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تسجيل مستخدم جديدSpectra and Scattering of Light Lattice Nuclei from Effective Field Theory
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An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For $m_pi=510~$MeV we obtain, respectively, $^4a_{rm nD}=2.3pm 1.3~$fm, $^2a_{rm nD}=2.2pm 2.1~$fm, and $B_{alpha}^{}=35pm 22~$MeV, while for $m_pi=805~$MeV $^4a_{rm nD}=1.6pm 1.3~$fm, $^2a_{rm nD}=0.62pm 1.0~$fm, and $B_{alpha}^{}=94pm 45~$MeV are found. Phillips- and Tjon-like correlations to the triton binding energy are established. Higher-order effects on the respective correlation bands are found insensitive to the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.
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We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to
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We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimantal data for nuclei with mass numbers $A=
2$ and $3$, or alternatively to results from lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mass nuclei. At NLO the nuclei $^{16}$O and $^{40}$Ca are bound with respect to decay into alpha particles. Binding energies per nucleon are 9-10 MeV and 30-40 MeV at pion masses of 140 MeV and 806 MeV, respectively.
An approach for relating the nucleon excited states extracted from lattice QCD and the nucleon resonances of experimental data has been developed using the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in the finite volume of
the lattice, the eigenstates of the Hamiltonian model can be related to the energy eigenstates observed in Lattice simulations. By taking the infinite-volume limit of HEFT, information from the lattice is linked to experiment. The approach opens a new window for the study of experimentally-observed resonances from the first principles of lattice QCD calculations. With the Hamiltonian approach, one not only describes the spectra of lattice-QCD eigenstates through the eigenvalues of the finite-volume Hamiltonian matrix, but one also learns the composition of the lattice-QCD eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the composition of the states in terms of the meson-baryon basis states considered in formulating the effective field theory. One also learns the composition of the resonances observed in Nature. In this paper, we will focus on recent breakthroughs in our understanding of the structure of the $N^*(1535)$, $N^*(1440)$ and $Lambda^*(1405)$ resonances using this method.
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