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We present the scale setting for a new set of gauge configurations generated with $$N_\mathrm{f}=3+1$$ Nf=3+1 Wilson quarks with a non-perturbatively determined clover coefficient in a massive O(a) improvement scheme. The three light quarks are degenerate, with the sum of their masses being equal to its value in nature and the charm quark has its physical mass. We use open boundary conditions in time direction to avoid the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. The decoupling of charm at low energy allows us to set the scale by measuring the value of the low-energy quantity $$t_0^\star /a^2$$ t0⋆/a2 , which is the flow scale $$t_0$$ t0 at our mass point, and comparing it to an $$N_\mathrm{f}=2+1$$ Nf=2+1 result in physical units. We present the details of the algorithmic setup and tuning procedure and give the bare parameters of ensembles with two lattice spacings $$a=0.054$$ a=0.054 fm and $$a=0.043$$ a=0.043 fm. We discuss finite volume effects and lattice artifacts and present physical results for the charmonium spectrum. In particular the hyperfine splitting between the $$\eta _c$$ ηc and $$J/\psi $$ J/ψ mesons agrees very well with its physical value.

The properties of charmonium states are or will be intensively studied by the B-factories Belle II and BESIII, the LHCb and PANDA experiments and at a future Super-c-tau Factory. Precise lattice calculations provide valuable input and several results have been obtained by simulating up, down and strange quarks in the sea. We investigate the impact of a charm quark in the sea on the charmonium spectrum, the renormalization group invariant charm-quark mass and the scalar charm-quark content of charmonium. The latter is obtained by the direct computation of the mass-derivatives of the charmonium masses. We do this investigation in a model, QCD with two degenerate charm quarks. The absence of light quarks allows us to reach very small lattice spacings down to 0.023 fm. By comparing to pure gauge theory we find that charm quarks in the sea affect the hyperfine splitting at a level below 2%. The most significant effects are 5% in the quark mass and 3% in the value of the charm quark content of the eta_c meson. Given that we simulate two charm quarks these estimates are upper bounds for the contribution of a single charm quark. We show that lattice spacings, 25 pages, 8 figures

We estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities $N_f=2+1$ lattice QCD simulations provide results that can be compared with experiments or whether $N_f=2+1+1$ QCD including the charm quark in the sea needs to be simulated. We consider two theories, $N_f=0$ QCD and QCD with $N_f=2$ charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum limit. The absence of light quarks allows us to simulate the $N_f=2$ theory at lattice spacings down to $0.023$ fm that are crucial for reliable continuum extrapolations. We find that sea charm quark effects are below $1\%$ for the decay constants of charmonium. Our results show that decoupling of charm works well up to energies of about $500$ MeV. We also compute the derivatives of the decay constants and meson masses with respect to the charm mass. For these quantities we again do not see a significant dynamical charm quark effect, albeit with a lower precision. For mesons made of a charm quark and a heavy antiquark, whose mass is twice that of the charm quark, sea effects are only about $0.1\%$ in the ratio of vector to pseudoscalar masses., Comment: Matches version accepted for publication in Eur.Phys.J.C. 30 pages, 7 figures

We present the scale setting for a new set of gauge configurations generated with $N_f=3+1$ Wilson quarks with a non-perturbatively determined clover coefficient in a massive O($a$) improvement scheme. The three light quarks are degenerate, with the sum of their masses being equal to its value in nature and the charm quark has its physical mass. We use open boundary conditions in time direction to avoid the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. The decoupling of charm at low energy allows us to set the scale by measuring the value of the low-energy quantity $t_0^\star/a^2$, which is the flow scale $t_0$ at our mass point, and comparing it to an $N_f=2+1$ result in physical units. We present the details of the algorithmic setup and tuning procedure and give the bare parameters of ensembles with two lattice spacings a=0.054 fm and a=0.043 fm. We discuss finite volume effects and lattice artifacts and present physical results for the charmonium spectrum. In particular the hyperfine splitting between the $\eta_c$ and $J/\psi$ mesons agrees very well with its physical value., Comment: 25 pages, 9 figures. Version accepted for publication in the European Physical Journal C

Monte-Carlo Simulations of QCD with dynamical up, down, strange and charm quarks are carried out on lattices with large volumes and fine lattice spacings using a new massive renormalisation and improvement scheme that is tailored towards situations with a dynamical charm quark. The lattice spacings of the generated ensembles are determined and first physical results, concerning the mass spectrum of mesons built from a charm and anti-charm quark, are presented.

Nuclear physics / B 943, 114612 (2019). doi:10.1016/j.nuclphysb.2019.114612, Effects of heavy sea quarks on the low energy physics are described by an effective theory where the expansion parameter is the inverse quark mass, 1/$M$. At leading order in 1/$M$ the dependence of any low energy quantity on $M$ is given in terms of the ratio of $\Lambda$ parameters of the effective and the fundamental theory. We define a function describing the scaling with the mass $M$. We find that its perturbative expansion is very reliable for the bottom quark and also seems to work very well at the charm quark mass. The same is then true for the ratios of $\Lambda^{(4)}/\Lambda^{(5)}$ and $\Lambda^{(3)}/\Lambda^{(4)}$, which play a major rôle in connecting lattice determinations of $\alpha^{(3)}_{MSbar}$ from the three-flavor theory with $\alpha^{(5)}_{MSbar}(M_Z)$. Also the charm quark content of the nucleon, relevant for dark matter searches, can be computed accurately from perturbation theory. We investigate a very closely related model, namely QCD with $N_f=2$ heavy quarks. Our non-perturbative information is derived from simulations on the lattice, with masses up to the charm quark mass and lattice spacings down to about 0.023 fm followed by a continuum extrapolation. The non-perturbative mass dependence agrees within rather small errors with the perturbative prediction at masses around the charm quark mass. Surprisingly, from studying solely the massive theory we can make a prediction for the ratio $Q^{\sqrt{t_0}}_{0,2}=[\Lambda \sqrt{t_0(0)}]_{N_f=2}/[\Lambda \sqrt{t_0}]_{N_f=0}$, which refers to the chiral limit in $N_f=2$. Here $t_0$ is the Gradient Flow scale of [1]. The uncertainty for $Q$ is estimated to be dominated by the statistical errors of below 2%. For the phenomenologically interesting $\Lambda^{(3)}/\Lambda^{(4)}$, we conclude that perturbation theory introduces errors which are at most at the 0.5% level, far smaller than other current uncertainties., Published by North-Holland Publ. Co., Amsterdam

We present first results of the scale setting for QCD with Nf=3+1 dynamical quarks on the lattice. We use a recently proposed massive renormalization scheme with a non-perturbatively determined clover coefficient. To relate the bare coupling of the simulations to a lattice spacing in fm, we measure the flow scale t0 in lattice units at a mass point with degenerate light quark masses and a physical charm quark mass, where its value in physical units is known. We discuss the setup, tuning procedure, simulation parameters and measurement results for ensembles with three different volumes and present a charmonium spectrum., Comment: 7 pages, 4 figures, v2: version submitted to the journal, Fig. 3 changed

We discuss the determination of the strong coupling $\alpha_{\bar{MS}}(m_{Z})$ or, equivalently, the QCD $\Lambda$ parameter. Its determination requires the use of perturbation theory in $\alpha_{s}$(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\Lambda$ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to $\alpha_{s}$ = 0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the $\Lambda$ parameter, while data around $\alpha_{s}$ ≈ 0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

21 pp., (2016)., We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale $t_0$, which allow to set the scale of the lattices generated by CLS with $2 + 1$ flavors of non-perturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses.

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 $��> 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $��_\overline{MS}^{(3)}=332(14)$~MeV is translated to $��_\overline{MS}(m_Z)=0.1179(10)(2)$ 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 $0.0002$., 7 pages, proceedings of FPCapri2016 conference

We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the $\Delta(1232)$ isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the $\Delta$-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the $\Delta$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0$) is larger than the value -3 characterizing a point particle and the fact that the transverse charge density in a $\Delta^+$ of maximal transverse spin projection is elongated along the axis of the spin., Comment: 35 pages, 10 figures

We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the $��(1232)$ isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the $��$-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the $��$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0$) is larger than the value -3 characterizing a point particle and the fact that the transverse charge density in a $��^+$ of maximal transverse spin projection is elongated along the axis of the spin., 35 pages, 10 figures

We present results on the mass of the nucleon and the $\Delta$ using two dynamical degenerate twisted mass quarks. The evaluation is performed at four quark masses corresponding to a pion mass in the range of 690-300 MeV on lattices of size 2.1 fm and 2.7 fm. We check for cutoff effects by evaluating these baryon masses on lattices of spatial size 2.1 fm with lattice spacings $a(\beta=3.9)=0.0855(6)$ fm and $a(\beta=4.05)=0.0666(6)$ fm, determined from the pion sector and find them to be within our statistical errors. Lattice results are extrapolated to the physical limit using continuum chiral perturbation theory. The nucleon mass at the physical point provides a determination of the lattice spacing. Using heavy baryon chiral perturbation theory at ${\cal O}(p^3)$ we find $a(\beta=3.9)=0.0879(12)$ fm, with a systematic error due to the chiral extrapolation estimated to be about the same as the statistical error. This value of the lattice spacing is in good agreement with the value determined from the pion sector. We check for isospin breaking in the $\Delta$-system. We find that $\Delta^{++,-}$ and $\Delta^{+,0}$ are almost degenerate pointing to small flavor violating effects., Comment: 7 pages, 9 figures. Talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany