Infrared Consistency of NSVZ and DRED Supersymmetric Gluodynamics

Pade approximant methods are applied to known terms of the DRED beta- function for N = 1 supersymmetric SU(3) Yang-Mills theory. Each of the [N|M] approximants with N + M less than or equal to 4 (M not equal to zero) constructed from this series exhibits a positive pole which precedes any zeros of the approximant, consistent with the same infrared-attractor pole behaviour known to characterise the exact NSVZ beta-function. A similar Pade-approximant analysis of truncations of the NSVZ series is shown consistently to reproduce the geometric-series pole of the exact NSVZ beta function.Comment: LaTeX, 15 page

The Canonical Structure of the Superstring Action

We consider the canonical structure of the Green-Schwarz superstring in $9 + 1$ dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in $2 + 1$ and $3 + 1$ dimensions. A key feature of this structure is that the primary Fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac Bracket (DB) then the second group of primary Fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary Fermionic first class constraints can be used to find the generator of a local Fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space-time to see if the Fermionic gauge symmetry can be made simpler than it is in $2 + 1$, $3 + 1$ and $9 + 1$ dimensions. With a $3 + 3$ dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first class Fermionic constraint.Comment: 24 pages, Latex2e; further comments and clarifications adde

Startling Equivalences in the Higgs-Goldstone Sector between Radiative and Lowest-Order Conventional Electroweak Symmetry Breaking

For the Higgs boson mass of $\sim 220$ GeV expected to arise from radiative electroweak symmetry breaking, we find the same lowest-order expressions as would be obtained from conventional electroweak symmetry breaking, given the same Higgs boson mass, for Higgs-Goldstone sector scattering processes identified with $W_L^ + W_L^- \to W_L^+ W_L^-$, $W_L^+ W_L^- \to Z_L Z_L$, as well as for Higgs boson decay widths $H \to W_L^+ W_L^-$, $H \to Z_L Z_L$. The radiatively broken case, however, leads to an order of magnitude enhancement over lowest-order conventional symmetry breaking for scattering processes $W_L^+ W_L^+ \to H H$, $Z_L Z_L \to H H$, as well as a factor of $\sim 30$ enhancement for $H H \to H H$.Comment: 6 pages, uses ws-ijmpa.cls written in Latex2E. Major revision in text and conclusions--different enhanced scattering processes found than the earlier version. To appear in the IJMPA proceedings issue for MRST 2005, Utica, N

The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V'(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".

Treatment of a System with Explicitly Broken Gauge Symmetries

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.Comment: 10 pages, LaTeX2e, typos correcte

Renormalization Mass Scale and Scheme Dependence in the Perturbative Contribution to Inclusive Semileptonic bb Decays

We examine the perturbative calculation of the inclusive semi-leptonic decay rate $\Gamma$ for the $b$-quark, using mass-independent renormalization. To finite order of perturbation theory the series for $\Gamma$ will depend on the unphysical renormalization scale parameter $\mu$ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit $\mu$-dependence of $\Gamma$, through powers of ln$(\mu)$, can be summed by using the renormalization group equation. We then find that this explicit $\mu$-dependence can be combined together with the implicit $\mu$-dependence of $\Gamma$ (through powers of both the running coupling $a(\mu)$ and the running $b$-quark mass $m(\mu)$) to yield a $\mu$-independent perturbative expansion for $\Gamma$ in terms of $a(\mu)$ and $m(\mu)$ both evaluated at a renormalization scheme independent mass scale $I\!\!M$ which is fixed in terms of either the "$\overline{MS}$ mass" $\overline{m}_b$ of the $b$ quark or its pole mass $m_{pole}$. At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients $c_i$ and $g_i$ of the perturbative expansions of the renormalization group functions $\beta(a)$ and $\gamma(a)$, associated with $a(\mu)$ and $m(\mu)$ respectively, to characterize the remaining renormalization scheme arbitrariness of $\Gamma$. We further show that all terms in the expansion of $\Gamma$ can be written in terms of the $c_i$ and $g_i$ coefficients and a set of renormalization scheme independent parameters $\tau_i$.Comment: 26 pages, 4 figures, typo correcte

The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic expansions in evaluation of such Bessel functions which also happen to have large argument. Large order Bessel functions also arise in the Peters-Mathews model of binary inspiralling stars emitting GW and several problems in potential scattering theory. Other applications also arise in a variety of problems in Applied Mathematics as well as in the Natural Sciences and present a challenge for High Performance Computing(HPC).Comment: 8 pages, Uses IEEE style files: Ieee.cls, Ieee.clo and floatsty.sty. Accepted for publication in High Performance Computing Symposium, May 15-18 (HPCS 2005) Guelph, Ontario, Canad

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($\mu$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $\mu$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $\mu$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.Comment: 12 pages, 3 figures, LaTe