Fermions as Global Correction: the QCD Case

It is widely believed that the fermion determinant cannot be treated in global acceptance-rejection steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorizations of the determinant that separate the ultraviolet from the infrared modes of the Dirac operator it is known that the latter show less variation under changes of the gauge field compared to the former. Using a factorization based on recursive domain decomposition allows for a hierarchical algorithm that starts with pure gauge updates of the links within the domains and ends after a number of filters with a global acceptance-rejection step. Ratios of determinants have to be treated stochastically and we construct techniques to reduce the noise. We find that the global acceptance rate is high on moderate lattice sizes and demonstrate the effectiveness of the hierarchical filter.Comment: 36 pages, 9 figures; improved version to be published in Comput.Phys.Commun., new results for the topological charge presented in Figure

Isospin Effects by Mass Reweighting

Most of today's lattice simulations are performed in the isospin symmetric limit of the light quark sector. Mass reweighting is a technique to include effects of isospin breaking in the sea quarks at moderate numerical cost. We will give a summary of our recent results on fine lattices with light quark masses and will show how light quark masses can be extracted by introducing suitable tuning conditions for the bare mass parameters. In general the reweighting factor introduces additional fluctuations and thus increases the statistical uncertainties. In the case of isospin reweighting this factor is a ratio of fermion determinants. The stochastic evaluation of the determinants potentially leads to stochastic noise in observables. We show the quark mass and the volume dependence of these fluctuations.Comment: 7 pages, 4 figures, 32st International Symposium on Lattice Field Theory - LATTICE 2014, Corrected (rescaled) x-axis of figures (1) and (2

Tuning of the strange quark mass with optimal reweighting

Quark mass reweighting can be used to tune the mass of dynamical quarks. The basic idea is to use gauge field ensembles generated at some bare mass parameters to evaluate observables at different bare sea quark masses. This involves the computation of so called reweighing factors which are given as ratios of fermion determinants. In the case of simulations including the strange quark, reweighting can be used to improve the approach towards physical quark masses. Optimal reweighting strategies combine a change of the strange quark mass with a change of the light quark masses in order to minimize the fluctuations of the reweighting factor. We present numerical test of such strategies for recent CLS2 simulations and a software package for mass reweighting based on openQCD.Comment: Lattice 2014, the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, N

One flavor mass reweighting in lattice QCD

One flavor mass reweighting can be used in lattice QCD computations to fine tune the quark masses to their physical values. We present a new method that utilizes an unbiased stochastic estimation of the one flavor determinant. The stochastic estimation is based on the integral representation of the determinant of a complex matrix, which we prove. In contrast to other methods it can also be applied in situations where the determinant has a complex phase. The stochastic error is controlled by determinant factorizations based on mass interpolation and Schur decomposition. As an example of an application we demonstrate how the method can be used to tune the up-down quark mass difference.Comment: 20 pages, 4 figures; condition in Eq. (7) corrected, numerical results unaffecte

Perturbative versus non-perturbative decoupling of heavy quarks

We simulate a theory with $N_f=2$ heavy quarks of mass $M$. At energies much smaller than $M$ the heavy quarks decouple and the theory can be described by an effective theory which is a pure gauge theory to leading order in $1/M$. We present results for the mass dependence of ratios such as $t_0(M)/t_0(0)$. We compute these ratios from simulations and compare them to the perturbative prediction. The latter relies on a factorisation formula for the ratios which is valid to leading order in $1/M$.Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japa

Lattice QCD investigation of the structure of the a0(980)a_0(980) meson

We investigate the quark content of the scalar meson $a_0(980)$ using lattice QCD. To this end we consider correlation functions of six different two- and four-quark interpolating fields. We evaluate all diagrams, including diagrams, where quarks propagate within a timeslice, e.g. with closed quark loops. We demonstrate that diagrams containing such closed quark loops have a drastic effect on the final results and, thus, may not be neglected. Our analysis shows that in addition to the expected spectrum of two-meson scattering states there is an additional energy level around the two-particle thresholds of $K + \bar{K}$ and $\eta + \pi$. This additional state, which is a candidate for the $a_0(980)$ meson, couples to a quark-antiquark as well as to a diquark-antidiquark interpolating field, indicating that it is a superposition of an ordinary $\bar{q} q$ and a tetraquark structure. The analysis is performed using AMIAS, a novel statistical method based on the sampling of all possible spectral decompositions of the considered correlation functions, as well as solving standard generalized eigenvalue problems.Comment: 11 pages, 10 figure

Bandgap and effective mass of epitaxial cadmium oxide

The bandgap and band-edge effective mass of single crystal cadmium oxide, epitaxially grown by metal-organic vapor-phase epitaxy, are determined from infrared reflectivity, ultraviolet/visible absorption, and Hall effect measurements. Analysis and simulation of the optical data, including effects of band nonparabolicity, Moss-Burstein band filling and bandgap renormalization, reveal room temperature bandgap and band-edge effective mass values of 2.16±0.02 eV and 0.21±0.01m0 respectively

Isospin-0 ππ\pi\pi s-wave scattering length from twisted mass lattice QCD

We present results for the isospin-0 $\pi\pi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical value (250$\sim$MeV), at 240$\sim$MeV (320$\sim$MeV) and at 330$\sim$MeV (400$\sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $\pi\pi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_\pi a^\mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.Comment: 21 pages, 5 figures, 6 table

Disconnected diagrams with twisted-mass fermions

The latest results from the Twisted-Mass collaboration on disconnected diagrams at the physical value of the pion mass are presented. In particular, we focus on the sigma terms, the axial charges and the momentum fraction, all of them for the nucleon. A detailed error analysis for each observable follows, showing the strengths and weaknesses of the one-end trick. Alternatives are discussed.Comment: Proceedings of the 34th annual International Symposium on Lattice Field Theory. 7 pages, 6 figure