Approximating the radiatively corrected Higgs mass in the Minimal Supersymmetric Model

To obtain the most accurate predictions for the Higgs masses in the minimal supersymmetric model (MSSM), one should compute the full set of one-loop radiative corrections, resum the large logarithms to all orders, and add the dominant two-loop effects. A complete computation following this procedure yields a complex set of formulae which must be analyzed numerically. We discuss a very simple approximation scheme which includes the most important terms from each of the three components mentioned above. We estimate that the Higgs masses computed using our scheme lie within 2 GeV of their theoretically predicted values over a very large fraction of MSSM parameter space.Comment: 31 pages, 10 embedded figures, latex with psfig.sty the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp95-09/ttp95-09.ps or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

A selection-quotient process for packed word Hopf algebra

In this paper, we define a Hopf algebra structure on the vector space spanned by packed words using a selection-quotient coproduct. We show that this algebra is free on its irreducible packed words. Finally, we give some brief explanations on the Maple codes we have used.Comment: 12 pages, conference proceedings, 5th International Conference on Algebraic Informatics, September 3-6, 201

Origin of the structural phase transition in Li7La3Zr2O12

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that relieves internal structural strain. Supervalent doping introduces vacancies into the Li sublattice, increasing the overall entropy and reducing the free energy gain from ordering, eventually stabilizing the cubic phase. We show that the critical temperature for cubic phase stability is lowered as Li vacancy concentration (dopant level) is raised and that an activated hop of Li ions from one crystallographic site to another always accompanies the transition. By identifying the relevant mechanism and critical concentrations for achieving the high conductivity phase, this work shows how targeted synthesis could be used to improve electrolytic performance

The mechanics of shuffle products and their siblings

We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name $\varphi$-shuffle products. Our paper is dedicated to a study of the latter class, from a combinatorial standpoint. We consider first how to extend Radford's theorem to the products in that class, then how to construct their bi-algebras. As some conditions are necessary do carry that out, we study them closely and simplify them so that they can be seen directly from the definition of the product. We eventually test these conditions on the products mentioned above

Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach

Using a quantum field theory renormalization group-like differential equation, we give a new proof of the recipe theorem for the Tutte polynomial for matroids. The solution of such an equation is in fact given by some appropriate characters of the Hopf algebra of isomorphic classes of matroids, characters which are then related to the Tutte polynomial for matroids. This Hopf algebraic approach also allows to prove, in a new way, a matroid Tutte polynomial convolution formula appearing in W. Kook {\it et. al., J. Comb. Series} {\bf B 76} (1999).Comment: 14 pages, 3 figure

Space-time domain decomposition for advection-diffusion problems in mixed formulations

This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time steps can be used in different parts of the domain. Global-in-time, non-overlapping domain-decomposition methods are coupled with operator splitting making possible the different treatment of the advection and diffusion terms. Two domain-decomposition methods are considered: one uses the time-dependent Steklov--Poincar{\'e} operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Robin transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains. A generalized Neumann-Neumann preconditioner is proposed for the first method. To illustrate the two methods numerical results for two-dimensional problems with strong heterogeneities are presented. These include both academic problems and more realistic prototypes for simulations for the underground storage of nuclear waste

Ultrasoft Renormalization in Non-Relativistic QCD

For Non-Relativistic QCD the velocity renormalization group correlates the renormalization scales for ultrasoft, potential and soft degrees of freedom. Here we discuss the renormalization of operators by ultrasoft gluons. We show that renormalization of soft vertices can induce new operators, and also present a procedure for correctly subtracting divergences in mixed potential-ultrasoft graphs. Our results affect the running of the spin-independent potentials in QCD. The change for the NNLL t-tbar cross section near threshold is very small, being at the 1% level and essentially independent of the energy. We also discuss implications for analyzing situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig

Proteins and polymers

Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native state structures and is not incompatible with the existence of structured building blocks such as $\alpha$-helices and $\beta$-strands. We present a discussion on how the notion of the thickness of a polymer chain, besides being useful in describing a chain molecule in the continuum limit, plays a vital role in interpolating between conventional polymer physics and the phase of matter associated with protein structures.Comment: 7 pages, 6 figure

1S and MSbar Bottom Quark Masses from Upsilon Sum Rules

The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules which relate the masses and the electronic decay widths of the $\Upsilon$ mesons to moments of the vacuum polarization function. The 1S mass is defined as half the perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound state, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues the pole mass definition. Compared to an earlier analysis by the same author, which had been carried out in the pole mass scheme, the 1S mass scheme leads to a much better behaved perturbative series of the moments, smaller uncertainties in the mass extraction and to a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking $\alpha_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the $\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\bar m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of pole and $\bar{MS}$ mass are known and if the error in the strong coupling is decreased.Comment: 20 pages, latex; numbers in Tabs. 2,3,4 corrected, a reference and a comment on the fitting procedure added, typos in Eqs. 2 and 23 eliminate