Antonin Portelli

Ab initio calculation of the neutron-proton mass difference

Weighing the neutron against the proton Elementary science textbooks often state that protons have the same mass as neutrons. This is not far from the truth—the neutron is about 0.14% heavier (and less stable) than the proton. The precise value is important, because if the mass difference were bigger or smaller, the world as we know it would likely not exist. Borsanyi et al. calculated the mass difference to high precision using a sophisticated approach that took into account the various forces that exist within a nucleon. The calculations reveal how finely tuned our universe needs to be. Science, this issue p. 1452 Lattice quantum chromodynamics and quantum electrodynamics are used to calculate mass differences between pairs of hadrons. 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.

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ( f π , f K , B K , m ud , m s , t 0 ½, 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 π , m K and m Ω to determine the two quark masses and the scale—all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including f π = 130.2(9) MeV; f K = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the ‾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 renormalization group invariant scheme, 0.750(15) and the ‾MS scheme at 3 GeV, 0.530(11).

Sigma term and strangeness content of octet baryons

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 Nf = 2 + 1 lattice ensembles include pion masses

Precision computation of the kaon bag parameter

Abstract Indirect CP violation in K → π π 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 phenomenon 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 a ≈ 0.054 fm to a ≈ 0.093 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 ( 3.5 GeV ) = 0.531 ( 6 ) stat ( 2 ) sys . A perturbative 2-loop conversion yields B K MS ¯ - NDR ( 2 GeV ) = 0.564 ( 6 ) stat ( 3 ) sys ( 6 ) PT and B ˆ K = 0.773 ( 8 ) stat ( 3 ) sys ( 8 ) PT , which is in good agreement with current results from fits to experimental data.

Isospin splittings in the light baryon octet from lattice QCD and QED

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 Nf=2+1 simulations with five 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.

Calculation of the Hadronic Vacuum Polarization Disconnected Contribution to the Muon Anomalous Magnetic Moment

We report the first lattice QCD calculation of the hadronic vacuum polarization (HVP) disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique that enables the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 48^{3}×96 physical-pion-mass lattice generated by the RBC and UKQCD Collaborations. We find the leading-order hadronic vacuum polarization a_{μ}^{HVP(LO)disc}=-9.6(3.3)(2.3)×10^{-10}, where the first error is statistical and the second systematic.

Lattice QCD at the physical point meets SU (2) chiral perturbation theory

We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (\chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) \chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (\xi-expansion). We find that these expansions begin showing signs of failure around M_\pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 \pm 1.3\pm 0.3 and B^\msbar(2 GeV)=2.58 \pm 0.07 \pm 0.02 GeV, and the related quark condensate, \Sigma^\msbar(2 GeV)=(271\pm 4\pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 \pm 0.5 \pm 0.4 and l_4=3.8 \pm 0.4 \pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.

Lattice calculation of the leading strange quark-connected contribution to the muon g - 2

A bstractWe present results for the leading hadronic contribution to the muon anomalous magnetic moment due to strange quark-connected vacuum polarisation effects. Simulations were performed using RBC-UKQCD’s Nf = 2 + 1 domain wall fermion ensembles with physical light sea quark masses at two lattice spacings. We consider a large number of analysis scenarios in order to obtain solid estimates for residual systematic effects. Our final result in the continuum limit is aμ(2)had,s = 53.1(9)(− 3+ 1) × 10− 10.

Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study

A bstractWe calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a 64 × 243 lattice with an inverse lattice spacing of a−1 = 1.78 GeV and an isospin symmetric pion mass of mπ = 340 MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than 1% for the up quark and 0.1% for the strange quark, although it should be noted that this is obtained using unphysical light quark masses. In addition to the results themselves, we compare the precision which can be reached for the same computational cost using each method. Such a comparison is also made for the meson electromagnetic mass-splittings.

Electromagnetic corrections to light hadron masses

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