Lattice Effective Field Theory Calculations for A = 3, 4, 6, 12 Nuclei

Institut für Kernphysik (IKP-3) and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany.
Physical Review Letters (Impact Factor: 7.73). 04/2010; 104(14):142501. DOI: 10.1103/PhysRevLett.104.142501
Source: PubMed

ABSTRACT We present lattice results for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our analysis includes isospin breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.

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    ABSTRACT: Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The result of a lattice QCD calculation corresponds to that of nature only in the limit when the volume of spacetime is taken to infinity and the spacing between discretized points on the lattice is taken to zero. A better understanding of these discretization and volume effects not only provides the connection to the infinite-volume continuum observables, but also leads to optimized calculations that can be performed with available computational resources. This thesis includes various formal developments in this direction, along with proposals for improvements, to be applied to the upcoming lattice QCD studies of nuclear and hadronic systems. Among these developments are i) an analytical investigation of the recovery of rotational symmetry with the use of suitably-formed smeared operators toward the continuum limit, ii) an extension of the Luscher finite-volume method to two-nucleon systems with arbitrary angular momentum, spin, parity and center of mass momentum, iii) the application of such formalism in extracting the scattering parameters of the 3S1-3D1 coupled channels, iv) an investigation of twisted boundary conditions in the single- and two-hadron sectors, with proposals for improving the volume-dependence of the deuteron binding energy upon proper choices of boundary conditions, and v) exploring the volume dependence of the masses of hadrons and light-nuclei due to quantum electrodynamic interactions, including the effects arising from particles' compositeness. The required background as well as a brief status report of the field pertinent to the discussions in this thesis are presented.
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    ABSTRACT: Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. We now introduce the technique of "symmetry-sign extrapolation" which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to control the sign oscillations without introducing unknown systematic errors. We benchmark this method by calculating the ground-state energies of the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter.
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    ABSTRACT: In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave mixing. Specifically we analyze the system of the low-energy interactions between protons and neutrons. We also analyze low-energy scattering for systems with arbitrary short-range interactions plus an attractive $1/r^{\alpha}$ tail for $\alpha\geq2$. In particular, we focus on the case of $\alpha=6$ and we derive the constraints of causality and unitarity also for these systems and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive $1/r^{6}$ tail. We argue that a similar universality class exists for any attractive potential $1/r^{\alpha}$ for $\alpha\geq2$. In the second part of the thesis we present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use L\"uscher's finite-volume relations to determine the $s$-wave, $p$-wave, and $d$-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.

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