Zohreh Davoudi

Moving multichannel systems in a finite volume with application to proton-proton fusion

The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present the result for three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the non-relativistic case, we pay close attention to processes that mix the 1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e), and show how to determine the transition amplitude of such processes directly from lattice QCD.

Three-particle scattering amplitudes from a finite volume formalism

We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume scattering amplitudes. The quantization condition presented is an integral equation that in general must be solved numerically. However, for systems with an attractive two-body force that supports a two-body bound-state, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the well-known 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 boson-diboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no two-body bound-state (with only scattering states and resonances) the Luscher formula gets power-law volume corrections and consequently fails to describe the three-particle system. These corrections are nonperturbatively included in the quantization condition presented.

Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD

Volume modications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modications

Restoration of rotational symmetry in the continuum limit of lattice field theories

We explore how rotational invariance is systematically recovered from calculations on hyper-cubic lattices through the use of smeared lattice operators that smoothly evolve into continuum operators with definite angular momentum as the lattice-spacing is reduced. Perturbative calculations of the angular momentum violation associated with such operators at tree level and at one loop are presented in

Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions

\ensuremath{\lambda}{\ensuremath{\phi}}^{4}

Finite-Volume Electromagnetic Corrections to the Masses of Mesons, Baryons and Nuclei

theory and QCD. Contributions from these operators that violate rotational invariance occur at tree-level, with coefficients that are suppressed by

Constraints on the Universe as a Numerical Simulation

\mathcal{O}({a}^{2})

Two-nucleon systems in a finite volume. II. S13-D13 coupled channels and the deuteron

in the continuum limit. Quantum loops do not modify this behavior in

Nuclear reactions from lattice QCD

\ensuremath{\lambda}{\ensuremath{\phi}}^{4}

Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double-β Decay Phenomenology

, nor in QCD if the gauge-fields are smeared over a comparable spatial region. Consequently, the use of this type of operator should, in principle, allow for Lattice QCD calculations of the higher moments of the hadron structure functions.