Pion and an improved static bag model

Journal Article · Tue Apr 01 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.1975· OSTI ID:5448068

Donoghue, J F; Johnson, K

Quark-model calculations involve an extended static object localized in space. We introduce new methods, involving momentum-space wave packets, which account for this localization. These methods have little effect on heavy states, whose sizes are large compared to their Compton size 1/m, but are very important for light particles such as the pion. In this treatment the pion's mass is naturally very small, and, in order to connect with a spontaneously broken chiral symmetry, we require that m/sub ..pi../ vanish when the light quarks are massless. Expanding about this limit (and also readjusting the fit to other hadrons), we obtain m/sub q/=(m-italic/sub u/+m/sub d/)/2=33 MeV. We calculate F/sub ..pi../ approx. = 145 MeV (using a normalization such that F/sub ..pi../ vertical-bar /sub exp/=93 MeV), F/sub K//F/sub ..pi../ approx. = 1, and various corrections to static properties of baryons. In addition we explore the relationship of our methods with chiral perturbation theory, deriving the formula m/sub ..pi../ /sup 2/=(m-italic/sub u/+m/sub d/) < ..pi..(p) vertical-bar q-bar(0)q(0) vertical-bar ..pi..(p) > in the appropriate approximation and commenting on the quark mass obtained from the nucleon's sigma term. Finally we discuss the bag model's use of the scalar density q-barq as an order parameter describing the separation of the spontaneously broken vacuum phase from the perturbative vacuum of the bag's interior.

• Research Organization: Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• DOE Contract Number: EY-76-C-02-3069
• OSTI ID: 5448068
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:7; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645205* -- High Energy Physics-- Particle Interactions &amp; Properties-Theoretical-- Strong Interactions
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645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BAG MODEL
BOSONS
BOUND STATE
CHIRAL SYMMETRY
COMPOSITE MODELS
ELEMENTARY PARTICLES
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
GOLDSTONE BOSONS
HADRONS
INTERACTIONS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL MODELS
MESONS
PARTICLE INTERACTIONS
PARTICLE MODELS
PCAC THEORY
PERTURBATION THEORY
PIONS
POSTULATED PARTICLES
PSEUDOSCALAR MESONS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUARK-ANTIQUARK INTERACTIONS
SU GROUPS
SU-2 GROUPS
SYMMETRY
SYMMETRY BREAKING
SYMMETRY GROUPS
VACUUM STATES