High-energy color-singlet--color-singlet scattering in non-Abelian gauge theories

Journal Article · Tue Mar 15 04:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.1736· OSTI ID:7312125

Stockham, C D

In the quark model, hadrons are thought to be singlet states with respect to ''color'' SU(3). Therefore, in this paper, we study singlet-singlet scattering in a non-Abelian gauge theory in which color SU(3) is the gauge symmetry. We avoid the difficult bound-state problem by representing the hadron as a scalar field phi, a color singlet, which interacts with the quarks through an effective coupling: Gphi summation/sup 3//sub i//sub 1/ psi-bar/sub i/psi/sub i/. We calculate the high-energy (s ..-->.. infinity,t < or = 0 fixed) phiphi scattering amplitude to sixth order in the quark-gluon coupling constant g. The calculation is done by using the ''infinite-momentum technique'' as developed by Chang and Ma. To justify this technique we also calculate high-energy fermion-fermion scattering in a non-Abelian gauge theory using a more rigorous method. We compare our result with an ''infinite-momentum technique'' calculation done by McCoy and Wu and a similar calculation done by Tyburski. The phiphi scattering amplitude is infrared finite. The total cross section for high-energy phiphi scattering is found to be sigma/sub phi phi/ = 64g/sup 4/G/sup 4/(2..pi..)/sup -12/..pi../sup 7/(N/sub 1/(b) - (3g/sup 2//8..pi../sup 2/) lnsN/sub 2/(b)), where N/sub 1/(b) and N/sub 2/(b) are positive functions depending only on b = (..mu../sup 2/ - 4m/sup 2/)/sup 1///sup 2//..mu.., where ..mu.. is the hadron mass and m is the quark mass.

• Research Organization: Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853
• OSTI ID: 7312125
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
BOUND STATE
COLOR MODEL
COMPOSITE MODELS
COUPLING CONSTANTS
CROSS SECTIONS
DIAGRAMS
ELEMENTARY PARTICLES
FEYNMAN DIAGRAM
GAUGE INVARIANCE
GLUON MODEL
HADRON-HADRON INTERACTIONS
HADRONS
INTERACTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE INTERACTIONS
PARTICLE MODELS
QUARK MODEL
RENORMALIZATION
SCATTERING AMPLITUDES
SU GROUPS
SU-3 GROUPS
SYMMETRY
SYMMETRY GROUPS
TOTAL CROSS SECTIONS