Nonlocal condensates and QCD sum rules for the pion wave function

Journal Article · Sat Feb 29 23:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.1754· OSTI ID:7235215

Mikhailov, S V ^[1]; Radyushkin, A V ^[2]

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1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russia) Rostov State University, Rostov on Don (Russia)
2. Continuous Electron Beam Accelerator Facility, Newport News, Virginia 23606 (United States) Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russia)

The QCD-sum-rule calculation of the pion wave function by Chernyak and Zhitnitsky (CZ) implicitly assumes that the correlation length of vacuum fluctuations is large compared to the typical hadronic scale {similar to}1/{ital m}{sub {rho}}, so that one can substitute the original nonlocal objects such as {l angle}{ital {bar q}}(0){ital q}({ital z}){r angle} by constant {l angle}{ital {bar q}}(0){ital q}(0){r angle}-type values. We outline a formalism enabling one to work directly with the nonlocal condensates, and construct a modified sum rule for the moments {l angle}{xi}{sup {ital N}}{r angle} of the pion wave function. The results are rather sensitive to the value of the parameter {lambda}{sub {ital q}}{sup 2}={l angle}{ital {bar q}D}{sup 2}{ital q}{r angle}/{l angle}{ital {bar q}q}{r angle} specifying the average virtuality of the vacuum quarks. Varying it from the most popular value {lambda}{sub {ital q}}{sup 2}=0.4 GeV{sup 2} up to the value {lambda}{sub {ital q}}{sup 2}=1.2 GeV{sup 2} suggested by the instanton-liquid model, we obtain {l angle}{xi}{sup 2}{r angle}=0.25--0.20, to be compared to the CZ value {l angle}{xi}{sup 2}{r angle}=0.43 obtained with {lambda}{sub {ital q}}{sup 2}=0.

• DOE Contract Number: AC05-84ER40150
• OSTI ID: 7235215
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 45:5; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662230* -- Quantum Chromodynamics-- (1992-)
662420 -- Properties of Mesons & Meson Resonances-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
DISTRIBUTION FUNCTIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD THEORIES
FORM FACTORS
FUNCTIONS
HADRONS
INSTANTONS
MESONS
PARTICLE PROPERTIES
PARTONS
PERTURBATION THEORY
PIONS
POSTULATED PARTICLES
PSEUDOSCALAR MESONS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARKS
QUASI PARTICLES
SUM RULES
VACUUM STATES
WAVE FUNCTIONS