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Stefan Schaefer

Publications and source records attributed to Stefan Schaefer.

At least 37 records · Page 2Linked to original sources
arXiv2017

Domain decomposition and multilevel integration for fermions

The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory. We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator. This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.

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arXiv2017

A local factorization of the fermion determinant in lattice QCD

We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by multiboson fields located on the boundaries of the blocks. The resultant multiboson domain-decomposed hybrid Monte Carlo passes extensive numerical tests carried out by measuring standard gluonic observables. The combination of the determinant factorization and of the one of the propagator, that we put forward recently, paves the way for multilevel Monte Carlo integration in the presence of fermions. We test this possibility by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and we observe a significant increase of the signal-to-noise ratio due to a two-level integration.

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arXiv2016

New extended interpolating operators for hadron correlation functions

New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalisation properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. The operators have been numerically implemented and a comparison to point sources and Jacobi smeared sources has been performed on the new CLS configurations.

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arXiv2016

The determination of $α_s$ by the ALPHA collaboration

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $α> 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $Λ_\overline{MS}^{(3)}=332(14)$~MeV is translated to $α_\overline{MS}(m_Z)=0.1179(10)(2)$ by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.

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arXiv2016

The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory

We present a precise computation of the topological susceptibility $χ_{_\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity $t_0^2χ_{_\mathrm{YM}}$ to the continuum and large $N$ limits with confidence. The accuracy of the final result represents a new quality in the verification of large $N$ scaling.

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arXiv2016

The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory

We compute the topological susceptibility of the SU(N) Yang-Mills theory in the large-N limit with a percent level accuracy. This is achieved by measuring the gradient-flow definition of the susceptibility at three values of the lattice spacing for N=3,4,5,6. Thanks to this coverage of parameter space, we can extrapolate the results to the large-N and continuum limits with confidence. Open boundary conditions are instrumental to make simulations feasible on the finer lattices at the larger N.

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arXiv2016

A multilevel algorithm for flow observables in gauge theories

We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a subset of the lattice. Together with a local action this allows for independent updates and consequently a convergence of the Monte Carlo process faster than the inverse square root of the number of measurements. We demonstrate the feasibility of this idea in the correlation functions of the topological charge and the energy density.

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arXiv2016

Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD

We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level integration scheme. The quark propagator is expanded in series of terms with a well defined hierarchical structure. The higher the order of a term, the (exponentially) smaller its magnitude, the less local is its dependence on the gauge field. Once inserted in a Wick contraction, the gauge-field dependence of the terms in the resulting series can be factorized so that it is suitable for multi-level Monte Carlo integration. We test the strategy in quenched QCD by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and a nucleon two-point function. In either cases we observe a significant exponential increase of the signal-to-noise ratio.

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arXiv2015

Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions

We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N_f=2+1 flavors of non-perturbatively improved Wilson fermions in the sea with the Luescher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t_0.

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arXiv2014

On the extraction of spectral quantities with open boundary conditions

We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by Lüscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.

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arXiv2013

Charm quark mass and D-meson decay constants from two-flavour lattice QCD

We present a computation of the charm quark's mass and the leptonic D-meson decay constants f_D and f_{D_s} in two-flavour lattice QCD with non-perturbatively O(a) improved Wilson quarks. Our analysis is based on the CLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the lattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at L*m_pi > 4, in order to perform controlled continuum and chiral extrapolations with small systematic uncertainties.

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arXiv2013

Improvement of N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action

We determine the parameter c_SW required for O(a)-improvement of the three flavor Wilson fermion action together with the tree-level Symanzik improved gauge action. The standard improvement condition is employed for a range of couplings. Additionally, we perform a check of the volume independence of c_SW and provide a preliminary estimate of the lattice spacing at our largest values of g_0^2.

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arXiv2012

Status and challenges of simulations with dynamical fermions

An overview over the current state of algorithms for dynamical fermion simulations is given. In particular some insight into the functioning of the determinant spitting techniques is discussed. The critical slowing down of the simulations towards the continuum limit and the role of the boundary conditions is also reviewed.

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arXiv2012

The strange quark mass and Lambda parameter of two flavor QCD

We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r_0 in physical units as well as an improved determination of the renormalization constant Z_A.

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arXiv2012

Lattice QCD with open boundary conditions and twisted-mass reweighting

Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into instabilities triggered by accidental near-zero modes of the lattice Dirac operator. As already noted in ref. [1], the first problem is bypassed if open boundary conditions are imposed in the time direction, while the second can potentially be overcome through twisted-mass determinant reweighting [2]. In this paper, we show that twisted-mass reweighting works out as expected in QCD with open boundary conditions and 2+1 flavours of O(a) improved Wilson quarks. Further algorithmic improvements are tested as well and a few physical quantities are computed for illustration.

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arXiv2011

Strange quark mass and Lambda parameter by the ALPHA collaboration

We determine f_K for lattice QCD in the two flavor approximation with non-perturbatively improved Wilson fermions. The result is used to set the scale for dimensionful quantities in CLS/ALPHA simulations. To control its dependence on the light quark mass, two different strategies for the chiral extrapolation are applied. Combining f_K and the bare strange quark mass with non-perturbative renormalization factors and step scaling functions computed in the Schroedinger Functional, we determine the RGI strange quark mass and the Lambda parameter in units of f_K.

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arXiv2011

Lattice QCD without topology barriers

As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.

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