Radiative kaon decay in the chiral perturbation theory

We analyze the possibility of experimental investigation of new low-energy relations between the values of resonance masses in the meson form factors and the differential rate of radiative kaon decay K ⁺ → π⁺ e ⁺ e ⁻(μ⁺μ⁻) at the current level of the experimental precision. A set of arguments is listed in favor that these relations can be a consequence of weak static interactions in the Standard Model. The results were presented at the 5th NA48 Mini-Workshop on Kaon Physics, CERN, Dec. 12, 2006. The text was submitted by the authors in English.     

Information theory and renormalization group flows

We present a possible approach to the study of the renormalization group (RG) flow based entirely on the information theory. The average information loss under a single step of Wilsonian RG transformation is evaluated as a conditional entropy of the fast variables, which are integrated out, when the slow ones are held fixed. Its positivity results in the monotonic decrease of the informational entropy under renormalization. This, however, does not necessarily imply the irreversibility of the RG flow, because entropy is an extensive quantity and explicitly depends on the total number of degrees of freedom, which is reduced. Only some size-independent additive part of the entropy could possibly provide the required Lyapunov function. We also introduce a mutual information of fast and slow variables as probably a more adequate quantity to represent the changes in the system under renormalization and evaluate it for some simple systems. It is shown that for certain real space decimation transformations the positivity of the mutual information directly leads to the monotonic growth of the entropy per lattice site along the RG flow and hence to its irreversibility.     

Wave function renormalization in heavy baryon chiral perturbation theory

We establish exact relations between relativistic form factors and amplitudes for single-baryon processes and the corresponding quantities calculated in the framework of heavy baryon chiral perturbation theory. A crucial ingredient for the proper matching is the first complete treatment of baryon wave function renormalization in heavy baryon chiral perturbation theory.     

Quantum chromodynamics predictions in renormalization scheme invariant perturbation theory

It has recently been shown that any physical quantity ℛ, in perturbation theory, can be obtained as a function of only the renormalization scheme (rs) invariants,ρ ₀,ρ ₁,ρ ₂, … Physical predictions, to any given order, are renormalization scheme independent in this approach. Quantum chromodynamics (qcd) predictions to second order, within thisrs-invariant perturbation theory, are given here for several processes. These lead to some novel relations between experimentally measurable quantities, which do not involve the unknownqcd scale parameter Λ. They can therefore be directly confronted with experiments and this has been done wherever possible. It is suggested that these relations can be used to probe the neglected higher order corrections.     

Radiative Kaon decays and CP violation in chiral perturbation theory

Chiral perturbation theory is a very useful framework for testing the standard model in processes where long-distance effects are expected to play an essential rôle. We analyze the rare K decays K⁰→γℓ⁺ℓ⁻, K⁺→π⁺γ3 and K_L→π⁰ℓ⁺ℓ⁻ in the effective chiral formulation of the standard model. These processes, like the decays K⁰→γγ, K⁺→π⁺ℓ⁺ℓ⁻, K_S→π⁰ℓ⁺ℓ⁻ and K⁰→π⁰γγ discussed in previous work, have the property that the corresponding amplitudes vanish to lowest order in chiral perturbation theory. Precise predictions for decay rates and spectra are made in terms of a few coupling constants not restricted by softly broken chiral symmetry alone. Special consideration is given to various possible tests of CP noninvariance in these decays, in particular to effects due to intrinsic CP violation in the amplitudes. We find that chiral perturbation theory correlates different CP-violating observables such as the charge asymmetries in K^±→π^±γγ and K^±→π^±ℓ⁺ℓ⁻, the one-photon exchange contribution to K_L→π⁰e⁺e⁻ and the transverse polarization in K_L →π⁰μ⁺μ⁻. Detailed numerical results are shown.     

Summing perturbation expansions by means of renormalization group considerations

Renormalization group considerations are used to sum divergent perturbation expansions encountered in QCD or other quantum field theories. The method works even in the case when these expansions, considered in a fixed renormalization scheme (RS), are factorially divergent and of asymptotically constant sign. The results assume the form of convergent (under certain circumstances) expansions in a set of functions of a free parameter which specifies the procedure involved. It is argued that the relation of our results to conventional, formal perturbation expansions in a fixed RS in fact suggests the physical interpretation of this parameter and specifies its value.     

Linear and nonlinear dynamic scaling relations in the renormalization group theory

Dynamic scaling relations in the presence of an external field are derived by extending Hubbard's static arguments to non-equilibrium systems using the RG theory. This confirms microscopically the scaling relations of the linear and non-linear critical slowing down.     

Real space renormalization group theory of the percolation model

A cluster expansion renormalization group method in real space is-developed to determine the critical properties of the percolation model. In contrast to previous renormalization group approaches, this method considers the cluster size distribution (free energy) rather than the site or bond probability distribution (coupling constants) and satisfies the basic renormalization group requirement of free energy conservation. In the construction of the renormalization group transformation, new couplings are generated which alter the topological structure of the clusters and which must be introduced in the original system. Predicted values of the critical exponents appear to converge to presumed exact values as higher orders in the expansion are considered. The method can in principle be extended to different lattice structures, as well as to different dimensions of space.This paper is dedicated to Prof. Philippe Choquard.     

Radiative perturbation theory for polarized radiances: 1. Theory

Radiative perturbation theory has proven to be a useful tool in radiative transfer calculations, especially in situations where repeated solution of the radiative transfer equation is required. So far however, its use has been restricted to non-polarized situations, including such applications as surface fluxes, UV indices, and the inversion of satellite radiance observations. Here, we extend the structure of radiative perturbation theory to incorporate the full Stokes formalism of polarization, to obtain the relevant equations for the first order term. This formalism will be applied to fluxes in a follow-up paper, and eventually to satellite observations.     

BRST string field theory from Wilson's renormalization group

Wilson “renormalization group” fixed point equations are derived for BRST symmetry in two-dimensional field theory. Their usefulness as equations of motions for string field theory is discussed.     

Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998     

The impact of renormalization group theory on magnetism

The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ε that is independent of spin structure and lattice symmetry. Normally the T^ε function holds up to ~0.85T_c where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the T^ε function are demonstrated for the spontaneous magnetization and for the heat capacity.     

Radiative quark mass generation and a fourth quark family

We study the possibility to calculate masses and mixing angles of the known three quark families from radiative corrections connecting them to a heavy fourth family. In a left-right symmetric electroweak model with chiral horizontal gauge interactions, we obtain for the heavy quark masses values in the TeV range.     

Dynamical mean field theory with the density matrix renormalization group

A new numerical method for the solution of the dynamical mean field theory's self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.