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Nuclear Physics with Lattice QCD

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.

 

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Nuclear Physics from Lattice QCD

 

Recent results

 

Quarkonium-Nucleus Bound States from Lattice QCD

Phys. Rev. D91, 114503 (2015)

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In this paper, we present lattice QCD calculations of the interactions of strange and charm quarkonia with light nuclei. In the plots, we represent the corresponding binding energies as a function of the atomic number. Both the strangeonium-nucleus and charmonium-nucleus systems are found to be relatively deeply bound when the masses of the three light quarks are set equal to that of the physical strange quark. Extrapolation of these results to the physical light-quark masses suggests that the binding energy of charmonium to nuclear matter is BphysNM ≲ 40  MeV.

 

img Magnetic moments of light nuclei from lattice quantum chromodynamics

Phys. Rev. Lett. 113, 252001 (2014)


We recently demonstrated for the first time that Quantum Chromodynamics (QCD) can be used to calculate the structure of nuclei from first principles. This study performed exploratory Lattice QCD calculations of the magnetic moments of light nuclear systems, at the SU(3) flavor symmetric point, corresponding to a pion mass of 800 MeV. When presented in terms of the natural nuclear magneton at the corresponding quark masses, the extracted magnetic moments were seen to be in close agreement with those of nature. Additionally, the magnetic moment of 3He was found to be close to that of the neutron, and that of the triton was close to that of the proton, in agreement with the expectations of the phenomenological shell-model, and therefore suggesting that this model structure is a robust feature of nuclei even away from the physical quark masses.

 

img Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry

Phys. Rev. D87 (2013) 034506


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 as determined in this work.

 

img Evidence for a Bound H Dibaryon from Lattice QCD

Phys. Rev. Lett. 106, 162001 (2011))


In this work 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/mπ)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.

Synopsis by Physical Review Letters Binding baryons on the lattice

 

img I=2 ππ S-wave Scattering


In this work 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, mπ ∼ 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).

 



The mission of the multi-institutional NPLQCD effort is to make predictions for the structure and interactions of nuclei using lattice QCD




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From left to right:
Silas R. Beane (U of Washington, Seattle), Emmanuel Chang (U of Washington, Seattle),
Zohreh Davoudi (MIT), William Detmold (MIT), Kostas Orginos (William & Mary and TJNAF),
Assumpta Parreño (U of Barcelona), Martin J. Savage (Institute for Nuclear Theory, Seattle),
Frank Winter (TJNAF), Brian Tiburzi (City College of New York)



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