Chiral Perturbation Theory Parameters Research Articles

Tests of quark–hadron duality in τ-decays

An exhaustive number of QCD finite energy sum rules for [Formula: see text]-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension d = 2 condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions d = 6 and d = 8, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark–hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic [Formula: see text]-decay in the kinematic region above s [Formula: see text] 2.2 GeV2 for these kernels.

CHIRON: a package for ChPT numerical results at two loops

This document describes the package CHIRON which includes two libraries, chiron itself and jbnumlib. CHIRON is a set of routines useful for two-loop numerical results in Chiral Perturbation Theory (ChPT). It includes programs for the needed one- and two-loop integrals as well as routines to deal with the ChPT parameters. The present version includes everything needed for the masses, decay constants and quark-antiquark vacuum-expectation-values. An added routine calculates consistent values for the masses and decay constants when the pion and kaon masses are varied. In addition a number of finite volume results are included: one-loop tadpole integrals, two-loop sunset integrals and the results for masses and decay constants. The numerical routine library jbnumlib contains the numerical routines used in chiron. Many are to a large extent simple C++ versions of routines in the CERNLIB numerical library. Notable exceptions are the dilogarithm and the Jacobi theta function implementations. This paper describes what is included in CHIRON v0.50.

Pion and kaon decay constants: Lattice versus resonance chiral theory

The Lattice results for the pion and kaon decay constants are analyzed within the Resonance Chiral Theory framework in the large ${N}_{C}$ limit. The approximately linear behavior of the observable at large light-quark mass is explained through the interaction with the lightest multiplet of scalar resonances. The analysis of the Lattice results allows to obtain the resonance mass ${M}_{S}=1049\ifmmode\pm\else\textpm\fi{}25\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$ and some of the Chiral Perturbation Theory parameters at leading order in $1/{N}_{C}$.

Form-factors and – scattering

The F and G form-factors of K ℓ4 and the quark condensates are calculated to O (p 6 ) in Chiral Perturbation theory (CHPT). Full formulas are presented as much as possible. A full refit of most of the O (p 4 ) CHPT parameters is done with a discussion of all inputs and underlying assumptions. We discuss the consequences for the vacuum expectation values, decay constants, pseudoscalar masses and π – π scattering.

Simulations of discrete quantum systems in continuous euclidean time

We propose a new method to study path integrals for discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is applied here to the Heisenberg quantum antiferromagnet using a continuous-time version of a loop cluster algorithm. This algorithm is exploited to confirm the predictions of chiral perturbation theory in the extreme low temperature regime, down to T = 0.01 J. A fit of the low-energy parameters of chiral perturbation theory gives excellent agreement with previous results and with experiments.

Fixing two chiral perturbation theory parameters by fitting pion-pion phase shifts

In this paper, we fix the parameters ℓ 1 and ℓ 2 of the one loop corrected chiral perturbation theory by fitting the low energy pion-pion S- and P- experimental phase-shifts. The corresponding values of the scattering lengths are calculated. Related approaches for data fitting, in particular the unitarization program of current algebra, are also discussed.

Simulations of Discrete Quantum Systems in Continuous Euclidean Time.

We propose a new method to study path integrals for discrete quantum systems in which we work directly in the Euclidean time continuum. The method is of general interest. Here it is applied to the Heisenberg quantum antiferromagnet using a continuous-time version of a loop cluster algorithm. This algorithm is exploited to confirm the predictions of chiral perturbation theory in the extreme low temperature regime, down to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.01J$. A fit of the low-energy parameters of chiral perturbation theory gives excellent agreement with previous results and with experiments.

Constraints on chiral perturbation theory parameters from QCD inequalities

We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that 2 m q ( μ) ⩽ B o ( μ) Z( μ). The use of further properties of the exact fermion propagator yields information on some higher order parameters.

K ℓ4 decays and the low-energy expansion

Tha amplitudes for the K ℓ4 decays are calculated to next-to-leading order in Chiral Perturbation Theory. These are then compared with the available experimental results on these decays. The values of the parameters L 1, 2, 3 previously determined from ππ scattering are compared with those obtained here. A short overview of the determination of the parameters of Chiral Perturbation Theory is included.