Lattice QCD Equation of State at Finite Chemical Potential from an Alternative Expansion Scheme.

In this Letter, we introduce a novel scheme for extrapolating the equation of state of QCD to finite chemical potential that features considerably improved convergence properties and allows us to extend its reach to unprecedentedly high baryonic chemical potentials. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to µ_{B}/T≤3.5. This novel expansion does not suffer from the shortcomings that characterize the traditional Taylor expansion method, such as difficulties inherent in performing such an expansion with a limited number of coefficients and the poor signal-to-noise ratio that affects Taylor coefficients determined from lattice calculations.

Leading hadronic contribution to the muon magnetic moment from lattice QCD.

The standard model of particle physics describes the vast majority of experiments and observations involving elementary particles. Any deviation from its predictions would be a sign of new, fundamental physics. One long-standing discrepancy concerns the anomalous magnetic moment of the muon, a measure of the magnetic field surrounding that particle. Standard-model predictions1 exhibit disagreement with measurements2 that is tightly scattered around 3.7 standard deviations. Today, theoretical and measurement errors are comparable; however, ongoing and planned experiments aim to reduce the measurement error by a factor of four. Theoretically, the dominant source of error is the leading-order hadronic vacuum polarization (LO-HVP) contribution. For the upcoming measurements, it is essential to evaluate the prediction for this contribution with independent methods and to reduce its uncertainties. The most precise, model-independent determinations so far rely on dispersive techniques, combined with measurements of the cross-section of electron-positron annihilation into hadrons3-6. To eliminate our reliance on these experiments, here we use ab initio quantum chromodynamics (QCD) and quantum electrodynamics simulations to compute the LO-HVP contribution. We reach sufficient precision to discriminate between the measurement of the anomalous magnetic moment of the muon and the predictions of dispersive methods. Our result favours the experimentally measured value over those obtained using the dispersion relation. Moreover, the methods used and developed in this work will enable further increased precision as more powerful computers become available.

Hadronic Vacuum Polarization Contribution to the Anomalous Magnetic Moments of Leptons from First Principles.

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.

Calculation of the axion mass based on high-temperature lattice quantum chromodynamics.

Unlike the electroweak sector of the standard model of particle physics, quantum chromodynamics (QCD) is surprisingly symmetric under time reversal. As there is no obvious reason for QCD being so symmetric, this phenomenon poses a theoretical problem, often referred to as the strong CP problem. The most attractive solution for this requires the existence of a new particle, the axion-a promising dark-matter candidate. Here we determine the axion mass using lattice QCD, assuming that these particles are the dominant component of dark matter. The key quantities of the calculation are the equation of state of the Universe and the temperature dependence of the topological susceptibility of QCD, a quantity that is notoriously difficult to calculate, especially in the most relevant high-temperature region (up to several gigaelectronvolts). But by splitting the vacuum into different sectors and re-defining the fermionic determinants, its controlled calculation becomes feasible. Thus, our twofold prediction helps most cosmological calculations to describe the evolution of the early Universe by using the equation of state, and may be decisive for guiding experiments looking for dark-matter axions. In the next couple of years, it should be possible to confirm or rule out post-inflation axions experimentally, depending on whether the axion mass is found to be as predicted here. Alternatively, in a pre-inflation scenario, our calculation determines the universal axionic angle that corresponds to the initial condition of our Universe.

Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.

In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 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. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.

Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point.

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_{ud}^{N}=0.0405(40)(35) and f_{s}^{N}=0.113(45)(40), which translates into σ_{πN}=38(3)(3) MeV, σ_{sN}=105(41)(37) MeV, and y_{N}=0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors 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).

Ab initio calculation of the neutron-proton mass difference.

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.

Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?

Recent results for moments of multiplicity distributions of net protons and net-electric charge from the STAR Collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest Collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryochemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.

Freeze-out parameters: lattice meets experiment.

We present our results for ratios of higher order fluctuations of electric charge as functions of the temperature. These results are obtained in a system of 2+1 quark flavors at physical quark masses and continuum extrapolated. We compare them to preliminary data on higher order moments of the net electric charge distribution from the STAR collaboration. This allows us to determine the freeze-out temperature and chemical potential from first principles. We also show continuum-extrapolated results for ratios of higher order fluctuations of baryon number. These will allow us to test the consistency of the approach, by comparing them to the corresponding experimental data (once they become available) and thus, extracting the freeze-out parameters in an independent way.

Ab initio determination of light hadron masses.

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-electron volts 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.

The order of the quantum chromodynamics transition predicted by the standard model of particle physics.

Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.