pi-pi and pi-K scatterings in three-flavour resummed chiral perturbation theory

The (light but not-so-light) strange quark may play a special role in the low-energy dynamics of QCD. The presence of strange quark pairs in the sea may have a significant impact of the pattern of chiral symmetry breaking : in particular large differences can occur between the chiral limits of two and three massless flavours (i.e., whether m_s is kept at its physical value or sent to zero). This may induce problems of convergence in three-flavour chiral expansions. To cope with such difficulties, we introduce a new framework, called Resummed Chiral Perturbation Theory. We exploit it to analyse pi-pi and pi-K scatterings and match them with dispersive results in a frequentist framework. Constraints on three-flavour chiral order parameters are derived.Comment: Proceedings of the EPS-HEP 2007 Conference, Manchester (UK). 3 pages, 1 figur

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order Lambda_QCD, fluctuations of sea s-s bar pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N_f=2 (m_u=m_d=0, m_s physical) and N_f=3 (m_u=m_d=m_s=0). This effect of vacuum fluctuations of s-s bar pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p^4) low-energy constants L_4 and L_6 of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit a numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with a special care. We investigate the impact of the fluctuations of s-s bar pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes (L around 2.5 fm).Comment: 31 pages, 9 figures. A few comments added and typos correcte

Chiral symmetry and spectrum of Euclidean Dirac operator

After recalling some connections between the Spontaneous Breakdown of Chiral Symmetry (SBChS) and the spectrum of the Dirac operator for Euclidean QCD on a torus, we use this tool to reconsider two related issues : the Zweig rule violation in the scalar channel and the dependence of SBChS order parameters on the number N_f of massless flavours. The latter would result into a great variety of SBChS patterns in the (N_f,N_c) plane, which could be studied through so-called Leutwyler-Smilga sum rules in association with lattice computations of the Dirac spectrum.Comment: 6 pages, no figure, class file included. Talk given at the XVII International School of Physics "QCD: Perturbative or Nonperturbative", Lisbon, Portugal, 29 September - 4 October 1999, to appear in the Proceeding

A note on renormalon models for the determination of alpha_s(M_tau)

The tau hadronic width provides a determination of the strong coupling constant alpha_s at low energies, since it can be related to a weighted integral of the Adler function in the complex energy plane. Using Operator Product Expansion, one sees that the sensitivity to alpha_s comes from the perturbative contribution, which can be obtained by integrating the perturbative expansion of the Adler function. Two different prescriptions proposed to perform this integral, called Fixed-Order Perturbation Theory and Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results for the strong coupling constant. Recently, models for the Adler function based on renormalon calculus have been proposed to determine which of the two methods is the most accurate, by comparing the resulting asymptotic series with the true value of the integral. We discuss the assumptions of such ansatz and the determination of their free parameters. We show that variations of this renormalon ansatz can yield opposite conclusions concerning the comparison of CIPT versus FOPT, and that such models are not constrained enough to provide a definite answer on this issue or to be exploited for a high-precision determination of alpha_s(m_tau^2).Comment: 28 pages, 5 figure

Renormalization of B-meson distribution amplitudes

We summarize a recent calculation of the evolution kernels of the two-particle B-meson distribution amplitudes $\phi_+$ and $\phi_-$ taking into account three-particle contributions. In addition to a few phenomenological comments, we give as a new result the evolution kernel of the combination of three-particle distribution amplitudes $\Psi_A-\Psi_V$ and confirm constraints on $\phi_+$ and $\phi_-$ derived from the light-quark equation of motion.Comment: 7 pages, 2 figures. Contribution to the proceedings of the Int. Workshop on Effective Field Theories: from the pion to the upsilon. Feb. 2009. Valencia, Spai

Radiative corrections in weak semi-leptoni processes at low energy: a two-step matching determination

We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the Standard Model. For this purpose, we follow a two-step procedure. A first matching, from the Standard Model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual $\log(M\_Z/M\_\rho)$ approximation.Comment: 28 pages, late