Massless Scalar Field Propagator in a Quantized Space-Time

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2<p^2<\infty$. Finally, we argue that the spectral function for the multiparticle states appears to saturate as $p^2$ probes just beyond the $1/a^2$ discretization scale. We speculate on the cosmological consequences of such a spectral function.Comment: 6 pages, 1 eps figure embedded in manuscrip

Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?

We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $\mu$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the SU(3) gauge coupling $z$, and the $SU(2) \times U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the $N^2LL...N^4LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction (MS) scheme to their form in the CW scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is $m_{H}=219\;GeV/c^2$ decreases to $m_{H}=188\;GeV/c^2$ at $N^{2}LL$ order and $m_{H}=163\;GeV/c^2$ at $N^{4}LL$ order. No reasonable estimate of $m_H$ can be made at orders $V_{NLL}$ or $V_{N^3LL}$. This is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of $m_H$. The mass $163\;GeV/c^2$ is argued to be an upper bound on $m_H$.Comment: 24 pages, 5 figures. Updated version contains new discussion, references, figures, and corrects errors in reference

Constraints on Higher-Order Perturbative Corrections in b→ub\to u Semileptonic Decays from Residual Renormalization-Scale Dependence

The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group invariant quantities. This technique is applied to the inclusive semileptonic process $b\to u \bar\nu_\ell\ell^-$ (explicitly known to two-loop order) to obtain bounds on the three- and four-loop perturbative coefficients that are not accessible via the renormalization group. Using the principle of minimal sensitivity, an estimate is obtained for the perturbative contributions to $\Gamma(b\to u \bar\nu_\ell\ell^-)$ that incorporates theoretical uncertainty from as-yet-undetermined higher order QCD corrections.Comment: latex2e using amsmath, 8 pages, 4 embedded eps figures. Revised version contains an additional figure and accompanying revision

Advances in startercultures and cultured foods

With 2005 retail sales close to $4.8 million, cultured dairy products are driving the growth of dairy foods consumption. Starter cultures are of great industrial significance in that they play a vital role in the manufacturing, flavor, and texture development of fermented dairy foods. Furthermore, additional interest in starter bacteria has been generated because of the data accumulating on the potential health benefits of these organisms. Today, starter cultures for fermented foods are developed mainly by design rather than by the traditional screening methods and trial and error. Advances in genetics and molecular biology have provided opportunities for genomic studies of these economically significant organisms and engineering of cultures that focuses on rational improvement of the industrially useful strain. Furthermore, much research has been published on the health benefits associated with ingesting cultured dairy foods and probiotics, particularly their role in modulating immune function. The aim of this review is to describe some of the major scientific advances made in starter and non-starter lactic acid bacteria during the past 10 yr, including genomic studies on dairy starter cultures, engineering of culture attributes, advances in phage control, developments in methods to enumerate lactic acid bacteria and probiotics in dairy foods, and the potential role of cultured dairy foods in modulation of immune function

Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics

We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group improvement of this series is equivalent to a closed-form summation of the first four towers of renormalization-group accessible logarithms to all orders of perturbation theory

The Nielsen Identities for the Two-Point Functions of QED and QCD

We consider the Nielsen identities for the two-point functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon self-energy and ghost propagator in terms of the gauge dependence of other, independent Green functions.Comment: 25 pages, plain TeX, 4 figures available upon request, MZ-TH/94-0

The circumburst environment of a FRED GRB: study of the prompt emission and X-ray/optical afterglow of GRB 051111

We report a multi-wavelength analysis of the prompt emission and early afterglow of GRB051111 and discuss its properties in the context of current fireball models. The detection of GRB051111 by the Burst Alert Telescope on-board Swift triggered early BVRi' observations with the 2-m robotic Faulkes Telescope North in Hawaii, as well as X-ray observations with the Swift X-Ray Telescope. The prompt gamma-ray emission shows a classical FRED profile. The optical afterglow light curves are fitted with a broken power law, with alpha_1=0.35 to alpha_2=1.35 and a break time around 12 minutes after the GRB. Although contemporaneous X-ray observations were not taken, a power law connection between the gamma-ray tail of the FRED temporal profile and the late XRT flux decay is feasible. Alternatively, if the X-ray afterglow tracks the optical decay, this would represent one of the first GRBs for which the canonical steep-shallow-normal decay typical of early X-ray afterglows has been monitored optically. We present a detailed analysis of the intrinsic extinction, elemental abundances and spectral energy distribution. From the absorption measured in the low X-ray band we find possible evidence for an overabundance of some alpha elements such as oxygen, [O/Zn]=0.7+/-0.3, or, alternatively, for a significant presence of molecular gas. The IR-to-X-ray Spectral Energy Distribution measured at 80 minutes after the burst is consistent with the cooling break lying between the optical and X-ray bands. Extensive modelling of the intrinsic extinction suggests dust with big grains or grey extinction profiles. The early optical break is due either to an energy injection episode or, less probably, to a stratified wind environment for the circumburst medium.Comment: accepted to A&A on Nov. 10 (14 pages, 8 figures