Silas R. Beane

Towards a Perturbative Theory of Nuclear Forces

NT@UW-01-06 LBNL 47692 RBRC-186 Towards a Perturbative Theory of Nuclear Forces S.R. Beane a , P.F. Bedaque b , M.J. Savage a,c , and U. van Kolck d,e arXiv:nucl-th/0104030 v1 9 Apr 2001 a Department of Physics, University of Washington, Seattle, WA 98195 b Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 c Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606 Department of Physics, University of Arizona, Tucson, AZ 85721 d e RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 Abstract We show that an expansion of nuclear forces about the chiral limit is formally consistent and is equivalent to KSW power counting in the 1 S 0 channel and Weinberg power counting in the 3 S 1 − 3 D 1 coupled channels. Numerical evidence suggests that this expansion converges. The feasibility of making contact between nuclear physics and lattice-QCD simulations is discussed.

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 uuddss, 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.

Two nucleons on a lattice

The two-nucleon sector is near an infrared fixed point of QCD and as a result the S-wave scattering lengths are unnaturally large compared to the effective ranges and shape parameters. It is usually assumed that a lattice QCD simulation of the two-nucleon sector will require a lattice that is much larger than the scattering lengths in order to extract quantitative information. In this Letter we point out that this does not have to be the case: lattice QCD simulations on much smaller lattices will produce rigorous results for nuclear physics.

Hyperon–nucleon scattering from fully-dynamical lattice QCD

Abstract We present results of the first fully-dynamical lattice QCD determination of hyperon–nucleon scattering. One s-wave phase shift was determined for nΛ scattering in both spin-channels at pion masses of 350, 490 and 590 MeV, and for n Σ − scattering in both spin channels at pion masses of 490 and 590 MeV. The calculations were performed with domain-wall valence quarks on dynamical, staggered gauge configurations with a lattice spacing of b ∼ 0.125 fm .

Variation of fundamental couplings and nuclear forces

Abstract The dependence of the nuclear force on standard model parameters plays an important role in bounding time and space variations of fundamental couplings over cosmological time scales. We discuss the quark-mass dependence of deuteron and di-neutron binding in a systematic chiral expansion. The leading quark-mass dependence of the nuclear force arises from one-pion exchange and from local quark-mass dependent four-nucleon operators with coefficients that are presently unknown. By varying these coefficients while leaving nuclear observables at the physical values of the quark masses invariant, we find scenarios where two-nucleon physics depends both weakly and strongly on the quark masses. While the determination of these coefficients is an exciting future opportunity for lattice QCD, we conclude that, at present, bounds on time and space variations of fundamental parameters from the two-nucleon sector are much weaker than previously claimed. This brings into question the reliability of coupling-constant bounds derived from more complex nuclei and nuclear processes.

The Deuteron and Exotic Two-Body Bound States from Lattice QCD

Results of a high-statistics, multi-volume Lattice QCD exploration of the deuteron, the di-neutron, the H-dibaryon, and the {Xi}-{Xi}- system at a pion mass of m{sub {pi}} ~ 390 MeV are presented. Calculations were performed with an anisotropic n{sub f} = 2+1 Clover discretization in four lattice volumes of spatial extent L ~ 2.0, 2.5, 3.0 and 4.0 fm, with a lattice spacing of b{sub s} ~ 0.123 fm in the spatial-direction, and b{sub t} ~ b{sub s}/3.5 in the time-direction. The {Xi}-{Xi}- is found to be bound by B{sub {Xi}-{Xi}} = 14.0(1.4)(6.7) MeV, consistent with expectations based upon phenomenological models and low-energy effective field theories constrained by nucleon-nucleon and hyperon-nucleon scattering data at the physical light-quark masses. We find weak evidence that both the deuteron and the di-neutron are bound at this pion mass, with binding energies of B{sub d} = 11(05)(12) MeV and B{sub nn} = 7.1(5.2)(7.3) MeV, respectively. With an increased number of measurements and a refined analysis, the binding energy of the H-dibaryon is B{sub H} = 13.2(1.8)(4.0) MeV at this pion mass, updating our previous result.

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 jsj 2, including the deuteron, di-neutron, H-dibaryon, 3 He, 3 He, 4 He, 4 He, and 4 He, are calculated in the limit of avor-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 nf = 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.

The Quark-Mass Dependence of Two-Nucleon Systems

Abstract We explore the quark-mass dependence of two-nucleon systems. Allowed regions for the scattering lengths in the 1S0 and 3S1 channels as functions of the light-quark masses are determined from the current uncertainty in strong-interaction parameters that appear at next-to-leading order in the effective field theory. Where experimental constraints are absent, as is the case for the quark-mass dependent four-nucleon operators, we use naive dimensional analysis. We find it likely that there is no bound state in the 1S0 channel in the chiral limit. However, given the present uncertainties in strong-interaction parameters it is unclear whether the deuteron is bound or unbound in the chiral limit.

Singular potentials and limit cycles

We show that a central 1/r{sup n} singular potential (with n{>=}{>=}2) is renormalized by a one-parameter square-well counterterm; low-energy observables are made independent of the square-well width by adjusting the square-well strength. We find a closed form expression for the renormalization-group evolution of the square-well counterterm.

I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD

We compute the I=2 pipi scattering length at pion masses of mpi~294, 348, and 484 MeV in fully-dynamical lattice QCD using Luschers finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, b~0.125 fm. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find mpia2=-0.0426±0.0006±0.0003±0.0018, in good agreement with experiment. The I=2 pipi scattering phase shift is calculated to be delta=-43±10±5° at |p|~544 MeV for mpi~484 MeV.