arXiv subjects

Michele Della Morte

Publications and source records attributed to Michele Della Morte.

At least 73 records · Page 4Linked to original sources

arXiv2009

New ideas for g-2 on the lattice

Using iso-spin symmetry the quark-connected and disconnected contributions to the hadronic vacuum polarisation in a theory with N_f=2 flavours can be described as independent correlation functions, respectively. We show how this allows to use twisted boundary conditions for the connected contribution in order to improve the q^2-resolution in lattice QCD. Furthermore we derive an exact relation between the connected and the disconnected contributions at NLO in chiral perturbation theory. We discuss extensions to theories with more than 2 dynamical flavours.

hep-lat↗

arXiv2009

Symmetries and exponential error reduction in YM theories on the lattice: theoretical aspects and simulation results

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We briefly illustrate the approach in the simple case of the one-dimensional harmonic oscillator and discuss in some detail its extension to the four-dimensional Yang Mills theories. We report on our recent new results in the SU(3) Yang--Mills theory on the relative contribution to the partition function of the parity-odd states.

hep-lat↗

arXiv2009

Symmetries and exponential error reduction in Yang-Mills theories on the lattice

The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.

hep-lat↗

arXiv2009

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.

hep-lat↗

arXiv2008

Non-perturbative quark mass dependence in the heavy-light sector of two-flavour QCD

We present preliminary results of the non-perturbative heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. These observables, which are derived from heavy-light Schroedinger functional correlation functions and computed over a range of renormalization group invariant heavy quark masses from the charm to beyond the bottom region, allow for a quantitative comparison with the predictions of HQET and are of practical relevance for solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume.

hep-lat↗

arXiv2008

On cutoff effects in lattice QCD from short to long distances

We discuss kinematical enhancements of cutoff effects at short and intermediate distances. Starting from a pedagogical example with periodic boundary conditions, we switch to the case of the Schroedinger Functional, where the theoretical analysis is checked by precise numerical data with Nf=2 dynamical O(a)-improved Wilson quarks. Finally we present an improved determination of the renormalization of the axial current in that theory.

hep-lat↗

arXiv2008

Heavy Quark Effective Theory computation of the mass of the bottom quark

We present a fully non-perturbative computation of the mass of the b-quark in the quenched approximation. Our strategy starts from the matching of HQET to QCD in a finite volume and finally relates the quark mass to the spin averaged mass of the Bs meson in HQET. All steps include the terms of order Lambda^2/Mb. Expanding on [1], we discuss the computation and renormalization of correlation functions at order 1/Mb. With the strange quark mass fixed from the Kaon mass and the QCD scale set through r0=0.5 fm, we obtain a renormalization group invariant mass Mb = 6.758(86) GeV or mb(mb)= 4.347(48) GeV in the MS-bar scheme. The uncertainty in the computed Lambda^2/Mb terms contributes little to the total error and Lambda^3/Mb^2 terms are negligible. The strategy is promising for full QCD as well as for other B-physics observables.

hep-ph↗

arXiv2008

Scaling test of two-flavor O(a)-improved lattice QCD

We report on a scaling test of several mesonic observables in the non-perturbatively O(a) improved Wilson theory with two flavors of dynamical quarks. The observables are constructed in a fixed volume of 2.4fm x (1.8fm)^3 with Schroedinger functional boundary conditions. No significant scaling violations are found. Using the kaon mass determined in \cite{cernI}, we update our estimate of the Lambda parameter to Lambda^(2)_{msbar}/m_K = 0.52(6).

hep-lat↗

arXiv2008

Heavy-strange meson decay constants in the continuum limit of quenched QCD

We improve a previous quenched result for heavy-light pseudoscalar meson decay constants with the light quark taken to be the strange quark. A finer lattice resolution (a ~ 0.05 fm) in the continuum limit extrapolation of the data computed in the static approximation is included. We also give further details concerning the techniques used in order to keep the statistical and systematic errors at large lattice sizes L/a under control. Our final result, obtained by combining these data with determinations of the decay constant for pseudoscalar mesons around the D_s, follows nicely the qualitative expectation of the 1/m-expansion with a (relative) 1/m-term of about -0.5 GeV/m_PS. At the physical b-quark mass we obtain F_{B_s} = 193(7) MeV, where all errors apart from the quenched approximation are included.

hep-lat↗

arXiv2007

Standard Model parameters and heavy quarks on the lattice

I review recent progresses in heavy quarks physics on the lattice. I focus on decay constants and form factors relevant for the extraction of CKM matrix elements from experimental data. B-\bar{B} mixing is also discussed. In the last part of the paper I describe phenomenological applications of Heavy Quark Effective Theory (HQET) on the lattice, presenting in some detail the recent non-perturbative determination of the b-quark mass including O(1/m_b) corrections.

hep-lat↗

arXiv2007

Towards a non-perturbative matching of HQET and QCD with dynamical light quarks

We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to include dynamical fermions. As a primary application, some elements of an HQET computation of the mass of the b-quark beyond the leading order with N_f=2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L ~ 0.5 fm, which will serve to quantitatively determine the heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. As a preparation for the latter, we report on our determination of the renormalization constants and improvement coefficients relating the renormalized current and subtracted bare quark mass in the relevant weak coupling region. The calculation of these coefficients employs a constant physics condition in the Schroedinger functional scheme, where the box size L is fixed by working at a prescribed value of the renormalized coupling.

hep-lat↗

arXiv2007

Heavy-light decay constant at the 1/m order of HQET

Following the strategy developed by the ALPHA collaboration, we present a method to compute non-perturbatively the decay constant of a heavy-light meson in HQET including the 1/m corrections. We start by a matching between HQET and QCD in a small volume to determine the parameters of the effective theory non-perturbatively. Observables in the effective theory are then evolved to larger volumes. In two steps a large enough volume is reached to determine the physical decay constant. Some preliminary results in the quenched approximation are shown.

hep-lat↗

arXiv2007

Non-perturbative renormalization of the static axial current in two-flavour QCD

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at beta=5.3.

hep-lat↗

arXiv2006

Exploring the HMC trajectory-length dependence of autocorrelation times in lattice QCD

We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be kept under control, we find a variation of the integrated autocorrelation times by a factor of about two in the quantities of interest. Trajectories longer than conventionally used are found to be superior both in the Nf=0 and Nf=2 examples considered here. We also provide evidence that they lead to faster thermalization of systems with light quarks.

hep-lat↗

arXiv2005

Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking

We simulate two dimensional QED with two degenerate Wilson fermions and plaquette gauge action. As a consequence of the Mermin-Wagner theorem, in the continuum limit chiral symmetry is realized a la Wigner. This property affects also the size of the cutoff effects. That can be understood in view of the fact that the leading lattice artifacts are described, in the continuum Symanzik effective theory, by chirality breaking terms. In particular, vacuum expectation values of non-chirality-breaking operators are expected to be O(a) improved in the chiral limit. We provide a numerical confirmation of this expectation by performing a scaling test.

hep-lat↗

arXiv2005

A quenched study of m_b in HQET beyond the leading order

A non perturbative method to compute the mass of the b quark including the 1/m term in HQET has been presented in a companion talk. Following this strategy, we find in the MS bar scheme m_b^{stat}(m_b) = 4.350(64) GeV for the leading term, and m_b^{(1)}(m_b) = -0.049(29) GeV for the next to leading order correction. This method involves several steps, including the simulation of the relativistic theory in a small volume, and of the effective theory in a big volume. Here we present some numerical details of our calculations.

hep-lat↗

arXiv2005

Restoring chiral symmetry to O(a^2) for dynamical Wilson fermions

We present results for the non-perturbative determination of the improvement and renormalization factors of the isovector axial current for lattice QCD with two flavors of dynamical Wilson quarks. The improvement and normalization conditions are formulated in terms of matrix elements of the PCAC relation in the Schroedinger functional setup and results are given in the form of interpolating formulae for bare gauge couplings beta=6/g_0^2>5.2.

hep-lat↗

arXiv2005

A strategy for the computation of m_b including 1/m terms

We consider HQET including the first order correction in 1/m. A strategy for the computation of the b-quark mass is discussed. Only two quantities Phi_1/2 have to be considered in order to match QCD and HQET, since the spin-dependent interaction is easily eliminated due to the spin symmetry of the static theory. Quite simple formulae relate the renormalization group invariant b-quark mass (M_b) to the B-meson mass. All entries in these formulae are non-perturbatively defined and can be computed in the continuum limit of the lattice regularized theory. For the numerically most critical part, we illustrate the cancellation of power divergences by a numerical example. Numerical results for the 1/m correction to M_b, are presented in a companion talk.

hep-lat↗