Relativistic $N$-particle energy shift in finite volume

Understand

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.