Abstract:
The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Pad\'e-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Pad\'e-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for n_f leq 6, and is shown to be in exact agreement with its true value in the n_f \to \infty limit. Asymptotic Pad\'e estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.

Abstract:
The three-loop contribution to the MS bar single-Higgs-doublet standard-model cross-section $\sigma(W_L^+ W_L^- \to Z_L Z_L)$ at s = (5M_H)^2 is estimated via least-squares matching of the asymptotic Pade-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expansion parameter for the W_L^+ W_L^- \to Z_L Z_L process is the non-asymptotically-free quartic scalar-field coupling of the standard model, suggesting that the least-squares matching be performed over the "infrared" mu^2 <= s region of the scale parameter. All three coefficients of logarithms within the three-loop term obtained by such matching are found to be within 6.6% relative error of their true values, as determined via renormalization-group methods. Surprisingly, almost identical results are obtained by performing the least squares matching over the mu^2 >= s region.

Abstract:
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.

Abstract:
Background: We describe a rare case of Candida albicans retropharyngeal infection with upper cervical spondylodiscitis associated with epidural abscess triggered by ingestion of a chicken bone. Case Description: A 63-year-old woman presented with posterior neck and bilateral shoulders pain three weeks after choking on a 2-centimeter chicken bone. Magnetic resonance imaging (MRI) revealed spondylodiscitis and epidural abscess with significant spinal cord compression at C2 and C3 levels. A Barium swallow showed a focal disruption of the posterior wall of the esophagus. A posterior upper cervical fixation (C2-C5) was initially performed. One week later an anterior decompressive procedure was carried out followed by iliac crest bony fusion, and repair of the esophageal defect. Intra-operative cultures showed heavy growth of Candida albicans. After a transitory post-operative neurologic worsening, and after six weeks of appropriate antifungal therapy, the patient achieved a full clinical and radiologic recovery. Conclusion: Prompt surgical debridement, fusion and stabilization combined with adequate antimicrobial agents are necessary to guarantee a good outcome and reverse the neurological deficits.

Abstract:
Asymptotic Pade-approximant methods are utilized to estimate the leading-order unknown (i.e., not-yet-calculated) contributions to the perturbative expansions of two-current QCD correlation functions obtained from scalar-channel fermion and gluon currents, as well as from vector-channel fermion currents. Such contributions to the imaginary part of each correlator are polynomials of logarithms whose coefficients (other than the constant term within the polynomial) may be extracted from prior-order contributions by use of the renormalization-group (RG) equation appropriate for each correlator. We find surprisingly good agreement between asymptotic Pade-approximant predictions and RG-determinations of such coefficients for each correlation function considered, although such agreement is seen to diminish with increasing numbers of quark flavours. The RG-determined coefficients we obtain are then utilized in conjunction with asymptotic Pade-approximant methods to predict the RG-inaccessible constant terms of the leading-order unknown contributions for all three correlators. The vector channel predictions lead to estimates for the order $(\alpha_s^4)$ contribution to $R(s) \equiv[\sigma(e^+ e^- \to hadrons) / \sigma(e^+ e^- \to \mu^+ \mu^-)]$ for three, four, and five flavours.

Abstract:
Within the context of massive N-component $\phi^4$ scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function $\beta_g$, the anomalous mass dimension $\gamma_m$, the vacuum-energy beta-function $\beta_v$, and the anomalous dimension $\gamma_2$ of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to $\beta_g$, $\gamma_m$, $\beta_v$, and are seen to be respectively within 5%, 18%, and 27% of their true values for $N$ between 1 and 5. We then extend asymptotic Pade-approximant methods to predict the presently unknown six-loop contributions to $\beta_g$, $\gamma_m$, and $\beta_v$. These predictions, as well as the six-loop prediction for $\gamma_2$, provide a test of asymptotic Pade-approximant methods against future calculations.

Abstract:
Pad\'e-improvement of four-loop beta-functions in massive phi^4 scalar field theory is shown to predict the known five-loop contribution with astonishing (0.2%) accuracy, supporting the applicability of Pade-summations for approximating all-orders MS-bar QCD beta-functions, as suggested by Ellis, Karliner, and Samuel. Surprisingly, the most general set of [2|2] approximants consistent with known two-, three-, and four-loop contributions to the QCD beta-function with up to six flavours fail to exhibit any zeros that could be interpreted as positive infrared fixed points, regardless of the unknown five-loop term. When they occur, positive zeros of such [2|2] approximants are preceded by singularities, leading to a double-valued beta-function that is decoupled entirely from the infrared region, similar to the beta-function of SUSY gluodynamics.