REVIEW
Constituent quark model study of the meson spectra
High Energy Physics - Phenomenology · Submitted 22 Nov 2004 · 119 references
Pith's verdict: A useful, candid full-spectrum quark-model template whose one overreach is the unscanned claim that the missing isoscalar scalars cannot exist for any parameter choice.
T0 · AI review
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Referee report
The paper
The paper claims
One quark-antiquark potential is asked to cover every meson, from the pion to the bottomonium states, and most masses land within tens of MeV.
The reading
What carries the argument
The load-bearing object is the flavour-dependent quark-quark potential of Eq. (17): $qbar q$ pairs in the light sector feel confinement, one-gluon exchange, and pion, $\sigma$, kaon and eta exchange; once a heavy quark is involved, only confinement and one-gluon exchange survive. Three pieces do the quantitative work. The screened confining potential $V_{CON} = {-a_c(1 - e^{-mu_c r}) + Delta}(lambda^c_i cdot lambda^c_j)$ saturates at large distance instead of rising forever, and its two parameters are fixed by two measured radial gaps, $rho$ to $rho(1450)$ and $J/psi$ to $psi(2S)$. The scalar/vector mixture $a_s = 0.777$ in the confinement spin-orbit term is fixed by requiring the $a_1(1260)$ to sit above the $a_2(1320)$, which a pure scalar confinement gets backwards. And the strong coupling is frozen per flavour sector, $alpha_s(mu) = alpha_0 / ln((mu^2 + mu_0^2)/Lambda_0^2)$ with $mu$ the reduced mass of the pair, with the contact-term regularisation radii scaling as $r_0(mu) = hat r_0/mu$ and $r_g(mu) = hat r_g/mu$ — this is what lets one parameter set reach from 0.14 GeV to 10 GeV. Noncentral terms are treated exactly on the diagonal and by matrix diagonalisation when they couple partial waves, e.g. the $^3S_1$-$^3D_1$ and $^3P_2$-$^3F_2$ blocks.
Extended reading notes
Core claim
The claim is that a generalized constituent quark model — screened confinement plus one-gluon exchange plus Goldstone-boson exchange, with parameters inherited from the two-nucleon and baryon sectors — gives an overall good fit to the measured meson spectrum across all flavours, and that the places where it fails are informative rather than fatal. The model reproduces the low-lying pseudoscalar and vector mesons, the $D$ and $D_s$ ground states, charmonium (including a prediction of $M[eta_c(2S)] = 3627$ MeV and a $2S/1S$ hyperfine ratio of 0.537, both inside the later Belle error bars), and bottomonium, with the $chi_{cJ}$ and $chi_{bJ}$ splittings right in order and magnitude. From that baseline the authors draw identifications: the $omega(1650)$ is a $3^3S_1$ rather than a $1^3D_1$; $eta(1440)$-region strength is dominantly $nbar n$; the $K_1(1270)$/$K_1(1400)$ pair requires a $1^+$ mixing angle near $55.7^circ$, far from the $5^circ$ of a gluon-only model. And they draw exclusions: no $qbar q$ slot exists for the $f_0(980)$, the $kappa(800)$, the $f_0(1500)$, the $K^*(1410)$, the $K_2(1580)$, or the new narrow $0^+$ charm states, which the authors suggest may be tetraquark or molecular objects that can carry positive parity without orbital excitation.
Load-bearing premise
Everything rests on identifying the reduced mass of the quark-antiquark pair with the momentum scale at which the strong coupling freezes and at which the contact-term regularisation radii scale, an identification asserted by analogy with a Coulombic system and justified only by appeal to a cited phenomenological study; the authors do acknowledge that the $0^+$ $D$ and $D_s$ states come out about 150 MeV too heavy and that forcing $a_s$ to 0.46 does not repair the charm-light sector, but they do not put the scaling ansatz itself in doubt.
Editorial extensions
If this is right
- States the model cannot place — $f_0(980)$, $kappa(800)$, $f_0(1500)$, $K^*(1410)$, $K_2(1580)$, $D_{sJ}^*(2317)$, $X(3872)$ — become a shopping list for glueball, hybrid, tetraquark or molecular interpretations rather than anomalies to be absorbed by parameter tuning.
- The model predicts unobserved partners that experiments can look for: a pure $sbar s$ $2^{-+}$ near 1853 MeV beside the $eta_2(1870)$, a $nbar n$ $3^{--}$ degenerate with the $phi_3(1850)$ near 1875 MeV, and a $sbar s$ $1^{+-}$ near 1973 MeV.
- Quantum-number assignments follow for states whose $J^{PC}$ is undetermined: the $K(1630)$ is read as $1^-$, the $D^*(2640)$ as $0^-$, and the $D_{sJ}(2573)$ as $2^+$.
- The $X(3872)$ is argued to be outside a $cbar c$ scheme on internal grounds: the model's $1D$ candidates sit 70–80 MeV below it and its $2P$ candidates about 40 MeV above, because the calculated $^3D_J$ splitting is about 25 MeV where roughly 100 MeV would be needed to bridge $psi(3770)$ and the $X(3872)$.
- The charmonium hyperfine ratio comes out at 0.537 for $2S/1S$, consistent with the higher-statistics Belle values and with the ratio of leptonic widths, $Gamma_{e^+e^-}[psi(2S)]/Gamma_{e^+e^-}[J/psi] = 0.44$ against $0.41 pm 0.07$ measured.
Reading between the lines
- The paper's real product is a decision procedure rather than a fit: because the parameters are frozen by non-meson data, a miss is evidence, whereas in a model fitted to the meson spectrum a miss is just a bad fit. That asymmetry is what makes the negative results on the light scalars worth more than the positive ones.
- If the reduced-mass freezing of $alpha_s$ is the thing that carries the heavy sector, then the acknowledged 150 MeV overshoot on the $0^+$ $D$ and $D_s$ states and the failure of the $a_s = 0.46$ rescue attempt point at short-range spin-orbit strength being flavour-dependent in a way the current ansatz cannot express — a testable defect, not just a numerical miss.
- The predicted unobserved partners are the cleanest handle on the whole scheme: an $sbar s$ $2^{-+}$ near 1853 MeV and a $nbar n$ $3^{--}$ near 1875 MeV either exist and confirm the flavour assignments, or their absence tells you the confinement spin-orbit mixture is wrong.
- Extending the same frozen-coupling logic to the baryon sector, where the parameters originated, would be a consistency check the paper does not run: the same $alpha_s(mu)$ should govern light baryons if the reduced-mass identification is more than a bookkeeping device.
Original abstract
The $q\bar q$ spectrum is studied in a generalized constituent quark model constrained in the study of the $NN$ phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The $q\bar q$ spectrum is studied in a generalized constituent quark model constrained in the study of the $NN$ phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The $q\bar q$ spectrum is studied in a generalized constituent quark model constrained in the study of the $NN$ phenomenology and the baryon spectrum. | contribution 0.69 | 0.83 | 0.07 | asserted 0.99 |
| s1 | An overall good fit to the available experimental data is obtained. | result 1.00 | 0.94 | 0.36 | asserted 1.00 |
| s2 | A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. | contribution 0.85 | 0.94 | 0.11 | asserted 0.97 |
| s3 | These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states. | interpretation 0.84 | 0.27 | 0.33 | hedged possibility 0.85 |
What was examined, and what was not
- arXiv listing abstract v2
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- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
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- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/0411299 by the authors.
References
How later papers used it
78 later papers cite it
2 later papers by other authors are listed below: 2 used its method or tool. 4 more papers by the same authors are listed: 4 used its method or tool.
Uses its method or tool 6 of 22 papers with this label · 4 by the same authors
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Used the constituent quark model proposed in this paper as its theoretical formalism.
Triply-heavy baryons in a constituent quark model (2019) · 1.00 · paraphrased: the licence does not allow quoting
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Followed the formulation of this paper to write the Hamiltonian.
How to understand the $\rho$ resonance from the quark model and $\pi\pi$ $P$-wave phase shift (2026) · 0.98 · paraphrased: the licence does not allow quoting
By the same authors
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Used the constituent quark model presented in this paper and updated in another work.
Canonical description of the new LHCb resonances (2016) (same authors) · 0.89 · paraphrased: the licence does not allow quoting
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Referred to this paper, updated in another work, for details of the constituent quark model, explicit expressions for all the potentials and the value of the model parameters.
The $D_{s0}(2590)^+$ as the dressed $c\bar s(2^1S_0)$ meson in a coupled-channels calculation (2021) (same authors) · 0.89 · paraphrased: the licence does not allow quoting
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Performed a coupled-channels calculation in the framework of the constituent quark model proposed in this paper.
Charmonium resonances in the 3.9 GeV/$c^2$ energy region and the $X(3915)/X(3930)$ puzzle (2017) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
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Performed a coupled-channels calculation within the framework of the constituent quark model of this paper for the I^G(J^PC)=1^+(1^+-) sector.
The $Z_c$ structures in a coupled-channels model (2018) (same authors) · 0.95 · paraphrased: the licence does not allow quoting
How the literature uses it
64 arXiv papers cite this in 118 sentences
Papers citing it · 78 sentences without a confident label
Uses its method or tool 18 papers
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Our theoretical formalism is the constituent quark model (CQM) proposed in Ref. [ref] (see references [ref] and [ref] for reviews).
Triply-heavy baryons in a constituent quark model · Introduction · 1.00
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In support of the experimental effort, we revisit herein the kaon spectrum using a constituent quark model [ref] in which the quark-antiquark interaction is based on the non-perturbative phenomena of dynamical chiral symmetry breaking and color confinement, plus the perturbative one-gluon exchange (OGE) force.
Kaon spectrum revisited · Introduction · 0.90
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The first ingredient of the present work is the non-relativistic constituent quark model (CQM) extensively described in Ref. [ref] , which allows us to build the theoretical $QQ̅$ and $H_Q$ spectrum and the $H_Q^(∗)H̅_Q^(∗)$ interaction.
Symmetries, partners and thresholds: the case of the $X_b$ · The model · 0.99
Uses its data or values 6 papers
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In the set (a), we will use bare masses of 5851 MeV and 5883 MeV for the $0^+$ and $1^+$ states, respectively, as deduced from the CQM of Refs. [ref] without including any correction to the OGE potential.
Lowest lying even-parity $\bar B_s$ mesons: heavy quark spin-flavor symmetry, chiral dynamics, and constituent quark model bare masses · Results · 0.99
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Table [ref] shows the involved model parameters fitted over all meson spectra [ref] , updated in Refs. [ref] .
Constituent-quark-model based coupled-channels calculation of the $\mathbf{bb\bar c\bar c}$ and $\mathbf{bc\bar b\bar c}$ tetraquark systems · Naive quark model · 0.90
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We have used values that have been fitted before through hadron [ref] , hadron-hadron [ref] and multiquark [ref] phenomenology.
Hidden-Bottom Pentaquarks · Introduction · 0.93
Compares with it 2 papers
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which align closely with those in constituent quark model [ref] .
$B \to D^{(*)} \tau \nu_{\tau}$ decay properties with RIQ model · Numerical results & analysis · 0.99
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It should be stressed that many specialized models [ref] describe their respective sectors considerably better than our present model.
The excited baryon spectrum from a unified quark model · Fit results · 0.86
Cites it as background 12 papers
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Among the wide range of chiral quark models developed in the last 50 years [ref] , our theoretical framework is a QCD-inspired constituent quark model (CQM) proposed in Ref. [ref] and extensively reviewed in Ref. [ref] .
Detailed derivation of the $\mathbf{^3P_0}$ strong decay model applied to baryons · Introduction · 0.87
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The latter present some puzzles: the strange mesons known as $D_s(2317)$ and $D_s(2460)$ are said to be lighter than expected from constitutent quark model predictions (for reviews, see e.g. [ref] ).
Puzzles of excited charm meson masses · Introduction · 0.84
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Due to the absence of a rigorous proof for the form of the confinement potential, there are currently three prevalent models: linear confinement potential [ref] , quadratic confinement potential, and confinement potential with screening effects [ref] .
Equivalence among color singlet, color octet and diquark structure in a chiral quark model · Chiral quark model · 0.93
Discussion
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