Trailing Edge Unification via an Intermediate Pati-Salam Group

We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $\alpha(M_z), \alpha_s(M_z)$ and $\sin^2\theta_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale.Comment: 7 pages, 4 embedded eps figur

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

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

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

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

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