An Illustrative Example of How Quark-Hadron Duality Might Work

B. Blok; Da-Xin Zhang; M. Shifman

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An Illustrative Example of How Quark-Hadron Duality Might Work

B. Blok, M. Shifman, Da-Xin Zhang

High Energy Physics - Phenomenology · Submitted 13 Sep 1997 · 23 references

Pith's verdict: A real numerical width law in the 't Hooft model wrapped around a ψ-function ansatz; the qualitative picture holds, but the damping exponent carries a wave-function systematic the error bar hides.

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CitationB. Blok, Da-Xin Zhang, M. Shifman. "An Illustrative Example of How Quark-Hadron Duality Might Work." arXiv:hep-ph/9709333 (1997). https://pith.science/paper/ZE4QU4DM

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Worth reading for one number and one idea, and the authors are reasonably clear about which is which. The number: in the 't Hooft model the widths of highly excited mesons grow as √a, Γ(a) = A μ/(π²Nc)√a, with A = 0.44 ± 0.05 from summing two-body channels up to a = 500 (Figs. 1–2). That is a real calculation, the fit is clean, and √a is what phase space suggests. The idea: once widths are switched on, the Breit-Wigner resummation turns the ψ-function spectral density into a smooth unit term plus an oscillating piece damped by exp(−αs/μ²), α = A/(π⁴Nc). The structure — exponential, oscillating, exponent ∝ 1/Nc — is the part they want kept, and it lines up with what Chibisov–Dikeman–Shifman–Uraltsev argued on much shakier grounds. Soft spots, in order of weight. Footnote 4 is the one that matters: with 't Hooft's older wave function the coefficient falls to A′ ≈ 0.007, a factor of roughly 50. The quoted ±0.05 is fit scatter only; the wave-function systematic is not in it, and since α is linear in A, the oscillation-zone boundary s₀ ~ π⁴Ncμ² moves by the same factor. The claim that the √a law is robust while A is not rests on exactly two approximate wave functions, both poor at the endpoints where the overlap integrals live. So read the exponent as order-of-magnitude, not a prediction. Second, the overlap integrals are available only by e-mail — acceptable for 1997, irritating now. Third, the four-dimensional section: B, C and Δm² are chosen so the curve resembles the ALEPH spectral density, and the resemblance is then reported as qualitative agreement. That is a parametrization, not a test, and to their credit they present it as an ansatz rather than a derivation. Who should read it: anyone working on duality violations in inclusive decays, or using the 't Hooft model as a laboratory. The two-dimensional width law is citable; the four-dimensional ψ-function ansatz is a useful straw man to argue against. Send it to a referee.

Referee report

Significance

The two-dimensional part is a real calculation rather than an ansatz: the numerical width determination of Figs. 1–2 is a genuine result, the √a law is stable across two different approximate wave functions, and the analytic-structure argument of Fig. 3 is correct — the map z = Q²(Q²/2π²µ²)^{−α} of Eq. (33) indeed produces a wedge of angle 4πα removed from the z plane, so the poles sit on unphysical sheets and the physical sheet retains only the q² ≥ 0 cut. The chain from Eq. (50) to Eq. (51) is also internally consistent: expanding σ̃ for timelike s gives Im part π²δs/Δm² with δ = B/(Ncπ), hence the exponent 2πBs/(NcΔm²) and the period 2πs/Δm² quoted in Eq. (51). The paper is candid about what it has not done (abstract s3, footnote 4, Sect. 5), and the qualitative conclusion is a useful, falsifiable-in-principle statement about the shape of duality violations. The weaknesses are in the propagation of systematic uncertainty and in the evidential weight assigned to the four-dimensional comparison, not in the internal logic of the two-dimensional derivation.

Major objections (4)

[Sect. 3.2, Eq. (22) and footnote 4] The quoted A = 0.44 ± 0.05 is presented as the coefficient of the √a law, but footnote 4 reports that the same calculation with the 't Hooft wave function of Eq. (12) gives A′ ~ 0.007, a factor of roughly fifty smaller. Since α = A/(π⁴Nc) in Eq. (44) is linear in A, the damping rate, the boundary s₀ ~ π⁴Ncµ², and the amplitude shown in Fig. 4 all inherit this factor. The ±0.05 therefore reflects only the fit scatter over the 500 levels and not the dominant systematic. The authors do state in footnote 4 that the √a law survives while A does not, and in Sect. 3.4 that the slow damping is specific to the 't Hooft model, which is a fair partial acknowledgment; but the main text and Eq. (22) should carry the systematic range explicitly, or the error bar should be relabelled as statistical. As written, a reader who takes Eq. (22) at face value will overestimate the precision of the predicted oscillation-zone boundary.
[Sect. 3.2, discussion of Ref. [17]] The paper notes that the same √a law was reported in Ref. [17], but that the coefficient there is claimed to be proportional to 1/√m and therefore to diverge in the chiral limit, and dismisses the overlap with the sentence 'The coincidence looks completely accidental.' This is a load-bearing point rather than a peripheral one: the entire two-dimensional analysis is carried out at γ = 0 (massless quarks, Eq. (11) with β = 0), so if the width coefficient really scales as 1/√m, the Breit–Wigner smearing picture on which Eqs. (29)–(35) rest would be singular in precisely the limit being studied. A one-sentence dismissal is not proportionate. The authors should either exhibit the source of the discrepancy (for example, by showing where the 1/√m factor would enter the overlap integrals of Eq. (17)) or state explicitly that their result is in conflict with Ref. [17] and explain why the massless limit is nonetheless under control.
[Sect. 3.4, Fig. 4] Fig. 4 is plotted with Nc = 3 over oscillations 40 to 65, i.e. excitation numbers a ~ 40–65. The paper argues in Sect. 3.2 that the relevant 1/Nc expansion parameter is √a/Nc, so that corrections are negligible at a = Const·Nc. At Nc = 3 and a ≈ 50 this parameter is √50/3 ≈ 1.6, well above unity, so the leading-1/Nc width formula of Eq. (21) is being used outside the regime in which the paper itself justifies it. The figure is presented as an illustration of the mechanism, and it may well be that the qualitative shape is insensitive to this, but the text should say so and should not let Fig. 4 stand as a quantitative demonstration at Nc = 3. Either plot at a larger Nc, or restrict the window to a ≲ Nc, or add an explicit caveat in the caption.
[Sect. 4, Figs. 5 and 6] The comparison between Fig. 5 and the ALEPH data of Fig. 6 is offered as evidence that the model 'properly captures all important features' of real spectral densities, but Fig. 5 is generated from Eq. (50) with three parameters (Δm² = 1 GeV², C = 0.6, B = 0.78) chosen to reproduce the visible bump structure. A three-parameter fit to a curve with a handful of visible features is not a test, and the sentence 'the qualitative similarity of our model with experiment is remarkable' overstates what the comparison establishes. The authors already concede that the ρ width comes out about 1.5 times the experimental value, which sits awkwardly with 'remarkable'. The figure should be labelled explicitly as a parameter fit, and the claim downgraded to the statement that the model is capable of reproducing the qualitative shape once its parameters are fixed — which is a consistency check, not a prediction.

Minor objections (7)

[Eq. (17)] The limits of the second integral in Eq. (17) are printed ambiguously, and the upper limit appears to exceed the range over which the wave functions are defined. Since the decay couplings and hence the whole width result depend on this expression, the limits should be checked and set clearly in proof.
[Sect. 3.2, Eq. (22)] The origin of the quoted uncertainty ±0.05 is not stated: it is unclear whether it is the scatter of the averaged widths about the fit of Fig. 2, the residual of the fit over the range a ≤ 500, or an estimate of the truncation of the sum in Eq. (19). This should be specified.
[Sect. 3.2, Eq. (19) and footnote 18] The numerical procedure is not documented: the truncation of the double sum over b and c, the treatment of the triangular-function endpoint, and any convergence check with a are all omitted. Footnote 18 offers the program by e-mail, which was standard practice, but a short appendix describing the method and stating the estimated numerical error would make the central result of Figs. 1–2 reproducible.
[Sect. 3.4, Eq. (43)] The '1' in the square bracket of Eq. (43) is attributed to the leading OPE term, but the decomposition of Eq. (39) into three pieces means that the ψ(−σ̃) and 1/σ̃ terms also contribute to the smooth part. A sentence confirming that these only renormalize the OPE corrections of Eq. (38) and do not shift the constant term would remove an ambiguity.
[Fig. 3(b)] The caption refers to a 'defect angle' without giving its value. Since the wedge angle is 4πα = 4A/(π³Nc), stating this explicitly would let the reader check the analytic-structure claim directly.
[Sect. 5] The closing remark that a component of the same structure is 'quite probable' in hard quantities without OPE, such as thrust, is speculative and is not supported anywhere in the paper. It should either be softened to an open question or backed by a concrete estimate.
[References and front matter] Several typographical errors should be corrected: Ref. [3] is dated 1977 but should be 1997; Ref. [17] reads 'M. Bishary' and is presumably Bishari; Ref. [21] reads 'N. Neurberger' and should be Neuberger; the Minnesota address gives ZIP code 54555 rather than 55455; the affiliation reads 'Technio n'; the text contains 'opresented' (Sect. 1) and 'dsip layed' (Fig. 4 caption); the acknowledgment has 'by by Grant'; and Ref. [23] has 'uncertanties'. Some of the broken spacing elsewhere in the manuscript may be a typesetting artifact and is not held against the authors.

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The paper

The paper claims

The mismatch between smooth quark-level predictions and the real hadron spectrum is not random noise but a damped oscillation, and in a solvable two-dimensional model of QCD its damping rate is set by how fast resonance widths grow with Exc

The reading

Quark-hadron duality is the working assumption that a smooth quark-gluon calculation, continued from the Euclidean to the Minkowski domain, reproduces the actual hadronic cross section at high energy. The paper asks what the *residual* looks like: the piece left over when the smooth curve is subtracted from the true spectral density. Working in the 't Hooft model, two-dimensional QCD in the limit of many colors where mesons are infinitely narrow and the spectrum is exactly solvable, the authors compute how the widths of highly excited mesons grow with excitation number and then resum the resonances in a Breit-Wigner form. The answer is that the leftover piece is an oscillation whose amplitude falls off exponentially with energy, with the exponent proportional to $1/N_c$ and fixed by the width growth law. The authors then propose the same functional form, with a different width scaling taken from a flux-tube argument, as a realistic description of four-dimensional QCD, and show that the resulting curve resembles measured $e^+e^-$ and $e^+e^-$/$e^+e^-$-annihilation spectral densities. If correct, this turns the vague statement that duality violations are exponentially small into a specific, parameterized shape that could be modelled or bounded in heavy-quark and tau-decay analyses.

What carries the argument

The load-bearing device is the psi-function ansatz: a spectral density of infinitely narrow, equally spaced resonances with equal residues gives a polarization operator proportional to the logarithmic derivative of the gamma function, $Π(Q^2) - Π(0) = -(N_c/2π) ψ(σ)$ with $σ = Q^2/(2π^2 μ^2) + 1/2$. Its asymptotic expansion has factorially growing, sign-alternating coefficients, which is what makes the truncated series a good approximation in the Euclidean domain yet blind to an oscillating component in the Minkowski domain. Switching on finite widths amounts to replacing $σ$ by a shifted variable $z = Q^2 (Q^2/2π^2 μ^2)^{-α}$ with $α = A/(π^4 N_c)$, which moves all poles onto the unphysical sheet and leaves the correct analytic structure. The reflection formula for $ψ$ then separates the smooth part from the oscillating part, and the imaginary part of the cotangent term produces the damped oscillation explicitly. In four dimensions the same construction is reused with the exponent rescaled by the linear width law.

Extended reading notes

Core claim

The paper's central claim is that the duality-violating component of a hadronic spectral density has a definite shape: an oscillation superimposed on the smooth operator-product-expansion curve, with an amplitude damped exponentially in energy, $1 + 2 e^{-2y}/(1 - e^{-2y})$-type behaviour reducing at high energy to $1 + 2e^{-2y}$ times a cosine. In the 't Hooft model the authors compute the decay widths of highly excited mesons to leading order in $1/N_c$ and report that the averaged width follows a square-root law in the excitation number, $G(a) = A$ times $m$ over $e^2 N_c$ times $a^{1/2}$ with $A = 0.44 ± 0.05$, holding numerically up to $a = 500$. Feeding this into a Breit-Wigner resummation of the two-scalar-current polarization operator gives a spectral density whose deviation from the smooth curve is $2 e^{-2y}$ times a cosine, with the damping exponent linear in $A$ and in $1/N_c$. The authors stress that the exponential-with-oscillation character is generic while the numerical rate is model-dependent, and they extend the same ansatz to four dimensions by replacing the square-root width law with a linear one, $G_n$ proportional to $m_n/N_c$, motivated by a flux-tube picture in which a quark-antiquark pair can be created anywhere along a tube of length proportional to $m_n$.

Load-bearing premise

The quantitative damping rate rests on computing overlap integrals with an approximate large-$n$ meson wave function, and the paper's own footnote records that the older wave function leaves the square-root law intact but changes the coefficient $A$ by roughly a factor of fifty, which propagates directly into the predicted exponent.

Editorial extensions

If this is right

The deviation from local quark-hadron duality is not an unconstrained nuisance but a specific damped oscillation, so its size at a given energy can be estimated once the resonance width law is known.
There is a sharp crossover energy, where the resonance width becomes comparable to the spacing between neighbouring resonances, below which the spectral density is a sequence of visible peaks and above which it is a smooth curve plus a small oscillation.
Because the damping exponent scales as $1/N_c$, the duality-violating component is a leading-order-in-$1/N_c$ effect in its onset and a subleading correction to the smooth term at high energy, which sharpens how $1/N_c$ bookkeeping should be applied to Minkowski observables.
The four-dimensional ansatz, with a linear width law $G_n$ proportional to $m_n/N_c$, reproduces the qualitative look of measured vector spectral densities in $e^+e^-$ annihilation and tau decays, including the broadening of the rho-like peak.
The same oscillating component should be expected in observables that lack a clean operator-product expansion, such as event-shape variables, where power corrections are already known to be needed.

Reading between the lines

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

If the width law really controls the damping rate, then measuring the residual oscillation in tau-decay spectral densities would be an indirect measurement of high-excitation meson widths, which are otherwise inaccessible.
The factor-of-order-fifty spread in the coefficient between two admissible large-$n$ wave functions suggests that the qualitative shape is robust but any quantitative use of the exponent requires an independent determination of the width law, for instance from lattice studies of excited-state decay widths.
Because the construction only needs the leading large-$n$ behaviour of the masses and residues, the same machinery could be applied to other confining theories with approximately linear Regge trajectories, where the psi-function ansatz would serve as a controlled null hypothesis for duality violations.
The paper's own comparison to data is qualitative; a natural next step would be a fit that treats the damping exponent as a free parameter and checks whether the fitted value is consistent with the $1/N_c$ scaling.

Original abstract

We discuss the issue of the local quark-hadron duality at high energies in two- and four-dimensional QCD. A mechanism of the dynamical realization of the quark-hadron duality in two- dimensional QCD in the limit of large number of colors, N_c -> \infty, (the 't Hooft model) is considered. A similar mechanism of dynamical smearing may be relevant in four-dimensional QCD. Although particular details of our results are model-dependent, the general features of the duality implementation conjectured previously get further support.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.55 · mentions code or data availability 0.02.

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

We discuss the issue of the local quark-hadron duality at high energies in two- and four-dimensional QCD. A mechanism of the dynamical realization of the quark-hadron duality in two- dimensional QCD in the limit of large number of colors, N_c -> \infty, (the 't Hooft model) is considered. A similar mechanism of dynamical smearing may be relevant in four-dimensional QCD. Although particular details of our results are model-dependent, the general features of the duality implementation conjectured previously get further support.

background contribution method result interpretation main claim

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss the issue of the local quark-hadron duality at high energies in two- and four-dimensional QCD.	contribution 0.55	0.73	0.06	unclear 0.69
s1	A mechanism of the dynamical realization of the quark-hadron duality in two- dimensional QCD in the limit of large number of colors, N_c -> \infty, (the 't Hooft model) is considered.	contribution 0.51	0.66	0.10	asserted 0.89
s2	A similar mechanism of dynamical smearing may be relevant in four-dimensional QCD.	interpretation 0.97	0.21	0.19	hedged possibility 0.98
s3	Although particular details of our results are model-dependent, the general features of the duality implementation conjectured previously get further support.	interpretation 0.87	0.64	0.70	hedged possibility 0.51

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from argument 0.58.

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arXiv listing abstract v1

not examined

full text
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P abstract

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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.** The width of the a-th state (in units of µπ−2N −1 c ) as a function of a up to a = 500. 9

**Figure 2.** Smeared widths in the same interval of a and the square-root fit, Eq. (21). 10

**Figure 3.** Analytical structure of the polarization operator. (

**Figure 4.** The spectral density corresponding to Eq. (34) in the ’t H

**Figure 5.** The imaginary part of the polarization operator correspo

**Figure 6.** The spectral density in the vector isoscalar channel mea

Figures reproduced from arXiv:hep-ph/9709333 by the authors.

References

Works cited (23)

[17]

M. Bishary, Ann. Phys. (N.Y.) 129 (1980) 435

View on Pith 1980
[1]

K. Wilson, Phys. Rev. 179 (1969) 1499; Phys. Rev. D3 (1971) 1818; Proc. 1971 Int. Symp. on Electron and Photon Interactions at High Energies, N. Mistry, Ed. (New York, 1972), p. 115; K. Wilson and J. Kogut, Phys. Reports 12 (1974) 75; A. M. Polyakov, 1970, unpublished

View on Pith 1969
[2]

M. Shifman, Theory of Preasymptotic Eﬀects in Weak Inclusive Decays, in Proc. Workshop on Continuous Advances in QCD , ed. A. Smilga (World Scientiﬁc, Singapore, 1994), page 249 [hep-ph/9405246]; Recent Progress in the Heavy Quark Theory , in Particles, Strings and Cosmology , Proc. PASCOS-95, ed. J. Bagger et al. (World Scientiﬁc, Singapore, 1996), page ...

View on Pith Pith review arXiv 1994
[3]

B. Chibisov, R. Dikeman, M. Shifman and N. Uraltsev, Int. J. Mod. Phys. A12 (1977) 2075

View on Pith 1977
[4]

V. Novikov, M. Shifman, A. Vainshtein, V. Zakharov, Nucl. Phys. B249 (1985) 445. 21

View on Pith 1985
[5]

B. Blok and T. Mannel, Mod. Phys. Lett. A11 (1996) 1263; B. Blok, M. Shifman, and N. Uraltsev, Nucl. Phys. B494 (1997) 237

View on Pith 1996
[6]

Z.X. Wang and D.R. Guo, Special Functions , (World Scientiﬁc, Singapore, 1989)

View on Pith 1989
[7]

G. ’t Hooft, Nucl. Phys. B75 (1974) 461 [Reprinted in G. ’t Hooft, Under the Spell of the Gauge Principle (World Scientiﬁc, Singapore 1994), page 443]; see also Ref. [8] for a discussion of subtleties in the regularization of the ’t Hooft model

View on Pith 1974
[8]

F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. Phys. (N.Y.) 208 (1991) 1

View on Pith 1991
[9]

C. Callan, N. Coote, and D. Gross, Phys. Rev. D13 (1976) 1649

View on Pith 1976
[10]

M. Einhorn, Phys. Rev. D14 (1976) 3451

View on Pith 1976
[11]

M. Einhorn, S. Nussinov, and E. Rabinovici, Phys. Rev. D15 (1977) 2282

View on Pith 1977
[12]

I. Bars and M. Green, Phys. Rev. D17 (1978) 537

View on Pith 1978
[13]

A. Zhitnitsky, Phys. Rev. D53 (1996) 5821

View on Pith 1996
[14]

P. Colangelo, C. Dominguez, and G. Nardulli, hep-ph/9705390

View on Pith Pith review arXiv
[15]

M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B147 (1979) 385

View on Pith 1979
[16]

W. Krauss and M. Staudacher, Phys. Lett. B388 (1997) 808

View on Pith 1997
[18]

The full answer and the program used to generate it can be obt ained from the authors via e-mail

View on Pith
[19]

A. Zhitnitsky, Sov. J. Nucl. Phys. 43 (1986) 999; 44 (1986) 139

View on Pith 1986
[20]

M. B. Green and G. Veneziano, Phys. Lett. B36 (1971) 477; A.Yu. Dubin, A.B. Kaidalov, and Yu.A. Simonov, Phys. Lett. B323 (1994) 41

View on Pith 1971
[21]

A. Casher, N. Neurberger and S. Nussinov, Phys. Rev. D20 (1979) 179

View on Pith 1979
[22]

R. Barate et al. (ALEPH Collab.), Measurement of the spectral functions of vector current hadronic τ decays, Preprint CERN PPE/97-013

View on Pith
[23]

V.M. Braun, Theoretical uncertanties in the determination of αs from hadronic event observables: the impact of nonperturbative eﬀects , Talk at Annual Meeting of Division of Particles and Fields of the APS (DPF‘96), Minneapolis, MN, August 10–15, 1996 [hep-ph/9610212]. 22

View on Pith Pith review arXiv 1996

Forward citations

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hep-ph 2014-10 conditional novelty 5.0 of 10

A duality-violation-aware fit to revised ALEPH tau-decay data gives the strong coupling at the tau mass as 0.296 (FOPT) to 0.310 (CIPT), below the standard-analysis value of 0.332.
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Modeling duality-violating contributions to the tau hadronic spectral functions lowers the extracted coupling to alpha_s(m_tau^2) = 0.307 +/- 0.019 (FOPT) and 0.322 +/- 0.026 (CIPT), versus OPAL's 0.324 and 0.348.
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States the same result 1 paper

Although particular details of our results are model-dependent (especially in the latter case), the general features of the duality implementation conjectured previously get further support.

How quark hadron duality in QCD may work · 0.99

Papers citing it · 34 sentences without a confident label

Builds on it 1 paper

Finally, we have also considered a model at finite $N_c$ [ref] and modified it to allow for the inclusion of perturbative (logarithmic) corrections.

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Uses its method or tool 4 papers

The model we will use to illustrate the possible role of DVs follows a suggestion of Refs. [ref] .

Unraveling duality violations in hadronic tau decays · The model · 0.85
To this end we model the tower of vector-meson resonances as in [ref] and connect it to the QCDF expressions via dispersion relations such that the asymptotic behaviour (i.e. far away from the resonances) of the perturbative result is reproduced.

$D \to \rho \,\ell^+\ell^-$ Decays in the QCD Factorization Approach · Introduction · 0.94
This ansatz, based on Regge theory, large-$N_c$, and analyticity [ref] , is given by [ref] [equation] Introducing the DV ansatz above adds four new fit parameters per channel on top of the OPE parameters considered in earlier studies.

On the Extraction of the Strong Coupling from Hadronic Tau Decay · Strategy · 0.92

Uses its data or values 1 paper

In this figure, the blue dashed curve shows the result of a physically motivated model for the vacuum polarization in the $I=1$ channel based on the experimental data obtained in non-strange hadronic $τ$ decays, supplemented by a successful model of duality violations at energies above the $τ$ mass [ref] (see Ref. [ref] for more details).

A Hybrid Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2)_\mu$ · Introduction · 0.87

Cites it as background 9 papers

These updates employ different methods: while perturbation theory and the operator product expansion (OPE) are central to both, they differ in the way they treat resonance effects, or, equivalently, violations of quark-hadron duality (DVs) [ref] .

The status of the strong coupling from tau decays in 2016 · Introduction · 0.90
The perturbative spectral density $ρ_pert(s,μ)$ vanishes below some “theoretical” threshold $s_th.$ For an interpolating current formed by a quark and an antiquark, of masses $m_1$ and $m_2,$ respectively, $s_th$ is given by $s_th=(m_1+m_2)^2.$ Therefore, referring by $Π_NP(τ,μ)$ to the Borel transform of the total nonperturbative contribution to the QCD spectral density $ρ_QCD(s),$ our Borel-transformed (or “Borelized”) correlation function $Π(τ)$ reads [equation] As the final step, any ignorance about the contributions of higher states to the spectral densities may be swept under the carpet by invoking the assumption of (global) quark–hadron duality [ref] , postulating that above — $τ$-dependent [ref] — effective thresholds $s_eff(τ)$ the solely perturbative contributions to the QCD-level correlator cancel the ones of all excited and continuum states to the hadronic correlator: [equati

On the description of exotic hadron states within QCD sum rules · QCD sum-rule formalism: the example of two-point correlation functions · 0.80
In the previous studies, this test is applied for hadronic spectral density functions [ref] related to $e^+e^-$ annihilation and $τ$ decays, deep inelastic scattering [ref] and heavy meson decays [ref] .

Quark-hadron duality for heavy meson mixings in the 't Hooft model · Introduction · 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] [17]

M. Bishary, Ann. Phys. (N.Y.) 129 (1980) 435

View on Pith 1980

[2] [1]

K. Wilson, Phys. Rev. 179 (1969) 1499; Phys. Rev. D3 (1971) 1818; Proc. 1971 Int. Symp. on Electron and Photon Interactions at High Energies, N. Mistry, Ed. (New York, 1972), p. 115; K. Wilson and J. Kogut, Phys. Reports 12 (1974) 75; A. M. Polyakov, 1970, unpublished

View on Pith 1969

[3] [2]

M. Shifman, Theory of Preasymptotic Eﬀects in Weak Inclusive Decays, in Proc. Workshop on Continuous Advances in QCD , ed. A. Smilga (World Scientiﬁc, Singapore, 1994), page 249 [hep-ph/9405246]; Recent Progress in the Heavy Quark Theory , in Particles, Strings and Cosmology , Proc. PASCOS-95, ed. J. Bagger et al. (World Scientiﬁc, Singapore, 1996), page ...

View on Pith Pith review arXiv 1994

[4] [3]

B. Chibisov, R. Dikeman, M. Shifman and N. Uraltsev, Int. J. Mod. Phys. A12 (1977) 2075

View on Pith 1977

[5] [4]

V. Novikov, M. Shifman, A. Vainshtein, V. Zakharov, Nucl. Phys. B249 (1985) 445. 21

View on Pith 1985

[6] [5]

B. Blok and T. Mannel, Mod. Phys. Lett. A11 (1996) 1263; B. Blok, M. Shifman, and N. Uraltsev, Nucl. Phys. B494 (1997) 237

View on Pith 1996

[7] [6]

Z.X. Wang and D.R. Guo, Special Functions , (World Scientiﬁc, Singapore, 1989)

View on Pith 1989

[8] [7]

G. ’t Hooft, Nucl. Phys. B75 (1974) 461 [Reprinted in G. ’t Hooft, Under the Spell of the Gauge Principle (World Scientiﬁc, Singapore 1994), page 443]; see also Ref. [8] for a discussion of subtleties in the regularization of the ’t Hooft model

View on Pith 1974

[9] [8]

F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. Phys. (N.Y.) 208 (1991) 1

View on Pith 1991

[10] [9]

C. Callan, N. Coote, and D. Gross, Phys. Rev. D13 (1976) 1649

View on Pith 1976

[11] [10]

M. Einhorn, Phys. Rev. D14 (1976) 3451

View on Pith 1976

[12] [11]

M. Einhorn, S. Nussinov, and E. Rabinovici, Phys. Rev. D15 (1977) 2282

View on Pith 1977

[13] [12]

I. Bars and M. Green, Phys. Rev. D17 (1978) 537

View on Pith 1978

[14] [13]

A. Zhitnitsky, Phys. Rev. D53 (1996) 5821

View on Pith 1996

[15] [14]

P. Colangelo, C. Dominguez, and G. Nardulli, hep-ph/9705390

View on Pith Pith review arXiv

[16] [15]

M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B147 (1979) 385

View on Pith 1979

[17] [16]

W. Krauss and M. Staudacher, Phys. Lett. B388 (1997) 808

View on Pith 1997

[18] [18]

The full answer and the program used to generate it can be obt ained from the authors via e-mail

View on Pith

[19] [19]

A. Zhitnitsky, Sov. J. Nucl. Phys. 43 (1986) 999; 44 (1986) 139

View on Pith 1986

[20] [20]

M. B. Green and G. Veneziano, Phys. Lett. B36 (1971) 477; A.Yu. Dubin, A.B. Kaidalov, and Yu.A. Simonov, Phys. Lett. B323 (1994) 41

View on Pith 1971

[21] [21]

A. Casher, N. Neurberger and S. Nussinov, Phys. Rev. D20 (1979) 179

View on Pith 1979

[22] [22]

R. Barate et al. (ALEPH Collab.), Measurement of the spectral functions of vector current hadronic τ decays, Preprint CERN PPE/97-013

View on Pith

[23] [23]

V.M. Braun, Theoretical uncertanties in the determination of αs from hadronic event observables: the impact of nonperturbative eﬀects , Talk at Annual Meeting of Division of Particles and Fields of the APS (DPF‘96), Minneapolis, MN, August 10–15, 1996 [hep-ph/9610212]. 22

View on Pith Pith review arXiv 1996