Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Abstract

We derive analytic expansions for the finite-volume energies of weakly-interacting twoparticle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of weakly-interacting systems on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear.

Three-particle scattering amplitudes from lattice QCD

“…Similar expansions have been calculated in the literature for more complicated cases. These include higher orders in 1/L, multi-particle states, the isospin-1 three-pion system, as well as excited states and non-identical particles [1,17,43,44,46,[76][77][78].…”

“…The central idea of this formalism is to connect the energy levels extracted from Euclidean correlation functions to infinitevolume scattering quantities. Subsequent theoretical developments [6][7][8][9][10][11][12][13][14][15][16][17] achieved a general two-particle formalism that can treat arbitrarily complex two-body systems below the particle production threshold.…”