Spectral functions in quantum chromodynamics and applications

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1981

OSTI ID:6647927

Tran, M D

The longitudinal and transverse spectral functions for arbitrary conserved and non-conserved vector and axial vector currents of massive quarks are calculated to first order in ..cap alpha../sub s/ and exact analytical expressions are given. As an intermediate step the form factors to the same order in ..cap alpha../sub s/ are determined. A remarkably simple result for the combination of the spectral functions corresponding to the Weinberg's first sum rule is derived. It behaves asymptotically like ..cap alpha../sub s/s/sup 2/ thus ensuring the convergence of the sum rule. The Weinberg's second sum rule is shown to fail to hold, a new sum rule is then proposed to replace the original one. The current algebra calculation of the pion electromagnetic mass difference is reexamined in the light of quantum chromodynamics. The old analysis cannot be upheld because of the failure of the Weinberg's second sum rule. After a modification based on Dashen's theorem, the proposed sum rule then can be used to obtain a mass difference close to experimental value. Using the derived QCD corrected spectral functions on finite Q/sup 2/ sum rules, the current couplings of the five low-lying mesons ..pi.., rho, K, K*, A/sub 1/ are computed. For values of quark masses m/sub u/ = m/sub d/ = 0.25 GeV, m/sub s/ = 0.4 GeV and of the QCD scale parameter ..lambda.. = 0.5 GeV, a striking agreement with experiment is obtained. We investigate decay properties of the intermediate vector bosons Z, W. Gluonic corrections to hadronic decay modes are calculated with the account of quark mass effect. Implications of the results for decay widths, branching ratios are examined. The ratio R of reaction e/sup +/e/sup -/ ..-->.. hadrons is calculated to first order in ..cap alpha../sub s/, the quark mass effect is shown to be important.

• Research Organization: California Univ., Los Angeles (USA)
• OSTI ID: 6647927
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRAIC CURRENTS
BRANCHING RATIO
CURRENTS
DECAY
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FUNCTIONS
HADRONIC PARTICLE DECAY
MASS
PARTICLE DECAY
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARKS
SPECTRAL FUNCTIONS
SUM RULES
VECTOR CURRENTS