Jochen Heitger

Computation of the strong coupling in QCD with two dynamical flavors

Abstract We present a non-perturbative computation of the running of the coupling α s in QCD with two flavors of dynamical fermions in the Schrodinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Λ-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Λ r 0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm . It translates into Λ MS ¯ ( 2 ) = 245 ( 16 ) ( 16 ) MeV [assuming r 0 = 0.5 fm ]. The last step still has to be improved to reduce the uncertainty.

Precision computation of the strange quark's mass in quenched QCD

We determine the renormalization group invariant quark mass corresponding to the sum of the strange and the average light quark mass in the quenched approximation of QCD, using as essential input the mass of the K-mesons. In the continuum limit we find (Ms+M)/FK=0.874(29), which includes systematic errors. Translating this non-perturbative result into the running quark masses in the MS scheme at μ=2 GeV and using the quark mass ratios from chiral perturbation theory, we obtain ms(2GeV)=97(4)MeV. With the help of recent results by the CP-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced FK by the nucleon mass to set the scale. This is a typical ambiguity in the quenched approximation.

Non-perturbative heavy quark effective theory

We explain how to perform non-perturbative computations in HQET on the lattice. In particular the problem of the subtraction of power-law divergences is solved by a non-perturbative matching of HQET and QCD. As examples, we present a full calculation of the mass of the b-quark in the combined static and quenched approximation and outline an alternative way to obtain the B-meson decay constant at lowest order. Since no excessively large lattices are required, our strategy can also be applied including dynamical fermions.

First results on the running coupling in QCD with two massless flavours

Abstract We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schrodinger functional scheme. The corresponding Λ-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic “experimentally” observable quantity. We find the non-perturbative evolution of the coupling important to eliminate a significant contribution to the total error in the estimated Λ-parameter.

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrodinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrodinger functional technique turns out to be much more efficient than the known alternatives.

Effective chiral Lagrangians and lattice QCD

We propose a general method to obtain accurate estimates for some of the “low-energy constants” in the one-loop effective chiral Lagrangian by means of simulating lattice QCD. In particular, the method is sensitive to those constants whose values are required to test the hypothesis of a massless up-quark. Initial tests performed in the quenched approximation confirm that good statistical precision can be achieved. As a byproduct we obtain an accurate estimate for the ratio of pseudoscalar decay constants, FK/Fπ , in the quenched approximation, which lies 10% below the experimental result. The quantities that serve to extract the low-energy constants also allow a test of the scaling behaviour of different discretizations of QCD and a search for the effects of dynamical quarks.

Non-perturbative renormalization of the static axial current in quenched QCD

We non-perturbatively calculate the scale dependence of the static axial current in the Schrodinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. The bare current in the O(a) improved theory as well as in the original Wilson regularization is thus connected to the renormalization group invariant one. The latter may then be related to the current at the B-scale defined such that its matrix elements differ from the physical (QCD) ones by O(1/M). At present, a (probably small) perturbative uncertainty enters in this step. As an application, we renormalize existing unimproved data on FBbare and extrapolate to the continuum limit. We also study an interesting function h(d/L,u) derived from the Schrodinger functional amplitude describing the propagation of a static quark–antiquark pair.

Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks

Abstract We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on N f = 2 gauge field ensembles, covering three lattice spacings a ≈ ( 0.08 – 0.05 ) fm and pion masses down to 190 MeV , a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read f B = 186 ( 13 ) MeV , f B s = 224 ( 14 ) MeV and f B s / f B = 1.203 ( 65 ) . A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible.

Parameters of heavy quark effective theory from N-f=2 lattice QCD

A bstractWe report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with Nf = 2 flavors of massless dynamical quarks. The effective theory is considered at the 1/mh order, and the heavy mass mh covers a range from slightly above the charm to beyond the beauty region. These HQET parameters are needed to compute, for example, the b-quark mass, the heavy-light spectrum and decay constants in the static approximation and to order 1/mh in HQET. The determination of the parameters is done non-perturbatively. The computation reported in this paper uses the plaquette gauge action and two different static actions for the heavy quark described by HQET. For the light-quark action we choose non-perturbatively O(a)-improved Wilson fermions.

Comparative benchmarks of full QCD algorithms

We report performance benchmarks for several algorithms that we have used to simulate the Schrodinger functional with two flavors of dynamical quarks. They include hybrid and polynomial hybrid Monte Carlo with preconditioning. An appendix describes a method to deal with autocorrelations for nonlinear functions of primary observables as they are met here due to reweighting.