Relativistic N-particle energy shift in finite volume
Fernando Romero-López, Akaki Rusetsky, Nikolas Schlage, Carsten Urbach
Abstract
A bstract We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/ L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L − 6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N -particle ground state energy shift in the complex φ 4 theory.