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SU ( N ) -Singlet Gluon Model in Less-Than-Four Dimensions

1973; American Physical Society; Volume: 8; Issue: 8 Linguagem: Inglês

10.1103/physrevd.8.2457

1538-4500

Sun-Sheng Shei, Tung‐Mow Yan,

High-Energy Particle Collisions Research

The interaction ${g}_{0}\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{\ensuremath{\mu}}\ensuremath{\psi}{\ensuremath{\varphi}}^{\ensuremath{\mu}}$ for an $\mathrm{SU}(N)$-singlet gluon and an $N$-component fermion is studied in a space-time of dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$, slightly less than four. Wilson's prescription for coupling-constant renormalization is applied so that the theory is scale-invariant at short distances with anomalous dimensions. General properties of the model at high energies are discussed by using Callan-Symanzik equations. Anomalous dimensions of various operators including the symmetric and traceless tensors are calculated to order $\ensuremath{\epsilon}$ and are generally large except for the energy-momentum tensor. A large correction to order $\ensuremath{\epsilon}$ is also found for the parton-model prediction of the "${e}^{+}\ensuremath{-}{e}^{\ensuremath{-}}$ annihilation" total cross section. These results are qualitatively different from those in $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ scalar field theory in which these corrections are found to be very small. We also discuss briefly how a normal scaling Ward identity may become anomalous in the limit $\ensuremath{\epsilon}\ensuremath{\rightarrow}0$.