The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically differ
ent universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of $300$ kilo-electron volts, which is greater than $0$ by $5$ standard deviations. We also determine the splittings in the $Sigma$, $Xi$, $D$ and $Xi_{cc}$ isospin multiplets, exceeding in some cases the precision of experimental measurements.
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 ad
ding 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.
We use the Wilson flow to define the gauge anisotropy at a given physical scale. We demonstrate the use of the anisotropic flow by performing the tuning of the bare gauge anisotropy in the tree-level Symanzik action for several lattice spacings and t
arget anisotropies. We use this method to tune the anisotropy parameters in full QCD, where we also exploit the diminishing effect of a well chosen smearing on the renormalization of the fermion anisotropy.
QCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a co
ntrolled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed N_t approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly.
We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on N_t=6 and 8 lattices. All our runs are performed with fixed global topology. Ou
r results are compared with staggered ones and a nice agreement is found.
Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and t
his is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.
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 o
f 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}).
We study the spectra of heavy-light and heavy-heavy mesons containing charm quarks, including higher spin states. We use two sets of $N_f = 2 + 1$ gauge configurations, one set from QCDSF using the SLiNC action, and the other configurations from the
Budapest-Marseille-Wuppertal collaboration, using the HEX smeared clover action. To extract information about the excited states, we choose a suitable basis of operators to implement the variational method.
Indirect CP violation in K rightarrow {pi}{pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomen
on was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from aapprox0.054 fm to aapprox0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data.
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 t
han 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.
