Unitary limit of two-nucleon interactions in strong magnetic fields

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m π ∼ 450 and 806 MeV in uniform, time-independent magnetic fields of strength | B | ∼ 10 19 - 10 20     G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems

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

Variational study of two-nucleon systems with lattice QCD

The low-energy spectrum and scattering of two-nucleon systems are studied with lattice quantum chromodynamics using a variational approach. A wide range of interpolating operators are used: dibaryon operators built from products of plane-wave nucleons, hexaquark operators built from six localized quarks, and quasilocal operators inspired by two-nucleon bound-state wave functions in low-energy effective theories. Sparsening techniques are used to compute the timeslice-to-all quark propagators required to form correlation-function matrices using products of these operators. Projection of these matrices onto irreducible representations of the cubic group, including spin-orbit coupling, is detailed. Variational methods are applied to constrain the low-energy spectra of two-nucleon systems in a single finite volume with quark masses corresponding to a pion mass of 806 MeV. Results for S- and D-wave phase shifts in the isospin singlet and triplet channels are obtained under the assumption that partial-wave mixing is negligible. Tests of interpolating-operator dependence are used to investigate the reliability of the energy spectra obtained and highlight both the strengths and weaknesses of variational methods. These studies and comparisons to previous studies using the same gauge-field ensemble demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and nonvariational methods, including missing energy levels and other discrepancies. While this study is inconclusive regarding the presence of two-nucleon bound states at this quark mass, it provides robust upper bounds on two-nucleon energy levels that can be improved in future calculations using additional interpolating operators and is therefore a step toward reliable nuclear spectroscopy from the underlying Standard Model of particle physics

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

Low-energy scattering and effective interaction of two baryons at m(pion) ~ 450 MeV from lattice quantum chromodynamics

The interactions between two-octet baryons are studied at low energies using lattice quantum chromodynamics (LQCD) with larger-than-physical quark masses corresponding to a pion mass of ~450 MeV and a kaon mass of ~ 596 MeV. The two-baryon systems that are analyzed range from strangeness S=0 to -4 and include the spin-singlet and triplet NN, ΣN (I=3/2), and ΞΞ states, the spin-singlet ΣΣ (I=2) and ΞΣ (I=3/2) states, and the spin-triplet ΞN (I=0) state. The corresponding s-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable are extracted using Lüscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet ΣN and ΞΞ channels are found to be repulsive and do not support bound states. Using results from previous studies of these systems at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with available experimental values and phenomenological predictions. The low-energy coefficients in pionless effective field theory (EFT) relevant for two-baryon interactions, including those responsible for SU(3) flavor-symmetry breaking, are constrained. The SU(3) flavor symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the SU(6) spin-flavor symmetry, predicted at large Nc. A remnant of an accidental SU(16) symmetry found previously at a larger pion mass is further observed. The SU(6)-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading SU(3) flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD

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

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