Frozen and broken color: A matrix Schroedinger equation in the semiclassical limit

Journal Article · Tue Jun 01 00:00:00 EDT 1982 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(82)90272-X· OSTI ID:6773970

Bjorken, J D; Orbach, H S

A simple one-dimensional theory is considered in which a colored spinless quark and antiquark are bound together by a confining, color-dependent potential. To investigate the dynamics underlying Lipkin's mechanism of hidden charge, and how his conclusions are modified in the presence of symmetry breaking. The case of ''frozen color'' is considered. Using semiclassical WKB formalism, the spectrum of bound states is constructed. To determine the charge of the constituents, deep-inelastic scattering of an external probe (e.g., lepton) from our one-dimensional meson is considered. The structure function, ..cap omega.., is calculated explicitly in the WKB limit and it is shown how Lipkin's mechanism is manifested, as well as how scaling behavior comes about. The dominant physical process is one of excitation of a semiclassical state by the hard collision of the probe with the quark or antiquark. These considerations are generalized to the case of broken color symmetry--but where the breaking is not so strong as to allow low-lying states to have a large amount of mixing with the colored states. In this case, the degeneracy of excited colored states can be broken. Again deep-inelastic scattering can be used to measure the charges of the constituents, and there will again be a distinct contribution from each type of ''classical'' state which can be excited by the external probe. However, in the general case, the charge measured via excitation of a given state can be energy dependent. Local excitation of color is found to guarantee global excitation of color. However, global existence of color does not guarantee the excitation of colored states via deep-inelastic processes. Finally, even in the absence of direct physical application, we have examined how to implement the WKB method for bound-state problems in the presence of internal degrees of freedom.

• Research Organization: SLAC National Accelerator Lab., Menlo Park, CA (United States)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 6773970
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 141:1
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COLOR MODEL
SEMICLASSICAL APPROXIMATION
SYMMETRY BREAKING
BOUND STATE
DEEP INELASTIC SCATTERING
HAMILTONIANS
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION
STRUCTURE FUNCTIONS
WKB APPROXIMATION
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INELASTIC SCATTERING
INTERACTIONS
LEPTON-BARYON INTERACTIONS
LEPTON-HADRON INTERACTIONS
LEPTON-NUCLEON INTERACTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PARTICLE MODELS
QUANTUM OPERATORS
QUARK MODEL
SCATTERING
WAVE EQUATIONS
645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties