D. R. T. Jones

Fermion masses and induction of the weak scale by supergravity

Abstract We discuss some problems which arise in a low-energy theory of strong and electroweak interactions when the weak scale is induced via supergravity. The main problem concerns the origin of quark and lepton masses. If the fermions obtain their masses in the conventional way via Yukawa couplings, then the low-energy supergap (mass difference between supersymmetric partners) is comparable to the mass of the lightest massive fermion. One solution would require that at least the light generations receive their mass indirectly via radiative corrections. Alternatively it might be that the SU(2) × U(1) breaking is induced radiatively.

The weak mixing angle and unification mass in supersymmetric SU(5)

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. Supersymmetric unified models (SUMS) offer a potential solution to the unnaturalness or gauge hierarchy puzzle of standard grand unified models (GUMS) of electroweak and strong interactions [ 1,2]. Attempts to build realistic SUMS face theoretical and phenomenological difficulties [2,3], but it has been emphasized [4] that the most naive extension of SU(5) will not substantially alter the successful prediction of the weak mixing angle Bw, whereas the unification mass scale M tends to increase by several orders of magnitude, thereby suppressing the proton decay rate beyond the range of feasible observation. Were this a universal feature of SUMS, the observation of proton decay would discourage further attempts to utilize supersymmetry to render GUMS natural*. In this paper, we reconsider the predictions for 8, and M in SUMS, emphasizing the sensitivity to the number of light Higgs doublets. We also extend the previous lowest order results to two loops, our motivation being twofold: (i) The accuracy of the one-loop approximation depends upon the size of higher order corrections, and, since SUMS generally will contain many more particles than GUMS, one might a priori expect higher order corrections to be relatively more important. (ii) Even a relatively modest change in the unification mass M produces a large change in the proton lifetime r a M4. Another topic treated in the course of this investigation is the change in the prediction of the quark-lepton ratio m,/m, in going from the minimal SU(5) GUM to the minimal SU(5) SUM. Remarkably enough, we find only a small change in this seemingly successful consequence of SU(5) unification. *See note added in proof.

More on the axial anomaly in supersymmetric Yang-Mills theory☆

The compatibility of the Adler-Bardeen theorem with the supermultiplet containing the axial, trace, and supercurrent anomalies in N = 1 supersymmetric Yang-Mills theory is re-examined (in component form). It is argued that consideration of the off-shell form of the supermultiplet removes the apparent paradox, at least at the two-loop level.

Heavy particles and the ϱ parameter in the standard model

Abstract A new formalism is presented for the calculation of the contribution δϱ to ϱ = Mw2/Mz2cos2θw from heavy particles transforming according to arbitrary representations of SU(2) × U(1). A conjecture for the necessary and sufficient conditions that δϱ⩾0 for all values of masses and mixing angles within a particular multiplet is formulated. A number of examples are given (all consistent with the conjecture) and the significance of improved knowledge of ϱ vis a vis the possible existence of undiscovered heavy particles discussed.

Two-loop renormalisation of d = 2 σ-models with torsion

Abstract A calculation of the two-loop s-function for σ-models with torsion is presented, for the bosonic and the N = 1 supersymmetric cases (using component fields). In the bosonic case the result agrees with a recent calculation by Hull and Townsend, while in the supersymmetric case, we obtain a vanishing two-loop s-function.

Observations on horizontal symmetries and flavor changing neutral currents

Abstract We present a detailed study of the possibility of having a horizontal gauge symmetry, in addition to SU(3) c × SU(2) L × U(1). Grand unification is not used as a constraint. We concentrate on the horizontal group SU(3) H . There are two main results. (i) The horizontal symmetry might break on two mass scales, one heavy and the other of order m z or a few m z . The K L -K S mass difference and other rare kaon and muon transitions are protected by a residual symmetry, but other flavor changing processes not involving the lightest fermion of each charge can be orders of magnitude larger, e.g. b →sl + l − , τ → μl + l − ,e + e − →bs¯, τμ,tc¯(while b→dl + l − , τ →el + l − and some others are forbidden). Some sectors should have relatively large flavor changing neutral currents. (ii) There is not enough new physics in the approach to explain fermion masses, but the structure of the model suggests that the lighter masses and the KM quark mixing angles might be generated radiatively. Unfortunately, careful analysis shows that the same symmetry that protects the K L -K S mass difference requires that the Cabibbo angle be identically zero to all orders. This suggests that it may be extremely difficult to make a realistic fundamental or effective SU(3) horizontal symmetry. While the model fails to generate the CKM angles, it is consistent with all low energy data and suggests a number of interesting reactions that might occur.