Consequences of Leading-Logarithm Summation for the Radiative Breakdown of Standard-Model Electroweak Symmetry

In the empirically sensible limit in which QCD, t-quark Yukawa, and scalar-field-interaction coupling constants dominate all other Standard-Model coupling constants, we sum all leading-logarithm terms within the perturbative expansion for the effective potential that contribute to the extraction of the Higgs boson mass via radiative electroweak symmetry breaking. A Higgs boson mass of 216 GeV emerges from such terms, as well as a scalar-field-interaction coupling constant substantially larger than that anticipated from conventional spontaneous symmetry breaking. The sum of the effective potential's leading logarithms is shown to exhibit a local minimum in the limit $\phi \to 0$ if the QCD coupling constant is sufficiently strong, suggesting (in a multiphase scenario) that electroweak physics may provide the mechanism for choosing the asymptotically-free phase of QCD.Comment: latex using aip proceedings class. 8 page write-out of presentation at MRST 2003 Conference (Syracuse

Improvement of Renormalization-Scale Uncertainties Within Empirical Determinations of the b-Quark Mass

Accurate determinations of the MS-bar b-quark mass $m_b(m_b)$ from $\sigma(e^+e^-\to{\rm hadrons})$ experimental data currently contain three comparable sources of uncertainty; the experimental uncertainty from moments of this cross-section, the uncertainty associated with $\alpha_s(M_z)$, and the theoretical uncertainty associated with the renormalization scale. Through resummation of all logarithmic terms explicitly determined in the perturbative series by the renormalization-group (RG) equation, it is shown that the renormalization-scale dependence is virtually eliminated as a source of theoretical uncertainty in $m_b(m_b)$. This resummation also reduces the estimated effect of higher-loop perturbative contributions, further reducing the theoretical uncertainties in $m_b(m_b)$. Furthermore, such resummation techniques improve the agreement between the values of the MS-bar b-quark mass extracted from the various moments of $R(s)=\sigma(e^+e^-\to{\rm hadrons})/\sigma_{pt}$ [$\sigma_{pt}=4\pi\alpha^2/(3s)$], obviating the need to choose an optimummoment for determining $m_b(m_b)$. Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark MS-bar and pole mass and in the relation between the pole and $1S$ mass.Comment: 19 pages, latex2e, 6 eps figures contained in latex file. Errors corrected in equations (20)--(22

Pade-Improved Estimate of Perturbative Contributions to Inclusive Semileptonic b→ub\to u Decays

Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic $b \to u$ decay rate. These improved estimates of the decay rate reduce the theoretical uncertainty in the extraction of the CKM matrix element $|V_{ub}|$ from the measured inclusive semileptonic branching ratio.Comment: 3 pages, latex, write-up of talk presented at DPF 200

Higher Order Stability of a Radiatively Induced 220 GeV Higgs Mass

The effective potential for radiatively broken electroweak symmetry in the single Higgs doublet Standard Model is explored to four sequentially subleading logarithm-summation levels (5-loops) in the dominant Higgs self-interaction couplant $\lambda$. We augment these results with all contributing leading logarithms in the remaining large but sub-dominant Standard Model couplants (t-quark, QCD and $SU(2)\otimes U(1)$ gauge couplants) as well as next to leading logarithm contributions from the largest of these, the t-quark and QCD couplants. Order-by-order stability is demonstrated for earlier leading logarithm predictions of an order 220 GeV Higgs boson mass in conjunction with fivefold enhancement of the value for $\lambda$ over that anticipated from conventional spontaneous symmetry breaking.Comment: revtex, 6 pages. Analysis and text is expanded in revised versio

On the Standard Approach to Renormalization Group Improvement

Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing N^{n}LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless $\lambda \phi^{4}$ model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.Comment: 6 page

Impeded Growth of Magnetic Flux Bubbles in the Intermediate State Pattern of Type I Superconductors

Normal state bubble patterns in Type I superconducting Indium and Lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be almost independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. On this basis, in the framework of the "current-loop" model [R.E. Goldstein, D.P. Jackson and A.T. Dorsey, Phys. Rev. Lett. 76, 3818 (1996)], we calculate the equilibrium diameter of an isolated bubble resulting from the competition between the Biot-and-Savart interaction of the Meissner current encircling the bubble and the superconductor-normal interface energy. A good quantitative agreement with the master curve is found over two decades of the magnetic Bond number. The isolation of each bubble in the superconducting matrix and the existence of a positive interface energy are shown to preclude any continuous size variation of the bubbles after their formation, contrary to the prediction of mean-field models.Comment: \'{e}quipe Nanostructures Quantique