Showing papers by "Heinrich Leutwyler published in 2001"
TL;DR: In this paper, the Roy equations admit physically acceptable solutions only within a band of the (a_0^0,a_ 0^2) plane, and it is shown that the data on the reactions e+e- -> pi pi and tau-to-pi pi nu reduce the width of this band quite significantly.
335 citations
TL;DR: In this article, the pion nucleon scattering amplitude is derived in terms of functions of a single variable and the result can be expressed as a set of integral equations that interrelate the lowest partial waves and are analogous to the Roy equations for ππ scattering.
Abstract: We derive a representation for the pion nucleon scattering amplitude that is valid to the fourth order of the chiral expansion. To obtain the correct analytic structure of the singularities in the low energy region, we have performed the calculation in a relativistic framework (infrared regularization). The result can be written in terms of functions of a single variable. We study the corresponding dispersion relations and discuss the problems encountered in the straightforward nonrelativistic expansion of the infrared singularities. As an application, we evaluate the corrections to the Goldberger-Treiman relation and to the low energy theorem that relates the value of the amplitude at the Cheng-Dashen point to the σ-term. While chiral symmetry does govern the behaviour of the amplitude in the vicinity of this point, the representation for the scattering amplitude is not accurate enough to use it for an extrapolation of the experimental data to the subthreshold region. We propose to perform this extrapolation on the basis of a set of integral equations that interrelate the lowest partial waves and are analogous to the Roy equations for ππ scattering.
177 citations
TL;DR: It is shown that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave pipi scattering lengths, and this result confirms the hypothesis that the quarkscondensate is the leading order parameter.
Abstract: We show that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave pipi scattering lengths. In view of this constraint, the new precision data on K(e(4)) decay allow a remarkably accurate determination of these quantities. The result confirms the hypothesis that the quark condensate is the leading order parameter.
125 citations
01 Mar 2001
TL;DR: In this paper, the sum rule determinations of m s and the chiral perturbation theory results for the ratios m u / m d and m s/m d are reviewed and a method for the extrapolation of lattice data to the physical values of m u and m d is outlined.
Abstract: The sum rule determinations of m s and the chiral perturbation theory results for the ratios m u / m d and m s / m d are reviewed and a method for the extrapolation of lattice data to the physical values of m u and m d is outlined.
36 citations
TL;DR: The role of the quark condensate for the low energy structure of QCD is discussed in some detail in this paper, where the dependence of M_pi on m_u and m_d and low energy theorems for the pi-pi scattering amplitude are reviewed.
Abstract: The role of the quark condensate for the low energy structure of QCD is discussed in some detail. In particular, the dependence of M_pi on m_u and m_d and the low energy theorems for the pi-pi scattering amplitude are reviewed. The new data on Ke4 decay beautifully confirm the standard picture, according to which the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.
1 citations
01 Dec 2001
TL;DR: In this article, the authors discuss the reasons why a considerable effort is made to resolve the low energy structure of QCD and the effective field theory used for this purpose is illustrated with the recent progress made in the predictions for pipi scattering and in understanding the low-energy properties of the theory in the large Nc limit.
Abstract: The reasons why a considerable effort is made to resolve the low energy structure of QCD are discussed. The effective field theory used for this purpose is illustrated with the recent progress made in the predictions for pipi scattering and in understanding the low energy properties of the theory in the large Nc limit.