[en] We discuss a novel method to calculate f_B on the lattice, introduced in [1], based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. This method avoids the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We show the results of a first estimate at finite lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22) MeV. We also obtain f_Bs = 192(9)(5)(24)MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two-scale problems in lattice QCD

[en] We describe how the Schroedinger functional and twisted mass QCD can be used to compute the kaon B-parameter B_K on the lattice with Wilson fermions. This new approach is expected to reduce the systematic uncertainties on B_K through a better control of its (nonperturbative) renormalisation. Preliminary results for the bare matrix element in a physical volume of 1.5³ x 4.5 fm⁴ are presented. The renormalisation of the matrix element in a Schroedinger functional scheme is also discussed

[en] We apply the Schroedinger Functional (SF) formalism to determine the renormalisation group running of four-fermion operators which appear in the effective weak Hamiltonian of the Standard Model. Our calculations are done using Wilson fermions and the parity-odd components of the operators. Preliminary results are presented for the operator O_VA (s-barγ_μd) (s-barγ_μγy5d)

[en] We report on recent results for the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. For the first time finite volume effects of this matrix element are investigated and come out to be surprisingly large. We use standard Wilson and non-pertirbatively improved clover actions in order to control better the extrapolation to the continuum limit. Moreover, we compute, fully nonperturbatively, the renormalization group invariant matrix element, which allows a comparison with experimental results in a broad range of energy scales. Finally, we discuss the remaining uncertainties, the extrapolation to the chiral limit and the quenched approximation

[en] We compute non-perturbatively the evolution of the twist-2 operators corresponding to the average momentum of non-singlet quark densities. The calculation is based on a finite-size technique, using the Schroedinger Functional, in quenched QCD. We find that a careful choice of the boundary conditions, is essential, for such operators, to render possible the computation. As a by-product we apply the non-perturbatively computed renormalization constants to available data of bare matrix elements between nucleon states

[en] The renormalisation group running of the quark mass is determined non-perturbatively for a large range of scales, by computing the step scaling function in the Schroedinger Functional formalism of quenched lattice QCD both with and without O(a) improvement. A one-loop perturbative calculation of the discretisation effects has been carried out for both the Wilson and the Clover-improved actions and for a large number of lattice resolutions. The non-perturbative computation yields continuum results which are regularisation independent, thus providing convincing evidence for the uniqueness of the continuum limit. As a byproduct, the ratio of the renormalisation group invariant quark mass to the quark mass, renormalised at a hadronic scale, is obtained with very high accuracy. (author)

[en] We discuss the usage of continuous external momenta for computing renormalization factors as needed to renormalize operator matrix elements. These kind of external momenta are encoded in special boundary conditions for the fermion fields. The method allows to compute certain renormalization factors on the lattice that would have been very difficult, if not impossible, to compute with standard methods. As a result we give the renormalization group invariant step scaling function for a twist-2 operator corresponding to the average momentum of non-singlet quark densities

[en] We compute charm and bottom quark masses in the quenched approximation and in the continuum limit of lattice QCD. We make use of a step scaling method, previously introduced to deal with two scale problems, that allows to take the continuum limit of the lattice data. We determine the RGI quark masses and make the connection to the MS-bar scheme. The continuum extrapolation gives us a value m_b^RGI=6.73(16) GeV for the b-quark and m_c^RGI=1.681(36) GeV for the c-quark, corresponding, respectively, to m_b^MS-bar(m_b^MS-bar=4.33(10) GeV and m_c^MS-bar(m_c^MS-bar=1.319(28) GeV. The latter result, in agreement with current estimates, is for us a check of the method. Using our results on the heavy quark masses we compute the mass of the B_c meson, M_Bc=6.46(15) GeV

[en] We compute the decay constants for the heavy-light pseudoscalar mesons in the quenched approximation and continuum limit of lattice QCD. Within the Schroedinger functional framework, we make use of the step scaling method, which has been previously introduced in order to deal with the two scale problem represented by the coexistence of a light and a heavy quark. The continuum extrapolation gives us a value f_Bs=192(6)(4) MeV for the B_s meson decay constant and f_Ds=240(5)(5) MeV for the D_s meson

[en] We present data from the ALPHA Collaboration about lattice calculation of SU(2) pure-gauge running coupling constant, obtained with two different definitions of the coupling itself, which show universality of the continuum limit and clarify the applicability of renormalized perturbation theory. ((orig.))