58 research outputs found
Hadron -hadron scattering in lattice quantum chromodynamics
Hadron-hadron and multi-hadron scattering calculations in fully dynamical, mixed-action Lattice Quantum Chromodynamics using the MILC gauge ensembles in a non-perturbative simulation are discussed. In particular, calculations of the pi+sum+, pi+xi 0, K+p, K+n, and K¯ 0xi0 scattering lengths are presented, and are the main subject of this dissertation. Using the two-flavor chiral expansion for extrapolation, the pion-hyperon scattering lengths are found to be ap+S+ = --0.197 +/- 0.017 fm, and ap+X0 = --0.098 +/- 0.017 fm, where the comprehensive error includes statistical and systematic uncertainties. Meson-meson and multi-meson lattice calculations by the NPLQCD collaboration are reviewed, and presented for completeness
Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction
The ground-state energies of 2, 3, 4 and 5 \pi^+'s in a spatial volume V (2.5
fm)^3 are computed with lattice QCD. By eliminating the leading contribution
from three-\pi^+ interactions, particular combinations of these n-\pi^+
ground-state energies provide precise extractions of the \pi^+\pi^+ scattering
length in agreement with that obtained from calculations involving only two
\pi^+'s. The three-\pi^+ interaction can be isolated by forming other
combinations of the n-\pi^+ ground-state energies. We find a result that is
consistent with a repulsive three-\pi^+ interaction for m_\pi < 352 MeV.Comment: 4 pages, 5 figure
High Statistics Analysis using Anisotropic Clover Lattices: (I) Single Hadron Correlation Functions
We present the results of high-statistics calculations of correlation
functions generated with single-baryon interpolating operators on an ensemble
of dynamical anisotropic gauge-field configurations generated by the Hadron
Spectrum Collaboration using a tadpole-improved clover fermion action and
Symanzik-improved gauge action. A total of 292,500 sets of measurements are
made using 1194 gauge configurations of size 20^3 x 128 with an anisotropy
parameter \xi= b_s/b_t = 3.5, a spatial lattice spacing of b_s=0.1227\pm 0.0008
fm, and pion mass of m_\pi ~ 390 MeV. Ground state baryon masses are extracted
with fully quantified uncertainties that are at or below the ~0.2%-level in
lattice units. The lowest-lying negative-parity states are also extracted
albeit with a somewhat lower level of precision. In the case of the nucleon,
this negative-parity state is above the N\pi threshold and, therefore, the
isospin-1/2 \pi N s-wave scattering phase-shift can be extracted using
Luescher's method. The disconnected contributions to this process are included
indirectly in the gauge-field configurations and do not require additional
calculations. The signal-to-noise ratio in the various correlation functions is
explored and is found to degrade exponentially faster than naive expectations
on many time-slices. This is due to backward propagating states arising from
the anti-periodic boundary conditions imposed on the quark-propagators in the
time-direction. We explore how best to distribute computational resources
between configuration generation and propagator measurements in order to
optimize the extraction of single baryon observables
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
The K+K+ Scattering Length from Lattice QCD
The K+K+ scattering length is calculated in fully-dynamical lattice QCD with
domain-wall valence quarks on the MILC asqtad-improved gauge configurations
with rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation
theory at next-to-leading order, which includes the leading effects of the
finite lattice spacing, is used to extrapolate the results of the lattice
calculation to the physical value of m_{K+}/f_{K+}. We find m_{K+} a_{K+K+} =
-0.352 +- 0.016, where the statistical and systematic errors have been combined
in quadrature.Comment: 17 pages, 12 figures. NPLQCD collaboratio
Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
The I=2 pipi scattering length is calculated in fully-dynamical lattice QCD
with domain-wall valence quarks on the asqtad-improved coarse MILC
configurations (with fourth-rooted staggered sea quarks) at four light-quark
masses. Two- and three-flavor mixed-action chiral perturbation theory at
next-to-leading order is used to perform the chiral and continuum
extrapolations. At the physical charged pion mass, we find m_pi a_pipi(I=2) =
-0.04330 +- 0.00042, where the error bar combines the statistical and
systematic uncertainties in quadrature.Comment: 20 pages, 7 figure
Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
The ground-state energies of systems containing up to twelve 's in a
spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice
QCD at a lattice spacing of ~ 0.125 fm for four different values of the light
quark masses. Clean signals are seen for each ground state, allowing for a
precise extraction of both the scattering length and
-interaction from a correlated analysis of systems containing
different numbers of 's. This extraction of the scattering
length is consistent with than that from the -system alone. The
large number of systems studied here significantly strengthens the arguments
presented in our earlier work and unambiguously demonstrates the presence of a
low energy -interaction. The equation of state of a
gas is investigated using our numerical results and the density dependence of
the isospin chemical potential for these systems agrees well with the
theoretical expectations of leading order chiral perturbation theory. The
chemical potential is found to receive a substantial contribution from the
-interaction at the lighter pion masses. An important
technical aspect of this work is the demonstration of the necessity of
performing propagator contractions in greater than double precision to extract
the correct results.Comment: 38 pages, 20 figure
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
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
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