The CKM Matrix from Lattice QCD

Lattice QCD plays an essential role in testing and determining the parameters of the CKM theory of flavor mixing and CP violation. Very high precisions are required for lattice calculations analysing CKM data; I discuss the prospects for achieving them. Lattice calculations will also play a role in investigating flavor mixing and CP violation beyond the Standard Model.Comment: To appear in Prog. Theor. Phys. Vol. 122, No.1 (Special Issue

Progress in QCD Using Lattice Gauge Theory

Review of results from lattice QCD of relevance to standard-model phenomenology, to appear in Annual Review of Nuclear and Particle Science. KEY WORDS: hadron masses, quark mixing (CKM) matrix, weak matrix elements, strong coupling constant.Comment: 41 pages LaTeX, FERMILAB-PUB-93/058-T. Figures and style file are uuencoded and appended. Figures embedded with epsf.sty, available from the serve

Expected Precision of Higgs Boson Partial Widths within the Standard Model

We discuss the sources of uncertainty in calculations of the partial widths of the Higgs boson within the Standard Model. The uncertainties come from two sources: the truncation of perturbation theory and the uncertainties in input parameters. We review the current status of perturbative calculations and note that these are already reaching the parts-per-mil level of accuracy for the major decay modes. The main sources of uncertainty will then come from the parametric dependences on alpha_s, m_b, and m_c. Knowledge of these parameters is systematically improvable through lattice gauge theory calculations. We estimate the precision that lattice QCD will achieve in the next decade and the corresponding precision of the Standard Model predictions for Higgs boson partial widths.Comment: 20 pages, 1 figure; v2: minor typo correction

Hierarchical modelling of temperature and habitat size effects on population dynamics of North Atlantic cod

Understanding how temperature affects cod (Gadus morhua) ecology is important for forecasting how populations will develop as climate changes in future. The effects of spawning-season temperature and habitat size on cod recruitment dynamics have been investigated across the North Atlantic. Ricker and Beverton and Holt stock–recruitment (SR) models were extended by applying hierarchical methods, mixed-effects models, and Bayesian inference to incorporate the influence of these ecosystem factors on model parameters representing cod maximum reproductive rate and carrying capacity. We identified the pattern of temperature effects on cod productivity at the species level and estimated SR model parameters with increased precision. Temperature impacts vary geographically, being positive in areas where temperatures are <5°C, and negative for higher temperatures. Using the relationship derived, it is possible to predict expected changes in population-specific reproductive rates and carrying capacities resulting from temperature increases. Further, carrying capacity covaries with available habitat size, explaining at least half its variability across stocks. These patterns improve our understanding of environmental impacts on key population parameters, which is required for an ecosystem approach to cod management, particularly under ocean-warming scenarios. Key words: carrying capacity , cod , hierarchical models , North Atlantic , temperature , uncertaint

Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term

We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry, radiative corrections do not change the coefficient of the \cs term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant \cs term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the \cs term is a discontinuous function over the phase diagram of the theory.Comment: Version to be published in Phys Lett B., minor additional change

On the Viability of Lattice Perturbation Theory

In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using instead ``renormalized'' coupling constants defined in terms of physical quantities, like the heavy-quark potential, greatly enhances the predictive power of lattice perturbation theory. The quality of these predictions is further enhanced by a method for automatically determining the coupling-constant scale most appropriate to a particular quantity. We present a mean-field analysis that explains the large renormalizations relating lattice quantities, like the coupling constant, to their continuum analogues. This suggests a new prescription for designing lattice operators that are more continuum-like than conventional operators. Finally, we provide evidence that the scaling of physical quantities is asymptotic or perturbative already at $\beta$'s as low as 5.7, provided the evolution from scale to scale is analyzed using renormalized perturbation theory. This result indicates that reliable simulations of (quenched) QCD are possible at these same low $\beta$'s.Comment: 3

Phase transitions in a gas of anyons

We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however now in the presence of a topological term added to the action corresponding to the total linking number between the loops. We compute the linking number using certain notions from knot theory. Adding the topological term converts the particles into anyons. Using the correspondence that the model is an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. We find the following new results. The system continues to exhibit a phase transition as a function of the anyon mass as it becomes small \cite{mnp}, although the phases do not change the manifestation of the symmetry. The Chern-Simons term has no effect on the Wilson loop, but it does affect the {\rm '}t Hooft loop. For a given configuration it adds the linking number of the 't Hooft loop with all of the dynamical vortex loops to the action. We find that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, which is unexpected.Comment: 6 pages, 5 figure