Renormalizability of the massive Yang-Mills theory

It is shown that the massive Yang-Mills theory is on mass-shell renormalizable. Thus the Standard Model of electroweak interactions can be modified by removing terms with the scalar field from the Lagrangian in the unitary gauge. The resulting electroweak theory without the Higgs particle is on mass-shell renormalizable and unitary.Comment: 9 page

Limits on Lorentz Violation from the Highest Energy Cosmic Rays

We place several new limits on Lorentz violating effects, which can modify particles' dispersion relations, by considering the highest energy cosmic rays observed. Since these are hadrons, this involves considering the partonic content of such cosmic rays. We get a number of bounds on differences in maximum propagation speeds, which are typically bounded at the 10^{-21} level, and on momentum dependent dispersion corrections of the form v = 1 +- p^2/Lambda^2, which typically bound Lambda > 10^{21} GeV, well above the Planck scale. For (CPT violating) dispersion correction of the form v = 1 + p/Lambda, the bounds are up to 15 orders of magnitude beyond the Planck scale.Comment: 24 pages, no figures. Added references, very slight changes. Version published in Physical Review

Relating Physical Observables in QCD without Scale-Scheme Ambiguity

We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for $\Lambda_{\overline{\rm MS}}$ as the pole in the associated 't Hooft scheme. A concrete application to $R(e^+e^- \to {\rm hadrons})$ is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-17

The order O(αˉ αˉs)O(\bar{\alpha}~\bar{\alpha}_s) and O(αˉ2)O(\bar{\alpha}^2) corrections to the decay width of the neutral Higgs boson to the bˉb\bar{b}b pair

We present the analytical expressions for the contributions of the order $O(\bar{\alpha}~\bar{\alpha}_s)$ and $O(\bar{\alpha}^2)$ corrections to the decay width of the Standard Model Higgs boson into the $\bar{b}b$-pair. The numerical value of the mixed QED and QCD correction of order $O(\bar{\alpha}~\bar{\alpha}_s)$ is comparable with the previously calculated terms in the perturbative series for $\Gamma(H^0\to\bar{b}b)$.Comment: LaTeX 5 pages, accepted for publication in Pisma Zh. Eksp. Teor. Fiz. v 66, N5 (1997

A multiloop improvement of non-singlet QCD evolution equations

An approach is elaborated for calculation of "all loop" contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the "nonforward" ER-BL equation from these diagrams that dominate for a large value of $b_0$, the first $\beta$-function coefficient. Calculations are performed in the covariant $\xi$-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter $\xi=-3$ generalizes the standard "naive nonabelianization" approximation. The solutions are obtained to the ER-BL evolution equation (taken at the "all loop" improved kernel), which are in form similar to one-loop solutions. A consequence for QCD descriptions of hard processes and the benefits and incompleteness of the approach are briefly discussed.Comment: 13 pages, revtex, 2 figures are enclosed as eps-file, the text style and figures are corrected following version, accepted for publication to Phys. Rev.

Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge

Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is renormalized to three loops in the MSbar scheme. The beta-functions and anomalous dimensions are computed as functions of the usual QED coupling and the additional coupling, xi, which is introduced as part of the nonlinear gauge fixing condition. Similar to the maximal abelian gauge of quantum chromodynamics, the renormalization of the gauge parameter is singular.Comment: 8 latex page

Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.Comment: 10 pages (Latex), 3 figures (Postscript

Commensurate Scale Relations in Quantum Chromodynamics

We use the BLM method to show that perturbatively-calculable observables in QCD can be related to each other without renormalization scale or scheme ambiguity. We define and study the commensurate scale relations. We show that the commensurate scales satisfy the renormalization group transitivity rule which ensures that predictions in PQCD are independent of the choice of an intermediate renormalization scheme. We generalize the BLM procedure to higher order. The application of this procedure to relate known physical observables in QCD gives surprisingly simple results. In particular, the annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule for polarized electroproduction are related through simple coefficients, which reinforces the idea of a hidden symmetry between these two observables.Comment: 35 pages (RevTeX), one PostScript figure included at the end. SLAC-PUB-6481, UMD Preprint #94-13

Five-loop renormalization group functions of O(n){O}(n)-symmetric ϕ4\phi^4-theory and \ep-expansions of critical exponents up to \ep^5

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the ${O}(n)$-symmetric $\phi^4$-theory in D=4-\ep dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and \ep-expansions are given for the critical exponents $\eta$, $\nu$, and $\omega$ up to order $\epsilon^5$.Comment: LaTeX file. For related work see the www address http://www.physik.fu-berlin.de/kleiner_re.html on our www homepage http://www.physik.fu-berlin.de/kleinert.htm