Filtered overlap: speedup, locality, kernel non-normality and Z_A~1

We investigate the overlap operator with a UV filtered Wilson kernel. The filtering leads to a better localization of the operator even on coarse lattices and with the untuned choice $\rho=1$. Furthermore, the axial-vector renormalization constant $Z_A$ is much closer to 1, reducing the mismatch with perturbation theory. We show that all these features persist over a wide range of couplings and that the details of filtering prove immaterial. We investigate the properties of the kernel spectrum and find that the kernel non-normality is reduced. As a side effect we observe that for certain applications of the filtered overlap a speed-up factor of 2-4 can be achieved.Comment: 30 pp, 23 fig

SU(2) Low-Energy Constants from Mixed-Action Lattice QCD

An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m_l / m_s <= 0.6, while pion masses are in the range 235 < m_\pi < 680 MeV. A two-flavor chiral perturbation theory analysis of the Lattice QCD calculations constrains the Gasser-Leutwyler coefficients bar{l}_3 and bar{l}_4 to be bar{l}_3 = 4.04(40)(+73-55) and bar{l}_4 = 4.30(51)(+84-60). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f_\pi / f = 1.062(26)(+42-40) where f is the decay constant in the chiral limit. The most recent scale setting by the MILC Collaboration yields a postdiction of f_\pi = 128.2(3.6)(+4.4-6.0)(+1.2-3.3) MeV at the physical pion mass.Comment: 28 pages, 9 figures; version 2 accepted for publication in PR

Ab initio Calculation of the np→dγ Radiative Capture Process

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process n p → d γ , and the photo-disintegration processes γ ( * ) d → n p . In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m π ∼ 450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m π ∼ 806     MeV , using only lattice QCD inputs, a cross section σ 806     MeV ∼ 17     mb is found at an incident neutron speed of v = 2 , 200     m / s . Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ lqcd ( n p → d γ ) = 334.9 ( + 5.2 − 5.4 )     mb is obtained at the same incident neutron speed, consistent with the experimental value of σ expt ( n p → d γ ) = 334.2 ( 0.5 )     mb

High statistics analysis using anisotropic clover lattices. II. Three-baryon systems

We present the results of an exploratory lattice QCD calculation of three-baryon systems through a high statistics study of one ensemble of anisotropic clover gauge-field configurations with a pion mass of m π ∼ 390     MeV . Because of the computational cost of the necessary contractions, we focus on correlation functions generated by interpolating operators with the quantum numbers of the Ξ 0 Ξ 0 n system, one of the least demanding three-baryon systems in terms of the number of contractions. We find that the ground state of this system has an energy of E Ξ 0 Ξ 0 n = 3877.9 ± 6.9 ± 9.2 ± 3.3     MeV corresponding to an energy shift due to interactions of δ E Ξ 0 Ξ 0 n = E Ξ 0 Ξ 0 n − 2 M Ξ 0 − M n = 4.6 ± 5.0 ± 7.9 ± 4.2     MeV . There are a significant number of time slices in the three-baryon correlation function for which the signal-to-noise ratio is only slowly degrading with time. This is in contrast to the exponential degradation of the signal-to-noise ratio that is observed at larger times, and is due to the suppressed overlap of the source and sink interpolating operators that are associated with the variance of the three-baryon correlation function onto the lightest eigenstates in the lattice volume (mesonic systems). As one of the motivations for this area of exploration is the calculation of the structure and reactions of light nuclei, we also present initial results for a system with the quantum numbers of the triton ( p n n ). This present work establishes a path to multibaryon systems, and shows that lattice QCD calculations of the properties and interactions of systems containing four and five baryons are now within sight

Meson-baryon scattering lengths from mixed-action lattice QCD

The π + Σ + , π + Ξ 0 , K + p , K + n , and ¯¯¯¯ K 0 Ξ 0 scattering lengths are calculated in mixed-action Lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations at four light-quark masses, and at two light-quark masses on the fine MILC configurations. Heavy-baryon chiral perturbation theory with two and three flavors of light quarks is used to perform the chiral extrapolations. To the order we work in the three-flavor chiral expansion, the kaon-baryon processes that we investigate show no signs of convergence. Using the two-flavor chiral expansion for extrapolation, the pion-hyperon scattering lengths are found to be a π + Σ + = − 0.197 ± 0.017     fm , and a π + Ξ 0 = − 0.098 ± 0.017     fm , where the comprehensive error includes statistical and systematic uncertainties

Magnetic moments of light nuclei from Lattice Quantum Chromodynamics

We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton, and 3 He , along with those of the neutron and proton. These calculations, performed at quark masses corresponding to m π ∼ 800     MeV , reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of 3 He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, μ 3 H ∼ μ p . The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations. Furthermore, deviations from the Schmidt limits are also found to be similar to those in nature for these nuclei. These findings suggest that at least some nuclei at these unphysical quark masses are describable by a phenomenological nuclear shell model

The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD

The pi+pi+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L~2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of b_s~0.123 fm in the spatial direction and b_t b_s/3.5 in the time direction. The phase-shift is determined from the energy-eigenvalues of pi+pi+ systems with both zero and non-zero total momentum in the lattice volume using Luscher's method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape-parameter P, in this channel and to examine the prediction of two-flavor chiral perturbation theory: m_pi^2 a r = 3+O(m_pi^2/Lambda_chi^2). Chiral perturbation theory is used, with the Lattice QCD results as input, to predict the scattering phase-shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data.Comment: 22 pages, 16 figure

Evidence for a Bound H-dibaryon from Lattice QCD

We present evidence for the existence of a bound H dibaryon, an I = 0 , J = 0 , s = − 2 state with valence quark structure u u d d s s , at a pion mass of m π ∼ 389     MeV . Using the results of lattice QCD calculations performed on four ensembles of anisotropic clover gauge-field configurations, with spatial extents of L ∼ 2.0 , 2.5, 3.0, and 3.9 fm at a spatial lattice spacing of b s ∼ 0.123     fm , we find an H dibaryon bound by B H ∞ = 16.6 ± 2.1 ± 4.6     MeV at a pion mass of m π ∼ 389     MeV

Hyperon-Nucleon Interactions from Quantum Chromodynamics and the Composition of Dense Nuclear Matter

The low-energy n Σ − interactions determine, in part, the role of the strange quark in dense matter, such as that found in astrophysical environments. The scattering phase shifts for this system are obtained from a numerical evaluation of the QCD path integral using the technique of lattice QCD. Our calculations, performed at a pion mass of m π ∼ 389     MeV in two large lattice volumes and at one lattice spacing, are extrapolated to the physical pion mass using effective field theory. The interactions determined from lattice QCD are consistent with those extracted from hyperon-nucleon experimental data within uncertainties and strengthen model-dependent theoretical arguments that the strange quark is a crucial component of dense nuclear matter

Charged multihadron systems in lattice QCD plus QED

Systems with the quantum numbers of up to 12 charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics (QCD+QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A nonrelativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charged hadrons and found to accurately reproduce the lattice QCD+QED results. QED effects on charged multihadron systems beyond Coulomb photon exchange are determined by comparing the two- and three-body interaction parameters extracted from the lattice QCD+QED results for charged and neutral multihadron systems