Quantum Chromodynamics (QCD) is the underlying theory governing the interaction between quarks and gluons, the strong force, and therefore, responsible for all the states of matter in the Universe. Analytical solutions of QCD in the low energy regime cannot be obtained due to the complexity of the quark-gluon dynamics. The only known non-perturbative method that systematically implements QCD from first principles is its formulation on a discretized space-time, lattice QCD. This numerical simulation of the theory consists in a Monte Carlo evaluation of a functional integral. Our goal is to extract information on hadronic interactions, relevant to nuclear processes, through Lattice QCD, using the enormous computing capabilities that the most modern supercomputers offer us, specially on those sectors where experiments are difficult to perform.

In this work we have calculated the binding energies of a range of nuclei and hypernuclei with atomic number
A up to 4 and strangeness 0, -1 and -2. The calculations were performed in the limit offlavor-SU(3) symmetry, at the
physical strange quark mass and in the absence of electromagnetic interactions.
The study includes the deuteron, di-neutron, H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He.
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.
In the figure, we show a compilation of the nuclear energy levels, with spin and parity J~~π~~, as determined in this work.

In
Evidence for a Bound H Dibaryon from Lattice QCD (Phys. Rev. Lett. 106, 162001 (2011))
we presented evidence for the existence of a bound H-dibaryon,
an I=0, J=0, s=-2 state with valence quark structure uuddss.
The infinite volume extrapolation of the results of Lattice QCD calculations performed
on four ensembles of anisotropic clover gauge-field configurations,
with spatial extents of 2.0, 2.5, 3.0 and 3.9 fm at
a spatial lattice spacing of 0.123 fm,
lead to an H-dibaryon bound by 16.6 ± 2.1 ± 4.6 MeV
at a pion mass of 389 MeV.
In the figure, the results of the Lattice QCD calculations of -i cot(δ) versus (q/m_{π})^{2}
at the two larger lattice sizes,
along with the infinite-volume extrapolation (red point). The dark (blue)
(light (green)) lines correspond to the statistical (systematic
and statistical uncertainties combined in quadrature) 68%
coincidence intervals calculated.

In I=2 ππ S-wave Scattering Phase Shift from Lattice QCD
we calculated the π^{+}π^{+} scattering
amplitude using Lattice QCD over a range of momenta below the inelastic threshold.
In the figure, we compare the experimental data with our Lattice QCD prediction for the phase shift
at the physical value
of the pion mass, m_{π} ∼ 140 MeV using NLO χPT, as a function of the
squared center-of-mass momentum.
The statistical and systematic uncertainties
have been combined in quadrature. The red vertical line denotes the inelastic 4π threshold.
Our predictions for the threshold scattering parameters, and hence the leading three terms in
the Effective Range Expansion, are consistent with determinations using the Roy equations
(inner blue and purple bands in the figure) and the predictions of χPT (solid purple curve).

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From left-top to right-bottom:

Silas R. Beane (U of New Hampshire and Bonn U), Emmanuel Chang (U of Washington), Saul Cohen (U of Washington),

William Detmold (MIT),
Parikshit Junnarkar (New Hampshire), Huey-Wen Lin (U of Washington), Thomas Luu (LLNL),

Kostas Orginos (William and Mary & JLab), Assumpta Parreño (U of Barcelona),

Martin J. Savage (U of Washington), André Walker-Loud (LBNL)