Anna Hasenfratz

Renormalization group study of scalar field theories

An approximate RG equation is derived and studied in scalar quantum field theories in d dimensions. The approximation allows for an infinite number of different couplings in the potential, but excludes interactions containing derivatives. The resulting non-linear partial differential equation can be studied by simple means. Both the gaussian and the non-gaussian fixed points are discribed qualitatively correctly by the equation. The RG flows n d = 4 and the problem of defining an “effective” field theory are discussed in detail.

The equivalence of the top quark condensate and the elementary Higgs field

Abstract Several recent works suggested to replace the fundamental Higgs boson by a top quark condensate in analogy with the Nambu-Jona-Lasinio (NJL) mechanism. We show that the field theoretically correct replacement is a generalized NJL model with the minimal choice of three independent interaction terms in the lagrangian. We demonstrate in the large- N color limit that the physics of this model is fully equivalent to the corresponding simplified Standard Model where the Higgs boson is represented by an elementary scalar field with the usual Yukawa- and self-interactions. The generalized NJL mechanism does not lead to new physical predictions or constraints and the complete parameter range of the simplified Standard Model is recovered. Since there exists a simple mapping between the couplings of these two models, it is difficult to give physical significance to notions like composite versus fundamental, or dynamical symmetry breaking in this scheme. We also present some new numerical results on the relevant phase diagrams.

The triviality bound of the four-component Φ4 model☆

Abstract The four-dimensional O(4) Φ4 scalar theory is investigated in the broken phase at different values of the quartic coupling λ. The scalar mass, the field expectation value and the wave function renormalization constant are calculated. We demonstrate the λ dependence of the ratio R s = m s 〈ϕ s ren 〉 and estimate its upper bound to be around 2.7(1).

Study of the 4-component Φ4 model

La theorie scalaire φ 4 O(4) en dimensions 4 est etudiee dans la phase brisee pour des valeurs variees du couplage quantique λ et de la masse nue, sans et, en partie aussi avec, une source externe. On etudie leffet de taille reticulaire finie et les etats de Goldstone. La valeur moyenne du champ, la constante de renormalisation de la fonction donde, f G (lequivalent de Goldstone de la constante de desintegration du pion) et la masse mσ de la particule scalaire massive, sont determinees. On obtient une limite superieure du rapport Rφ=mσ|f G , impliquant une limite superieure du couplage quantique renormalise. Il correspond a une limite superieure de 8.2 (5) sur le rapport de masse de Higgs sur la masse W aux valeurs du cut-off 1/mσ=2.5

Hopping parameter expansion for the meson spectrum in SU(3) lattice QCD

The low-lying pseudoscalar and vector mesons containing u, d, s and c quarks are studied by the method of the hopping parameter expansion combined with a Monte Carlo simulation at 1g2 = 0.0, 0.7, 0.9, 0.925, 0.95 and 1.0. The effect of virtual quark loops is taken into account. Meson masses, quark masses, the lattice scale and Ku, Ks and Kc as functions of g2 are determined.

Canonical ensembles and nonzero density quantum chromodynamics

We study QCD with nonzero chemical potential on 44 lattices by averaging over the canonical partition functions, or sectors with fixed quark number. We derive a condensed matrix of size 2×3×L3 whose eigenvalues can be used to find the canonical partition functions. We also experiment with a weight for configuration generation which respects the Z(3) symmetry which forces the canonical partition function to be zero for quark numbers that are not multiples of three.

The Equivalence of the SU(N) Yang-Mills theory with a purely fermionic model

Abstract We investigate the detailed conditions under which a purely fermionic model with current-current interaction goes over to a renormalizable, asymptotically free SU( N c ) gauge theory. We argue that a necessary condition is to require the number of fermions N f > 11 2 N c , but this condition might not be sufficient. We consider the sufficient N c → ∞ limit.

Non-perturbative study of the strongly coupled scalar-fermion model

Abstract We study the one-component scalar model coupled via a Yukawa term to (naive) fermions in the quenched approximation. While for weak Yukawa coupling we reproduce the perturbative behaviour, we find a drastically different situation for strong coupling, indicating the existence of an ultraviolet stable tricritical point. We argue that this is not the artifact of the quenched approximation.

Upper bound estimate for the Higgs mass from the lattice regularized Weinberg-Salam model

Abstract There are indications that, as a consequence of the trivality of the scalar φ 4 theory, the Weinberg-Salam model is massive free field theory. However, considering theWS model as an effective field theory, an upper bound for the Higgs mass can exist. We have studied this phenomenon by simulating the SU(2) gauge Higgs model on a lattice. The results indicate that R max = m H / m W | max = 9.3 ± 1. However, serious finite size effects make it unfeasible to explore the region m H ⩽ Λ cutoff with Monte Carlo simulation.

Goldstone bosons and finite size effects: A numerical study of the O(4) model

We study the 4-component φ4 model in 4 dimensions in the broken phase where the Goldstone modes dominate the finite size effects. Chiral perturbation theory relates the quantities measured at non-vanishing external source and in a finite volume to the low energy parameters v (the field expectation value) and F (the pion decay constant) defined at infinite volume in the limit of vanishing external source. We analyze high statistics Monte Carlo data for the field expectation value and the Goldstone propagator by means of such expansions and we find very good agreement with the theoretically expected functional behaviour. It is possible to identify non-leading terms in the finite volume expansion and determine corresponding scale parameters. We also explore some alternative methods applicable at vanishing external source. Our analysis demonstrates that in a situation where the light Goldstone bosons control the dynamics of the system at large distances one may determine the infinite volume, zeri external source quantities from finite volume simulations in a theoretically controlled way.