RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses

In this paper the formulae are collected which are needed for the computation of the strong coupling constant and quark masses at different energy scales and for different number of active flavours. All equations contain the state-of-the-art QCD corrections up to three- and sometimes even four-loop order. For the practical implementation {\tt Mathematica} is used and a package containing useful procedures is provided.Comment: 32 pages, ps figures included, accepted for publication in Computer Physics Communication

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

On a modification of algebraic multilevel iteration method for finite element matrices *

A M S subject classification: 65F10, 65N20 Ларин М.Р. О модификации алгебраического многоуровневого итерационного ме-тода для решения конечно-элементных систем линейных алгебраических уравнений // Сиб. журн. вычисл. математики / РАН. Сиб. отд-ние.--Новосибирск, 2007.--Т. 10, № 1.--С. 101-116. В настоящее время многосеточные и многоуровневые методы очень популярны для решения раз-реженных систем линейных алгебраических уравнений. Они обладают как широкой областью примене-ния, так и эффективностью. В работе [6] был предложен алгебраический многоуровневый итерационный (AMLI) метод для решения конечно-элементных систем линейных алгебраических уравнений. Однако этот метод имеет два ограничения на свойства исходной матрицы, которые могут нарушаться на практи-ке. C целью избежать их и улучшить качество AMLI-предбуславливателя предлагается и анализируется семейство итерационных параметров релаксации. Ключевые слова: алгебраический многоуровневый метод, метод сопряженных градиентов с пре-добуславливателем, системы линейных алгебраических уравнений, метод конечных элементов. Today, multigrids and multilevel methods for solving a sparse linear system of equations are well known. They are both robust and efficient. I

Boundary Layer Protuberance Simulations in Channel Nozzle Arc-Jet

Two protuberance designs were modeled in the channel nozzle of the NASA Johnson Space Center Atmospheric Reentry Materials and Structures Facility with the Data-Parallel Line Relaxation computational fluid dynamics code. The heating on the protuberance was compared to nominal baseline heating at a single fixed arc-jet condition in order to obtain heating augmentation factors for flight traceability in the Boundary Layer Transition Flight Experiment on Space Shuttle Orbiter flights STS-119 and STS-128. The arc-jet simulations were performed in conjunction with the actual ground tests performed on the protuberances. The arc-jet simulations included non-uniform inflow conditions based on the current best practices methodology and used variable enthalpy and constant mass flow rate across the throat. Channel walls were modeled as fully catalytic isothermal surfaces, while the test section (consisting of Reaction Cured Glass tiles) was modeled as a partially catalytic radiative equilibrium wall. The results of the protuberance and baseline simulations were compared to the applicable ground test results, and the effects of the protuberance shock on the opposite channel wall were investigated

Nonperturbative ghost dynamics in the maximal Abelian gauge

We construct the effective potential for the ghost condensate in the maximal Abelian gauge. This condensate is an order parameter for a global continuous symmetry, which is spontaneously broken since a nonvanishing value of lowers the vacuum energy. The associated Goldstone mode turns out to be unphysical.Comment: 16 pages. v2: version accepted for publication in JHE

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

Symbolic Algebra and Renormalization of Gauge Theories

Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of gauge theories. This scheme is readily implemented using the general purpose package, Mathematica. The techniques discussed are used to calculate renormalization group functions for a non-abelian $SU(m)$ gauge theory with massless fermions in a representation R, in the two-loop approximation, and to simplify some expressions arising in electroweak calculations at the two loop level.Comment: 16 pages, LaTex, 2 diagrams drawn with FEYNMAN, uses cite.sty Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-41.T193.ps Accepted for publication in Computer Physics Communicatio

Higher moments of nucleon spin structure functions in heavy baryon chiral perturbation theory and in a resonance model

The third moment $d_2$ of the twist-3 part of the nucleon spin structure function $g_2$ is generalized to arbitrary momentum transfer $Q^2$ and is evaluated in heavy baryon chiral perturbation theory (HBChPT) up to order ${\mathcal{O}}(p^4)$ and in a unitary isobar model (MAID). We show how to link $d_2$ as well as higher moments of the nucleon spin structure functions $g_1$ and $g_2$ to nucleon spin polarizabilities. We compare our results with the most recent experimental data, and find a good description of these available data within the unitary isobar model. We proceed to extract the twist-4 matrix element $f_2$ which appears in the $1/Q^2$ suppressed term in the twist expansion of the spin structure function $g_1$ for proton and neutron.Comment: 30 pages, 7 figure