[Show abstract][Hide abstract] ABSTRACT: We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic
traps with external spin-orbit potentials and short range two-body
interactions. Using a truncated basis of total angular momentum eigenstates,
non-perturbative results are presented for experimentally realistic forms of
the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus
couplings in equal parts, and a Weyl-type coupling. The technique is easily
adapted to bosonic systems and other forms of spin-orbit coupling.
Physical Review A 12/2014; 91(4). DOI:10.1103/PhysRevA.91.043606 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: At the Forschungszentrum Juelich (FZJ) we have started a long-term program
that aims to determine beyond-the-Standard-Model (BSM) matrix elements using
the gradient flow, and to understand the impact of BSM physics in nucleon and
nuclear observables. Using the gradient flow, we propose to calculate the QCD
component of key beyond the Standard Model (BSM) matrix elements related to
quark and strong theta CP violation and the strange content within the nucleon.
The former set of matrix elements impacts our understanding of Electric Dipole
Moments (EDMs) of nucleons and nuclei (a key signature of BSM physics), while
the latter contributes to elastic recoil of Dark Matter particles off nucleons
and nuclei. If successful, these results will lay the foundation for extraction
of BSM observables from future low-energy, high-intensity and high-accuracy
experimental measurements.
[Show abstract][Hide abstract] ABSTRACT: One of the overarching goals of nuclear physics is to rigorously compute
properties of hadronic systems directly from the fundamental theory of strong
interactions, Quantum Chromodynamics (QCD). In particular, the hope is to
perform reliable calculations of nuclear reactions which will impact our
understanding of environments that occur during big bang nucleosynthesis, the
evolution of stars and supernovae, and within nuclear reactors and high
energy/density facilities. Such calculations, being truly ab initio, would
include all two-nucleon and three- nucleon (and higher) interactions in a
consistent manner. Currently, lattice QCD provides the only reliable option for
performing calculations of some of the low- energy hadronic observables. With
the aim of bridging the gap between lattice QCD and nuclear many-body physics,
the Institute for Nuclear Theory held a workshop on Nuclear Reactions from
Lattice QCD on March 2013. In this review article, we report on the topics
discussed in this workshop and the path planned to move forward in the upcoming
years.
Journal of Physics G Nuclear and Particle Physics 06/2014; 42(2). DOI:10.1088/0954-3899/42/2/023101 · 2.78 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The energy spectra of two nucleons in a cubic volume provide access to
the two phase shifts and one mixing angle that define the S matrix in
the S13-D13 coupled channels containing the deuteron. With the aid of
recently derived energy quantization conditions for such systems, and
the known scattering parameters, these spectra are predicted for a range
of volumes. It is found that extractions of the infinite-volume deuteron
binding energy and leading scattering parameters, including the S-D
mixing angle at the deuteron pole, are possible from lattice QCD
calculations of two-nucleon systems with boosts of |P|≤(2π)/(L)3
in volumes with 10fm≲L≲14fm. The viability of extracting the
asymptotic D/S ratio of the deuteron wave function from lattice QCD
calculations is discussed.
Physical Review D 12/2013; 88(11):114507-. DOI:10.1103/PhysRevD.88.114507 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore the use of twisted boundary conditions in extracting the nucleon
mass and the binding energy of two-baryon systems, such as the deuteron, from
Lattice QCD calculations. Averaging the results of calculations performed with
periodic and anti-periodic boundary conditions imposed upon the light-quark
fields, or other pair-wise averages, improves the volume dependence of the
deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L.
However, a twist angle of pi/2 in each of the spatial directions improves the
volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging
the binding energy with a random sampling of twist angles improves the volume
dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard
deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest
lattice volumes. Using the experimentally determined phase shifts and mixing
angles, we determine the expected energies of the deuteron states over a range
of cubic lattice volumes for a selection of twisted boundary conditions.
Physical Review D 11/2013; 89(7). DOI:10.1103/PhysRevD.89.074509 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The origin of mass is one of the deepest mysteries in science. Neutrons and protons, which account for almost all visible mass in the Universe, emerged from a primordial plasma through a cataclysmic phase transition microseconds after the Big Bang. However, most mass in the Universe is invisible. The existence of dark matter, which interacts with our world so weakly that it is essentially undetectable, has been established from its galactic-scale gravitational effects. Here we describe results from the first truly physical calculations of the cosmic phase transition and a groundbreaking first-principles investigation into composite dark matter, studies impossible with previous state-of-the-art methods and resources. By inventing a powerful new algorithm, "DSDR," and implementing it effectively for contemporary supercomputers, we attain excellent strong scaling, perfect weak scaling to the LLNL BlueGene/Q two million cores, sustained speed of 7.2 petaflops, and time-to-solution speedup of more than 200 over the previous state-of-the-art.
Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis; 11/2013
[Show abstract][Hide abstract] ABSTRACT: I provide a short overview of the current status of nuclear physics calculations using lattice quantum chromodynamics (LQCD). I give an heuristic description of how LQCD calculations are performed and how nuclear scattering data are extracted from these calculations, emphasizing the overlap between traditional nuclear many-body theory and LQCD calculations. I look at the Ω
−Ω
− system as a concrete example, and in so doing demonstrate the predictive nature of LQCD calculations as applied to nuclear physics.
Few-Body Systems 08/2013; 54(7-10). DOI:10.1007/s00601-013-0695-0 · 0.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The quantization condition for interacting energy eigenvalues of the
two-nucleon system in a finite cubic volume is derived in connection to the
nucleon-nucleon scattering amplitudes. This condition is derived using an
auxiliary (dimer) field formalism that is generalized to arbitrary partial
waves in the context of non-relativistic effective field theory. The
quantization condition presented gives access to the scattering parameters of
the two-nucleon systems with arbitrary parity, spin, isospin, angular momentum
and center of mass motion, from a lattice QCD calculation of the energy
eigenvalues. In particular, as it includes all non-central interactions, such
as the two-nucleon tensor force, it makes explicit the dependence of the mixing
parameters of nucleon-nucleon systems calculated from lattice QCD when there is
a physical mixing among different partial-waves, e. g. S-D mixing in the
deuteron channel. We provide explicit relations among scattering parameters and
their corresponding point group symmetry class eigenenergies with orbital
angular momentum l smaller than or equal to 3, and for center of mass boost
vectors of the form 2\pi (2n_1, 2n_2, 2n_3)/L, 2\pi (2n_1, 2n_2, 2n_3+1)/L and
2\pi (2n_1+1, 2n_2+1, 2n_3)/L. L denotes the special extent of the cubic volume
and n_1,n_2,n_3 are integers. Our results are valid below inelastic thresholds
up to exponential volume corrections that are governed by the pion mass.
[Show abstract][Hide abstract] ABSTRACT: The scattering lengths and effective ranges that describe low-energy
nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry
at the physical strange-quark mass with Lattice Quantum Chromodynamics. The
calculations are performed with an isotropic clover discretization of the quark
action in three volumes with spatial extents of L \sim 3.4 fm, 4.5fm and 6.7
fm, and with a lattice spacing of b \sim 0.145 fm. With determinations of the
energies of the two-nucleon systems (both of which contain bound states at
these up and down quark masses) at rest and moving in the lattice volume,
Luscher's method is used to determine the low-energy phase shifts in each
channel, from which the scattering length and effective range are obtained. The
scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) =
9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) =
{4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1)
= 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) =
3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the
two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes
exact in the limit of large-N_c. In both spin channels, the phase shifts change
sign at higher momentum, near the start of the t-channel cut, indicating that
the nuclear interactions have a repulsive core even at the SU(3)-symmetric
point.
Physical Review C 01/2013; 88(2). DOI:10.1103/PhysRevC.88.024003 · 3.73 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: I provide a short overview of the current status of nuclear physics
calculations using lattice Quantum Chromodynamics (LQCD). I demonstrate,
at a very high level, how LQCD calculations are performed and how
nuclear scattering data are extracted from these calculations,
emphasizing the overlap between traditional nuclear many-body theory and
LQCD calculations. I look at the Ω-Ω-
system as a concrete example, and in so doing demonstrate the predictive
nature of LQCD calculations as applied to nuclear physics.
Journal of Physics Conference Series 12/2012; 403(1):2041-. DOI:10.1088/1742-6596/403/1/012041
[Show abstract][Hide abstract] ABSTRACT: The low-energy nΣ^{-} 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.
[Show abstract][Hide abstract] ABSTRACT: The binding energies of a range of nuclei and hypernuclei with atomic number
A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron,
H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He, 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.
[Show abstract][Hide abstract] ABSTRACT: The π+π+ s-wave scattering phase shift is determined below the inelastic threshold using lattice QCD. Calculations were performed at a pion mass of mπ∼390 MeV with an anisotropic nf=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 bs∼0.123 fm in the spatial direction and bt∼bs/3.5 in the time direction. The phase shift is determined from the energy eigenvalues of π+π+ systems with both zero and nonzero total momentum in the lattice volume using Lüscher’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: mπ2ar=3+O(mπ2/Λχ2). 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.
[Show abstract][Hide abstract] ABSTRACT: We explore the interactions of two strangeness -3 baryons in multiple spin
channels with lattice QCD. This system provides an ideal laboratory for
exploring the interactions of multi-baryon systems with minimal dependence on
light quark masses. Model calculations of the two-$\Omega^-$ system in two
previous works have obtained conflicting results, which can be resolved by
lattice QCD. The lattice calculations are performed using two different volumes
with $L\sim2.5$ and 3.9 fm on anisotropic clover lattices at $m_\pi \sim 390$
MeV with a lattice spacing of $a_s \sim 0.123$ fm in the spatial direction and
$a_t\sim{a}_s/3.5$ in the temporal direction. Using multiple interpolating
operators from a non-displaced source, we present scattering information for
two ground state $\Omega^-$ baryons in both the S=0 and S=2 channels. For S=0,
$k\cot\delta$ is extracted at two volumes, which lead to an extrapolated
scattering length of $a^{\Omega\Omega}_{S=0}=0.16 \pm 0.22 \ \text{fm}$,
indicating a weakly repulsive interaction. Additionally, for S=2, two separate
highly repulsive states are observed. We also present results on the
interactions of the excited strangeness -3, spin-1/2 states with the ground
spin-3/2 states for the spin-1 and spin-2 channels. Results for these
interactions are consistent with attractive behavior.
[Show abstract][Hide abstract] ABSTRACT: 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 ~ 390 MeV are presented. Calculations were performed with an anisotropic
n_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_s ~ 0.123 fm in the
spatial-direction, and b_t ~ b_s/3.5 in the time-direction. The Xi-Xi- is found
to be bound by B_{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_d =
11(05)(12) MeV and B_{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_H = 13.2(1.8)(4.0) MeV at this pion mass, updating our previous
result.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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(pi) similar to 389 MeV. Using the results of lattice QCD calculations performed on four ensembles of anisotropic clover gauge-field configurations, with spatial extents of L similar to 2.0, 2.5, 3.0, and 3.9 fm at a spatial lattice spacing of b(s) similar to 0.123 fm, we find an H dibaryon bound by B(infinity)(H) = 16.6 +/- 2.1 +/- 4.6 MeV at a pion mass of m(pi) similar to 389 MeV.
[Show abstract][Hide abstract] ABSTRACT: The volume dependence of the octet baryon masses and relations among them are
explored with Lattice QCD. Calculations are performed with 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, with an anisotropic lattice spacing of b_s ~ 0.123 fm in
the spatial direction, and b_t = b_s/3.5 in the time direction, and at a pion
mass of m_pi ~ 390 MeV. The typical precision of the ground-state baryon mass
determination is ~0.2%, enabling a precise exploration of the volume dependence
of the masses, the Gell-Mann--Okubo mass relation, and of other mass
combinations. A comparison of the volume dependence with the predictions of
heavy baryon chiral perturbation theory is performed in both the SU(2)_L X
SU(2)_R and SU(3)_L X SU(3)_R expansions. Predictions of the three-flavor
expansion for the hadron masses are found to describe the observed volume
dependences reasonably well. Further, the Delta-N-pi axial coupling constant is
extracted from the volume dependence of the nucleon mass in the two-flavor
expansion, with only small modifications in the three-flavor expansion from the
inclusion of kaons and etas. At a given value of m_pi L, the finite-volume
contributions to the nucleon mass are predicted to be significantly smaller at
m_pi ~ 140 MeV than at m_pi ~ 390 MeV due to a coefficient that scales as ~
m_pi^3. This is relevant for the design of future ensembles of lattice
gauge-field configurations. Finally, the volume dependence of the pion and kaon
masses are analyzed with two-flavor and three-flavor chiral perturbation
theory.
Physical Review D 04/2011; 84(01). DOI:10.1103/PhysRevD.84.039903 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The current constraints from lattice QCD on the existence of the H-dibaryon
are discussed. With only two significant lattice QCD calculations of the
H-dibaryon binding energy at approximately the same lattice spacing, the forms
of the chiral and continuum extrapolations to the physical point are not
determined. In this brief report, we consider the constraints on the H-dibaryon
imposed by two simple chiral extrapolations. In both instances, the
extrapolation to the physical pion mass allows for a bound H-dibaryon or a
near-threshold scattering state. Further lattice QCD calculations are required
to clarify this situation.
Modern Physics Letters A 03/2011; 26(34). DOI:10.1142/S0217732311036978 · 1.20 Impact Factor