Few-Body Bound States and Resonances in Finite Volume
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Sebastian König
Few-Body Bound States and Resonances in Finite Volume
Received: 5 March 2020 / Accepted: 4 May 2020 © The Author(s) 2020
Abstract Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with more constituents. This work is relevant not only for nuclear physics, where lattice methods are now able to calculate few- and manynucleon states, but also for other fields such as simulations of cold atoms. This article discusses recent progress regarding the extraction of few-body bound-state and resonance properties from finite-volume calculations of systems with an arbitrary number of constituents.
1 Introduction It is well known from the pioneering work of Lüscher [1–3] that simulating physical systems in a finite volume can be used as a tool to extract physical properties. The bound-state relation connects the finitevolume correction of binding energies to the asymptotic properties of the two-particle wavefunction, whereas for elastic scattering physical scattering parameters are encoded in the volume dependence of discrete energy levels. Resonances, i.e., short-lived, unstable states, are manifest in this discrete spectrum as avoided crossing of energy levels as the size of the volume is varied [4–6]. All this work is based on the fact that the physical S-matrix governs the volume dependence of energy levels and is widely used in Lattice QCD (LQCD). It has been extended in several directions, including non-zero angular momenta [7–9], moving frames [6,10–13], generalized boundary conditions [14–18], particles with intrinsic spin [19], and perturbative Coulomb corrections [20]. To date, most results have been obtained for two-body systems. As numerical techniques, such as LQCD and in particular lattice effective field theory (LEFT) [21–23], progress to calculate states with an increasing number of constituents, understanding the volume dependence of more complex systems is of great relevance. This is particularly true for the study of few-body resonances in light of recent efforts to observe [24] and calculate [25–33] few-neutron resonances in nuclear physics. This contribution has been presented during the ceremony of the Few-Body Systems Award for young professionals. S. König (B) Department of Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany E-mail: [email protected] S. König ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany S. König Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
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S. König
Early studies of the triton and Efimov trimers in finite volume [34–37] derived explicit results for these bound systems. Gene
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