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

How far can you go ? Surprises and pitfalls in three-flavour chiral extrapolations

The presence of strange sea quark pairs 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). We recall some indications of such a scenario in QCD, in relation with the peculiar dynamics of the scalar sector. We explain how this could affect the convergence of three-flavour chiral series, commonly used to extrapolate the results of lattice simulations. Finally, we indicate how lattice simulations with three dynamical flavours could unveil such an effect through the quark-mass dependence of light meson masses and decay constants.Comment: 7 pages, 4 figures, Presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

QCD factorisation and flavour symmetries illustrated in B_d,s -> KK decays

We present a new analysis of B_d,s -> KK modes within the SM, relating them in a controlled way through SU(3)-flavour symmetry and QCD-improved factorisation. We propose a set of sum rules for B_d,s -> K^0 \bar K^0 observables. We determine B_s -> KK branching ratios and CP-asymmetries as functions of A_dir(B_d -> K^0 \bar K^0), with a good agreement with current experimental measurements of CDF. Finally, we predict the amount of U-spin breaking between B_d -> pi+ pi- and B_s -> K+K-.Comment: 4 pages, 2 figures. Talk given at the 4th International Workshop on the CKM Unitarity Triangle (CKM2006), 12-16 December 2006, Nagoya, Japan, to appear in the proceedings (KEK Report

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

Estimation for L\'{e}vy processes from high frequency data within a long time interval

In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$ tends to infinity, $\Delta=\Delta_n$ tends to zero while $n\Delta_n$ tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the L\'{e}vy density and to provide a bound for the global ${\mathbb{L}}^2$-risk. Estimators of the drift and of the variance of the Gaussian component are also studied. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework.Comment: Published in at http://dx.doi.org/10.1214/10-AOS856 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org