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REVIEW 3 major objections 4 minor 101 references

Towards a theory of baryon resonances

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that a resonance is an S-matrix pole and that chiral-symmetric analysis finds two poles in the $D_0^\ast(2400)$ region.

desk verdict A competent and readable expert review of resonance methods, but the PDG-change call on D*0(2400) rests on a single model-dependent continuation and would need stability tests to carry that weight. read the letter →

arxiv 1908.06706 v1 pith:PWQYJLET submitted 2019-08-19 nucl-th hep-exhep-lathep-phnucl-ex

Ulf-G. Mei{ss}ner This is my paper · ORCID
classification nucl-thhep-exhep-lathep-phnucl-ex
keywords baryonresonancesS-matrixpolesunphysicalRiemannsheetstwo-polestructureunitarizedchiralperturbationtheorylatticeQCDRoperresonancecomplex-massscheme
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 talk argues that a resonance is not a bump in a cross section but a pole of the scattering amplitude on an unphysical Riemann sheet, and that only lattice QCD and chiral effective field theories can locate such poles systematically and model-independently. The payoff is a concrete claim about the heavy-light spectrum: the region of the $D_0^\ast(2400)$ contains two S-matrix poles, not one, so the standard particle listings should be updated accordingly. The same two-pole pattern, traced to group theory, is extended to the $D_1$, $B_0^\ast$, and $B_1$ states. The talk also computes the widths of the $\Delta(1232)$ and the Roper $N^\ast(1440)$ at two-loop order in baryon chiral perturbation theory, finding consistency with measured values.

What carries the argument

The load-bearing object is the S-matrix pole on an unphysical Riemann sheet, located by analytic continuation of the scattering amplitude. The operational machinery is unitarized chiral perturbation theory (UCHPT), whose $T$-matrix satisfies $T^{-1}=V^{-1}-G$, with $V$ the chiral potential and $G$ the two-point loop function; chiral symmetry fixes which channels couple and how the potential behaves as masses move. In finite volume, $G$ is replaced by a modified loop function $\tilde G(s,L)$ that encodes the quantization of momenta, so lattice energy levels can be postdicted and poles found in the complex plane. For baryon widths, the talk uses the complex-mass scheme at two loops, treating unstable-particle masses as complex pole positions, with a power counting in which $m_R-m_N\sim\epsilon$, $m_R-m_\Delta\sim\epsilon^2$, and $M_\pi\sim\epsilon^2$.

What would settle it

Two concrete tests: an SU(3)-symmetric lattice calculation with $M_\phi>575$ MeV should show the sextet pole becoming a bound state, and a direct lattice determination of the Roper couplings $g_R$ and $h_R$ should find them consistent with $g_A$ and $h_A$; failure of either would undercut the corresponding claim.

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Extended reading notes

Core claim

The paper's central claim is that every resonance is an S-matrix pole on an unphysical Riemann sheet, so resonance parameters are meaningless unless extracted from a pole search in the complex energy plane. Applying that rule to the coupled channels $D\pi$, $D\eta$, $D_s\bar K$ with isospin $I=1/2$, the talk reports that a chiral-symmetric reanalysis of existing lattice data yields two poles in the $D_0^\ast(2400)$ region, at about $2105$ MeV and $2451$ MeV, with the lower pole falling below the $D_{s0}^\ast(2317)$; this dissolves the puzzle that the charm-strange state is lighter than its charm-light counterpart. The two poles follow from the SU(3) decomposition $\bar 3\otimes 8 = \bar 3 \oplus 6 \oplus 15$, where the anti-triplet and sextet are attractive. The same machinery predicts two-pole structures for the $D_1$, $B_0^\ast$, and $B_1$ states, and the talk states that the time is ripe to change the listings for the $D_0^\ast$ and $D_1$ accordingly.

Load-bearing premise

The Roper width prediction assumes the Roper–pion and $\Delta$–Roper–pion couplings equal the nucleon axial couplings (the maximal-mixing assumption); if they differ, the quoted $\Gamma(R\to N\pi\pi)$ shifts and the agreement with the measured value is not guaranteed.

Editorial extensions

If this is right

  • If the two-pole claim is right, the standard listings should show two states for $D_0^\ast$ and $D_1$, with the lower $D_0^\ast$ pole below $D_{s0}^\ast(2317)$.
  • The predicted two-pole structures for $B_0^\ast$ and $B_1$ give a direct test: future measurements should see a near-threshold pole plus a higher pole, with cusp structures at the $D\eta$ and $D_s\bar K$ thresholds.
  • A lattice calculation with SU(3)-symmetric quark masses and $M_\phi>575$ MeV should turn the sextet pole into a bound state, testing the group-theoretic origin of the double pole.
  • The two-loop widths for $\Delta(1232)$ and the Roper, obtained without model assumptions, tie the hadron spectrum to chiral EFT parameters that lattice QCD can determine.

Reading between the lines

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

  • Extension: if the two-pole pattern is as generic as the talk suggests, single-entry listings in other heavy-light channels may also conceal pole pairs; re-running the same chiral-symmetric pole search on those channels would reveal them.
  • Extension: the talk's insistence on complex-plane poles implies a methodological standard: lattice analyses should report pole locations, not just phase shifts, and should use chiral-symmetric extrapolations when moving below the real axis.
  • Extension: the Roper width prediction's dependence on maximal mixing suggests a concrete lattice program: determine $g_R$ and $h_R$ directly; if they deviate from $g_A$ and $h_A$, the $\pi\pi$ width would likely move outside the current error bars.
  • Extension: the same finite-volume UCHPT machinery could be applied to open-charm baryons, where similar threshold-coupled channels may show analogous two-pole structures.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This manuscript, written as a talk summary, argues that a systematic and model-independent theory of hadron resonances must be built on lattice QCD and effective field theories, with resonances defined as S-matrix poles on unphysical Riemann sheets. It reviews the Luescher formalism for finite-volume spectra, its extension to coupled channels via unitarized chiral perturbation theory (UCHPT), and uses these tools to present a two-pole structure for the D*0(2400) from a re-analysis of Hadron Spectrum Collaboration lattice data, supported by LHCb angular-moment data. The later sections discuss hadroproduction of molecular states such as the X(3872), the calculation of the Delta(1232) and Roper N*(1440) widths in the complex-mass scheme of baryon chiral perturbation theory, and ambiguities in isolating 'pion cloud' effects. The paper concludes with take-home lessons emphasizing pole-structure analysis, chiral-symmetry constraints on extrapolations, and the role of hadronic molecules.

Significance. If the claims hold, the paper would strengthen the case that finite-volume lattice data, when continued to the complex plane with chiral-symmetric amplitudes, reveal a two-sheet structure for heavy-light scalar/axial mesons that should be reflected in the PDG listings. The presentation has real virtues: it states a crisp and widely accepted definition of resonances, emphasizes the necessity of coupled-channel analyses, and provides concrete falsifiable tests, notably the SU(3)-limit sextet bound state for M_phi > 575 MeV and the confrontation with LHCb angular-moment data. At the same time, the strongest quantitative claims are not accompanied in this manuscript by the stability and sensitivity analyses needed to make them archival-level results; they are summaries of already-published work. The paper therefore serves well as an expert overview, but its evidence base for the PDG recommendation is thinner than the rhetoric.

major comments (3)
  1. [Sec. 4, Fig. 6 and Table 1] The assertion that 'time is ripe to change these entries in the PDG' for the D*0 and D1 relies on a second pole near 2451 MeV that arises from a single UCHPT continuation of the HSC lattice levels at M_pi ~ 390 MeV. The manuscript does not demonstrate that this pole is stable under variations of the subtraction constant a(mu) in G(s), under inclusion of N2LO chiral corrections to V(s), or under alternative unitarization prescriptions. Since the HSC's own eleven K-matrix parametrizations found only one S-wave pole (Sec. 4), this second pole is a model-dependent outcome. To support the PDG recommendation, please provide a stability analysis of the pole trajectory, or clearly soften the claim to a scenario that requires further checks.
  2. [Sec. 6.2, Eqs. (29)-(30)] The prediction for the Roper two-pion width uses g_R = g_A and h_R = h_A, the 'maximal mixing assumption', and the paper itself acknowledges that improved determinations of g_R and h_R are needed. Equation (29) contains terms quadratic and quartic in these couplings, so deviations of order 10-20% from g_A and h_A can shift the central value by an amount comparable to the quoted LEC and higher-order uncertainties. The claim that Eq. (30) is consistent with the PDG value of (67 +/- 10) MeV is thus contingent on an untested assumption. Please quantify the sensitivity by varying g_R and h_R over a physically reasonable range, or present the result explicitly as conditional on maximal mixing.
  3. [Sec. 4, LEC fitting and data overlap] The LECs h_2,...,h_5 are stated to be 'obtained from a fit to lattice data' in Ref. [32], and the same UCHPT framework is then used to postdict the HSC finite-volume levels (upper panel of Fig. 6) and to extract the poles. The manuscript does not state whether the lattice data used to fix the LECs are independent of the HSC data set [24] being re-analyzed. If there is overlap, the agreement in the upper panel is a fit rather than a postdiction, and the poles inherit the fit's assumptions. Please clarify the data sets and, if they are independent, state that explicitly; if they are not, the pole extraction should be reframed as an interpolation within a single framework.
minor comments (4)
  1. [References] Reference [85] is missing a closing parenthesis in the year: it reads 'Phys. Lett. B 760, 736 (2016.'
  2. [Sec. 2] The phrase 'with very few exception of well-isolated' should be 'with very few exceptions'.
  3. [Table 2] The table header 'sigma(pp/bar-p) -> X(3872))' contains an unmatched parenthesis.
  4. [Sec. 6.1, Eq. (23)] Equation (23) is quoted without an uncertainty estimate, yet Fig. 13 uses it to draw a quantitative correlation band; please either provide the uncertainty or explicitly refer to the error analysis in the original publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the D*0 two-pole and Roper width claims are predictions from fixed inputs, not refits of the target observables.

full rationale

The paper does not exhibit any derivation that reduces by construction to its own inputs. The D*0 two-pole claim is based on finite-volume UCHPT (Eqs. 9-11) with LECs fixed in Ref. [32] from lattice channels, after which the HSC energy levels of Ref. [24] are postdicted with no new parameters and the poles are located by analytic continuation. Although Refs. [33] and [39] are from the same collaboration, the result is independently testable: the higher pole is checked against LHCb angular moments, a lattice test is proposed (sextet pole becoming a bound state for Mphi > 575 MeV), and Table 1 predicts B*0 and B1 states, so the self-citations carry external falsifiability rather than circular force. The Roper width in Sec. 6.2 is likewise not a disguised fit: g_piNR is fixed from the PDG one-pion width, gR=gA and hR=hA are adopted under the explicitly named maximal mixing assumption, and the resulting Gamma(R -> N pi pi) is a genuinely different observable not used in any fit. The paper even states that improved determinations of gR and hR are needed, which is a transparent limitation rather than a circular step. The Delta-width parameter reduction of Eq. (22) is renormalization-group content, and the resulting correlation is compared to an independent analysis of pion-nucleon scattering. No self-definitional identification, fitted-input-as-prediction, uniqueness-theorem importation, or ansatz-smuggling-by-citation is present; the proceedings-level self-citations are normal and non-load-bearing in the circularity sense.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

No new entities are introduced. The free parameters are couplings and LECs carried over from the cited calculations; the axioms are the standard EFT assumptions plus two explicitly flagged choices (power counting and maximal mixing) introduced to make the Roper calculation tractable.

free parameters (6)
  • gπNR (Roper-nucleon-pion coupling) = 0.47 ± 0.04
    Fixed to reproduce the PDG width Γ(R→Nπ) = (123.5 ± 19.0) MeV in Eq. (28); then used to predict Γ(R→Nππ).
  • g_R (Roper-pion coupling) = set equal to g_A = 1.27
    Chosen under the maximal mixing assumption [89]; not measured in this paper, central to Eq. (29).
  • h_R (Delta-Roper-pion coupling) = set equal to h_A = 1.42 ± 0.02
    Chosen under the maximal mixing assumption; determines the Roper two-pion width.
  • h1 (heavy-light chiral LEC) = 0.42
    Fixed from the D_s-D mass splitting (Sec. 4); used in the Dφ UCHPT amplitude.
  • h2, h3, h4, h5 (heavy-light chiral LECs) = from fit to lattice data (Ref [32])
    Fitted to Dπ and DKbar scattering lattice data; the two-pole D*0 result depends on them.
  • cutoff Λ for X(3872) hadroproduction = range [0.5, 1.0] GeV
    A regulator range chosen following Ref [67]; results in Table 2 span that range.
assumptions (7)
  • domain assumption SU(3) chiral symmetry breaking pattern with eight pseudo-Goldstone bosons and spontaneous symmetry breaking.
    Used throughout to justify CHPT and UCHPT as the EFTs; central to Eq. (10) and Eq. (12).
  • domain assumption Unitarized CHPT T-matrix form T^{-1} = V^{-1} - G (Eq. 9) is a valid resummation of the chiral potential.
    The two-pole and molecular results rely on this unitarization; alternative schemes (K-matrix) are warned against in Sec. 4.
  • domain assumption The complex-mass scheme preserves symmetry and unitarity order-by-order when applied to unstable particles.
    Invoked in Sec. 6 to justify computing resonance widths with complex-valued masses; quoted from [77] without proof in this text.
  • ad hoc to paper The chiral power counting near the Roper pole: m_R-m_N~ε, m_R-m_Δ~ε^2, m_Δ-m_N~ε^2, M_π~ε^2 (Eq. 26).
    This counting defines the small parameter for the two-loop Roper calculation; if invalid, the quoted width formula does not follow.
  • ad hoc to paper Maximal mixing assumption g_R = g_A and h_R = h_A.
    Explicitly assumed in Sec. 6.2 to reduce the number of unknown couplings and produce a definite prediction for Γ(R→Nππ).
  • domain assumption The deuteron and X(3872) share the same range of forces, R ~ 300 MeV (two-pion exchange).
    Used to criticize the Bignamini et al. production bound; without it the rebuttal in Sec. 5 loses force.
  • domain assumption The 3bar and 6 channels in the SU(3) decomposition 3bar⊗8 = 3bar ⊕ 6 ⊕ 15 are attractive, leading to two zero-width poles.
    Group theory gives the decomposition, but the attractiveness assignment is dynamical; used to explain the D*0 two-pole structure (Eq. 12).

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Cite this review

Pith. "Pith review of Towards a theory of baryon resonances." pith.science (2026). https://pith.science/paper/PWQYJLET

@misc{pith2026190806706,
  author       = {Pith},
  title        = {Pith review of: Towards a theory of baryon resonances},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PWQYJLET}},
  note         = {Machine review of arXiv:1908.06706}
}
read the original abstract

In this talk, I discuss methods that allow for a systematic and model-independent calculation of the hadron spectrum. These are lattice QCD and/or its corresponding Effective Field Theories. Assorted results are shown and I take the opportunity to discuss some misconceptions often found in the literature.

Figures

Figures reproduced from arXiv: 1908.06706 by the authors.

Figure 1
Figure 1. The imaginary part of a single-channel amplitude in the presence of a resonance. The solid dots indicate the allowed positions for resonance poles. Figure from [2]. width, their photo-couplings, etc. . In particular, these in￾trinsic properties do not depend on the experiment or the￾ory (model). Most importantly, resonances correspond to S-matrix poles on unphysical Riemann sheets, as de￾picted in [PITH_FULL_IMAGE:… view at source ↗
Figure 2
Figure 2. Modulus of the analytic continuation of the J P = 1/2 − πN scattering amplitude into the complex s-plane. Shown is the (- - - + + +) Riemann sheet. The two poles at √ s = (1.51 − i0.14) GeV and √ s = (1.69 − i0.05), corresponding to the S 11(1535) and the S 11(1650), respectively, are clearly visi￾ble. The stars and black dots refer to other determinations as listed in [3]. For the definitions of the sheets, see e.g… view at source ↗
Figure 3
Figure 3. The S-wave amplitude f0+ for K − p → K − p for I = 0 in the complex energy plane clearly showing the two poles in the region of the Λ(1405). The red band indicates that the (+ + - - - - + + + +) Riemann sheet is only connected to the real energy axis between the KN¯ and the πΣ thresholds. For the definitions of the sheets, see e.g. Ref. [5]. Figure courtesy of Maxim Mai. 3 Lesson 2: Well separated resonances Well se… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The πN phase shift of the ∆ channel as a function of the center-of-mass momentum k. The solid line is the phase gen￾erated from the physical mass and width of the ∆-resonance. The dashed horizontal line indicates the 90◦ crossing of the phase. used a Nf = 2 clover acti…
Figure 7
Figure 7. Figure 7: Comparison of the S-wave amplitude determined from the calculation of [39] with the S-wave anchor points from the experimental analysis, shown as the data points [42]. The red (solid) line gives the best fit results and the grey band quanti￾fies the uncertainties. The …
Figure 8
Figure 8. Figure 8: Typical near-threshold line shapes that emerge for compact (left panel) and molecular states (right panel). The dashed perpendicular lines indicate the location of the threshold. Note the cusp at the threshold for the molecular scenario. The x-axis shows M = m1 + m2 + …
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: A triangle diagram illustrating the long-distance con￾tribution to the transition between two heavy particles A and B with the emission of a light particle C. The two vertical dashed lines denote the two relevant cuts. Figure from [2]. with (dσ[HH0 (k)]/dk)MC the cros…
Figure 12
Figure 12. Figure 12: One and two-loop self-energy diagrams contributing to the width of the delta resonance up-to-and-including fifth or￾der according to the standard power counting. The dashed and double solid lines represent the pions and the delta resonances, respectively. The double (…

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Works this paper leans on

101 extracted references · 76 canonical work pages

  1. [32]

    Liu et al., Phys

    L. Liu et al., Phys. Rev. D 87, 014508 (2013)

    work page 2013

  2. [24]

    Moir et al., JHEP 1610, 011 (2016)

    G. Moir et al., JHEP 1610, 011 (2016)

    work page 2016

  3. [1]

    R. G. Moorhouse, quote from the 1960ties

  4. [2]

    F. K. Guo et al., Rev. Mod. Phys. 90, 015004 (2018)

    2018

  5. [3]

    P. C. Bruns et al., Phys. Lett. B 697, 254 (2011)

    2011

  6. [4]

    J. A. Oller et al., Phys. Lett. B 500, 263 (2001)

    2001

  7. [5]

    Cieplý et al., Nucl

    A. Cieplý et al., Nucl. Phys. A 954, 17 (2016)

    2016

  8. [6]

    Lüscher, Commun

    M. Lüscher, Commun. Math. Phys. 105, 153 (1986)

    1986

Show all 101 references
  1. [7]

    U. J. Wiese, Nucl. Phys. Proc. Suppl. 9, 609 (1989)

    1989

  2. [8]

    Rummukainen et al

    K. Rummukainen et al. , Nucl. Phys. B 450, 397 (1995)

    1995

  3. [9]

    Bonn-Jülich-QCDSF collaboration, unpublished (2010)

    2010

  4. [10]

    Morningstar, these proceedings

    C. Morningstar, these proceedings

  5. [11]

    Petschlies, these proceedings

    M. Petschlies, these proceedings

  6. [12]

    C. B. Lang et al., Phys. Rev. D 87, 054502 (2013)

    2013

  7. [13]

    Verduciet al., PoS LATTICE 2014, 121 (2014)

    V . Verduciet al., PoS LATTICE 2014, 121 (2014)

    2014

  8. [14]

    Leskovec et al., Few Body Syst

    L. Leskovec et al., Few Body Syst. 59, 95 (2018)

    2018

  9. [15]

    Werner et al., arXiv:1907.01237 [hep-lat]

    M. Werner et al., arXiv:1907.01237 [hep-lat]

    1907 arXiv

  10. [16]

    He et al., JHEP 0507, 011 (2005)

    S. He et al., JHEP 0507, 011 (2005)

    2005

  11. [17]

    Lage et al., Phys

    M. Lage et al., Phys. Lett. B 681, 439 (2009)

    2009

  12. [18]

    Bernardet al., JHEP 1101, 019 (2011)

    V . Bernardet al., JHEP 1101, 019 (2011)

    2011

  13. [19]

    R. A. Brice ˜no et al., Phys. Rev. D88, 094507 (2013)

    2013

  14. [20]

    R. A. Brice ˜no et al., Phys. Rev. D88, 034502 (2013)

    2013

  15. [21]

    Döring et al., Eur

    M. Döring et al., Eur. Phys. J. A 47, 139 (2011)

    2011

  16. [22]

    Döring et al., Eur

    M. Döring et al., Eur. Phys. J. A 48, 114 (2012)

    2012

  17. [23]

    R. A. Brice ˜no et al., Phys. Rev. D95, 074510 (2017)

    2017

  18. [25]

    see http://pdg.lbl.gov/

  19. [26]

    J. M. M. Hall et al., Phys. Rev. Lett. 114, 132002 (2015)

    2015

  20. [27]

    Molina et al

    R. Molina et al. , Phys. Rev. D 94, 056010 (2016) Addendum: [Phys. Rev. D 94, 079901 (2016)]

    2016

  21. [28]

    Kaiser et al., Nucl

    N. Kaiser et al., Nucl. Phys. A 594, 325 (1995)

    1995

  22. [29]

    Oset et al., Nucl

    E. Oset et al., Nucl. Phys. A 635, 99 (1998)

    1998

  23. [30]

    M. F. M. Lutz et al., Nucl. Phys. A 700, 193 (2002)

    2002

  24. [31]

    F. K. Guo et al., Phys. Lett. B 666, 251 (2008)

    2008

  25. [33]

    Albaladejo et al., Phys

    M. Albaladejo et al., Phys. Lett. B 767, 465 (2017)

    2017

  26. [34]

    Jido et al., Nucl

    D. Jido et al., Nucl. Phys. A 725, 181 (2003)

    2003

  27. [35]

    E. E. Kolomeitsev et al. , Phys. Lett. B 582, 39 (2004)

    2004

  28. [36]

    F. K. Guo et al., Phys. Lett. B 641, 278 (2006)

    2006

  29. [37]

    F. K. Guo et al., Eur. Phys. J. A 40, 171 (2009)

    2009

  30. [38]

    Z. H. Guo et al., Phys. Rev. D 92, 094008 (2015)

    2015

  31. [39]

    M. L. Du et al., Phys. Rev. D 98, 094018 (2018)

    2018

  32. [40]

    Aaij et al

    R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 92, 012012 (2015)

    2015

  33. [41]

    Aaij et al

    R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 91, 092002 (2015) Erratum: [Phys. Rev. D 93, 119901 (2016)]

    2015

  34. [42]

    Aaij et al

    R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 94, 072001 (2016)

    2016

  35. [43]

    M. L. Du et al., Phys. Rev. D 99, 114002 (2019)

    2019

  36. [44]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. 137, B672 (1965)

    1965

  37. [45]

    Morgan et al., Phys

    D. Morgan et al., Phys. Lett. B 258, 444 (1991)

    1991

  38. [46]

    N. A. Tornqvist, Phys. Rev. D 51, 5312 (1995)

    1995

  39. [47]

    Baruet al., Phys

    V . Baruet al., Phys. Lett. B 586, 53 (2004)

    2004

  40. [48]

    Braaten et al., Phys

    E. Braaten et al., Phys. Rev. D 76, 094028 (2007)

    2007

  41. [49]

    Aceti et al., Phys

    F. Aceti et al., Phys. Rev. D 86, 014012 (2012)

    2012

  42. [50]

    Z. H. Guo et al., Phys. Rev. D 93, 096001 (2016)

    2016

  43. [51]

    Mai, these proceedings

    M. Mai, these proceedings

  44. [52]

    Oset, these proceedings

    E. Oset, these proceedings

  45. [53]

    Aaij et al

    R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 115 072001 (2015)

    2015

  46. [54]

    Aaij et al

    R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 122, 222001 (2019)

    2019

  47. [55]

    J. J. Wu et al., Phys. Rev. Lett. 105, 232001 (2010)

    2010

  48. [56]

    Chen et al., Phys

    R. Chen et al., Phys. Rev. Lett. 115 132002 (2015)

    2015

  49. [57]

    T. J. Burns, Eur. Phys. J. A 51, 152 (2015)

    2015

  50. [58]

    Roca et al., Phys

    L. Roca et al., Phys. Rev. D 92, 094003 (2015)

    2015

  51. [59]

    Chen et al., Phys

    R. Chen et al., Phys. Rev. D 100, 011502 (2019)

    2019

  52. [60]

    F. K. Guo et al., Phys. Rev. D 99 091501 (2019)

    2019

  53. [61]

    T. J. Burns et al., arXiv:1908.03528 [hep-ph] (2019)

    2019 arXiv

  54. [62]

    Bignamini et al

    C. Bignamini et al. , Phys. Rev. Lett. 103, 162001 (2009)

    2009

  55. [63]

    Albaladejo et al

    M. Albaladejo et al. , Chin. Phys. C 41, 121001 (2017)

    2017

  56. [64]

    Artoisenet et al., Phys

    P. Artoisenet et al., Phys. Rev. D 81, 114018 (2010)

    2010

  57. [65]

    F. K. Guo et al. , Commun. Theor. Phys. 61, 354 (2014)

    2014

  58. [66]

    F. K. Guo et al., Eur. Phys. J. C 74, 3063 (2014)

    2014

  59. [67]

    F. K. Guo et al., Phys. Rev. D 88, 054007 (2013)

    2013

  60. [68]

    F. K. Guo et al., JHEP 1405, 138 (2014)

    2014

  61. [69]

    Bauer [CDF Collaboration], Int

    G. Bauer [CDF Collaboration], Int. J. Mod. Phys. A 20, 3765 (2005)

    2005

  62. [70]

    Chatrchyan et al

    S. Chatrchyan et al. [CMS Collaboration], JHEP 1304, 154 (2013)

    2013

  63. [71]

    Fleming et al., Phys

    S. Fleming et al., Phys. Rev. D 76, 034006 (2007)

    2007

  64. [72]

    P. F. Bedaque et al., Ann. Rev. Nucl. Part. Sci. 52, 339 (2002)

    2002

  65. [73]

    D. L. Canham et al., Phys. Rev. D80 014009 (2009)

    2009

  66. [74]

    Z0 Physics

    R. G. Stuart, in “Z0 Physics”, ed. J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, 1990), p. 41

    1990

  67. [75]

    Denner et al., Nucl

    A. Denner et al., Nucl. Phys. B 560, 33 (1999)

    1999

  68. [76]

    Djukanovic et al., Phys

    D. Djukanovic et al., Phys. Lett. B 680, 235 (2009)

    2009

  69. [77]

    Denner et al., Nucl

    A. Denner et al., Nucl. Phys. Proc. Suppl. 160, 22 (2006)

    2006

  70. [78]

    Beenakker et al., Nucl

    W. Beenakker et al., Nucl. Phys. B 338, 349 (1990)

    1990

  71. [79]

    Gegelia et al., Phys

    J. Gegelia et al., Phys. Lett. B 763, 1 (2016)

    2016

  72. [80]

    H. B. Tang et al., Phys. Lett. B 387, 9 (1996)

    1996

  73. [81]

    Krebs et al., Phys

    H. Krebs et al., Phys. Lett. B 683, 222 (2010)

    2010

  74. [82]

    M. J. G. Veltman, Physica 29, 186 (1963)

    1963

  75. [83]

    Siemens et al., Phys

    D. Siemens et al., Phys. Lett. B 770, 27 (2017)

    2017

  76. [84]

    D. L. Yao et al., JHEP 1605, 038 (2016)

    2016

  77. [85]

    Gegelia et al., Phys

    J. Gegelia et al., Phys. Lett. B 760, 736 (2016

    2016

  78. [86]

    Borasoy et al., Phys

    B. Borasoy et al., Phys. Lett. B 641, 294 (2006)

    2006

  79. [87]

    Djukanovic et al., Phys

    D. Djukanovic et al., Phys. Lett. B 690, 123 (2010)

    2010

  80. [88]

    Long et al., Nucl

    B. Long et al., Nucl. Phys. A 870-871, 72 (2011)

    2011

  81. [89]

    S. R. Beane et al., J. Phys. G 31, 921 (2005)

    2005

  82. [90]

    Gelenava, Eur

    M. Gelenava, Eur. Phys. J. A 54, 88 (2018)

    2018

  83. [91]

    Burkert,these proceedings

    V . Burkert,these proceedings

  84. [92]

    Pagels, Phys

    H. Pagels, Phys. Rept. 16, 219 (1975)

    1975

  85. [93]

    Bernardet al., Phys

    V . Bernardet al., Phys. Rev. Lett. 67, 1515 (1991)

    1991

  86. [94]

    Bernard et al

    V . Bernard et al. , Nucl. Phys. A 635, 121 (1998) [Erratum-ibid. A 642, 563 (1998) 563]

    1998

  87. [95]

    Meißner, AIP Conf

    U.-G. Meißner, AIP Conf. Proc. 904, 142 (2007)

    2007

  88. [96]

    E. M. Henley et al., 100 Years of Subatomic Physics (World Scientific, Singapore, 2013) 199–229

    2013

  89. [97]

    M. B. V oloshin et al. , JETP Lett. 23, 333 (1976) [Pisma Zh. Eksp. Teor. Fiz. 23, 369 (1976)]

    1976

  90. [98]

    N. A. Tornqvist, Z. Phys. C 61, 525 (1994)

    1994

  91. [99]

    R. A. Brice ˜no, et al., Phys. Rev. Lett. 118, 022002 (2017)

    2017

  92. [100]

    Guo et al., Phys

    D. Guo et al., Phys. Rev. D 98, 014507 (2018)

    2018

  93. [101]

    Pang,these proceedings

    J.-Y . Pang,these proceedings

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