A new look at scalar mesons

A. Polosa; F. Piccinini; L. Maiani; V. Riquer

REVIEW

A new look at scalar mesons

L. Maiani, A. Polosa, F. Piccinini, V. Riquer

High Energy Physics - Phenomenology · Submitted 1 Jul 2004 · 13 references

Pith's verdict: A tidy tetraquark proposal whose spectroscopy argument is stronger than its decay evidence, which the abstract oversells.

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arXiv IDhep-ph/0407017 (version 2)

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CitationA. Polosa, F. Piccinini, L. Maiani, V. Riquer. "A new look at scalar mesons." arXiv:hep-ph/0407017 (2004). https://pith.science/paper/SWFSFYN7

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The thing to know up front: the spectroscopy argument is the good part, the decay fit is the weak part, and the abstract presents them as equally solid. It's worth a referee, but the decay claim needs to be cut down to size in revision or in your own reading of it. What's actually new, given that Jaffe proposed four-quark scalars back in 1977 and the paper says so: the OZI-respecting mass formula (Eqs. 3-7), the single-amplitude switch decay scheme (Eq. 12), and the charm/beauty extrapolation. The best physics in the paper is the inverted spectrum — the isolated I=0 state lightest, strange states next — which is precisely what a q-qbar nonet gets wrong and what makes f0(980) awkward in the standard assignment. That is a real argument, not a fit. Now the soft spots. The mass sector is four parameters (alpha, beta, c, d) against four masses, so Eq. 7 is a consistency relation that outputs the mixing angle; it tests nothing. Fine as a parametrization, but it is not evidence. The decay sector is one parameter A = 2.6 GeV fitted to the Table II widths it then reproduces, with kappa to K-pi at 138 MeV against 410 plus or minus 100. The stress-test note is right and it lands harder than the paper admits. In Eq. 18 both a0 to K-Kbar and kappa to K-pi carry the same (a - b), so their ratio is fixed by phase space at roughly 6 while the data want roughly 34. Turning on b = -0.7 GeV fixes a0 to K-Kbar (23 down to about 12 MeV) and pushes kappa to 66 MeV. No choice of (a, b, c) fits both. The paper says the kappa width is 'too low' but treats it as a number to note rather than a structural failure of the single-amplitude picture. That is the one place I would push in review. Also worth flagging: f0 degenerate with a0 is assumed rather than derived, and sigma is doing a lot of work at 478 plus or minus 24 plus or minus 17 when the paper itself explores 370 to 570 in Eq. 8. The heavy-quark predictions are the cleanest part: falsifiable, not used to fix any constant, and the narrow exotic states are a genuine experimental target. Who should read it: anyone working on light scalar spectroscopy or tetraquark hunting at Belle and PEPII. Serious paper, real idea, overstated decay claim. Send it out.

Referee report

Significance

If the identification holds, the paper reorganizes the light scalar nonet and removes a long-standing embarrassment of the quark model, namely that no qq̄ assignment ever reproduced the f0/a0 degeneracy pattern or the proximity of the σ and κ to threshold. The strongest single piece of evidence is qualitative and stated clearly: the tetraquark nonet has an inverted spectrum, with the isolated I = 0 state lightest and the strange states next, which is what the data show and what the qq̄ assignment does not give. The decay analysis is genuinely economical, reducing a large set of OZI-allowed amplitudes to fixed numerical multiples of one constant, and the heavy-quark section makes falsifiable predictions (narrow open- and hidden-charm states with exotic quantum numbers) that can be tested at the B factories and in fixed-target experiments. These are real virtues and should be weighed alongside the quantitative caveats below.

Major objections (2)

[Abstract, sentence s1; §'Quantum numbers and mass formulae', Eqs. (3)–(8)] The abstract states that the nonet 'obeys mass formulae which respect, to a good extent, the OZI rule', but Eq. (3) contains four free parameters (α, β, c, d) and the inputs are the four masses of Table I, with f0 held degenerate with a0. Eq. (7) is therefore a definition of the mixing angle in terms of the masses, not a test of the mass formula, and the mass sector as written has no predictive content beyond the parametrization. The genuine content is twofold and should be stated as such: the qualitative inverted ordering (σ lightest, κ next, a0 ≈ f0 heaviest), which is a real success relative to the qq̄ assignment, and the smallness of φ, which is the quantitative expression of OZI conservation. The latter is, moreover, controlled by the least well known input: Eq. (8) shows tan 2φ moving from −0.07 to −0.31 as the σ mass is varied over 570 to 370 MeV, so the 'good extent' to which the OZI rule is respected is not sharply determined by the data. I would ask the authors to rephrase the abstract and the opening of the mass section so that the reader can see which statements are predictions and which are consistency conditions, and to state explicitly that the small mixing angle is conditional on the σ mass.
[Abstract, sentence s2; §'Strong decays', Eqs. (12)–(13), Table II, Eqs. (17)–(19)] The claim that OZI-allowed decays are 'reasonably reproduced by a single amplitude' is stronger than Table II supports. With A = 2.6 GeV fixed essentially by σ → ππ (345 vs 324 ± 50 MeV), the a0 → K K̄ rate comes out at 23 MeV against 12 ± 3 MeV and the κ → Kπ rate at 138 MeV against 410 ± 100 MeV, a factor of three low; the text acknowledges only the κ discrepancy. The extended fit does not repair this, and the reason is structural rather than numerical: in Eq. (18) the a0 → K K̄ and κ → Kπ amplitudes both carry the same factor (a − b), so their ratio is fixed by phase space and isospin Clebsch-Gordan coefficients at roughly six, whereas the central experimental values give a ratio near thirty. No choice of (a, b, c) can fit both channels, and indeed the fit that brings a0 → K K̄ into line (a − b = 1.8 GeV) drives κ → Kπ down to 66 MeV. Two further points compound this. First, b = −0.7 GeV is about a quarter of A = 2.6 GeV, which is not a small OZI-violating correction and sits uneasily with the OZI-conservation narrative of the mass section. Second, the constant-amplitude ansatz of Eq. (12) has no momentum dependence, and the κ → Kπ channel lies closest to threshold, exactly where such dependence would matter most. I would ask the authors either to soften the abstract claim to something like 'the pattern of OZI-allowed decays is qualitatively reproduced, with the κ channel presently discrepant', or to present a channel-by-channel comparison with stated uncertainties and to say which channels drive A. The sub-threshold treatment of a0 → K K̄, where the width is obtained by averaging the momentum over a Breit-Wigner and yields ⟨p⟩ ≈ 84 MeV, should also be shown with an error band, since the result is sensitive to that procedure.

Minor objections (7)

[Notation, Eqs. (2), (6), (8)] The paper states that mass-squared is denoted by the particle's symbol, so that 'σ' in Eq. (8) means m_σ² while 'σ' elsewhere is the resonance itself; the same symbol is also used for the physical and the unprimed OZI-basis state. A short notational table, or a distinct symbol for the mass-squared quantities, would remove a real source of confusion in Eqs. (6)–(8).
[Table II] The layout of Table II makes it difficult to associate each calculated number with its experimental counterpart, particularly for the f0 row where the gπ and gK entries are interleaved with the branching-ratio limits. A cleaner column structure, with calculated and experimental values in adjacent labelled columns, would help the reader check the fit.
[§'Strong decays', paragraph before Eq. (17)] The text first says that 'in the exact SU(3) limit there is only one amplitude, A, to describe this process' and shortly afterwards that 'in the exact SU(3) limit there are four couplings'. The two statements refer to different things, the switch diagram alone versus all SU(3)-invariant operators, but the distinction should be made explicit in the sentence rather than left to the reader.
[§'Open and hidden charm scalar mesons'] The estimate of widths ≈ O(10) MeV is said to follow 'by scaling from Eq. (13)', but the scaling is not shown. Since these are among the paper's falsifiable predictions, at least the assumed value of A, the relevant phase-space momentum and the isospin factor should be given explicitly so that the estimate can be reproduced.
[Eq. (11) and Eq. (10)] The pseudoscalar mixing is specified only through sin φ_PS = 0.19. Giving the corresponding η–η′ mixing angle in the conventional θ_PS convention, together with the mass formula used, would let readers compare directly with other analyses of a0 → πη.
[Figure 1] The figure is purely schematic and the caption does not indicate the quark-flow convention used to derive the relative signs in Eq. (9) and Eq. (12). A sentence in the caption fixing the sign convention would make the amplitude computation checkable.
[References and typography] There are several typographical slips that should be corrected: 'whishes' in the Acknowledgments, 'FermiLab' for Fermilab, 'T¨ ornqvist' in Ref. [1], and a comma for a period in 'Phys. Lett, 5(1963) 165' in Ref. [9]. The meson names a(980) and f(980) in the opening paragraph should carry their subscripts, a0(980) and f0(980), to match Table I and the rest of the paper.

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The paper

The paper claims

The four light scalar mesons below 1 GeV are argued to be four-quark states — a diquark bound to an antidiquark — rather than ordinary quark-antiquark P-wave mesons, with a single quark-pair-switch amplitude accounting for their strongdecay

The reading

The paper argues that the four light scalar mesons below 1 GeV — the $sigma$ (about 480 MeV), the $kappa$ (about 800 MeV), the $f_0(980)$ and the $a_0(980)$ — are not ordinary quark-antiquark P-wave states but S-wave bound states of a diquark and an antidiquark, four quarks in all. The motivation is the long-standing failure of the quark-antiquark assignment: the $f_0(980)$ behaves as though it were built from strange quarks, whereas in a well-behaved quark-antiquark nonet the $I=0$ partner of the $a_0(980)$ should be nearly degenerate with it. Placing the four states in a nine-member flavour nonet built from fully antisymmetric diquarks, the authors find a mass formula that reproduces the observed ordering — the isolated $I=0$ state lightest, the strange states next — with only a small mixing between the two neutral $I=0$ members. The same picture then explains the decays: a single amplitude for swapping a quark-antiquark pair between the diquark and the antidiquark turns the state into two colourless pseudoscalar mesons and reproduces the OZI-allowed rates at roughly the right size. If this is correct, the ordinary quark-antiquark scalar nonet lies higher in mass, and a family of narrow charmed and beauty tetraquarks with exotic quantum numbers should exist.

What carries the argument

The load-bearing object is the diquark-antidiquark nonet: each scalar is a bound $[q_1q_2][bar q_3 bar q_4]$ with the diquark in the fully antisymmetric combination of colour anti-triplet, flavour anti-triplet and spin zero, so that $sigma^circ = [ud][bar u bar d]$, $kappa = [ud][bar s bar d]$, and the $a_0$/$f^circ$ pair is built from $[su][bar s bar u]$ and $[sd][bar s bar d]$. The mass argument runs through a tensor mass operator, $M^2 = frac{1}{2}{Tr(S^2 m) + sqrt{3} c, Tr(S lambda_8) Tr S + frac{3}{2} d [Tr(S lambda_0)]^2}$, whose $I=0$ block reduces to a $2 times 2$ matrix in $f^circ$ and $sigma^circ$ and yields one relation fixing the mixing angle from the masses. The decay argument runs through the switch amplitude: the effective Lagrangian $L = A[f^circ(-bar K K/sqrt{2} + eta_q eta_s) - sigma^circ(pi cdot pi/2 + eta_q^2/2) + a_0(bar K tau_3 K/sqrt{2} - pi^0 eta_s) + ldots]$ makes every partial width a fixed numerical multiple of $A^2$, with $Gamma(S to i) = frac{A^2}{8pi} frac{p}{M^2} x_{S to i}$. The extended version of the same Lagrangian, with couplings $a$, $b$, $c$ multiplying $epsilon_{jlm}epsilon_{ikn}$ structures, is what produces the linear spacing test.

Extended reading notes

Core claim

On the paper's own terms the result has two halves. First, the spectrum: writing the most general SU(3)-breaking mass operator for a nonet of scalar fields and using squared masses, the authors show that the measured masses of $sigma$, $kappa$, $f_0(980)$ and $a_0(980)$ follow from a four-parameter formula in which the OZI rule is respected, leaving one relation that fixes the $f_0$–$sigma$ mixing angle, $tan 2varphi approx -0.07$ to $-0.31$ depending on the $sigma$ mass, with $tan 2varphi = -0.48$ the point where the $sigma$ mass-squared would vanish. Second, the decays: if a quark-antiquark pair is switched between the diquark and the antidiquark, the state converts into two colourless pseudoscalar mesons, and in the exact SU(3) limit a single amplitude $A$ controls every OZI-allowed channel. With $A = 2.6$ GeV the calculated rates land near the measured ones for $sigma to pi pi$ (345 MeV against $324 pm 50$ MeV) and for the two $a_0$ channels, while the $kappa$ width comes out low, as the authors state. Adding the remaining SU(3)-invariant couplings, the three OZI-allowed amplitudes are found to be nearly equally spaced with $b = -0.7$ GeV, which the authors read as reinforcing the four-quark assignment. The paper closes by classifying open- and hidden-charm analogues, $[cq][bar q bar q]$ and $[cq][bar c bar q]$, which fall into $6 oplus bar 3$ and $8 oplus 1$ multiplets and should be narrow, of order 10 MeV, with conspicuous exotic decay modes.

Load-bearing premise

The decay pattern is assumed to follow from one SU(3)-invariant constant $A$ with no momentum dependence and negligible OZI-violating contributions, even though the paper's own extended fit finds the OZI-violating coupling $b = -0.7$ GeV, which is not small.

Editorial extensions

If this is right

The ordinary quark-antiquark P-wave scalar nonet — the partner of the established axial and tensor nonets — must lie above 1 GeV, so the scalar spectroscopy below 1 GeV is reclassified wholesale.
The mass ordering is inverted relative to a quark-antiquark nonet: the isolated $I=0$ state is lightest and the strange members heavier, which is the signature the paper points to as most evident in favour of four-quark structure.
Open-charm states $[cq][bar q bar q]$ should appear as an $a_{cbar s}$/$f_{cbar s}$ pair with charges $0, +1, +2$ and thresholds near $D_s pi$ at 2104 MeV and $DK$ at 2367 MeV, alongside isodoublets $delta_c$ and $S_c$ with $S_c to Dpi$ at 2004 MeV.
Hidden-charm states $[cq][bar c bar q]$ should give a degenerate isotriplet-isosinglet complex with decays to $eta_c pi$ (threshold 3115 MeV) and $Dbar D$ (3739 MeV).
Because quark-pair annihilation is suppressed by asymptotic freedom, the heavy tetraquark widths should be of order 10 MeV, giving narrow states with exotic quantum numbers rather than broad resonances.

Reading between the lines

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

The sharpest near-term test is not the $sigma$, whose mass is poorly known, but the $kappa$: the one-parameter fit undershoots its width by roughly a factor of three, so a better determination of the $kappa$ pole and its coupling to $Kpi$ would either restore the single-amplitude picture or force momentum dependence into the switch amplitude.
The predicted open-charm states sit within tens of MeV of $Dpi$, $DK$ and $D_s pi$ thresholds, so they would show up as threshold cusps or triangular singularities rather than clean Breit-Wigners; searches keyed to resonance peaks may miss them.
The paper's own unresolved item — the OZI-forbidden $f_0 to pi pi$ coming out too small — is naturally tied to the $kappa$: if that decay proceeds through an off-shell $Kbar K$ loop with $K^*$ and $kappa$ exchange, then the same object that fixes the $kappa$ width also fixes the $f_0 to pi pi$ rate, making the two anomalies a single measurement.
The inverted mass ordering is a generic consequence of four-quark binding rather than of this particular mass operator, so it is the natural target for lattice calculations of the lightest scalar nonet, independent of any model of the decay amplitudes.

Original abstract

Light scalar mesons are found to fit rather well a diquark-antidiquark description. The resulting nonet obeys mass formulae which respect, to a good extent, the OZI rule. OZI allowed strong decays are reasonably reproduced by a single amplitude describing the switch of a qbar-q pair, which transforms the state into two colourless pseudoscalar mesons. Predicted heavy states with one or more quarks replaced by charm or beauty are briefly described; they should give rise to narrow states with exotic quantum numbers.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,562 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.14 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Light scalar mesons are found to fit rather well a diquark-antidiquark description. The resulting nonet obeys mass formulae which respect, to a good extent, the OZI rule. OZI allowed strong decays are reasonably reproduced by a single amplitude describing the switch of a qbar-q pair, which transforms the state into two colourless pseudoscalar mesons. Predicted heavy states with one or more quarks replaced by charm or beauty are briefly described; they should give rise to narrow states with exotic quantum numbers.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Light scalar mesons are found to fit rather well a diquark-antidiquark description.	result 0.98	0.84	0.73	asserted 0.98
s1	The resulting nonet obeys mass formulae which respect, to a good extent, the OZI rule.	result 0.98	0.79	0.12	asserted 0.93
s2	OZI allowed strong decays are reasonably reproduced by a single amplitude describing the switch of a qbar-q pair, which transforms the state into two colourless pseudoscalar mesons.	result 0.83	0.80	0.14	asserted 0.90
s3	Predicted heavy states with one or more quarks replaced by charm or beauty are briefly described; they should give rise to narrow states with exotic quantum numbers.	result 0.60	0.73	0.08	hedged possibility 0.76

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from argument 0.79.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (13)

[1]

N.A. T¨ ornqvist, Z. Phys. C68 (1995) 647

View on Pith 1995
[2]

S. Eidelman et al., Phys. Lett. B592 (2004) 1

View on Pith 2004
[3]

F.E. Close and N.A. Tornqvist, J. Phys. G28 (2002) R249 and references therein

View on Pith 2002
[4]

J. Weinstein and N. Isgur, Phys. Rev. Lett. 48(1982) 659

View on Pith 1982
[5]

R.L. Jaﬀe, Phys. Rev. D15 (1977) 281; R.L. Jaﬀe and F.E. Low, Phys. Rev. D19 (1979) 2105; M. Alford and R.L. Jaﬀe, Nucl. Phys. B578 (2000) 367

View on Pith 1977
[6]

S. Nussinov, hep-ph/0307357; M. Karliner and H.J. Lip- kin, hep-ph/0307243. R.L. Jaﬀe and F. Wilczek, Phys. Rev. Lett. 91 (2003) 232003

View on Pith Pith review arXiv 2003
[7]

KLOE Collaboration (A. Aloisio et al. ), Phys. Lett. B537 (2002) 21; E.M. Aitala et al. , Phys. Rev. Lett. 86 (2001) 770

View on Pith 2002
[8]

E.M. Aitala et al. , Phys. Rev. Lett. 89 (2002) 121801

View on Pith 2002
[9]

G. Zweig, CERN report S419/TH412 (1964), unpub- 5 lished; S. Okubo, Phys. Lett, 5(1963) 165; J. Iizuka, K. Okada and O. Shito, Prog. Theor. Phys. 35 (1966) 1061

View on Pith 1964
[10]

H. Lipkin, Phys. Lett. B70, 113 (1977); D. Black, A.H. Fariborz, F. Sannino and J. Schechter, Phys. Rev. D59, 074026 (1999) where, unlike this paper, deriva- tive couplings were used; J.R. Pelaez, Phys. Rev. Lett. 92, 102001 (2004); M. Alford and R.L. Jaﬀe, Nucl.Phys. B578, 367 (2000) for lattice studies; A nice review with a complete list of reference ca...

View on Pith Pith review arXiv 1977
[11]

G.C. Rossi and G. Veneziano, Nucl. Phys. B123 (1977) 507; Phys. Lett. B70, 255 (1977); for a recent update see hep-th/0404262

View on Pith Pith review arXiv 1977
[12]

D. Barberis et al., Phys. Lett. B453 (1999) 325

View on Pith 1999
[13]

K. Terasaki, “Charmed Scalar Mesons and Related” , hep-ph/0405146

View on Pith Pith review arXiv

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How later papers used it

92 later papers cite it

Evidence: substantial. 83 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 129 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 cited it as support. 2 more papers by the same authors are listed: 1 used its data or values and 1 cited it as support.

Uses its data or values 1 of 2 papers with this label · 1 by the same authors

By the same authors

Took the mass value of the sigma from this paper to show values giving a ratio compatible with the experimental one.

A note on large N scalar QCD_2 (2008) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

Cites it as support 2 of 6 papers with this label · 1 by the same authors

Said that the tetraquark function is supported by spectroscopy of scalar mesons, citing this paper.

Production of $f_{0}(980)$ meson at the LHC: Color evaporation versus color-singlet gluon-gluon fusion (2020) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Believed there are solid reasons to understand the observed sub-GeV scalar meson nonet as four-quark states, as in this paper.

Update on Counting Valence Quarks at RHIC (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

86 arXiv papers cite this in 122 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 75 sentences without a confident label

Builds on it 1 paper

A fresh look at more recent light-quark scalar meson data using the diquark model [ref] inspired an extension of the approach [ref] to the then-newly discovered heavy-quark exotics; this extension, to be discussed below, constitutes the basis of modern heavy-quark diquark models.

Heavy-Quark QCD Exotica · General Considerations: Nature of Diquarks · 0.95

Uses its data or values 2 papers

In Figure [ref] we show a set of values $(M_s,M_f)$ which give a ratio $μ_(σ)/μ_(π)$ compatible with the experimental one, taking the mass value of the $σ$ from [ref] .

A note on large N scalar QCD_2 · Introduction · 0.96
The decay proceeds through $P$-wave and the matrix element is given by: [equation] The quark exchange amplitude considered above has been studied first in [ref] were a rather good fit of the scalar meson decays to pseudoscalar, $S→PP$, was obtained associating to this amplitude a coupling strength $A≃2.6$ GeV.

Higher Tetraquark Particles · Introduction · 0.87

Cites it as support 4 papers

We believe that there are solid reasons to understand the observed sub-GeV scalar meson nonet as four-quark states [ref] .

Update on Counting Valence Quarks at RHIC · Introduction · 1.00
Then, the light scalar states $f_0(500)$, $f_0(980)$, $K_0^∗(800)$, and $a_0(980)$ are (most likely) predominantly four quark-states [see e.g. Refs. [ref] and refs. therein].

$a_{0}(980)$ revisited · Introduction · 0.96
This is in agreement with various other works on this topic [ref] : virtual kaon-kaon pairs near the corresponding threshold are important for the dynamical generation of the resonance $a_0(980)$.

Dynamical generation of hadronic resonances in effective models with derivative interactions · Branching ratios and coupling constants for $a_0(980)$ · 0.98

Cites it as background 33 papers

The original discussion of tetraquark states as candidates for the light scalar mesons was presented in Ref. [ref] and revisited in Ref. [ref] .

Decay of light scalar mesons into vector-photon and into pseudoscalar mesons · The Lagrangian · 1.00
Dealing with these problems, models of dynamical generation[For a general discussion concerning dynamical generation see Ref. [ref] and references therein.] began to offer one possible solution and hence received more and more attention from the community [ref] (for other approaches, see e.g. Refs. [ref] ).

Dynamical generation of hadronic resonances · Introduction · 0.92
We now turn to the concrete examples of the well-known scalar resonances $f_0(500)$, $f_0(980)$, $f_0(1370)$ and $f_0(1500)$ and calculate their decays into pions [ref] (for a discussion of the internal structure of these states in terms of quarks and gluons see also e.g. Refs. [ref] ).

The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays · Specific examples · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

N.A. T¨ ornqvist, Z. Phys. C68 (1995) 647

View on Pith 1995

[2] [2]

S. Eidelman et al., Phys. Lett. B592 (2004) 1

View on Pith 2004

[3] [3]

F.E. Close and N.A. Tornqvist, J. Phys. G28 (2002) R249 and references therein

View on Pith 2002

[4] [4]

J. Weinstein and N. Isgur, Phys. Rev. Lett. 48(1982) 659

View on Pith 1982

[5] [5]

R.L. Jaﬀe, Phys. Rev. D15 (1977) 281; R.L. Jaﬀe and F.E. Low, Phys. Rev. D19 (1979) 2105; M. Alford and R.L. Jaﬀe, Nucl. Phys. B578 (2000) 367

View on Pith 1977

[6] [6]

S. Nussinov, hep-ph/0307357; M. Karliner and H.J. Lip- kin, hep-ph/0307243. R.L. Jaﬀe and F. Wilczek, Phys. Rev. Lett. 91 (2003) 232003

View on Pith Pith review arXiv 2003

[7] [7]

KLOE Collaboration (A. Aloisio et al. ), Phys. Lett. B537 (2002) 21; E.M. Aitala et al. , Phys. Rev. Lett. 86 (2001) 770

View on Pith 2002

[8] [8]

E.M. Aitala et al. , Phys. Rev. Lett. 89 (2002) 121801

View on Pith 2002

[9] [9]

G. Zweig, CERN report S419/TH412 (1964), unpub- 5 lished; S. Okubo, Phys. Lett, 5(1963) 165; J. Iizuka, K. Okada and O. Shito, Prog. Theor. Phys. 35 (1966) 1061

View on Pith 1964

[10] [10]

H. Lipkin, Phys. Lett. B70, 113 (1977); D. Black, A.H. Fariborz, F. Sannino and J. Schechter, Phys. Rev. D59, 074026 (1999) where, unlike this paper, deriva- tive couplings were used; J.R. Pelaez, Phys. Rev. Lett. 92, 102001 (2004); M. Alford and R.L. Jaﬀe, Nucl.Phys. B578, 367 (2000) for lattice studies; A nice review with a complete list of reference ca...

View on Pith Pith review arXiv 1977

[11] [11]

G.C. Rossi and G. Veneziano, Nucl. Phys. B123 (1977) 507; Phys. Lett. B70, 255 (1977); for a recent update see hep-th/0404262

View on Pith Pith review arXiv 1977

[12] [12]

D. Barberis et al., Phys. Lett. B453 (1999) 325

View on Pith 1999

[13] [13]

K. Terasaki, “Charmed Scalar Mesons and Related” , hep-ph/0405146

View on Pith Pith review arXiv