arXiv subjects
Publications and source records attributed to Rainer Sommer.
We have calculated the step scaling function and the running coupling of QCD in the Schroedinger functional scheme with four flavors of O(a) improved Wilson quarks. Comparisons of our non-perturbative results with 2-loop and 3-loop perturbation theory as well as with non-perturbative data for only two flavors are made.
We have determined the non-perturbative O(a)-improvement coefficient c_sw for four flavors of Wilson quarks with the plaquette gauge action in a range of beta >= 5. The data are fitted with several Pade approximation formulae to get an impression of the stability. A small extrapolation below beta=5 seems acceptable.
We carry out a thorough analysis with the GEVP method to obtain ground-state and first-excited-state masses and decay constants of bottom-strange (pseudo-scalar and vector) mesons. This computation is done for quenched, nonperturbatively renormalized HQET, including order $1/m_b$ terms. The continuum limit is obtained using three lattice spacings and two static actions.
Simulations of QCD are known to suffer from serious critical slowing down towards the continuum limit. This is particularly prominent in the topological charge. We investigate the severeness of the problem in the range of lattice spacings used in contemporary simulations and propose a method to give more reliable error estimates.
In this talk I want to convey an idea about the perspectives for precise lattice QCD computations. Some emphasis is put on the field of flavour physics, where lattice QCD seems to be needed the most in the quantitative interpretation of present and future experiments (in particular this is the reason for section 4.3). I do not want to discuss the latest numbers but will focus on the principle, the challenges and the perspectives. I mainly address those in the audience who know little about the field and therefore take a bit of a bird's-eye view of the field. So I do not hesitate to also list trivial facts (e.g. section 4.2) and my personal opinion on what is relevant for the future.
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.
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.
We present a preliminary analysis of the charm quark mass and the mass and decay constant $f_{D_s}$ of the $D_s$ meson obtained from dynamical simulations of $N_f = 2$ Wilson QCD on the large and fine lattices simulated by the CLS effort.
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.
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.
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).
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.
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.
We demonstrate how HQET and the Step Scaling Method for B-physics, pioneered by the Tor Vergata group, can be combined to reach a further improved precision. The observables considered are the mass of the b-quark and the B_s-meson decay constant. The demonstration is carried out in quenched lattice QCD. We start from a small volume, where one can use a standard O(a)-improved relativistic action for the b-quark, and compute two step scaling functions which relate the observables to the large volume ones. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m_b. The physical point m_b is then reached by an interpolation of the continuum results in 1/m. The essential, expected and verified, feature is that the step scaling fuctions have a weak mass-dependence resulting in an easy interpolation to the physical point. With r_0=0.5fm and the experimental B_s and K masses as input, we find F_Bs=191(6)MeV and the renormalization group invariant mass M_b=6.88(10)GeV, translating into m_b(m_b)=4.42(6)GeV in the MSbar scheme. This approach seems very promising for full QCD.
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.
We carry out the non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B mesons. We obtain its two-loop anomalous dimension in a Schr"odinger functional scheme by successive one-loop conversions to the lattice MS scheme and the MS-bar scheme. We then compute the scale evolution of the operator non-perturbatively in the N_f=0 theory between $μ\approx 0.3$ GeV and $μ\approx 100$ GeV, where contact is made with perturbation theory. The overall renormalization factor that converts the bare lattice operator to its renormalization group invariant form is given for the Wilson gauge action and two standard discretizations of the heavy-quark action. As an application, we find that this factor brings the previous quenched predictions of the B* - B mass splitting closer to the experimental value than found with a perturbative renormalization. The same renormalization factor is applicable to the spin-dependent potentials of Eichten and Feinberg.
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice.
We compute the mass of the b-quark and the B_s meson decay constant in quenched lattice QCD using a combination of HQET and the standard relativistic QCD Lagrangian. We start from a small volume, where one can directly deal with the b-quark, and compute the evolution to a big volume, where the finite size effects are negligible through step scaling functions which give the change of the observables when L is changed to 2L. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m_b. The point m_b is then reached by an interpolation of the continuum results. With r_0=0.5 fm and the experimental B_s and K masses we find f_Bs=191(6) MeV and the renormalization group invariant mass M_b=6.89(11) GeV, translating into m_b(m_b)=4.42(7) GeV in the MS-bar scheme.