Higher-order effects of asymptotically free field theories. [Structure functios, parton model, sum rules, effective coupling constant]

Journal Article · Tue Feb 01 04:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.730· OSTI ID:7225962

Calvo, M

Several experimental consequences of non-Abelian asymptotically free gauge theories are derived, in particular, second-order corrections to the moments of the nonsinglet pieces of the structure functions of deep-inelastic lepton-hadron scattering are calculated. These results are then used to obtain corrections to the parton-model sum rules, as well as to derive some direct functional relationships among the structure functions. If asymptotic behavior is assumed, the second-order correction terms involve calculable and uncalculable contributions; however, by considering suitable combinations of structure functions, the latter can be eliminated, thus obtaining some definite predictions. It is also found that some of these correction terms increase as one calculates higher moments of the structure functions. This remarkable fact, which is likely to persist in higher orders, suggests that all the functional relationships that are derived here and elsewhere have questionable validity near threshold; however, away from this region, where higher-order terms become negligible, they provide an important test of these theories. It is also shown that no similar predictions can be made for the singlet pieces of the structure functions since they always involve uncalculable constants. The question of the asymptotic region is discussed and it is indicated that the present range of energies (25 GeV in electroproduction and 150 GeV in neutrino production) is sufficiently high to test these theoretical asymptotic predictions. By making some reasonable assumptions, it is found that the effective coupling constant in these ranges of energies is > or =1 so that according to these models, the asymptotic region has not yet been achieved. However, by regarding the expansion in terms of the effective coupling constant as an experimentally measurable parameter, it is possible (but not certain) that one obtains measurable theoretical predictions within the range of present energies.

• Research Organization: Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 7225962
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:3; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645203* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Weak Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
CHIRAL SYMMETRY
COMPOSITE MODELS
COUPLING CONSTANTS
DEEP INELASTIC SCATTERING
EQUATIONS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
INELASTIC SCATTERING
INTERACTIONS
INVARIANCE PRINCIPLES
LEPTON-BARYON INTERACTIONS
LEPTON-HADRON INTERACTIONS
LEPTON-NUCLEON INTERACTIONS
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE INTERACTIONS
PARTICLE MODELS
PARTON MODEL
QUARK MODEL
SCATTERING
SPINORS
STRUCTURE FUNCTIONS
SU GROUPS
SU-3 GROUPS
SUM RULES
SYMMETRY
SYMMETRY GROUPS