Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $mu_B geq (2-2.5)T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second, higher order
coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio. In this work, we present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to $mu_B/Tle3.5$.
Many low-energy, particle-physics experiments seek to reveal new fundamental physics by searching for very rare scattering events on atomic nuclei. The interpretation of their results requires quantifying the non-linear effects of the strong interact
ion on the spin-independent couplings of this new physics to protons and neutrons. Here we present a fully-controlled, ab-initio calculation of these couplings to the quarks within those constituents of nuclei. We use lattice quantum chromodynamics computations for the four lightest species of quarks and heavy-quark expansions for the remaining two. We determine each of the six quark contributions with an accuracy better than 15%. Our results are especially important for guiding and interpreting experimental searches for our universes dark matter.
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on differential
equations, the most widely used models of epidemic spread are plagued by an approximation that is not justified in the case of the current COVID-19 pandemic. Taking the example of data from New York City, we show that currently used models significantly underestimate the initial basic reproduction number ($R_0$). The correct description, based on integral equations, can be implemented in most of the reported models and it much more accurately accounts for the dynamics of the epidemic after sharp changes in $R_0$ due to restrictive public congregation measures. It also provides a novel way to determine the incubation period, and most importantly, as we demonstrate for several countries, this method allows an accurate monitoring of $R_0$ and thus a fine-tuning of any restrictive measures. Integral equation based models do not only provide the conceptually correct description, they also have more predictive power than differential equation based models, therefore we do not see any reason for using the latter.
We compute the leading order hadronic vacuum polarization (LO-HVP) contribution to the anomalous magnetic moment of the muon, $(g_mu-2)$, using lattice QCD. Calculations are performed with four flavors of 4-stout-improved staggered quarks, at physica
l quark masses and at six values of the lattice spacing down to 0.064~fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. The infinite-volume limit is taken thanks to simulations performed in volumes of sizes up to 11~fm. Our result for the LO-HVP contribution to $(g_mu-2)$ has a total uncertainty of 0.8%. Compared to the result of the dispersive approach for this contribution, ours significantly reduces the tension between the standard model prediction for $(g_mu-2)$ and its measurement.
We study the density of states method as well as reweighting to explore the low temperature phase diagram of QCD at finite baryon chemical potential. We use four flavors of staggered quarks, a tree-level Symanzik improved gauge action and four stout
smearing steps on lattices with $N_s=4,6,8$ and $N_t=6 - 16$. We compare our results to that of the phase quenched ensemble and also determine the pion and nucleon masses. In the density of states approach we applied pion condensate or gauge action density fixing. We found that the density of states method performs similarly to reweighting. At $T approx 100$ MeV, we found an indication of the onset of the quark number density at around $mu/m_N sim 0.16 - 0.18$ on $6^4$ lattices at $beta=2.9$.
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 pe
rformed directly at the physical values of the quark masses and in volumes of linear extent larger than $6,mathrm{fm}$. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain $a_e^mathrm{LO-HVP}=189.3(2.6)(5.6)times 10^{-14}$, $a_mu^mathrm{LO-HVP}=711.1(7.5)(17.4)times 10^{-10}$ and $a_tau^mathrm{LO-HVP}=341.0(0.8)(3.2)times 10^{-8}$, where the first error is statistical and the second is systematic.
We present a determination of the corrections to Dashens theorem and of the individual up and down quark masses from a lattice calculation based on quenched QED and $N_f=2+1$ QCD simulations with 5 lattice spacings down to 0.054 fm. The simulations f
eature 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 Dashenss theorem we obtain $epsilon=0.73(2)(5)(17)$, 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, $m_u=2.27(6)(5)(4) , MeV$ and $m_d=4.67(6)(5)(4) , MeV$ in the $overline{MS}$ 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.
We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with 2+1+1 flavors of staggered fermions directly at the physical
values of the quark masses and in volumes of linear extent larger than 6fm. The continuum limit is carried out using six different lattice spacings. All connected and disconnected contributions are calculated, up to and including those of the charm.
In a previous letter (arXiv:1306.2287) we determined the isospin mass splittings of the baryon octet from a lattice calculation based on quenched QED and $N_f{=}2{+}1$ QCD simulations with 5 lattice spacings down to $0.054~mathrm{fm}$, lattice sizes
up to $6~mathrm{fm}$ and average up-down quark masses all the way down to their physical value. Using the same data we determine here the corrections to Dashens theorem and the individual up and down quark masses. For the parameter which quantifies violations to Dashenss theorem, we obtain $epsilon=0.73(2)(5)(17)$, 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, $m_u=2.27(6)(5)(4)~mathrm{MeV}$ and $m_d=4.67(6)(5)(4)~mathrm{MeV}$ in the $bar{mathrm{MS}}$ scheme at $2~mathrm{GeV}$ 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.
We calculate the QCD cross-over temperature, the equation of state and fluctuations of conserved charges at finite density by analytical continuation from imaginary to real chemical potentials. Our calculations are based on new continuum extrapolated
lattice simulations using the 4stout staggered actions with a lattice resolution up to $N_t=16$. The simulation parameters are tuned such that the strangeness neutrality is maintained, as it is in heavy ion collisions.
