The 1/N Expansion for Baryons

Aneesh V. Manohar; Elizabeth Jenkins; Roger Dashen

REVIEW

The 1/N Expansion for Baryons

Roger Dashen, Elizabeth Jenkins, Aneesh V. Manohar

High Energy Physics - Phenomenology · Submitted 1 Nov 1993 · 42 references

Pith's verdict: A foundational, honest paper: the group theory is solid, the Nc=3 extrapolation is the soft part, and the authors say so themselves.

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arXiv IDhep-ph/9310379 (version 1)

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CitationAneesh V. Manohar, Elizabeth Jenkins, Roger Dashen. "The 1/N Expansion for Baryons." arXiv:hep-ph/9310379 (1993). https://pith.science/paper/BJP45WMD

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Editor's note

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This is the paper that turned the 1/Nc expansion for baryons from power-counting folklore into a real calculational scheme. The core move is clean: unitarity on pion-baryon scattering forces the contracted SU(4) spin-flavor algebra (Sect. 2), and the induced-representation machinery of Sect. 3 classifies all its irreducible representations. That formalism is the genuinely new piece, and it is done properly — Mackey's theorem is the right tool, and the little-group analysis is careful. The Nf=3 extension without assuming SU(3) (Sects. 6-8) is the other real contribution; the kaon and eta coupling results hold irrespective of the strange quark mass, which is a stronger statement than the SU(3) literature usually makes. The mass relations of Sect. 10 (eqs. 10.14-10.17) are derived from the operator structure, not fitted, and the observation that the order-Nc non-analytic correction is SU(3) singlet while the order-one piece is octet is a nice, checkable statement. The chiral-loop cancellation in Sect. 12 is the kind of result that only becomes visible once you have the full tower, and it explains why earlier loop calculations looked badly behaved. Credit where due: this is careful work, and the derivations are internally consistent throughout. Now the soft spots, in proportion. The stress-test concern about the K=0 identification is real but the authors flag it themselves in Sect. 5.3 — they say plainly that it is not proved that the baryons annihilated by eqs. (5.3) and (5.9) are the lowest-lying ones. The supporting argument is quark-model/Skyrme, and the post-hoc agreement with data is consistent with it, but it is an assumption, not a theorem. That is the load-bearing soft spot, and it is acknowledged. The Nc=3 extrapolation is the second: three methods give F/D = 0.56, 0.58, 0.67, a spread of about 0.1 that the paper attributes to 1/Nc^2 without quantifying. The mass-relation comparisons in eq. 10.21 give central values with no error bars or chi-squared. These are minor-to-moderate, not fatal — the paper is honest about all of them. Who should read it: anyone working on baryon structure, large Nc, or chiral perturbation theory for baryons. It is a standard reference for a reason. It deserves a serious referee, and I would cite it without hesitation.

Referee report

Significance

If the framework holds, this is a substantial and durable contribution: it converts large-Nc QCD for baryons from a set of qualitative power-counting statements into a calculational scheme with parameter-free relations among measurable quantities. The strengths are real and should be named. The derivation of the contracted algebra from unitarity is clean and does not smuggle in model assumptions. The induced-representation classification is a correct application of a standard mathematical theorem, and it makes the correspondence with the Skyrme model transparent rather than coincidental. The predictions are falsifiable and are stated as such: F/D = 2/3 + O(1/Nc^2), the mass relations of eqs. (10.14)-(10.17), the equal-spacing rule for the pion couplings of Sect. 9.1, and the claim that the leading chiral logarithm in the axial currents cancels to two orders in 1/Nc. The mass-relation analysis of Sect. 10 is particularly valuable because it explains, rather than merely records, why some SU(3) relations work far better than naive ms counting would suggest. The discussion in Sect. 12.3 of the non-commutativity of the Nc -> infinity and mq -> 0 limits is a genuinely useful clarifying贡献

Major objections (3)

[Sect. 1.1 (first bullet) and Sect. 9, eqs. (9.30)-(9.32)] The summary of results states 'The F/D ratio for the baryon axial currents is determined to be 2/3 + O(1/Nc^2), in good agreement with the experimental value of 0.58 +/- 0.04.' Sect. 9 itself is more careful: three equally legitimate extrapolations to Nc = 3 give 1/sqrt(3) = 0.58 (eq. 9.30), 2/3 = 0.67 (eq. 9.31), and 5/9 = 0.56 (eq. 9.32), and the text notes that 'the range of the three values implies an O(1/Nc^2) correction of about 0.1.' A theoretical spread of 0.1 is roughly 15% and is two and a half times the quoted experimental error of 0.04, so the phrase 'good agreement' in the summary overstates what the calculation establishes. The summary bullet and the abstract should quote the spread as the theoretical uncertainty, e.g. F/D = 0.6 +/- 0.1, rather than selecting the quark-model value 2/3 and comparing it to 0.58 +/- 0.04 as though the theory error were below the experimental one. This is a framing and bookkeeping issue, not an error in the derivation, but it is load-bearing for the paper's headline claim.
[Sect. 6, eq. (6.16) and Sect. 7] In Sect. 6 the operator X^{ia}_1 proportional to J_s^i I^a is identified as the one candidate 1/Nc correction with the correct transformation properties, and its exclusion is deferred: 'This term can be shown to be absent by considering the process pi + B -> pi + K + B' ... This discussion is deferred to the next section on kaon couplings.' Sect. 7 then states only that the consistency conditions (7.18)-(7.20) 'can be used to show that the term in g(K) in eq. (6.19) of order 1/Nc is at most linear in K and that X^{ia}_1 does not contain terms of the form J_s I, as was stated in the previous section.' The demonstration is asserted rather than carried out. Since the absence of this operator is what makes the ratios of pion couplings within a tower free of 1/Nc corrections, and hence what licenses the O(1/Nc^2) accuracy claimed throughout Sects. 6 and 9, the argument should be given explicitly, even if only in a short appendix.
[Sect. 5.3] The authors state plainly that the identification of the physical baryons with the induced representations on the orbit X^{ia}_0 proportional to delta^{ia} 'is not rigorous because it has not been proved that the baryons annihilated by the operators eqs. (5.3) and (5.9) are the lowest lying baryons.' I do not raise this as a new finding, since it is acknowledged and supported by both the quark-model counting of Sect. 5.2 and the Skyrme correspondence of Sect. 4. What remains unresolved is that the abstract and the summary of results present the coupling and mass relations as predictions of QCD, without carrying this conditionality forward. A sentence in Sect. 1.1 and in the abstract stating that the relations hold for baryons in the maximally symmetric orbit, and that the identification of the observed baryons with that orbit is supported but not proved, would make the logical status of the results accurate without weakening them.

Minor objections (7)

[Sect. 6, eq. (6.12)] The exclusion of the two operators epsilon^{ijk} X^{ja}_0 J^k and epsilon^{abc} X^{ib}_0 I^c on the grounds that they 'do not transform under time reversal in the same manner as an axial current' and 'can be removed by phase redeﬁnition of the baryon states of order 1/Nc' is stated in one sentence. A brief explicit demonstration of the phase redefinition would help the reader verify the claim.
[Tables 1 and 2] The captions do not state the normalization convention for the reduced amplitudes M, N, and L. The text notes in a parenthetical after eq. (9.19) that the normalization of L relative to M depends on how the spin invariants for B and T are normalized; this convention should be stated in the table captions so that the entries can be used without reconstructing it from the surrounding text.
[Sect. 9.2] The statement that the F/D ratio for the baryon magnetic moments is 2/3, 'in good agreement with the experimental value of 0.72,' gives no reference for the extraction of 0.72. A citation should be supplied, as it is for the axial value of 0.58 +/- 0.04.
[Sect. 11, eq. (11.12)] The claim that the consistency condition (6.11) admits the single non-trivial SU(3) solution lambda' N_c d^{ABC} X^{iB}_0 T^C is asserted rather than derived. One or two sentences indicating why no other d-symbol structures survive would make this section self-contained.
[Sect. 10, eq. (10.21)] The experimental values quoted in parentheses (205 = 195, 191 = 215, and so on) are given without a source. The mass compilation used should be cited.
[Sect. 7] There are typographical errors to correct in proof: 'derivatively couplied kaon ﬁeld' in the sentence following eq. (7.1), and 'The coupling constant constant g(K)' in Sect. 6.
[Fig. 7] The SU(3) weight diagram is rendered as a field of small marks whose structure is not legible at the size reproduced. The figure should be redrawn with the states labelled, since the argument of Sect. 9 about extrapolating from the top of the weight diagram depends on the reader seeing its shape.

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The paper

The paper claims

The paper constructs a systematic $1/N_c$ expansion for QCD baryons and argues that a contracted spin-flavor symmetry fixes axial-coupling ratios, masses, and magnetic moments up to $O(1/N_c^2)$.

The reading

The paper asks whether QCD's baryons become tractable when the number of colors $N_c$ is taken large. In that limit the pion couples to a baryon through an axial current that grows like $N_c$, and requiring pion-baryon scattering not to violate unitarity forces the current operators to commute at leading order. The authors turn this consistency condition into a contracted spin-flavor algebra and classify its irreducible representations with the method of induced representations. The payoff is a set of parameter-free relations among baryon axial couplings, masses, and magnetic moments, with corrections ordered by powers of $1/N_c$; extrapolated to $N_c=3$, these relations describe the measured deviations from exact spin-flavor symmetry.

What carries the argument

The load-bearing device is the contracted $SU(4)$ algebra generated by spin $J^i$, isospin $I^a$, and axial operators $X^{ia}$ with $[X^{ia},X^{jb}]=0$ at leading order. It is derived by demanding that the would-be $N_c$-growing pion-baryon scattering amplitude cancel. The irreducible representations are constructed as induced representations: choose an orbit of the $3×3$ matrix $X_0$ under spin and isospin, take the little group of a standard point, and dress it with angular momentum $K$; the lowest baryons correspond to $X_0∝1$ and $2K=N_s$, the number of strange quarks. Matrix elements then reduce to Clebsch-Gordan and $6j$ symbols, producing the coupling ratios and mass relations.

Extended reading notes

Core claim

The central claim is that the baryon sector of large-$N_c$ QCD possesses a contracted $SU(4)$ spin-flavor symmetry, and that this symmetry, together with the assumption that the lowest baryons sit in the simplest induced representation, fixes the ratios of baryon axial couplings and the form of baryon masses up to $O(1/N_c^2)$. In particular, the axial-current $F/D$ ratio is $2/3+O(1/N_c^2)$, the same leading ratio holds for magnetic moments, all pion-baryon coupling ratios are determined, kaon couplings respect strange-quark spin symmetry at leading order, and mass relations such as $Σ^*-Σ=Ξ^*-Ξ$ hold without assuming $SU(3)$. The paper argues that the observed departures from exact spin-flavor symmetry are accurately accounted for by the subleading $1/N_c$ terms, so the expansion is quantitative at $N_c=3$, not merely qualitative.

Load-bearing premise

The identification of the physical baryons with the simplest induced representation, the orbit where $X_0$ is proportional to the identity and $2K$ equals the number of strange quarks, is not proved; the authors state in Sect. 5.3 that it has not been shown that the baryons annihilated by their symmetric quark operators are the lowest-lying ones.

Editorial extensions

If this is right

The axial-current ratio $F/D$ is predicted to be $2/3$ up to $1/N_c^2$, close to the measured $0.58±0.04$; the magnetic-moment ratio has the same leading value, and the gap between the two is a calibrated $1/N_c^2$ effect.
Ratios of all pion-baryon couplings are fixed to $O(1/N_c^2)$, and kaon-baryon couplings are fixed at leading order without assuming $SU(3)$, so the same relations apply even for a heavy strange quark.
The mass relations $Σ^*-Σ=Ξ^*-Ξ$ and companions hold to $O(1/N_c^2)$ without $SU(3)$; violations of the Gell-Mann–Okubo formula are at most $O(1/N_c)$.
Chiral-loop corrections to the axial currents cancel through two orders in $1/N_c$ and are suppressed by $1/N_c$, while the leading nonanalytic mass correction is an $SU(3)$ singlet and the next is octet, protecting the Gell-Mann–Okubo pattern.
The expansion gives a quantitative error budget for extrapolating from $N_c=∞$ to $N_c=3$, with the observed $15$–$20%$ discrepancy between axial and magnetic $F/D$ serving as a measure of the first neglected $1/N_c^2$ terms.

Reading between the lines

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

If the induced-representation identification can be derived rather than assumed, the same route should give controlled $1/N_c$ relations for baryons with one heavy quark and for exotic hadron sectors, because the method only needs a contracted symmetry and a little-group classification.
The paper's logic suggests a general diagnostic: when a model relation such as a quark-model or Skyrme-model ratio works unexpectedly well, check whether it follows from a contracted algebra, since that would explain the success without committing to the model's dynamics.
The mass-relation pattern implies a practical ordering for tests: relations requiring both large $N_c$ and $SU(3)$ should be more accurate than either symmetry alone predicts, so experimental effort is best spent on the few relations where the two protections coincide.
A lattice study that varies the number of colors, even at small $N_c$, could test the predicted scaling of the $F/D$ splitting and the mass-relation residuals, turning the extrapolation assumption into an empirical curve.

Original abstract

A systematic expansion in 1/N is constructed for baryons in QCD. Predictions of the 1/N expansion at leading and subleading order for baryon axial current coupling constant ratios such as F/D, baryon masses and magnetic moments are derived. The baryon sector of QCD has a light quark spin-flavor symmetry at leading order in 1/N. The formalism of induced representations for contracted Lie algebras is introduced to explain the consequences of this symmetry. Relations are first derived for the simplest case of two light flavors of quarks. The generalization of the large N expansion to N_f = 3 flavors is subtle and is treated using several complementary methods. The 1/N expansion severely restricts the form of SU(3) breaking in the baryon sector. Extrapolation of the large N results to N=3 permits quantitative comparison with experimental data. Deviations of the measured quantities from exact spin-flavor symmetry predictions are accurately described by the subleading 1/N corrections. Implications of the 1/N expansion for baryon chiral perturbation theory are discussed.

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, 7,365 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.45 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A systematic expansion in 1/N is constructed for baryons in QCD. Predictions of the 1/N expansion at leading and subleading order for baryon axial current coupling constant ratios such as F/D, baryon masses and magnetic moments are derived. The baryon sector of QCD has a light quark spin-flavor symmetry at leading order in 1/N. The formalism of induced representations for contracted Lie algebras is introduced to explain the consequences of this symmetry. Relations are first derived for the simplest case of two light flavors of quarks. The generalization of the large N expansion to N_f = 3 flavors is subtle and is treated using several complementary methods. The 1/N expansion severely restricts the form of SU(3) breaking in the baryon sector. Extrapolation of the large N results to N=3 permits quantitative comparison with experimental data. Deviations of the measured quantities from exact spin-flavor symmetry predictions are accurately described by the subleading 1/N corrections. Implications of the 1/N expansion for baryon chiral perturbation theory are discussed.

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	A systematic expansion in 1/N is constructed for baryons in QCD.	contribution 0.96	0.90	0.18	asserted 1.00
s1	Predictions of the 1/N expansion at leading and subleading order for baryon axial current coupling constant ratios such as F/D, baryon masses and magnetic moments are derived.	result 0.68	0.91	0.30	asserted 1.00
s2	The baryon sector of QCD has a light quark spin-flavor symmetry at leading order in 1/N.	result 0.74	0.49	0.16	asserted 1.00
s3	The formalism of induced representations for contracted Lie algebras is introduced to explain the consequences of this symmetry.	method 0.91	0.76	0.04	asserted 0.98
s4	Relations are first derived for the simplest case of two light flavors of quarks.	method 0.80	0.84	0.03	asserted 0.98
s5	The generalization of the large N expansion to N_f = 3 flavors is subtle and is treated using several complementary methods.	method 0.80	0.77	0.04	asserted 0.99
s6	The 1/N expansion severely restricts the form of SU(3) breaking in the baryon sector.	result 0.88	0.66	0.19	asserted 1.00
s7	Extrapolation of the large N results to N=3 permits quantitative comparison with experimental data.	method 0.56	0.65	0.15	asserted 0.86
s8	Deviations of the measured quantities from exact spin-flavor symmetry predictions are accurately described by the subleading 1/N corrections.	result 0.94	0.73	0.54	asserted 1.00
s9	Implications of the 1/N expansion for baryon chiral perturbation theory are discussed.	interpretation 0.82	0.63	0.06	unclear 0.71

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

Figures

**Figure 1.** Graphs contributing to pion-baryon scattering at le

Showing 2 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9310379 by the authors.

References

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M.A. Luty and J. March-Russell, LBL-34778, [hep-ph/9310369] 57 Figure Captions Fig. 1. Graphs contributing to pion-baryon scattering at le ading order in the 1 /Nc ex- pansion. Fig. 2. The leading diagram for the two point function of two a xial currents in large Nc. Only the quark line is shown. An arbitrary number of internal gluons can be exchanged bet...

View on Pith Pith review arXiv

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hep-lat 2016-06 accept novelty 6.0 of 10

Meson, baryon and static-potential observables in SU(N) gauge theory with two dynamical flavors follow leading large-N scaling to within roughly 15 percent for N = 3, 4, 5, with N = 2 the clear outlier.
Octet-baryon axial-vector charges and SU(3)-breaking effects in the semileptonic hyperon decays
hep-ph 2014-05 conditional novelty 6.0 of 10

Covariant baryon chiral perturbation theory at O(p^3) with explicit decuplets describes semileptonic hyperon decay axial charges with roughly 20 percent next-to-leading corrections, yielding D=0.623(61)(17) and F=0.44...
Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
hep-ph 2013-12 accept novelty 6.0 of 10

The authors compute the gauge-coupling terms of the one-loop anomalous dimension matrix for the 59 dimension-six SMEFT operators, completing the full 2499 x 2499 matrix.
Nucleon Generalized Parton Distributions from Full Lattice QCD
hep-lat 2007-05 conditional novelty 6.0 of 10

Two-plus-one-flavor lattice QCD at pion masses down to 350 MeV yields the lowest moments of nucleon generalized parton distributions, including quark momentum fractions and the up/down split of proton spin.
Nucleon form-factors of the energy momentum tensor in the chiral quark-soliton model
hep-ph 2007-02 accept novelty 6.0 of 10

The chiral quark-soliton model yields parameter-free predictions for the nucleon's energy-momentum-tensor form factors, including a negative d1 and a stability mechanism balancing quark-core repulsion against pion-clo...
Reconciling threshold and subthreshold expansions for pion-nucleon scattering
nucl-th 2016-10 conditional novelty 5.0 of 10

Including the Δ(1232) explicitly and using covariant baryon ChPT both reduce the low-energy constants of pion-nucleon scattering to natural size and bring predicted threshold parameters closer to the Roy-Steiner values.
On Gauge Invariance and Minimal Coupling
hep-ph 2013-04 accept novelty 5.0 of 10

Minimal coupling is ill-defined as an operator-classification principle in effective field theory, so claims that non-minimally-coupled Higgs operators are loop-suppressed are unjustified.
Charmed and strange baryon resonances with heavy-quark spin symmetry
hep-ph 2012-02 conditional novelty 5.0 of 10

An SU(8) spin-flavor coupled-channel model predicts charmed baryon resonances across one, two, and three charm sectors and tentatively assigns the Xi_c(2790) and Xi_c(2815) to a heavy-quark spin symmetry doublet.
Singly and Doubly Charmed J=1/2 Baryon Spectrum from Lattice QCD
hep-lat 2009-09 conditional novelty 5.0 of 10

Full-QCD lattice simulation yields M_Xi_cc = 3665 (+0/-78) MeV and M_Omega_cc - M_Xi_cc = 98 +/- 26 MeV, with the splitting free of the leading lattice discretization error.
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hep-ph 2004-09 conditional novelty 5.0 of 10

Diquark correlations, not free quarks, organize hadron spectroscopy: they explain why exotic multiquark states are almost absent and predict that any pentaquarks sit in a positive-parity antidecuplet.
SU(N) gauge theories at large N
hep-th 2012-10 accept novelty 3.0 of 10

Lattice simulations of SU(N) gauge theories for N up to about 8, extrapolated in 1/N, are consistent with a smooth confining 't Hooft limit whose pure-glue corrections scale as 1/N^2.
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hep-th 2019-07 unverdicted

Lecture notes on lattice methods for formal TASI students covering basics, confinement, chiral fermions, and case studies in the 3D Ising model and QCD.

How later papers used it

56 later papers cite it

Evidence: some. 54 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 107 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 used its method or tool.

Uses its method or tool 1 of 7 papers with this label

Recovered this paper's general two reduction rules through operator identities, eliminating operator products with contracted flavor or spin indices and those with symmetric or antisymmetric combinations of d and f symbols.

Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons (2014) · 0.88 · paraphrased: the licence does not allow quoting

How the literature uses it

51 arXiv papers cite this in 100 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 · 67 sentences without a confident label

Builds on it 1 paper

Formally they follow from the results [ref] upon the replacement $N_c →N_l$.

Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons · Large-$N_c$ operator analysis · 0.93

Uses its method or tool 6 papers

Owing to the operator identities the general two reduction rules of [ref] are recovered: * All operator products in which two flavor indices are contracted using $δ_ab$, $f_abc$ or $d_abc$ or two spin indices on $G$'s are contracted using $δ_ij$ or $ε_ijk$ can be eliminated. * All operator products in which two flavor indices are contracted using symmetric or antisymmetric combinations of two different $d$ and/or $f$ symbols can be eliminated.

Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons · Large-$N_c$ operator analysis · 0.88
Conservatively assuming the neutron is associated to a state with vanishing strangeness ($S=0$), it is easy to see that the neutron corresponds to [ref] |n)=C_nα_d+^†(α_u+^†α_d-^†-α_u-^†α_d+^†)^N_c+1/2|0), with $C_n$ a normalization chosen so that $(n|n)=1$.

A strange contribution to the neutron EDM · A systematic approach · 0.80
The baryon current Eq. ([ref]) can be constructed using the large-$N_c$ $SU(4)$ spin-flavor symmetry and expanded in the generators ${ 1̂, Î^a, Ŝ^i, Ĝ^ia} (i, a = 1,2,3)$ [ref] .

Target normal single-spin asymmetry in inclusive electron-nucleon scattering with two-photon exchange: Analysis using $1/N_c$ expansion · Currents and amplitudes · 0.91

Cites it as background 20 papers

The phenomenological analysis of large $N_c$ baryons relies upon three features: the large number of quarks in the baryon wave function [$N_c$ in the $N_c^F$ counting, $N_c(N_c-1)/2$ in the $N_c^AS$ counting] and their combinatorics [ref] , the 't Hooft scaling [ref] $g_YM ∼ N_c^-1/2$ of the QCD coupling constant, and the existence of a ground-state multiplet completely symmetric under the combined spin-flavor symmetry, which is the generalization of the old SU(6) 56-plet [ref] .

All you need is N: Baryon spectroscopy in two large N limits · Operator analysis and mass relations · 0.91
In the $N_c →∞$ limit of QCD, the dynamics is characterized by the emergent SU(2$N_f$) spin-flavor symmetry (here $N_f = 2$) [ref] .

QCD angular momentum in $N \rightarrow \Delta$ transitions · $N →Δ$ transition angular momentum in $1/N_c$ expansion · 0.93
The contracted group is related to the full SU(4) algebra [equation] through the contraction [equation] One representation for the operators ${S,I, G}$ [ref] uses bosonic-quark operators, [equation] where the $q^†$ and $q$ are creation and annihilation operators, respectively, for the light quark flavors and $σ^i$ ($τ^a$) are Pauli matrices in spin (isospin) space.

Implications of Large-$N_c$ QCD for the NN Interaction · Determining large-scaling · 0.81

Discussion

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