Organizers:R. Briceno University of Washington briceno@u.washington.edu
Z. Davoudi
T. Luu
Talks and Abstracts Application form |
Nuclear Reactions from Lattice QCDMarch 11-12, 2013 Talks and Abstracts
Petr Navratil - "Ab initio many-body calculations of nuclear scattering and reactions" Zohreh Davoudi - "Three-particle scattering amplitudes from a finite volume formalism" ABSTRACT: As a first step toward determining nuclear reaction cross sections from the underlying theory of QCD, the finite volume two-body Luscher technology needs to be extended to the three-body sector. In particular, the elements of the physical S-matrix for three-nucleon processes needs to be related to the spectral information of the three-nucleon systems obtained from lattice QCD calculations in a finite Euclidean space-time. In this talk, I will report on a recent development in this direction and discuss the hopes and the challenges ahead. Based on this finite volume three-body formalism, I will also show how a two-body Luscher formula for bound-state particle scattering below the bound-state breakup is recovered up to exponential corrections in the size of the bound-state wavefunction. This result would lead to a reliable determination of nucleon-deuteron scattering phase shifts from lattice QCD. Maxwell Hansen - "Towards a relativistic, model-independent relation between the finite-volume spectrum and three-particle scattering amplitudes" ABSTRACT: We present progress in generalizing Luescher's relation between the finite-volume spectrum and the \(S\)-matrix, to energies above the inelastic threshold. Specifically we consider a scalar field theory, which has a G-parity like-symmetry that prevents even-odd coupling and has no bound states, but is otherwise arbitrary. Assuming center of mass energies between three and five particle masses, we sum all finite-volume Feynman diagrams to derive a relation between the finite-volume spectrum and the scattering amplitudes of the infinite-volume theory. Both two-to-two and three-to-three amplitudes enter the final result. We conclude by showing how the low momentum limit of our result reproduces the known finite-volume expansion of the three-particle threshold energy through \(\mathcal O(L^-6)\). Dean Lee - "Progress towards nuclear scattering and reactions in lattice effective field theory" ABSTRACT: I review current progress in lattice effective field theory for nuclear scattering and reactions. For elastic scattering I discuss the use of Luescher's finite volume method for the scattering of nuclei. In particular I explain the origin of topological phases in finite volume corrections to the nuclear binding energies. For nuclear reactions, I discuss recent progress in the construction of cluster wavefunctions for lattice simulations. I then show how these are used to construct multi-channel adiabatic Hamiltonians for reaction calculations. Sinya Aoki - "Extensions of the HAL QCD approach to inelastic and multi-paricle scatterings in lattice QCD" ABSTRACT: After a brief introduction of the HAL QCD (Hadron to Atomic-nuclei from Lattice QCD) approach to baryon-baryon interactions in lattice QCD, I discuss extensions of this method. I first consider a construction of energy-independent but non-local potentials above inelastic thresholds, in terms of the Nambu-Bethe-Salpeter (NBS) wave functions defined in QCD. As an explicit example, I consider NN → NN + π scattering processes. In the second part, I derive asymptotic behavior of the NBS wave function at large separations for systems with more than 2 particles in quantum field theories. I give an explicit relation between the asymptotic behavior and the on-shell S-matrix, which justifies the calculation of three nuclear potentials in QCD. I also give two numerical results in lattice QCD, three nuclear forces and a two-body inelastic scattering of Λ Λ → ΛΛ, N Ξ, ΣΣ.Raul Briceno - "Nuclear Physics in a Box" ABSTRACT: I review issues regarding three-body partial wave mixing in a finite volume, which led us to generalize the "dimer formalism" for arbitrary partial waves in the two-body scalar and nuclear sectors. I will present this formalism and briefly derive the quantization condition for two nucleons in a finite volume with periodic boundary conditions. The result holds for arbitrary momenta below the two-pion production threshold. I will pay close attention to the positive parity sector and consider the implication of the quantization condition for the four smallest boosts. |