CLS 2+1 flavor simulations at physical light- and strange-quark masses

We report recent efforts by CLS to generate an ensemble with physical light- and strange-quark masses in a lattice volume of 192x96^3 at $\beta=3.55$ corresponding to a lattice spacing of 0.064 fm. This ensemble is being generated as part of the CLS 2+1 flavor effort with improved Wilson fermions. Our simulations currently cover 5 lattice spacings ranging from 0.039 fm to 0.086 fm at various pion masses along chiral trajectories with either the sum of the quark masses kept fixed, or with the strange-quark mass at the physical value. The current status of simulations is briefly reviewed, including a short discussion of measured autocorrelation times and of the main features of the simulations. We then proceed to discuss the thermalization strategy employed for the generation of the physical quark-mass ensemble and present first results for some simple observables. Challenges encountered in the simulation are highlighted.Comment: 7 pages, 8 figures; Proceedings, 35th International Symposium on Lattice Field Theory (Lattice2017): Granada, Spai

η\eta and η′\eta^\prime masses and decay constants

We present preliminary results for the masses and decay constants of the $\eta$ and $\eta^\prime$ mesons using CLS $N_f = 2+1$ ensembles. One of the major challenges in these calculations are the large statistical fluctuations due to disconnected quark loops. We tackle these by employing a combination of noise reduction techniques which are tuned to minimize the statistical error at a fixed cost. On the analysis side we carefully assess excited states contributions by using a direct fit approach.Comment: 8 pages, 7 figures, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain. v2: corrected axis labe

Using NSPT for the Removal of Hypercubic Lattice Artifacts

The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI'-MOM scheme a large part of these artifacts can be calculated and subtracted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.Comment: 7 pages, 6 figures, talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, USA; PoS(LATTICE2014)29

Discretization Errors for the Gluon and Ghost Propagators in Landau Gauge using NSPT

The subtraction of hypercubic lattice corrections, calculated at 1-loop order in lattice perturbation theory (LPT), is common practice, e.g., for determinations of renormalization constants in lattice hadron physics. Providing such corrections beyond 1-loop order is however very demanding in LPT, and numerical stochastic perturbation theory (NSPT) might be the better candidate for this. Here we report on a first feasibility check of this method and provide (in a parametrization valid for arbitrary lattice couplings) the lattice corrections up to 3-loop order for the SU(3) gluon and ghost propagators in Landau gauge. These propagators are ideal candidates for such a check, as they are available from lattice simulations to high precision and can be combined to a renormalization group invariant product (Minimal MOM coupling) for which a 1-loop LPT correction was found to be insufficient to remove the bulk of the hypercubic lattice artifacts from the data. As a bonus, we also compare our results with the ever popular H(4) method.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Properties of the η and η' mesons from lattice QCD

In this thesis we compute masses, decay constants and gluonic matrix elements of the flavour-diagonal pseudoscalar mesons η and η' from lattice QCD. To control all relevant systematic errors we employ Nf = 2 + 1 flavour simulations along two distinct quark mass trajectories leading to and including the physical point. The continuum extrapolation is guided by four lattice spacings. The ensembles were generated within the coordinated lattice simulations initiative, and we set their relative scales in this work. We discuss noise reduction techniques for the efficient calculation of the disconnected contributions that are important building blocks of the relevant correlation functions of the η and η' system. The physical states are no flavour eigenstates, and hence sophisticated analysis methods are required to extract them from the data. We develop a matrix generalization of the effective mass method which we employ in conjunction with additional techniques to determine masses and matrix elements. The physical point extrapolation employs next-to-leading order large-Nc chiral perturbation theory, and we determine all relevant low energy constants. For the first time also their renormalization scale dependence is taken into account, and this provides an important check of the range of validity of this effective field theory with implications on many existing phenomenological analyses. Our physical point results for the masses are in agreement with experimental values and read Mη = 554.7(9.2) MeV and Mη' = 930(21) MeV. The determination of the four η and η' decay constants is the first from first principles and we obtain F8 = 115.0(2.8) MeV and θ8 = −25.8(2.3)◦ in the octet channel and F0 = 100.1(3.0) MeV and θ0 = −8.1(1.8)◦ for the singlet in the MS scheme at 2 GeV. These results are in excellent agreement with phenomenological determinations and at a similar level of precision. Finally, we connect these axialvector decay constants with pseudoscalar and gluonic matrix elements to test the axial Ward identities, and predict the anomalous matrix elements to be aη = = 0.0170(10) GeV^3 and aη' = = 0.0381(84) GeV^3 at the physical point and µ = 2 GeV

Lattice simulations with Nf=2+1N_f=2+1 improved Wilson fermions at a fixed strange quark mass

The explicit breaking of chiral symmetry of the Wilson fermion action results in additive quark mass renormalization. Moreover, flavour singlet and non-singlet scalar currents acquire different renormalization constants with respect to continuum regularization schemes. This complicates keeping the renormalized strange quark mass fixed when varying the light quark mass in simulations with $N_f=2+1$ sea quark flavours. Here we present and validate our strategy within the CLS (Coordinated Lattice Simulations) effort to achieve this in simulations with non-perturbatively order-$a$ improved Wilson fermions. We also determine various combinations of renormalization constants and improvement coefficients.Comment: 18 pages, 11 Figures, V2: References added/updated, all fits rerun with improved statistics for ensemble N204, also using the final values for the improvement coefficients A and b_P-b_A (very minor impact), The figures have been replotted accordingly. (The differences with respect to V1 are invisible to the human eye). Minor change

Light-cone distribution amplitudes of the baryon octet

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using $N_f=2+1$ flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.Comment: Update to the version published in JHE

Scale setting and the light baryon spectrum in Nf=2+1N_f=2+1 QCD with Wilson fermions

We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing $N_f=2+1$ flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from $a\approx 0.10\,$fm down to below $0.04\,$fm. The light pion mass varies from $M_{\pi}\approx 429\,$MeV down to $127\,$MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than $2.3\,$fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales $\sqrt{t_{0,{\rm ph}}}=0.1449^{(7)}_{(9)}\,$fm and $t_0^*\approx t_{0,{\rm ph}}$ from the octet cascade ($\Xi$ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass $m_N=941.7^{(6.5)}_{(7.6)}\,$MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the $\Omega$ baryon sigma~terms $\sigma_{\pi N}=43.9(4.7)\,$MeV, $\sigma_{\pi\Lambda}=28.2^{(4.3)}_{(5.4)}\,$MeV, $\sigma_{\pi\Sigma}=25.9^{(3.8)}_{(6.1)}\,$MeV, $\sigma_{\pi\Xi}=11.2^{(4.5)}_{(6.4)}\,$MeV and $\sigma_{\pi\Omega}=6.9^{(5.3)}_{(4.3)}\,$MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.Comment: 128 pages, many figure