arXiv subjects

Ulli Wolff

Publications and source records attributed to Ulli Wolff.

At least 55 records · Page 3Linked to original sources

arXiv2005

Towards a non-perturbative computation of the RGI strange quark mass with two dynamical flavors

The non-perturbative running of the quark mass in the Schroedinger functional scheme is computed over a large energy range (covering scales differing by two orders of magnitude). This allows to relate lattice estimates of the running quark mass to the renormalization group invariant mass. The result is used in a preliminary computation of the strange quark mass in the theory with two flavors of non-perturbatively improved Wilson quarks. A more detailed discussion of the calculation can be found in [1].

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arXiv2005

Cutoff effects in the O(N) sigma model at large N

The computation of the step scaling function for the finite size mass-gap in the O(N) sigma model at large N is reviewed. Practically exact nonperturbative results become available for both finite and vanishing lattice spacing. We use them as a testbed to investigate standard procedures of continuum extrapolation in lattice field theory.

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arXiv2005

Non-perturbative quark mass renormalization in two-flavor QCD

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O(a) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schroedinger Functional scheme. Using existing data for the scale r_0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.

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arXiv2005

Cutoff Effects in O(N) Nonlinear Sigma Models

In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of the finite volume massgap at N=3,4,8 and a large N-study of the leading as well as next-to-leading terms in 1/N. The latter exact results are demonstrated to follow Symanzik's form of the asymptotic cutoff dependence. At the same time, when fuzzed with artificial statistical errors and then fitted like the Monte Carlo results, a picture similar to N=3 emerges. We hence cannot conclude a truly anomalous cutoff dependence but only relatively large cutoff effects, where the logarithmic component is important. Their size shrinks at larger N, but the structure remains similar. The large N results are particularly interesting as we here have exact nonperturbative control over an asymptotically free model both in the continuum limit and on the lattice.

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arXiv2005

Non-perturbative renormalization of the axial current with dynamical Wilson fermions

We present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor Z_A. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schroedinger functional setup we calculate Z_A(g_0^2) as well as the vector current normalization factor Z_V(g_0^2) for beta = 6/g_0^2 >= 5.2.

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arXiv2004

Computation of the strong coupling in QCD with two dynamical flavours

We present a non-perturbative computation of the running of the coupling alpha_s in QCD with two flavours of dynamical fermions in the Schroedinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Lambda-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Lambda*r_0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm. It translates into Lambda_{MSbar}^{(2)}=245(16)(16) MeV [assuming r_0=0.5 fm]. The last step still has to be improved to reduce the uncertainty.

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arXiv2004

Impact of large cutoff-effects on algorithms for improved Wilson fermions

As a feasibility study for a scaling test we investigate the behavior of algorithms for dynamical fermions in the N_f=2 Schroedinger functional at an intermediate volume of 1 fm^4. Simulations were performed using HMC with two pseudo-fermions and PHMC at lattice spacings of approximately 0.1 and 0.07 fm. We show that some algorithmic problems are due to large cutoff-effects in the spectrum of the improved Wilson-Dirac operator and disappear at the smaller lattice spacing. The problems discussed here are not expected to be specific to the Schroedinger functional.

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arXiv2003

Numerical confirmation of analytic predictions for the finite volume mass gap of the XY-model

Recent exact predictions for the massive scaling limit of the two dimensional XY-model are based on the equivalence with the sine-Gordon theory and include detailed results on the finite size behavior. The so-called step-scaling function of the mass gap is simulated with very high precision and found consistent with analytic results in the continuum limit. To come to this conclusion, an also predicted form of a logarithmic decay of lattice artifacts was essential to use for the extrapolation.

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arXiv2003

Dynamical fermions by global acceptance steps

A study of principle is conducted on the inclusion of the fermionic determinant as a Metropolis acceptance correction. It is carried out in the 2-D Schwinger model to prepare later applications to the Schr"odinger functional. A mixed stochastic/determistic acceptance step is found that allows to include some problematic modes in a way to avoid the collapse of the acceptance rate due to fluctuations.

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arXiv2003

Dynamical fermions as a global correction

In the simplified setting of the Schwinger model we present a systematic study on the simulation of dynamical fermions by global accept/reject steps that take into account the fermion determinant. A family of exact algorithms is developed, which combine stochastic estimates of the determinant ratio with the exploitation of some exact extremal eigenvalues of the generalized problem defined by the `old' and the `new' Dirac operator. In this way an acceptable acceptance rate is achieved with large proposed steps and over a wide range of couplings and masses.

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arXiv2001

Schrödinger functional at N_f=-2

We study the Schrödinger functional coupling for lattice Yang-Mills theory coupled to an improved bosonic spinor field, which corresponds to QCD with minus two light flavors. This theory serves as a less costly testcase than QCD for the scaling of the coupling.

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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.

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arXiv2001

Nonstandard Cutoff Effects in the Nonlinear Sigma Model

High precision measurements of the renormalized zero-momentum 4-point coupling g_R and of the Luscher-Weisz-Wolff running coupling gbar(L) = L*m(L) performed with two different lattice actions in the non-perturbative region confirm the earlier observations, that the cutoff effects look linear, in contrast to perturbative considerations. The use of different actions allows one to make a more reliable estimate on the continuum limit. The measurements were done for infinite volume correlation length up to 350.

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arXiv2001

Schr"odinger functional at negative flavour number

The scaling of the Schr"odinger functional coupling is studied numerically and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved bosonic spinor field. This corresponds to QCD with minus two light flavours and is used as a numerically less costly test case for real QCD. A suitable algorithm is developed, and the influence of the matter fields on the continuum limit and the lattice artefacts are studied in detail.

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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.

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arXiv2001

Two Loop Computation of the Schroedinger Functional in Lattice QCD

We compute the Schroedinger functional (SF) for the case of lattice QCD with Wilson fermions (with and without SW improvement) at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size techniques with negligible systematic errors. In addition our results enable the implementation of two-loop O(a) improvement in SF-simulations.

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arXiv2001

Helicity modulus as renormalized coupling in the O(3) sigma-model

For the family of O(n) invariant nonlinear sigma-models we consider boundary conditions that are periodic up to an O(n) rotation. The helicity modulus is related to the change in free energy under variations of the corresponding angle. It defines a nonperturbative finite volume running coupling similar to the Schr"odinger functional for QCD. For the two-dimensional O(3)-model we investigate this quantity by analytical and numerical techniques. We establish its universal continuum relation to the finite volume massgap coupling at all scales and coupling strengths.

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arXiv2000

Comparative Benchmarks of full QCD Algorithms

We report performance benchmarks for several algorithms that we have used to simulate the Schr"odinger 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.

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