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arXiv · 2010.11715

Relativistic $N$-particle energy shift in finite volume

Fernando Romero-López·Akaki Rusetsky·Nikolas Schlage·Carsten Urbach
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Abstract

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 $\varphi^4$ theory.

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Fernando Romero-López, Akaki Rusetsky, Nikolas Schlage, Carsten Urbach. 2020-10-22. Relativistic $N$-particle energy shift in finite volume. https://doi.org/10.1007/jhep02(2021)060

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