Michael T. Vaughn

TWO-LOOP RENORMALIZATION GROUP EQUATIONS IN A GENERAL QUANTUM FIELD THEORY

The two-loop renormalization group equations in a general renormalizable field theory with scalar, spin-12, and (vector) gauge fields are considered. In this paper, the anomalous dimensions associated with the wave function renormalizations of the fields are computed in a general Rξ gauge. The wave function renormalization of the gauge field in background field gauge, and hence the two-loop β function for the gauge coupling, are also evaluated.

Two-loop renormalization group equations in a general quantum field theory (II). Yukawa couplings

Abstract The two-loop β-functions for the Yukawa couplings are computed in a general renormalizable quantum field theory with scalar, spin 1 2 , and (vector) gauge fields associated with a general gauge group G. A more explicit form is given for the two-loop β-functions for the Yukawa couplings of the Higgs doublet in the minimal QCD-electroweak theory based on SU(3) × SU(2) × U(1).

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, spin-12, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (−MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).

Regularization dependence of running couplings in softly broken supersymmetry

Abstract We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N = 1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional regularization does not. We find expressions for the differences between running couplings in the modified minimal subtraction schemes of these two regularization methods, to one-loop order. We also find the two-loop renormalization group equations for gaugino masses in both schemes, and discuss the application of these results to the Minimal Supersymmetric Standard Model.

Decoupling of the epsilon -scalar mass in softly broken supersymmetry.

It has been shown recently that the introduction of an unphysical [epsilon]-scalar mass [ital [tilde m]] is necessary for the proper renormalization of softly broken supersymmetric theories by dimensional reduction (DR). In these theories, both the two-loop [beta] functions of the scalar masses and their one-loop finite corrections depend on [ital [tilde m]][sup 2]. We find, however, that the dependence on [ital [tilde m]][sup 2] can be completely removed by slightly modifying the DR renormalization scheme. We also show that previous DR calculations of one-loop corrections in supersymmetry which ignored the [ital [tilde m]][sup 2] contribution correspond to using this modified scheme.

Fermion and Higgs Masses as Probes of Unified Theories

Abstract The effects of Yukawa couplings of order of the gauge couplings in the SU(3) × SU(2) × U(1) renormalization group equations governing the evolution of observable parameters such as m b m τ and the Higgs mass are studied systematically to one-loop order. These parameters are found to give useful constraints on the mass of the t quark, and of possible heavier fermion families, in theories with SU(5)-like boundary conditions at unification energies.

Tensor methods for the exceptional group E6

Abstract We present a tensor formalism to describe irreducible representations of the exceptional group E6. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E6 irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E6 representations 27, 78, 351, 351′.

Renormalization Group Constraints on Unified Gauge Theories. 2. Yukawa and Scalar Quartic Couplings

Renormalization group constraints on the behavior of Yukawa and scalar quartic couplings in unified gauge theories are examined. Yukawa couplings are generally asymptotically free whenever the gauge couplings are, but scalar quartic couplings can be asymptotically free only for simple scalar multiplets in large groups with large fermion content. The infrared behavior of Yukawa and scalar quartic couplings implied by the renormalization group equations has interesting and phenomenologically useful consequences: infrared fixed points (or quasifixed points) lead to bounds on masses of fermions and scalars, while scalar quartic couplings can be driven out of the domain of positivity of the classical potential, with possible implications for patterns of symmetry breaking.

Asymptotic freedom constraints on grand unified gauge theories

Constraints on the fermion and Higgs scalar content of grand unified gauge theories, imposed by the requirement of asymptotic freedom for the gauge couplings, are derived for models which have fermion representations with only color singlets and color triplets. The constraintnf≦16 on the numbernf of flavors of color triplet quarks in pure QCD is removed. Definitive limits are placed on the representation content of theories based on the exceptional groups.

Renormalization of scalar quartic and Yukawa couplings in unified gauge theories based onE6

Renormalization group equations for scalar and Yukawa couplings in gauge theories based on the exceptional groupE6 are analyzed. Asymptotic freedom is possible only for a limited set of scalar fields, and then only if several fermion generations are present. The infrared behavior of the scalar quartic coupling constants is striking: they are necessarily driven out of the region of positivity of the classical potential. Some useful group theoretic relations inE6 are given in an Appendix.