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Title: Tagging the pion quark structure in QCD

Abstract

We combine the constraints on the pion quark structure available from perturbative QCD, nonperturbative QCD (nonlocal QCD sum rules and light-cone sum rules) with the analysis of current data on F{sub {pi}}{sub {gamma}}{sub {gamma}}{sub *}(Q{sup 2}), including recent high-precision lattice calculations of the second moment of the pion's distribution amplitude. We supplement these constraints with those extracted from the renormalon approach by means of the twist-four contributions to the pion distribution amplitude in order to further increase stability with respect to related theoretical uncertainties. We show which regions in the space of the first two nontrivial Gegenbauer coefficients a{sub 2} and a{sub 4} of all these constraints overlap, tagging this way the pion structure to the highest degree possible at present.

Authors:
; ;  [1]
  1. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)
Publication Date:
OSTI Identifier:
20776906
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevD.73.056002; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCURACY; AMPLITUDES; DISTRIBUTION; LATTICE FIELD THEORY; LIGHT CONE; PARTICLE STRUCTURE; PIONS; QUANTUM CHROMODYNAMICS; QUARKS; SUM RULES

Citation Formats

Bakulev, A.P., Mikhailov, S.V., and Stefanis, N.G. Tagging the pion quark structure in QCD. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.056002.
Bakulev, A.P., Mikhailov, S.V., & Stefanis, N.G. Tagging the pion quark structure in QCD. United States. doi:10.1103/PhysRevD.73.056002.
Bakulev, A.P., Mikhailov, S.V., and Stefanis, N.G. Wed . "Tagging the pion quark structure in QCD". United States. doi:10.1103/PhysRevD.73.056002.
@article{osti_20776906,
title = {Tagging the pion quark structure in QCD},
author = {Bakulev, A.P. and Mikhailov, S.V. and Stefanis, N.G.},
abstractNote = {We combine the constraints on the pion quark structure available from perturbative QCD, nonperturbative QCD (nonlocal QCD sum rules and light-cone sum rules) with the analysis of current data on F{sub {pi}}{sub {gamma}}{sub {gamma}}{sub *}(Q{sup 2}), including recent high-precision lattice calculations of the second moment of the pion's distribution amplitude. We supplement these constraints with those extracted from the renormalon approach by means of the twist-four contributions to the pion distribution amplitude in order to further increase stability with respect to related theoretical uncertainties. We show which regions in the space of the first two nontrivial Gegenbauer coefficients a{sub 2} and a{sub 4} of all these constraints overlap, tagging this way the pion structure to the highest degree possible at present.},
doi = {10.1103/PhysRevD.73.056002},
journal = {Physical Review. D, Particles Fields},
number = 5,
volume = 73,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2006},
month = {Wed Mar 01 00:00:00 EST 2006}
}
  • We propose a generalization of the QCD sum rule method for determining the pion wave function {Phi}{sub {pi}} ({ital x}) by introducing nonlocal quark condensates, {l angle}{ital {bar q}}(0){ital q}({ital z}){r angle}{equivalent to}{ital M}({ital z}{sup 2}), {l angle}{ital {bar q}}(0){ital {cflx n}{cflx A}}{sub {mu}}({ital y}){ital q}({ital z}){r angle}={ital M}{sub {mu}} ({ital y},{ital z}), etc. We show that the QCD sum rules for the moments of {Phi}{sub {pi}}({ital x}) are very sensitive to the form of the coordinate dependence of the distributions {ital M}({ital z}{sup 2}), {ital M}{sub {mu}} ({ital y},{ital z}),... . We obtain modified sum rules and possible ans{umltmore » a}tze for the nonlocal condensates. We find that for distributions with a width determined by the standard value {lambda}{sup 2}{sub {ital q}}={l angle}{ital {bar q}}{del}{sup 2}{ital q}{r angle}/{l angle}{ital {bar q}q}{r angle}=0.4 GeV{sup 2}, {Phi}{sub {pi}} ({ital x}) should differ substantially from the wave function proposed by Chernyak and Zhitnitskii. We discuss the form of {Phi}{sub {pi}} ({ital x}).« less
  • We evaluate generalized parton distributions of the pion in two chiral quark models: the spectral quark model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the {alpha} representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules, and soft-pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the t-dependence. The QCD evolution of those parton distributions is carried outmore » to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the parton distribution function and the parton distribution amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.« less
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