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

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

QCD constraints on isospin-dense matter and the nuclear equation of state

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential bounds the partition function for a baryon chemical potential, these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time

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

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

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

Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry

The binding energies of a range of nuclei and hypernuclei with atomic number A ≤ 4 and strangeness | s | ≤ 2 , including the deuteron, dineutron, H-dibaryon, 3 He , 3 Λ He , 4 He , 4 Λ He , and 4 Λ Λ He , are calculated in the limit of flavor-SU(3) symmetry at the physical strange-quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from lattice QCD calculations performed with n f = 3 dynamical light quarks using an isotropic clover discretization of the quark action in three lattice volumes of spatial extent L ∼ 3.4     fm , 4.5 fm, and 6.7 fm, and with a single lattice spacing b ∼ 0.145     fm

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

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