The triviality bound on the Higgs mass; its value and what it means

Older lattice work exploring the Higgs mass triviality bound is briefly reviewed. It indicates that a strongly interacting scalar sector in the minimal standard model cannot exist; on the other hand low energy QCD phenomenology might be interpreted as an indication that it could. We attack this puzzle using the $1/N$ expansion and discover a simple criterion for selecting a lattice action that is more likely to produce a heavy Higgs particle. Depending on the precise form of the limitation put on the cutoff effects, our large $N$ calculations, when combined with old numerical data, suggest that the Higgs mass bound might be around 750 $GeV$, which is higher than the $\sim 650~GeV$ previously obtained. Preliminary numerical work indicates that an increase of at least 19\% takes place at $N=4$ on the $F_4$ lattice when the old simple action is replaced with a new action (still containing only nearest neighbor interactions) if one uses the lattice spacing as the physical cutoff for both actions. It appears that, while a QCD like theory could produce $M_H / F ~ \sim 6$, a meaningful ``minimal elementary Higgs'' theory cannot have M_H/ F~ \gtapprox 3. Still, even at 750 $GeV$, the Higgs particle is so wide ($\sim 290~$GeV), that one cannot argue any more that the scalar sector is weakly coupled.Comment: 8 pages. Latex file with 4 ps figures included. Preprint RU-92-22, SCRI-92-11

Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

In the domain-wall formulation of chiral fermion, the finite separation between domain-walls ($L_s$) induces an effective quark mass ($m_{\rm eff}$) which complicates the chiral limit. In this work, we study the size of the effective mass as the function of $L_s$ and the domain-wall height $m_0$ by calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator in the topologically-nontrivial background fields. We find that, just like in the free case, $m_{\rm eff}$ decreases exponentially in $L_s$ with a rate depending on $m_0$. However, quantum fluctuations amplify the wall effects significantly. Our numerical result is consistent with a previous study of the effective mass from the Gell-Mann-Oakes-Renner relation.Comment: 10 pages, an appendix and minor changes adde

The staggered domain wall fermion method

A different lattice fermion method is introduced. Staggered domain wall fermions are defined in 2n+1 dimensions and describe 2^n flavors of light lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As the size of the extra dimension becomes large, 2^n chiral flavors with the same chiral charge are expected to be localized on each boundary and the full SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give a different perspective into the inherent flavor mixing of lattice fermions and by design present an advantage for numerical simulations of lattice QCD thermodynamics. The chiral and topological index properties of the SDWF Dirac operator are investigated. And, there is a surprise ending...Comment: revtex4, 7 figures, minor revisions, 2 references adde

Adjoint Wilson Line in SU(2) Lattice Gauge Theory

The behavior of the adjoint Wilson line in finite-temperature, $SU(2)$, lattice gauge theory is discussed. The expectation value of the line and the associated excess free energy reveal the response of the finite-temperature gauge field to the presence of an adjoint source. The value of the adjoint line at the critical point of the deconfining phase transition is highlighted. This is not calculable in weak or strong coupling. It receives contributions from all scales and is nonanalytic at the critical point. We determine the general form of the free energy. It includes a linearly divergent term that is perturbative in the bare coupling and a finite, nonperturbative piece. We use a simple flux tube model to estimate the value of the nonperturbative piece. This provides the normalization needed to estimate the behavior of the line as one moves along the critical curve into the weak coupling region.Comment: 21 pages, no figures, Latex/Revtex 3, UCD-93-1

Solomonoff Induction Violates Nicod's Criterion

Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201

High Energy Physics from High Performance Computing

We discuss Quantum Chromodynamics calculations using the lattice regulator. The theory of the strong force is a cornerstone of the Standard Model of particle physics. We present USQCD collaboration results obtained on Argonne National Lab's Intrepid supercomputer that deepen our understanding of these fundamental theories of Nature and provide critical support to frontier particle physics experiments and phenomenology.Comment: Proceedings of invited plenary talk given at SciDAC 2009, San Diego, June 14-18, 2009, on behalf of the USQCD collaboratio