Light quark masses in quantum chromodynamics and chiral symmetry breaking

Becchi, C.; Narison, Stéphan; Rafael, Eduardo de; Ynduráin, Félix

doi:10.1007/bf01546328

Cited by 171 publications

(201 citation statements)

References 21 publications

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“…where the perturbative ambiguities ∆M ren k have been given in (44). These conditions are indeed satisfied with (70).…”

Section: Cancellation Of Renormalon Ambiguitiesmentioning

confidence: 55%

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The physics of hadrons

Neubert

1996

Nuclear Physics B

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The calculation of perturbative corrections to the spectral moments observable in hadronic τ decays is reconsidered. The exact order-α 3 s results and the resummation procedure of Le Diberder and Pich are compared with a partial resummation of the perturbative series based on the analysis of so-called renormalon chains. The perturbative analysis is complemented by a model-independent description of power corrections. For the contributions of dimension four and six in the OPE, it is demonstrated how infrared renormalon ambiguities in the definition of perturbation theory can be absorbed by a redefinition of nonperturbative parameters. We find that previous determinations of QCD parameters from a measurement of spectral moments in τ decays have underestimated the theoretical uncertainties. Given the present understanding of the asymptotic behaviour of perturbation theory, the running coupling constant can be measured at best with a theoretical uncertainty δα s (m 2 τ ) ≃ 0.05, and the gluon condensate with an uncertainty of order its magnitude. Two weighted integrals of the hadronic spectral function are constructed, which can be used to test the absence of dimension-two operators and to measure directly the gluon condensate.

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“…where the perturbative ambiguities ∆M ren k have been given in (44). These conditions are indeed satisfied with (70).…”

Section: Cancellation Of Renormalon Ambiguitiesmentioning

confidence: 55%

“…[4]. For the corrections of dimension two and four, the results are [44]- [47] O (0+1) 2 = −3 1 + 13 3…”

Section: Power Correctionsmentioning

confidence: 95%

The physics of hadrons

Neubert

1996

Nuclear Physics B

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“…We have considered the renormalization-group (RG) improvement of the sum rules [19] and anomalous dimensions for condensates [20,21] in Eq. (2), where µ 0 is the renormalization scale for condensates, and…”

Section: Qcd Sum Rule For I = 0 Scalar Channelmentioning

confidence: 99%

Constraint on the light quark mass mq from QCD sum rules in the I=0 scalar channel

et al. 2017

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In this paper, we reanalyze the I = 0 scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous Hölder-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances σ and f0(980), we obtain a prediction for light quark mass mq(2 GeV) = 1 2 (mu(2 GeV) + m d (2 GeV)) = 4.7 +0.8 −0.7 MeV, which is consistent with the PDG (Particle Data Group) value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of σ and f0(980) at 2 GeV, which are approximately 0.64 − 0.83 GeV and 0.40 − 0.48 GeV respectively.

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“…However, in higher orders, additional subtractions are required. Using the Ward-identity relating the divergence of the vector (axialvector) two-point function to the scalar (pseudoscalar) two-point function [3,23], we can express Π Γ (q) in terms of 4 Lorentz-scalar two-point functions Π I (q 2 ), with I ∈ {S, P, V, A}. Then the vector (axialvector) two-point function can be written as…”

Section: The Coefficient Functionsmentioning

confidence: 99%

Current correlators to all orders in the quark masses

Jamin

Münz

1993

Z. Phys. C - Particles and Fields

103

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The contributions to the coefficient functions of the quark and the mixed quarkgluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short-and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms of non-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.

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Light quark masses in quantum chromodynamics and chiral symmetry breaking

Cited by 171 publications

References 21 publications

The physics of hadrons

The physics of hadrons

Constraint on the light quark mass mq from QCD sum rules in the I=0 scalar channel

Current correlators to all orders in the quark masses

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