+e- -> Lambda Lambda-bar cross-section data (DM2, BaBar, BESIII) in Sec IV; from Ref. [125].
Lambda-Lambda potential radius a = 0.45 fm
Fitted together with V0 in Sec IV.
Lambda-Lambda production constant g = 237
Fitted normalization of the cross section, Sec IV.
Dipole form factor scale s0 = 1 GeV^2
Hand-fixed in Eq. (28) and used for all baryon processes ('We fixed the parameter s0 equal to 1 GeV^2').
Lambda_c S-wave potential US and radius aS = -1180 MeV, 0.98 fm
Fitted to BESIII e+e- -> Lambda_c Lambda_c-bar cross section and |GE/GM|, Table I.
Lambda_c D-wave potential UD and radius aD = -170 MeV, 1.93 fm
Table I, fitted as above.
Lambda_c tensor potential UT and radius aT = -64 MeV, 0.75 fm
Table I, fitted as above.
Lambda_c production constant GS = 155.4
Table I, overall normalization.
Tensor regularization b = 10 fm^-1
Chosen for numerical convenience; authors state results are insensitive to b (Eq. (43)).
NbarN potential parameters = Given in Ref. [147]
Depths and radii for pion exchange, isoscalar/isovector wells, imaginary parts; fitted to pbarp scattering and e+e- -> pbarp/n barn data (Sec VI).
D-meson potential parameters = Given in Refs. [154, 156]
Isoscalar and isovector well parameters and six-channel production constants; fitted to BaBar, Belle, CLEO, BESIII data (Sec VIII).
B-meson potential parameters = Three sets in Ref. [167]
Fitted to total e+e- -> B(*) Bbar(*) cross sections; three variants give different exclusive predictions (Sec IX).
Inelastic coefficients for e+e- -> 3(pi+pi-) = A=0.12, B=3.2e-3 nb/MeV, C=0.9 nb
Fitted to data in Sec VII, Eq. (46).
Inelastic coefficients for e+e- -> 2(pi+pi-pi0) = A=0.5, B=4.8e-3 nb/MeV, C=3.6 nb
Fitted to data in Sec VII, Eq. (46).
Inelastic coefficients for e+e- -> K+K-pi+pi- = A=0.12, B=-6.6e-5 nb/MeV^2, C=2e-3 nb/MeV, D=4.2 nb
Fitted to data in Sec VII, Eq. (47).
Illustrative two-channel model parameters = U11=U22=-540 MeV (or -640 MeV), a=2 fm, g1=1, g2=0.5/0.3, U12 in [-50, 140] MeV
Not fitted to data; illustrative choices in Sec III.
Channel production constants g_j for D/B systems = Given in Refs. [154, 167]
Fitted and used in Eq. (24) for multichannel production.

assumptions (9)

domain assumption Electron-positron annihilation proceeds through a single virtual photon
Sec II: 'we assume that electron-positron annihilation occurs only through one virtual photon in the intermediate state'.
domain assumption Short-distance quark-production amplitude factorizes and is slowly varying, so it can be pulled out of the final-state integral as a constant
Sec II, before Sec II A: 'the factors describing quark production can be factored out of the integral as a constant'.
domain assumption The hadron pair is described by a nonrelativistic Schrödinger equation with a local potential
Sec II A, Eq. (12); used throughout.
domain assumption Rectangular-well potentials with the chosen radii and depths are sufficient to describe the final-state interaction
Sec II C and later sections; authors argue insensitivity to parametrization but do not prove it.
domain assumption Annihilation of Lambda Lambda-bar and Lambda_c Lambda_c-bar into light mesons is small, so the potentials can be taken real
Sec IV: 'the interaction potential V(r) between Lambda and Lambda-bar can be considered real'; Sec V states the same for Lambda_c.
domain assumption Tensor forces are the only source of the deviation of |GE/GM| from unity for Lambda_c
Sec V, Eqs. (39)-(41).
ad hoc to paper D_s D_s-bar mixes weakly with D(*) Dbar(*) and can be neglected
Sec VIII: 'we expect that, due to the presence of s quarks, the D_s D_sbar state will weakly mix'.
domain assumption Isovector interaction has a weak effect on B(*) Bbar(*) cross sections summed over charge states
Sec IX: 'the admixture of the isovector state arising from the B(*)-meson interaction is small'.
ad hoc to paper Psi(3770) and Upsilon(4S) can be described as virtual levels in the meson-meson channels, with the c-cbar/b-bbar component not dominating the transition matrix element
Sec VIII and Sec IX: 'the exact psi(3770) wave function contains not only the contribution of the c-cbar state but also contributions from other states'.

invented entities (3)

Lambda Lambda-bar bound state near -30 MeV independent evidence
purpose: Explains anomalies at sqrt(s)=2.2 GeV in e+e- to K+K-pi+pi-, 2(K+K-), phi K+K- and related channels (Sec IV).
The state is predicted from fitted V0 and a, but the paper cites independent data anomalies at 2.2 GeV as corroboration; no direct observation is claimed.
Lambda_c Lambda_c-bar bound state near -40 MeV (sqrt(s) ~ 4530 MeV) independent evidence
purpose: Explains near-threshold cross-section behavior and gives a search target in other processes (Sec V).
The state is a consequence of the fitted potentials in Table I; no independent detection is presented, but the predicted mass provides a falsifiable handle.
Virtual levels in D D-bar and B B-bar channels underlying psi(3770) and Upsilon(4S) independent evidence
purpose: Redescribes the established resonances as final-state interaction effects rather than pure quark-antiquark states (Secs VIII, IX).
The virtual-level interpretation is tied to the fitted meson-meson potentials; it predicts charged/neutral production ratios (Fig. 17) that can be measured.

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Cite this review

Pith. "Pith review of Near-threshold resonances in $e^+e^-$ annihilation." pith.science (2026). https://pith.science/paper/XHENVMRQ

@misc{pith2026260808769,
  author       = {Pith},
  title        = {Pith review of: Near-threshold resonances in $e^+e^-$ annihilation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHENVMRQ}},
  note         = {Machine review of arXiv:2608.08769}
}

read the original abstract

Near-threshold resonances have been discovered in many hadron pair production processes, resulting in a significant increase in reaction cross sections at low relative velocities of the produced particles. The natural cause of such resonances is the interaction between slow hadrons in the final state. Our review demonstrates that, in virtually all known cases, final-state interactions successfully explain the results of numerous experiments demonstrating a nontrivial energy dependence of cross sections for processes near reaction thresholds. A comprehensive study of near-threshold resonances in various processes can provide new information about the interaction between hadrons at large distances.

Figures

Figures reproduced from arXiv: 2608.08769 by the authors.

**Figure 2.** Dependences of the gain |F0| 2 (a) and the cross section for the production of a hadronic pair (18) (b) on the energy for L = 0, M = 1 GeV, a = 2 fm and a few values of V0 (indicated below the graphs). for several values of the potential well parameters. For the hadron mass M = 1 GeV and the potential radius a = 2 fm, the third bound state in the potential well appears at a depth V0 = 600 MeV. Consequently, at a sma… view at source ↗

**Figure 3.** Energy dependences of the elastic cross section ( [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

Figures from the paper (14 more)

**Figure 4.** Figure 4: Energy dependences of the cross sections [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

**Figure 5.** Figure 5: Energy dependences of the cross sections [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

**Figure 6.** Figure 6: Energy dependence of the cross section of the process [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]

**Figure 7.** Figure 7: Energy dependence of the cross section e +e − → ΛcΛ¯ c (a), the ratio of the electromagnetic form factors |GE/GM| (b), the absolute value of the magnetic form factor |GM| (c) and the electric form factor |GE| (d). Experimental data are taken from Refs. [69, 70]. elect…

**Figure 8.** Figure 8: Effect of the Coulomb interaction on the energy dependence of the cross section of the [PITH_FULL_IMAGE:figures/full_fig_p029_8.png]

**Figure 9.** Figure 9: Comparison of our predictions for partial nucleon-antinucleon scattering cross sections [PITH_FULL_IMAGE:figures/full_fig_p032_9.png]

**Figure 10.** Figure 10: Energy dependence of the pp¯ (a, c) and nn¯ (b, d) production cross sections in e +e − annihilation. The bottom row shows the near-threshold energy region in more detail. Experimental data taken from the BaBar collaborations [31], CMD-3 [33, 34], SND [41], and BESIII…

**Figure 11.** Figure 11: Energy dependence of the electromagnetic form factors of proton (a, c) and neutron (b, [PITH_FULL_IMAGE:figures/full_fig_p034_11.png]

**Figure 12.** Figure 12: Energy dependences of elastic (dashed lines), inelastic (dotted lines) and total (solid [PITH_FULL_IMAGE:figures/full_fig_p036_12.png]

**Figure 13.** Figure 13: Energy dependence of process cross sections [PITH_FULL_IMAGE:figures/full_fig_p038_13.png]

**Figure 14.** Figure 14: Comparison with experimental data of our predictions for the energy dependence of [PITH_FULL_IMAGE:figures/full_fig_p041_14.png]

**Figure 15.** Figure 15: Comparison with experimental data of our predictions for the energy dependence of [PITH_FULL_IMAGE:figures/full_fig_p042_15.png]

**Figure 16.** Figure 16: Energy dependence of our predictions for the sum of the cross sections for the produc [PITH_FULL_IMAGE:figures/full_fig_p045_16.png]

**Figure 17.** Figure 17: Predictions for the energy dependence of the ratios [PITH_FULL_IMAGE:figures/full_fig_p047_17.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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