Loops, Cutoffs and Anomalous Gauge Boson Couplings

We discuss several issues regarding analyses which use loop calculations to put constraints on anomalous trilinear gauge boson couplings (TGC's). Many such analyses give far too stringent bounds. This is independent of questions of gauge invariance, contrary to the recent claims of de Rujula et. al., since the lagrangians used in these calculations ARE gauge invariant, but the SU(2)_L X U(1)_Y symmetry is nonlinearly realized. The real source of the problem is the incorrect use of cutoffs -- the cutoff dependence of a loop integral does not necessarily reflect the true dependence on the heavy physics scale M. If done carefully, one finds that the constraints on anomalous TGC's are much weaker. We also compare effective lagrangians in which SU(2)_L X U(1)_Y is realized linearly and nonlinearly, and discuss the role of custodial SU(2) in each formulation.Comment: talk presented at the XXVI International Conference on High Energy Physics, Dallas, USA, August 1992, plain TeX, 12 pages, 3 figures (not included), UdeM-LPN-TH-105, McGill-92/3

The comprehension revolution : a twenty-year history of process and practice related to reading comprehension

Includes bibliographie

Noise-Induced Stabilization of Planar Flows I

We show that the complex-valued ODE \begin{equation*} \dot z_t = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0, \end{equation*} which necessarily has trajectories along which the dynamics blows up in finite time, can be stabilized by the addition of an arbitrarily small elliptic, additive Brownian stochastic term. We also show that the stochastic perturbation has a unique invariant measure which is heavy-tailed yet is uniformly, exponentially attracting. The methods turn on the construction of Lyapunov functions. The techniques used in the construction are general and can likely be used in other settings where a Lyapunov function is needed. This is a two-part paper. This paper, Part I, focuses on general Lyapunov methods as applied to a special, simplified version of the problem. Part II of this paper extends the main results to the general setting.Comment: Part one of a two part pape