Nonlocal condensates and QCD sum rules for the pion wave function

Михайлов, С. В.; Radyushkin, Anatoly

doi:10.1103/physrevd.45.1754

Cited by 192 publications

(256 citation statements)

References 16 publications

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“…Refs. [26,27,28,29] and references therein) the non-local quark condensate, 16) plays an important role. In our approach 17) and, consequently, after performing the Fourier-Bessel transform, 18) where x denotes the Minkowski coordinate.…”

Section: B Quark Condensatementioning

confidence: 99%

Spectral quark model and low-energy hadron phenomenology

Arriola

Broniowski

2003

Phys. Rev. D

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We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations, valid at the low-energy scale of the model, can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc. These quantities, obtained at a low-energy scale of the model, have correct properties, as requested by symmetries and anomalies. They also have pure twist expansion, free of logarithmic corrections, as requested by the QCD factorization property.

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Section: B Quark Condensatementioning

confidence: 99%

Spectral quark model and low-energy hadron phenomenology

Arriola

Broniowski

2003

Phys. Rev. D

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“…(ii) How to improve the nonperturbative input by employing a pion DA which incorporates the nonperturbative features of the QCD vacuum in terms of a nonlocal quark condensate [64,65,66,67,68]. This accounts for the possibility that vacuum quarks can flow with a nonzero average virtuality λ 2 q , in an attempt to connect dynamic properties of the pion, like its electromagnetic form factor, directly with the QCD vacuum structure (we refer to [34] for further details).…”

Section: Introductionmentioning

confidence: 99%

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Bakulev¹,

Passek‐Kumerički²,

Schroers³

et al. 2004

Phys. Rev. D

118

252

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We present an investigation of the pion's electromagnetic form factor F π (Q 2 ) in the spacelike region utilizing two new ingredients: (i) a double-humped, endpoint-suppressed pion distribution amplitude derived before via QCD sum rules with nonlocal condensates-found to comply at the 1σ level with the CLEO data on the πγ transition-and (ii) analytic perturbation theory at the level of parton amplitudes for hadronic reactions. The computation of F π (Q 2 ) within this approach is performed at NLO of QCD perturbation theory (standard and analytic), including the evolution of the pion distribution amplitude at the same order. We consider the NLO corrections to the form factor in the MS scheme with various renormalization scale settings and also in the α Vscheme. We find that using standard perturbation theory, the size of the NLO corrections is quite sensitive to the adopted renormalization scheme and scale setting. The main results of our analysis are the following: (i) Replacing the QCD coupling and its powers by their analytic images, both dependencies are diminished and the predictions for the pion form factor are quasi scheme and scale-setting independent. (ii) The magnitude of the factorized pion form factor, calculated with the aforementioned pion distribution amplitude, is only slightly larger than the result obtained with the asymptotic one in all considered schemes. (iii) Including the soft pion form factor via local duality and ensuring the Ward identity at Q 2 = 0, we present predictions that are in remarkably good agreement with the existing experimental data both in trend and magnitude.

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“…In the analysis here, we use the general parameterization for the nonlocal quark condensate [22], [23] q(x)q(0) = qq…”

Section: The Qcd Sum Rulesmentioning

confidence: 99%

Light-cone wave functions of heavy baryons

2012

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We present a classification of the three-quark light-cone distribution amplitudes (LCDAs) for ground-state heavy baryons with the spin parities J P = 1/2 + and J P = 3/2 + in QCD in the heavy-quark symmetry limit and calculate several lowest moments of LCDAs based on QCD sum rules. We propose simple model functions for the heavy-baryon distribution amplitudes and analyze their dependence on the energy scale.

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Nonlocal condensates and QCD sum rules for the pion wave function

Cited by 192 publications

References 16 publications

Spectral quark model and low-energy hadron phenomenology

Spectral quark model and low-energy hadron phenomenology

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Light-cone wave functions of heavy baryons

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