Searcharxiv⌕ Search

arXiv subjects

D. R. T. Jones

Publications and source records attributed to D. R. T. Jones.

At least 19 recordsLinked to original sources
arXiv2026

Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$

We assess the accuracy of our previous Asymptotic Padé predictions of the five-loop QCD $β$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of $N_F$ (the number of flavours) were correct to within $1\%$. Furthermore an examination of recent results in $λϕ^4$ theory indicates that the Asymptotic Padé methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop Asymptotic Padé predictions for the QCD $β$-function and quark mass anomalous dimension, and also for the eight-loop $β$-function in $O(N)$ $λϕ^4$ theory.

hep-ph↗
arXiv2025

Anomalous dimensions for $ϕ^n$ in scale invariant $d=3$ theory

Recently it was shown that the scaling dimension of the operator $ϕ^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.

hep-th↗
arXiv2022

Scaling dimensions at large charge for cubic $ϕ^3$ theory in six dimensions

The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed point, and the $O(N)$ model with scalar cubic interactions at its infra-red fixed point are conjectured to be equivalent. This has been checked by comparing various features of the two models at their respective fixed points. Recently, the scaling dimensions of a family of operators of fixed charge $Q$ have been shown to match at the FPs up to $\cal{O}\left(\frac{1}{N^2}\right)$at leading order (LO) and next-to-leading order (NLO) in $Q$ using a semiclassical computation which is valid to all orders in the coupling. Here we perform a complementary but overlapping comparison using a perturbative calculation in six dimensions, up to three-loop order in the coupling, to compare these critical scaling dimensions beyond NLO in $Q$, in fact to all relevant orders in $Q$. We also obtain the corresponding results at $\cal{O}\left(\frac{1}{N^3}\right)$ for the cubic theory.

hep-th↗
arXiv2021

Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions

Recently it was shown that the scaling dimension of the operator $ϕ^n$ in $λ(\barϕϕ)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-ε$, for generic values of $λn$, and this was verified to two loop order in perturbation theory at leading and subleading $n$. This result was subsequently generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to four loops in perturbation theory at leading and subleading $Q$. More recently, similar semiclassical calculations have been performed for the classically scale-invariant $U(N)\times U(N)$ theory in four dimensions, and verified up to two loops, once again at leading and subleading $Q$. Here we extend this verification to four loops. We also consider the corresponding classically scale-invariant theory in three dimensions, similarly verifying the leading and subleading semiclassical results up to four loops in perturbation theory.

hep-th↗
arXiv2015

Gradient flows in three dimensions

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and supersymmetric cases.

hep-th↗
arXiv2011

Anomaly Mediation and Cosmology

We consider an extension of the MSSM wherein anomaly mediation is the source of supersymmetry breaking, and the tachyonic slepton problem is solved by a gauged U(1) symmetry, which is broken at high energies in a manner preserving supersymmetry, thereby also facilitating the see-saw mechanism for neutrino masses and a natural source for the Higgs mu-term. We show that these favourable outcomes can occur both in the presence and the absence of a large Fayet-Iliopoulos (FI) D-term associated with the new U(1). We explore the cosmological consequences of the model, showing that it naturally produces a period of hybrid inflation, terminating in the production of cosmic strings. In spite of the presence of a U(1) (even with an FI term), inflation is effected by the F-term, with a D-flat tree potential (the FI term, if present, being cancelled by non-zero squark and slepton fields). Calculating the 1-loop corrections to the inflaton potential, we estimate the constraints on the parameters of the model from Cosmic Microwave Background data. We will see that a consequence of these constraints is that the Higgs mu-term necessarily small. We briefly discuss the mechanisms for baryogenesis via conventional leptogenesis, the out-of-equilibrium production of neutrinos from the cosmic strings, or the Affleck-Dine mechanism. Cosmic string decays also boost the relic density of dark matter above the low value normally obtained in AMSB scenarios.

hep-ph↗
arXiv2009

Bounds on scalar masses in two Higgs doublet models

A thorough analysis of stability and perturbativity bounds is performed in several versions of the two-Higgs doublet model, for both CP-conserving and spontaneously broken CP minima. LEP results further aid in establishing very strict constraints on the mass of the lighter Higgs particle.

hep-ph↗
arXiv2009

Flavour Violation in Anomaly Mediated Supersymmetry Breaking

We study squark flavour violation in the anomaly mediated supersymmetry broken (AMSB) minimal supersymmetric standard model. Analytical expressions for the three-generational squark mass matrices are derived. We show that the anomaly-induced soft breaking terms have a decreasing amount of squark flavour violation when running from the GUT to the weak scale. Taking into account inter-generational squark mixing, we work out non-trivial constraints from B -> Xs gamma and Bs -> mu mu, which complement each other, as well as B -> tau nu decays. We further identify a region of parameter space where the anomalous magnetic moment of the muon and the B -> Xs gamma branching ratio are simultaneously accommodated. Since anomaly mediation is of the minimal flavour-violating type, the generic flavour predictions for this class of models apply, including a CKM-induced (and hence small) Bs-Bsbar-mixing phase.

hep-ph↗
arXiv2009

The non-anticommutative supersymmetric U(1) gauge theory

We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for renormalisability, showing in detail how the eliminated and uneliminated forms of the theory lead to equivalent results.

hep-th↗
arXiv2008

The non-anticommutative supersymmetric Wess-Zumino model

We discuss the non-anticommutative (N=1/2) supersymmetric Wess-Zumino model in four dimensions. Firstly we introduce differential operators which implement the non-anticommutative supersymmetry algebra acting on the component fields and action. Then we perform the renormalisation of the model up to two-loop order, including the complete set of terms necessary for renormalisability. We show that (at least up to this order) the results obtained when we eliminate the auxiliary field after renormalisation are equivalent to those obtained when we eliminate the auxiliary fields before quantisation.

hep-th↗
arXiv2007

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 U(1) compatible with a straightforward GUT embedding.

hep-ph↗
arXiv2007

Four-loop beta 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 DR-bar scheme and put special emphasis on the additional couplings which have to be taken into account. This concerns the epsilon-scalar--quark Yukawa coupling as well as the vertex containing four epsilon-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.

hep-ph↗
arXiv2006

Anomaly Mediation and Dimensional Transmutation

We show how a sparticle spectrum characteristic of anomaly mediation can arise from a theory whose Lagrangian contains no explicit mass scale. The scale of supersymmetry breaking is governed by the gravitino mass, which is the vacuum expectation value of the F-term of the conformal compensator field, and the tachyonic slepton problem is resolved by the breaking of a U(1) gauge symmetry at a scale determined by dimensional transmutation.

hep-ph↗