R. Briceno
University of Washington

Z. Davoudi
University of Washington

T. Luu
Lawrence Livermore

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Laura Lee
(206) 685-3509

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INT Workshop INT-13-53W

Nuclear Reactions from Lattice QCD
March 11-12, 2013

Talks and Abstracts

Petr Navratil - "Ab initio many-body calculations of nuclear scattering and reactions"

The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of nuclear forces with two-nucleon, three-nucleon and possibly even four-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. I will present new ab initio many-body approaches capable of describing both bound and scattering states in light nuclei simultaneously. I will discuss results for nucleon scattering on 4He, for resonances of exotic nuclei, e.g., 6,7He, for reactions important for astrophysics, such as 7Be(p,gamma)8B radiative capture, and for 3H(d,n)4He fusion.

Zohreh Davoudi - "Three-particle scattering amplitudes from a finite volume formalism"

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"

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"

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"

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"

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.