D. R. Timothy Jones

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.

Four-loop β function and mass anomalous dimension in dimensional reduction

Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the scheme and put special emphasis on the additional couplings which have to be taken into account. This concerns the ?-scalar?quark Yukawa coupling as well as the vertex containing four ?-scalars. For a supersymmetric Yang Mills theory, we find, in contrast to a previous claim, that the evanescent Yukawa coupling equals the strong coupling constant through three loops as required by supersymmetry.

The effective potential, the renormalisation group and vacuum stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.

The Four-loop DRED gauge beta-function and fermion mass anomalous dimension for general gauge groups

We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated using the dimensional reduction scheme. In the special case of a supersymmetric theory we confirm previous calculations of both the gauge beta-function and the gaugino mass beta-function.

Comment on “Bare Higgs mass at Planck scale”

The standard model (SM) Higgs-like particle of mass 125GeV recently discovered at the LHC [1, 2] has resulted in a revival of interest in the old Veltman observation [3] that it is possible to arrange cancellation of the quadratic divergence in the Higgs mass by imposing a certain relation upon the coupling constants of the theory [4]-[8]. In the notation of [4], the quadratic divergence at one loop is proportional to

Gauss-Bonnet coupling constant in classically scale-invariant gravity

We discuss the renormalization of higher-derivative gravity, both without and with matter fields, in terms of two primary coupling constants rather than three. A technique for determining the dependence of the Gauss-Bonnet coupling constant on the remaining couplings is explained, and consistency with the local form of the Gauss-Bonnet relation in four dimensions is demonstrated to all orders in perturbation theory. A similar argument is outlined for the Hirzebruch signature and its coupling. We speculate upon the potential implications of instantons on the associated nonperturbative coupling constants.

Strictly anomaly mediated supersymmetry breaking

We consider an MSSM extension with anomaly mediation as the source of supersymmetry-breaking, and a U(1) symmetry which solves the tachyonic slepton problem, and introduces both the see-saw mechanism for neutrino masses, and the Higgs mu-term. We compare its spectra with those from so-called minimal anomaly mediated supersymmetry breaking. We find a Standard Model-like Higgs of mass 125 GeV with a gravitino mass of 140 TeV and tan(beta)=16. However, the muon anomalous magnetic moment is 3 sigma away from the experimental value. The model naturally produces a period of hybrid inflation, which can exit to a false vacuum characterised by large Higgs vevs, reaching the true ground state after a period of thermal inflation. The scalar spectral index is reduced to approximately 0.975, and the correct abundance of neutralino dark matter can be produced by decays of thermally-produced gravitinos, provided the gravitino mass (and hence the Higgs mass) is high. Naturally light cosmic strings are produced, satisfying bounds from the Cosmic Microwave Background. The complementary pulsar timing and cosmic ray bounds require that strings decay primarily via loops into gravitational waves. Unless the loops are extremely small, the next generation pulsar timing array will rule out or detect the string-derived gravitational radiation background in this model.

Fermion Mass Hierarchy and Proton Stability from Non-anomalous U(1)(F) in SUSY SU(5)

We present a realistic supersymmetric SU(5) model combined with a nonanomalous U(1){sub F} symmetry. We find a set of U(1){sub F} charges which automatically lead to the realistic mass hierarchy and mixing patterns for quarks, leptons, and neutrinos. All gauge anomalies, including the [U(1){sub F}]{sup 3} anomaly, are canceled in our model without invoking the Green-Schwarz mechanism or having exotic fields. Proton decay mediated by dimension-5 operators is automatically suppressed in our model, because the scale set by the largest right-handed neutrino mass is much less than the GUT scale.

Renormalizable, asymptotically free gravity without ghosts or tachyons

We analyse scale invariant quadratic quantum gravity incorporating non-minimal coupling to a multiplet of scalar fields in a gauge theory, with particular emphasis on the consequences for its interpretation resulting from a transformation from the Jordan frame to the Einstein frame. The result is the natural emergence of a de Sitter space solution which, depending the gauge theory and region of parameter space chosen, can be free of ghosts and tachyons, and completely asymptotically free. In the case of an SO(10) model, we present a detailed account of the spontaneous symmetry breaking, and we calculate the leading (two-loop) contribution to the dilaton mass.

Anomaly mediation, Fayet-Iliopoulos D-terms and the renormalisation group

We address renormalisation group evolution issues that arise in the Anomaly Mediated Supersymmetry Breaking scenario when the tachyonic slepton problem is resolved by Fayet-Iliopoulos term contributions. We present typical sparticle spectra both for the original formulation of this idea and an alternative using Fayet-Iliopoulos terms for a U1 compatible with a straightforward GUT embedding.