The Great Dictator

Abstract not availabl

Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories

In the absence of a tree-level scalar-field mass, renormalization-group (RG) methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series for the effective-potential functions utilized in radiative symmetry breaking. For scalar-field electrodynamics, such a summation of leading logarithm contributions leads to upper bounds on the magnitudes of both gauge and scalar-field coupling constants, and suggests the possibility of an additional phase of spontaneous symmetry breaking characterized by a scalar-field mass comparable to that of the theory's gauge boson. For radiatively-broken electroweak symmetry, the all-orders summation of leading logarithm terms involving the dominant three couplings (quartic scalar-field, t-quark Yukawa, and QCD) contributing to standard-model radiative corrections leads to an RG-improved potential characterized by a 216 GeV Higgs boson mass. Upon incorporation of electroweak gauge couplants we find that the predicted Higgs mass increases to 218 GeV. The potential is also characterized by a quartic scalar-field coupling over five times larger than that anticipated for an equivalent Higgs mass obtained via conventional spontaneous symmetry breaking, leading to a concomitant enhancement of processes (such as $W^+ W^- \to ZZ$) sensitive to this coupling. Moreover, if the QCD coupling constant is taken to be sufficiently strong, the tree potential's local minimum at $\phi = 0$ is shown to be restored for the summation of leading logarithm corrections. Thus if QCD exhibits a two-phase structure similar to that of $N = 1$ supersymmetric Yang-Mills theory, the weaker asymptotically-free phase of QCD may be selected by the large logarithm behaviour of the RG-improved effective potential for radiatively broken electroweak symmetry.Comment: latex2e using amsmath, 36 pages, 7 eps figures embedded in latex. Section 8.3 errors asociated with electroweak coupling effects are correcte

Murchison Widefield Array rapid-response observations of the short GRB 180805A

Abstract Here we present stringent low-frequency (185 MHz) limits on coherent radio emission associated with a short-duration gamma-ray burst (SGRB). Our observations of the short gamma-ray burst (GRB) 180805A were taken with the upgraded Murchison Widefield Array (MWA) rapid-response system, which triggered within 20s of receiving the transient alert from the Swift Burst Alert Telescope, corresponding to 83.7 s post-burst. The SGRB was observed for a total of 30 min, resulting in a $3\sigma$ persistent flux density upper limit of 40.2 mJy beam–1. Transient searches were conducted at the Swift position of this GRB on 0.5 s, 5 s, 30 s and 2 min timescales, resulting in $3\sigma$ limits of 570–1 830, 270–630, 200–420, and 100–200 mJy beam–1, respectively. We also performed a dedispersion search for prompt signals at the position of the SGRB with a temporal and spectral resolution of 0.5 s and 1.28 MHz, respectively, resulting in a $6\sigma$ fluence upper-limit range from 570 Jy ms at DM $=3\,000$ pc cm–3 ( $z\sim 2.5$ ) to 1 750 Jy ms at DM $=200$ pc cm–3 ( $z\sim 0.1)$ , corresponding to the known redshift range of SGRBs. We compare the fluence prompt emission limit and the persistent upper limit to SGRB coherent emission models assuming the merger resulted in a stable magnetar remnant. Our observations were not sensitive enough to detect prompt emission associated with the alignment of magnetic fields of a binary neutron star just prior to the merger, from the interaction between the relativistic jet and the interstellar medium (ISM) or persistent pulsar-like emission from the spin-down of the magnetar. However, in the case of a more powerful SGRB (a gamma-ray fluence an order of magnitude higher than GRB 180805A and/or a brighter X-ray counterpart), our MWA observations may be sensitive enough to detect coherent radio emission from the jet-ISM interaction and/or the magnetar remnant. Finally, we demonstrate that of all current low- frequency radio telescopes, only the MWA has the sensitivity and response times capable of probing prompt emission models associated with the initial SGRB merger event.</jats:p

Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure

Bosonic Excitations in Random Media

We consider classical normal modes and non-interacting bosonic excitations in disordered systems. We emphasise generic aspects of such problems and parallels with disordered, non-interacting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of non-interacting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low frequency limit, above a critical dimension $d_c$, which in different circumstances takes the values $d_c=2$ and $d_c=0$. For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\rho(\omega) \propto \omega^4$ is a universal feature in systems with ground states that depend on the disorder realisation. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension