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

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 CKM Parameters

The Cabibbo-Kobayashi-Maskawa matrix is a key element to describe flavour dynamics in the Standard Model. With only four parameters, this matrix is able to describe a large range of phenomena in the quark sector, such as CP violation and rare decays. It can thus be constrained by many different processes, which have to be measured experimentally with a high accuracy and computed with a good theoretical control. With the advent of the B factories and the LHCb experiment taking data, the precision has significantly improved recently. The most relevant experimental constraints and theoretical inputs are reviewed and fits to the CKM matrix are presented for the Standard Model and for some topical model-independent studies of New Physics.Comment: Invited contribution to Annual Review of Nuclear and Particle Science, Volume 6

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

Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived. The impact of these equivalence results is that it justifies the use of the Euler scheme instead of the discretized diffusion process for inference purposes.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1216 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Filtering the Wright-Fisher diffusion

We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent and the conditional distribution of y(ti) only depends on x(ti). When this conditional distribution has a specific form, we prove that the model ((x(ti), y(ti)), i 1) is a computable filter in the sense that all distributions involved in filtering, prediction and smoothing are exactly computable. These distributions are expressed as finite mixtures of parametric distributions. Thus, the number of statistics to compute at each iteration is finite, but this number may vary along iterations.Comment: 24 page

Penalized nonparametric mean square estimation of the coefficients of diffusion processes

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and diffusion coefficients obtained by a penalized least squares approach. Our estimators belong to a finite-dimensional function space whose dimension is selected by a data-driven method. We provide non-asymptotic risk bounds for the estimators. When the sampling interval tends to zero while the number of observations and the length of the observation time interval tend to infinity, we show that our estimators reach the minimax optimal rates of convergence. Numerical results based on exact simulations of diffusion processes are given for several examples of models and illustrate the qualities of our estimation algorithms.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5173 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm