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

Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thric

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

A Global Photometric Analysis of 2MASS Calibration Data

We present results from the application of a global photometric calibration (GPC) procedure to calibration data from the first 2 years of The Two Micron All Sky Survey (2MASS). The GPC algorithm uses photometry of both primary standards and moderately bright `tracer' stars in 35 2MASS calibration fields. During the first two years of the Survey, each standard was observed on approximately 50 nights, with about 900 individual measurements. Based on the photometry of primary standard stars and secondary tracer stars and under the assumption that the nightly zeropoint drift is linear, GPC ties together all calibration fields and all survey nights simultaneously, producing a globally optimized solution. Calibration solutions for the Northern and Southern hemisphere observatories are found separately, and are tested for global consistency based on common fields near the celestial equator. Several results from the GPC are presented, including establishing candidate secondary standards, monitoring of near-infrared atmospheric extinction coefficients, and verification of global validity of the standards. The solution gives long-term averages of the atmospheric extinction coefficients, A_J=0.096, A_H=0.026, A_{K_s}=0.066 (North) and A_J=0.092, A_H=0.031, A_{K_s}=0.065 (South), with formal error of 0.001. The residuals show small seasonal variations, most likely due to changing atmospheric content of water vapor. Extension of the GPC to approximately 100 field stars in each of the 35 calibration fields yields a catalog of more than two thousand photometric standards ranging from 10th to 14th magnitude, with photometry that is globally consistent to $\sim 1$.Comment: 19 pages, 10 figures; Submitted to AJ. The table of secondary standards is available from ftp://nova.astro.umass.edu/pub/nikolaev/ or ftp://anon-ftp.ipac.caltech.edu/pub/2mass/globalcal

Editorial : Innate Immunity in Normal and Adverse Pregnancy

Non peer reviewe