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Rainer Sommer

Publications and source records attributed to Rainer Sommer.

139 records · Page 8Linked to original sources
arXiv1999

String breaking in SU(2) gauge theory with scalar matter fields

We investigate the static potential in the confinement phase of the SU(2) Higgs model on the lattice, where this model is expected to have properties similar to QCD. We observe that Wilson loops are inadequate to determine the potential at large distances, where the formation of two color-neutral mesons is expected. Introducing smeared fields and a suitable matrix correlation function, we are able to overcome this difficulty. We observe string breaking at a distance $r_b \approx 1.8 r_0$, where the length scale $r_0$ has a value $r_0 \approx 0.5 fm$ in QCD. The method presented here may lead the way towards a treatment of string breaking in QCD.

hep-lat↗
arXiv1997

The $Λ$-parameter and $m_s$ of quenched QCD

We explain how scale dependent renormalized quantities can be computed using lattice QCD. Two examples are used: the running coupling and quark masses. A reliable computation of the $Λ$-parameter in the quenched approximation is presented.

hep-ph↗
arXiv1997

Non-perturbative renormalization of QCD

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schrödinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the $Λ$-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement.

hep-ph↗
arXiv1997

O(a) improved lattice QCD

We review the O(a) improvement of lattice QCD with special emphasis on the motivation for performing the improvement programme non-perturbatively and the general concepts of on-shell improvement. The present status of the calculations of various improvement coefficients (perturbative and non-perturbative) is reviewed, as well as the computation of the isospin current normalization constants $Z_A$ and $Z_V$. We comment on recent results for hadronic observables obtained in the improved theory.

hep-lat↗
arXiv1996

Non-perturbative determination of the axial current normalization constant in O(a) improved lattice QCD

A finite-size technique is employed to compute the normalization constant $Z_A$ of the isovector axial current in lattice QCD. The calculation is carried out in the quenched approximation for values of the bare gauge coupling $g_0$ ranging from 0 to 1. In the lattice action and the lattice expression for the axial current we include the counterterms required for O(a) improvement, with non-perturbatively determined coefficients. With little additional work the normalization constant $Z_V$ of the improved isospin current is also obtained.

hep-lat↗
arXiv1996

Non-perturbative O(a) improvement of lattice QCD

The coefficients multiplying the counterterms required for O($a$) improvement of the action and the isovector axial current in lattice QCD are computed non-perturbatively, in the quenched approximation and for bare gauge couplings $g_0$ in the range $0 \leq g_0 \leq 1$. A finite-size method based on the Schrödinger functional is employed, which enables us to perform all calculations at zero or nearly zero quark mass. As a by-product the critical hopping parameter $κ_c$ is obtained at all couplings considered.

hep-lat↗
arXiv1996

Chiral symmetry and O(a) improvement in lattice QCD

The dominant cutoff effects in lattice QCD with Wilson quarks are proportional to the lattice spacing a. In particular, the isovector axial current satisfies the PCAC relation only up to such effects. Following a suggestion of Symanzik, they can be cancelled by adding local O(a) correction terms to the action and the axial current. We here address a number of theoretical issues in connection with the O(a) improvement of lattice QCD and then show that chiral symmetry can be used to fix the coefficients multiplying the correction terms.

hep-lat↗
arXiv1995

Non-perturbative renormalization of lattice QCD at all scales

A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization constant, the running coupling at zero quark masses and the scale evolution of the renormalized axial density. The non-perturbative calculation of O(a) correction terms (as they appear in Symanzik's improvement programme) is another important field of application.

hep-lat↗
arXiv1995

The running coupling from the QCD Schrödinger functional -- a one-loop analysis

Starting from the Schrödinger functional, we give a non-perturbative definition of the running coupling constant in QCD. The spatial boundary conditions for the quark fields are chosen such that the massless Dirac operator in the classical background field has a large smallest eigenvalue. At one-loop order of perturbation theory, we determine the matching coefficient to the $\MSbar$-scheme and discuss the quark mass effects in the $β$-function. To this order, we also compute the Symanzik improvement coefficient necessary to remove the $\Oa$ lattice artefacts originating from the boundaries. For reasonable lattice resolutions and the standard Wilson action, lattice artefacts are found to be only weakly dependent on the lattice spacing $a$, while they vanish quickly with the improved action of Sheikholeslami and Wohlert.

hep-lat↗
arXiv1994

Beauty Physics in Lattice Gauge Theory

We summarize the present status of lattice gauge theory computations of the leptonic decay constants $f_D$ and $f_B$. The various sources of systematic errors are explained in a manner easily understood by the non--expert. The results obtained by the different groups are then systematically compared. As a result, we derive estimates for $f_D$ and $f_B$ in the quenched approximation through an appropriate combination of the data available from the different groups. Since we account for a possible lattice spacing dependence, the final errors are quite large. However, it is now well known how these uncertainties can be reduced. For the decay constant of heavy--light pseudoscalar mesons with masses of 1-2~GeV, an interesting comparison of a full QCD result with the corresponding simulation in the quenched approximation can be done. Effects of sea quarks of mass $m_s$ are below the statistical accuracy of these simulations. Related quantities, like $B$--parameters, the spectrum of beauty--hadrons and the breaking of the QCD string are discussed briefly.

hep-lat↗
arXiv1993

A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory

A non-perturbative finite-size scaling technique is used to study the evolution of the running coupling (in a certain adapted scheme) in the SU(3) Yang-Mills theory. At low energies contact is made with the fundamental dynamical scales, such as the string tension K, while at larger energies the coupling is shown to evolve according to perturbation theory. In that regime the coupling in the MS-bar scheme of dimensional regularization is obtained with an estimated total error of a few percent.

hep-lat↗
arXiv1992

Computation of the Running Coupling in the SU(2) Yang-Mills Theory

A finite-size scaling technique is applied to the SU(2) gauge theory (without matter fields) to compute a non-perturbatively defined running coupling alpha(q) for a range of momenta q given in units of the string tension K. We find that already at rather low q, the evolution of alpha(q) is well described by the 2-loop approximation to the Callan-Symanzik beta-function. At the highest momentum reached, q=20 sqrt(K), we obtain alpha_MSbar(q)=0.187 +/- 0.005 +/- 0.009 for the running coupling in the MSbar scheme of dimensional regularization.

hep-lat↗