Introduction to Chiral Perturbation Theory

A brief introduction to chiral perturbation theory, the effective field theory of quantum chromodynamics at low energies, is given.Comment: 26 pages, 11 figures. Lectures given at the summer school ISSSMB 2006 in Akyaka, Turkey, September 200

Baryogenesis from a right-handed neutrino condensate

We show that the baryon asymmetry of the Universe can be generated by a strongly coupled right handed neutrino condensate which also drives inflation. The resulting model has only a small number of parameters, which completely determine not only the baryon asymmetry of the Universe and the mass of the right handed neutrino but also the inflationary phase. This feature allows us to make predictions that will be tested by current and planned experiments. As compared to the usual approach our dynamical framework is both economical and predictive.Comment: 13 pages, 3 figures. Typos corrected and several points clarified. Results unchanged. New references adde

Prebiotic Homochirality as a Critical Phenomenon

The development of prebiotic homochirality on early-Earth or another planetary platform may be viewed as a critical phenomenon. It is shown, in the context of spatio-temporal polymerization reaction networks, that environmental effects -- be them temperature surges or other external disruptions -- may destroy any net chirality previously produced. In order to understand the emergence of prebiotic homochirality it is important to model the coupling of polymerization reaction networks to different planetary environments.Comment: 6 Pages, 1 Figure, In Press: Origins of Life and Evolution of Biosphere

QCD axion and quintessential axion

The axion solution of the strong CP problem is reviewed together with the other strong CP solutions. We also point out the quintessential axion(quintaxion) whose potential can be extremely flat due to the tiny ratio of the hidden sector quark mass and the intermediate hidden sector scale. The quintaxion candidates are supposed to be the string theory axions, the model independent or the model dependent axions.Comment: 15 pages. Talk presented at Castle Ringberg, June 9-14, 200

Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure

d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference

Convergence properties of η→3π\eta\to 3\pi decays in chiral perturbation theory

Theoretical efforts to describe and explain the $\eta\to 3\pi$ decays reach far back in time. Even today, the convergence of the decay widths and some of the Dalitz plot parameters seems problematic in low energy QCD. In the framework of resummed CHPT, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series, where NNLO remainders are assumed to be small. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters $a$ and $d$ can be described very well too. When the parameters $b$ and $\alpha$ are concerned, we find a mild tension for the whole range of the free parameters, at less than 2$\sigma$ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable. Also, the distribution of the theoretical uncertainties is found to be significantly non-gaussian, so the consistency cannot be simply judged by the 1$\sigma$ error bars.Comment: 57 pages, 5 figure

Physics Opportunities of e+e- Linear Colliders

We describe the anticipated experimental program of an e+e- linear collider in the energy range 500 GeV -- 1.5 TeV. We begin with a description of current collider designs and the expected experimental environment. We then discuss precision studies of the W boson and top quark. Finally, we review the range of models proposed to explain the physics of electroweak symmetry breaking and show, for each case, the central role that the linear collider experiments will play in elucidating this physics. (to appear in Annual Reviews of Nuclear and Particle Science)Comment: 93 pages, latex + 23 figures; typos corrections + 1 reference adde