arXiv subjects

Rainer Sommer

Publications and source records attributed to Rainer Sommer.

At least 127 records · Page 7Linked to original sources

arXiv2002

Non-perturbative determination of Z_A^{stat} in quenched QCD

We non-perturbatively calculate the renormalization factor of the static axial vector current in O(a) improved quenched lattice QCD. Its scale dependence is mapped out in the Schroedinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. We also obtain Z_A^{stat} for Wilson fermions in order to renormalize existing unimproved data on F_B^{bare} non-perturbatively.

hep-lat↗

arXiv2002

O(a) improvement of lattice QCD with two flavors of Wilson quarks

We consider O(a) improvement for two flavor lattice QCD. The improvement term in the action is computed non-perturbatively for a large range of the bare coupling. The position of the critical line and higher order lattice artifacts remaining after improvement are estimated. We also discuss the behavior of the HMC algorithm in our simulations.

hep-lat↗

arXiv2002

Fundamental parameters of QCD

The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant alpha_s and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of alpha_s and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required.

physics.comp-ph↗

arXiv2001

The Schroedinger functional coupling in quenched QCD at low energies

Existing non-perturbative computations of the running coupling of quenched QCD in the Schroedinger functional scheme are extended to scales mu lying much deeper in the low-energy regime. We are able to reach 1/mu ~ 0.9 fm, where a significant deviation from its perturbative evolution is observed.

hep-lat↗

arXiv2001

Heavy Quark Effective Theory at one-loop order: An explicit example

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic character of the 1/m-expansion. In general, deviations from the m-to-infinity limit turn out to be small and are well described by the first non-trivial terms when m is a factor 2-3 above the external scale. We also investigate the mass dependence of discretization errors, and find that the behaviour of the correlation functions at finite lattice spacing differs significantly from that in the continuum limit when the quark mass is large.

hep-lat↗

arXiv2001

An explicit example of HQET at one-loop order of perturbation theory

As an explicit example of HQET, we construct correlation functions containing a heavy-light axial current, both in the static approximation and in full QCD. This enables us to investigate the size of finite mass effects. As we use the lattice regularisation, we can also check the mass dependence of discretisation errors.

hep-lat↗

arXiv2001

A strategy to compute the b-quark mass with non-perturbative accuracy

We describe a strategy for a non-perturbative computation of the b-quark mass to leading order in 1/m in the Heavy Quark Effective Theory (HQET). The approach avoids the perturbative subtraction of power law divergencies, and the continuum limit may be taken. First numerical results in the quenched approximation demonstrate the potential of the method with a preliminary result m_b(4GeV)=4.56(2)(7) GeV. In principle, the idea may also be applied to the matching of composite operators or the computation of 1/m corrections in HQET.

hep-lat↗

arXiv2001

Testing perturbation theory on the nf=0 static quark potential

The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling $α_{qq}(μ=1/r)=(C_f)^{-1} r^2 F(r)$. Since the Lambda-parameter of the $\nf=0$ theory is known from previous work, the perturbative prediction contains no free parameter. It is confronted with recent non-perturbative results. For $α< 0.3$ where the truncation error of the perturbative expression is naively estimated to be moderate, it is really quite accurate and large ``non-perturbative terms'' are excluded.

hep-ph↗

arXiv2001

The Nf=0 heavy quark potential from short to intermediate distances

We study the potential of a static quark anti-quark pair in the range 0.05fm \leq r \leq 0.8fm, employing a sequence of lattices up to 64^4. Lattice artifacts in potential and force are investigated theoretically as well as numerically and continuum quantities are obtained by extrapolation of the results at finite lattice spacing. Consistency of the numerical results with the form of scaling violations predicted by an analysis `a la Symanzik is found. The scale r_0/a is determined for the Wilson action up to beta=6.92.

hep-lat↗

arXiv2001

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

We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-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 indispensable to avoid untolerable errors in the estimated Lambda-parameter.

hep-lat↗

arXiv2000

Renormalization and O(a)-improvement of the static-light axial current

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schrödinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC- simulations. We evaluate its lattice spacing effects in perturbation theory.

hep-lat↗

arXiv2000

Non-perturbative results for the coefficients b_m and b_a-b_p in O(a) improved lattice QCD

We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.

hep-lat↗

arXiv2000

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, F_K/F_pi, 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.

hep-lat↗

arXiv2000

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the Lambda-parameter of the theory is obtained with a total error of 8%.

hep-lat↗

arXiv1999

Low energy physics from the QCD Schrödinger functional

We review recent work by the ALPHA and UKQCD Collaborations where masses and matrix elements were computed in lattice QCD using Schrödinger functional boundary conditions and where the strange quark mass was determined in the quenched approximation. We emphasize the general concepts and our strategy for the computation of quark masses.

hep-lat↗

arXiv1999

Renormalization of the static-light axial current

We discuss the determination of the heavy-light axial current renormalization in the static approximation, using a new method based on the Schrödinger Functional (SF). Previous perturbative results for the renormalization constant are confirmed.

hep-lat↗

arXiv1999

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 $(M_s + M_{light})/F_K=0.874(29)$, which includes systematic errors. Translating this non-perturbative result into the running quark masses in the $\msbar$-scheme at $μ=2 GeV$ and using the quark mass ratios from chiral perturbation theory, we obtain $\mbar_s(2 GeV)=97(4) MeV$. With the help of recent results by the CP-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced $F_K$ by the nucleon mass to set the scale. This is a typical ambiguity in the quenched approximation.

hep-lat↗

arXiv1999

Hadron masses and matrix elements from the QCD Schr"odinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schr"odinger 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 Schr"odinger functional technique turns out to be much more efficient than the known alternatives.

hep-lat↗