Lattice study of the Coleman--Weinberg mass in the SU(2)-Higgs model

Radiative symmetry breaking is a well known phenomenon in perturbation theory. We study the problem in a non-perturbative framework, i.e. lattice simulations. The example of the bosonic sector of the SU(2)-Higgs model is considered. We determine the minimal scalar mass which turns out to be higher than the mass value given by 1-loop continuum perturbation theory.Comment: Contribution to ICHEP-02, Amsterdam, 24-31 July 2002, 2 pages, 1 figur

Mass Deformed Exact S-parameter in Conformal Theories

We use the exact expression for the S parameter in the perturbative region of the conformal window to establish its dependence on the explicit introduction of fermion masses. We demonstrate that the relative ordering with which one sends to zero either the fermion mass or the external momentum leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories.Comment: 4 pages, 2 figures. 2column

Perturbative and non-perturbative studies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings

We present a calculation of the O(g^2,\lambda) perturbative corrections to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings. These corrections are obtained by a one-loop calculation requiring the rotational invariance of the gauge and Higgs boson propagators in the continuum limit. The coupling anisotropies are also determined from numerical simulations of the model on appropriate lattices. The one-loop perturbation theory and the simulation results agree with high accuracy. It is demonstrated that rotational invariance is also restored for the static potential determined from space-space and space-time Wilson loops.Comment: 27pages, Latex, 7 figures (7 eps, 3 ps files), correction of misprint

Intrinsic volumes of inscribed random polytopes in smooth convex bodies

Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the $s$-th intrinsic volumes $V_s(K_n)$ of $K_n$ for $s\in\{1, ..., d\}$. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of $K_n$. The essential tools are the Economic Cap Covering Theorem of B\'ar\'any and Larman, and the Efron-Stein jackknife inequality

On the multiplicity of arrangements of congruent zones on the sphere

Consider an arrangement of $n$ congruent zones on the $d$-dimensional unit sphere $S^{d-1}$, where a zone is the intersection of an origin symmetric Euclidean plank with $S^{d-1}$. We prove that, for sufficiently large $n$, it is possible to arrange $n$ congruent zones of suitable width on $S^{d-1}$ such that no point belongs to more than a constant number of zones, where the constant depends only on the dimension and the width of the zones. Furthermore, we also show that it is possible to cover $S^{d-1}$ by $n$ congruent zones such that each point of $S^{d-1}$ belongs to at most $A_d\ln n$ zones, where the $A_d$ is a constant that depends only on $d$. This extends the corresponding $3$-dimensional result of Frankl, Nagy and Nasz\'odi (2016). Moreover, we also examine coverings of $S^{d-1}$ with congruent zones under the condition that each point of the sphere belongs to the interior of at most $d-1$ zones

Electroweak phase transition by four dimensional simulations

The finite temperature phase transition in the SU(2)-Higgs model at a Higgs boson mass $M_H \simeq 35$ GeV is studied in numerical simulations on four dimensional lattices with time-like extensions up to $L_t=5$. $T_c/M_H$ is extrapolated to the continuum limit and a comparison with the perturbative prediction is made. A one-loop calculation to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings is presented. Our numerical simulations show that the above perturbative result is applicable in the phenomenologically interesting parameter region.Comment: 3 pages, Latex, 3 figures, Talk presented at LATTICE96(electroweak) by Z. Fodo

Interface Tension of the Electroweak Phase Transition

In our nonperturbative lattice investigation we study the interface tension of the finite-temperature electroweak phase transition. In this analysis the Higgs mass has been chosen to be about $35$ GeV. At the transition point of a finite volume system, tunnelling between the symmetric and the Higgs phase takes place. This phenomenon leads to a splitting of the ground state, which can be used to determine the interface tension. The result obtained this way agrees with the result of the two-coupling method and with the prediction of the perturbative approach.Comment: 10 pages, five figures in uuencoded PS format, Latex + epsf.st

Strange Particles and Neutron Stars - Experiments at Gsi

Experiments on strangeness production in nucleus-nucleus collisions at SIS energies address fundamental aspects of modern nuclear physics: the determination of the nuclear equation-of-state at high baryon densities and the properties of hadrons in dense nuclear matter. Experimental data and theoretical results will be reviewed. Future experiments at the FAIR accelerator aim at the exploration of the QCD phase diagram at highest baryon densities.Comment: %Invited talk given at the International Invited talk given at the International Symposium on Heavy Ion Physics (ISHIP 2006) April 3-6 2006, FIAS, Frankfurt, Germany Frankfurt, German

The status of pentaquark spectroscopy on the lattice

The present work is a summary of the status of lattice pentaquark calculations. After a pedagogic introduction to the basics of lattice hadron spectroscopy we give a critical comparison of results presently available in the literature. Special emphasis is put on presenting some of the possible pitfalls of these calculations. In particular we discuss at length the choice of the hadronic operators and the separation of genuine five-quark states from meson-baryon scattering states.Comment: 13 pages LaTeX, 1 eps figur