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 different 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 Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.

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We continue our investigation of 2 + 1 flavor QCD thermodynamics using dynamical Wilson fermions in the fixed scale approach. Two additional pion masses, approximately 440 MeV and 285 MeV, are added to our previous work at 545 MeV. The simulations were performed at 3 or 4 lattice spacings at each pion mass. The renormalized chiral condensate, strange quark number susceptibility and Polyakov loop is obtained as a function of the temperature and we observe a decrease in the light chiral pseudo-critical temperature as the pion mass is lowered while the pseudocritical temperature associated with the strange quark number susceptibility or the Polyakov loop is only mildly sensitive to the pion mass. These findings are in agreement with previous continuum results obtained in the staggered formulation. * Electronic address: borsanyi@uni-wuppertal.de †

We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon, and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of u, d, s, and c quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than 6 fm. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain a_{e}^{LO-HVP}=189.3(2.6)(5.6)×10^{-14}, a_{μ}^{LO-HVP}=711.1(7.5)(17.4)×10^{-10} and a_{τ}^{LO-HVP}=341.0(0.8)(3.2)×10^{-8}, where the first error is statistical and the second is systematic.

We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density in the`immediate neighbourhood' of the point it is just visiting. We focus on the most natural process with these properties that we call`true self-repelling motion'. This is the continuous counterpart to the integer-valued`true' self-avoiding walk, which had been studied among others by the ®rst author. One of the striking properties of true self-repelling motion is that, although the couple t Y occupation-time measure of at time t is a continuous Markov process, is not driven by a stochastic dierential equation and is not a semi-martingale. It turns out, for instance, that it has a ®nite variation of order 3/2, which contrasts with the ®nite quadratic variation of semi-martingales. One of the key-tools in the construction of is a continuous system of coalescing Brownian motions similar to those that have been constructed by Arratia [A1, A2]. We derive various properties of (existence and properties of the occupation time densities v t x, local variation, etc.) and an identity that shows that the dynamics of can be very loosely speaking described as follows: Àd t is equal to the gradient (in space) of v t x, in a generalized sense, even though x U 3 v t x is not dierentiable.

We present a QCD calculation of the u, d and s scalar quark contents of nucleons based on 47 lattice ensembles with N f = 2 + 1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f N ud = 0.0405(40)(35) and f N s = 0.113(45)(40), which translates into σπN = 38(3)(3) MeV, σsN = 105(41)(37) MeV and yN = 0.20 (8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).

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We modify the usual Erdős-Rényi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state.