We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.Comment: 22 pages plus three PostScript figures (appended), Liverpool preprint LTH 288, University of Michigan preprint UM-TH-92-2

Eective Lagrangians can be used to parametrize the eects of physics beyond the standard model. Assuming the complete theory is a gauge theory, w e determine which eective operators may be generated at tree level, and which are only generated at loop level. The latter are be suppressed by factors of 1=16 2 and will therefore be quite dicult to detect. In particular, all operators changing the Standard-Model structure of the triple-gauge-vector couplings fall into this category. W e also point out that in certain cases, dimension-eight operators may be more important than dimension-six operators. We discuss both the linear and non-linear representation of the Higgs sector.

We consider the predictions for the weak mixing angle 0w and the scale M of unification in a supersymmetric extension of SU(5). with particular emphasis on the sensitivity to the number of Higgs multiplets. In the one-loop approximation, we also calculate the ratio nrJrn,. We discuss generally the effects of an intermediate threshold between the weak interaction scale and M and estimate the sensitivity of 6'w and M to the scale of supersymmetry breaking The evolution of the coupling constants of the supersymmetric SU(3) 8 SU(2) @ U(1) effective gauge theory is described and the two-loop corrections to 6', and M are calculated.

We explore in the supergravity context the possibility that a Higgs scalar may drive inflation via a non-minimal coupling to gravity characterised by a large dimensionless coupling constant. We find that this scenario is not compatible with the MSSM, but that adding a singlet field (NMSSM, or a variant thereof) can very naturally give rise to slow-roll inflation. The inflaton is necessarily contained in the doublet Higgs sector and occurs in the D-flat direction of the two Higgs doublets.

No abstract

The impact of new interactions at very high energies on the spontaneous breaking of chiral symmetry in gauge field theories is studied. Described at low energies by higher dimension operators, these interactions can enhance the chiral condensate and even the Goldstone boson decay constant relative to the confinement scale. This can lead to important consequences in technicolor theories, including realistically large quark and lepton masses and the possibility of new physics at energies below the weak scale. In addition, small differences in strength of the four-fermion interactions, due say to isospin or flavor breaking, can be greatly magnified in the resulting quark and lepton mass spectrum.

We discuss interacting quantum field theory in de Sitter space and argue that the Mottola-Allen vacuum ambiguity is an artifact of free field theory. The nature of the nonthermality of the MA-vacua is also clarified. We propose analyticity of correlation functions as a fundamental requirement of quantum field theory in curved spacetimes. In de Sitter space, this principle determines the vacuum unambiguously and facilitates the systematic development of perturbation theory.

We use the effective potential to give a simple derivation of Veltman's formula for the quadratic divergence in the Higgs self-energy. We also comment on the effect of going beyond the one-loop approximation. PACS number(s1: 14.80.Gt, 12.10.Dm There has been some interest recently [I-81 in the nature of the quadratic divergences present in renormalizable field theories, both in general and in the standard model (SM). The quadratic divergences in the SM in the Higgs self-energy are indicative of the fact that the "natural" order of magnitude of the Higgs-boson mass is at least -M, where M represents the scale of new physics beyond the standard model [9]. Much of the interest in supersymmetric theories (from a phenomenological point of view) derives from the fact that [excluding U(1) D terms] they are quite generally free of quadratic divergences [lo]. They thus admit the possibility of "naturally" light scalar particles.Quadratic divergences in the SM context were first studied by Veltman [9] in the context of dimensional regularization. H e showed that, as long as regularization by dimensional reduction [lo] (DRED) is employed rather than conventional dimensional regularization (DREG), the requirement of the absence of quadratic divergences at one loop in the standard model can be expressed by the formula Here m,, rn , , m Z , and m , are the masses of the Higgs boson, W boson, Z boson, and top quark, respectively. For simplicity, we have dropped contributions from the lighter quarks and leptons. The generalization of this relation to an arbitrary renormalizable gauge theory may be found in Ref. [I]. In the same reference, it was noted that imposing both Eq. (1) itself and that it be renormalization group ( R G ) invariant leads to two constraints which cannot be simultaneously satisfied for any m , and m,, while in Ref. [4] it was shown that, if stronginteraction contributions to the R G evolution are ignored, then the predictions m , = 115 GeV and mn = 180 GeV are obtained. We will comment later on the effect of higher orders on these predictions.Although originally derived in the context of DRED, Eq. (1) is reproduced by any straightforward regularization method that does not involve continuation in dimen-'present address: DAMTP, University of Liverpool, P.O. Box 147, Liverpool L69 3BX United Kingdom. sion, for example, nonlocal regularization [4] or point splitting 181. We shall see why below, when we provide a particularly simple derivation of Eq. (1). With DREG, on the other hand, a different expression is obtained 191. This arises as follows. The coefficients of the m & term and the m i term in Eq. (1) are in fact 2 ( d ' -1 ) and( d l -1 ), respectively, where d'=g,,g~"' and g,,, is the metric tensor. With DRED, d 1 = 4 because the continuation to d dimensions is done by compactification, while, in DREG, d ' = d since the whole Lagrangian is continued to d dimensions. Then the fact that with either D R E D or D R E G quadratic divergences are manifested as poles at d =4-2/L (where L is the number of lo...