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We report on our ongoing determination of the charm quark mass and the masses and decay constants of various charmed mesons, obtained within a mixed-action setup. We employ $N_f=2+1$ CLS ensembles combined with a Wilson twisted mass valence action that eliminates the leading $O(a)$ effects from our target observables. Alongside our preliminary results, we will discuss an exploration of GEVP techniques aimed at optimizing the precision in view of the extension of the computation to heavier quark masses. We study the chiral-continuum extrapolation of decay constants for charm quark observables and the renormalized charm quark mass., Comment: Proceedings of the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology

QCD topological susceptibility at high temperature, $\chi_t(T)$, provides an important input for the estimate of the axion abundance in the present Universe. While the model independent determination of $\chi_t(T)$ should be possible from the first principles using lattice QCD, existing methods fail at high temperature, since not only the probability that non-trivial topological sectors appear in the configuration generation process but also the local topological fluctuations get strongly suppressed. We propose a novel method to calculate the temperature dependence of topological susceptibility at high temperature. A feasibility test is performed on a small lattice in the quenched approximation, and the results are compared with the prediction of the dilute instanton gas approximation. It is found that the method works well especially at very high temperature and the result is consistent with the instanton calculus down to $T\sim 2\, T_c$ within the statistical uncertainty., Comment: 27 pages, 8 figures. Method clarified, matches published version

In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $K\to\pi\pi$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the effects of this error are negligible compared to the overall errors on our calculation., Comment: 2 pages, 1 figure

We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1\sigma$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability., Comment: 9 pages, 3 figures. Updated to match published version

We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $K\to\pi\pi$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}\simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $\Delta I=1/2$ rule, Re$A_0$/Re$A_2\simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $\epsilon^\prime/\epsilon$ is Re($\epsilon^\prime/\epsilon)_\textrm{EWP}=-(6.6\pm 1.0)\times 10^{-4}$., Comment: 46 pages, 12 figures

We present results for several light hadronic quantities ($f_\pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_\pi$, $m_K$ and $m_\Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_\pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11)., Comment: 131 pages, 30 figures. Updated to match published version

While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here we include these effects by adding them to valence quarks in a lattice QCD calculation based on $N_f=2+1$ simulations with 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment., Comment: 5 pages, 3 figures. Version accepted for publication by Phys. Rev. Lett

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to about 190 MeV in large volumes (M_\pi L > 4), and three values of the lattice spacing. Our main results are the nucleon sigma term \sigma_{\pi N} = 39(4)(^{+18}_{-7}) and the strangeness content y_{N} = 0.20(7)(^{+13}_{-17}). Under the assumption of validity of covariant baryon \chi PT in our range of masses one finds y_{N} = 0.276(77)(^{+90}_{-62})., Comment: LaTeX. 15 pages, 5 figures. Text and results corrected according to Erratum [Phys. Rev. D 93, 039905(E) (2016)]

A status report is given for a joint project of the Budapest-Marseille-Wuppertal collaboration and the Regensburg group to study the quark mass-dependence of octet baryons in SU(3) Baryon XPT. This formulation is expected to extend to larger masses than Heavy-Baryon XPT. Its applicability is tested with 2+1 flavor data which cover three lattice spacings and pion masses down to about 190 MeV, in large volumes. Also polynomial and rational interpolations in M_\pi^2 and M_K^2 are used to assess the uncertainty due to the ansatz. Both frameworks are combined to explore the precision to be expected in a controlled determination of the nucleon sigma term and strangeness content., Comment: Lattice 2010

At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. We will present preliminary results for electromagnetic corrections to light hadron masses, based on simulations in which a $\mathrm{U}(1)$ degree of freedom is superimposed on $N_f=2+1$ QCD configurations from the BMW collaboration., Comment: 7 pages, 2 figures, The XXVIII International Symposium on Lattice Field Theory, June 14-19,2010, Villasimius, Sardinia Italy

While the masses of light hadrons have been extensively studied in lattice QCD simulations, there exist only a few exploratory calculations of the strong decay widths of hadronic resonances. We will present preliminary results of a computation of the rho meson width obtained using $N_f=2+1$ flavor simulations. The work is based on L\"uscher's formalism and its extension to moving frames., Comment: The XXVIII International Symposium on Lattice Field Theory, June 14-19,2010, Villasimius, Sardinia Italy

More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab-initio calculation of the masses of protons, neutrons and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega electronvolts are used to extrapolate to the physical point with lattice sizes of approximately four times the inverse pion mass. Three lattice spacings are used for a continuum extrapolation. Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties., Comment: 22 pages, 3 Tables, 8 Figures. Published in Science (21 November 2008) with Supporting Online Material. Submission to arXiv has been delayed by 6 months to respect the journal's embargo policy

The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational resources, one of them can always cheat perfectly. Here we analyze in detail how the performance of a quantum coin tossing experiment should be compared to classical protocols, taking into account the inevitable experimental imperfections. We then report an all-optical fiber experiment in which a single coin is tossed whose randomness is higher than achievable by any classical protocol and present some easily realisable cheating strategies by Alice and Bob., Comment: 13 pages