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

Journal Article · Tue Mar 15 00:00:00 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), Vol. 15:6
• Country of Publication: United States
• Language: English

Related Subjects

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