arXiv subjects
Publications and source records attributed to I. Jack.
We calculate the four-loop $β$-function for the generalised Wess-Zumino model. We use the result and Padé-Borel summation to discuss the domain of attraction of the quasi-infra-red fixed point of the top-quark Yukawa coupling in the supersymmetric standard model, and argue that the domain is in fact substantial.
We explore a more general class of soft supersymmetry-breaking masses and interactions than that usually considered, both in general and in the MSSM context, where our results for the one-loop $β$-functions correct some errors in the literature. We identify a new class of one-loop finite supersymmetric theories.
We investigate the infra-red stability of the fixed points in the evolution of the Yukawa couplings, $A$-parameters and soft scalar masses in a broad class of supersymmetric theories. We show that the issue of stability is essentially determined in all three cases by the eigenvalues of the same matrix. In a very wide range of physically interesting theories it follows that, in the asymptotically free case, the existence of stable infra-red fixed points for the Yukawa couplings implies stable infra-red fixed points for the $A$-parameters and soft scalar masses.
We explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $β$-function, we derive the transformation of $α^{\DRED}$ to $α^{\NSVZ}$ through terms of order $α^4$. We thus incidentally determine $β_α^{\DRED}$ through four loops, and we compare our result to a previous Padé Approximant prediction.
We present an exact formula for the $β$-function for the soft-breaking scalar mass in an N=1 supersymmetric gauge theory, in the form of an operator acting on the anomalous dimension. In particular we give the exact form for the correction due to the $ε$-scalar mass, and show that it has a particularly simple form in the renormalisation scheme corresponding to the exact NSVZ gauge $β$-function.
We demonstrate that the soft supersymmetry-breaking terms in a N=1 theory can be linked by simple renormalisation group invariant relations which are valid to all orders of perturbation theory. In the special case of finite N=1 theories, the soft terms preserve finiteness to all orders.
We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop β-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous β-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop β-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.
We present an elegant exact formula for the gaugino $β$-function in a softly-broken supersymmetric gauge theory, of the form $β_M = {\cal O}(β_g/g)$, where $β_g$ is the gauge $β$ function and ${\cal O}$ is a simple differential operator acting on the gauge coupling $g$ and the Yukawa coupling.
We discuss issues that arise in the regularisation of supersymmetric theories. (To appear in the book `Perspectives on Supersymmetry', World Scientific, Editor G. Kane.)
We present a prediction for the four loop $β$-function for SQCD based on the method of Asymptotic Padé Approximants.
We present calculations of the leading and $O(1/N_f)$ terms in a large-$N_f$ expansion of the $β$-functions and anomalous dimensions for various supersymmetric gauge theories, including supersymmetric QCD. In the case of supersymmetric QCD, we show that our $O(1/N_f)$ approximation displays an infra-red fixed point in the conformal window $3N_c/2 < N_f < 3N_c$.
We present calculations of the leading and O(1/N) terms in a large-N expansion of the β-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N is the number of a class of the chiral superfields in the theory.
We present the supersymmetric standard model three-loop $β$-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.
We investigate the connection between the NSVZ and the DRED forms of the gauge $β$-function in an $N=1$ supersymmetric gauge theory. We construct a coupling constant redefinition that relates the two forms up to four loops. By abelian calculations, we are able to infer the complete non-abelian form of $β_g^{(3)DRED}$, and also $β_g^{(4)DRED}$ except for one undetermined parameter.
We calculate the three loop gauge $β$-function for an abelian $N=1$ supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ $β$-function, and by generalising this redefinition to the non-abelian case we derive the DRED three loop gauge $β$-function for the non-abelian case.
We calculate the three loop anomalous dimension for a general $N=1$ supersymmetric gauge theory. The result is used to probe the possible existence of renormalisation invariant relationships between the Yukawa and gauge couplings.
We show that in a special class of theories the commonly assumed universal form of the soft supersymmetry--breaking terms is approached in the infra--red limit. The resulting universal scalar mass and trilinear coupling are predicted in terms of the gaugino mass.
We calculate the particle spectrum of the SSM which follows from the assumption that the commonly assumed universal form of the soft supersymmetry --breaking terms is invariant under renormalisation. It is argued that this ``strong'' universality might be approached as an infra--red fixed point for the unified theory above the unification scale.