On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD
Abstract
One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear processes which would impact our understanding of environments ranging from big bang nucleosynthesis, stars and supernovae, to nuclear reactors and highenergy density facilities. Such calculations, being truly abinitio, would include all twonucleon and threenucleon (and higher) interactions in a consistent manner. Currently, lattice QCD (LQCD) provides the only reliable option for performing calculations of lowenergy hadronic observables. LQCD calculations are necessarily performed in a finite Euclidean spacetime. As a result, it is necessary to construct formalism that maps the finitevolume observables determined via LQCD to the infinitevolume quantities of interest. For 2 → 2 bosonic elastic scattering processes, Martin Luscher first showed that one can obtain the physical scattering phase shifts from the finite volume (FV) twoparticle spectrum (for lattices with spatial extents that are much larger than the range of interactions). This thesis discusses the extension of this formalism for three important classes of systems. Chapter 1 discusses key aspects of the standard model, paying close attention to QCD at lowenergies and the necessity of effective field theories (EFTs) and LQCD. Chapter 2 reviews the result by Luscher for two bosons with arbitrary momentum. After a detailed derivation of the quantization condition for two bosons below the inelastic threshold, it is straightforward to determine the spectrum of a system with arbitrary number of channels composed of two hadrons with nonzero total momentum. In Section 2.3, Luscher's result is rederived using the auxilary field formalism, also known as the "dimer formalism". Chapter 3 briefly reviews the complexity of the nuclear sector, as compared to the scalar sector, and it shown that this rich structure can be recovered by the generalization of the auxilary field formalism for the two nucleon system. Using this formalism, the quantization condition for two nonrelativistic nucleons1 in a finite volume is derived. The result presented hold for a two nucleon system with arbitrary partialwaves, spin and parity. Provided are the explicit relations among scattering parameters and their corresponding point group symmetry class eigenenergies with orbital angular momentum l < 4. Finally, Chapter 4 presents the quantization condition for the spectrum of three identical bosons in a finite volume. Unlike the twobody analogue, the quantization condition of the threebody sector is not algebraic and in general requires numerically solving an integral equation. However, for systems with an attractive twobody force that supports a twobody boundstate, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the wellknown Luscher formula with exponential corrections in volume that scale with the diboson binding momentum. To accurately determine infinite volume phase shifts, it is necessary to extrapolate the phase shifts obtained from the Luscher formula for the bosondiboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no twobody boundstate (with only scattering states and resonances) the Luscher formula gets powerlaw volume corrections and consequently fails to describe the threeparticle system. These corrections are nonperturbatively included in the quantization condition presented.
 Publication:

Ph.D. Thesis
 Pub Date:
 2013
 DOI:
 10.48550/arXiv.1311.6032
 arXiv:
 arXiv:1311.6032
 Bibcode:
 2013PhDT.......271B
 Keywords:

 Physics, Radiation;Physics, Elementary Particles and High Energy;
 High Energy Physics  Lattice
 EPrint:
 Ph.D. Thesis, 147 pages, 21 figures