Fate of Multiparticle Resonances: From $Q$-Balls to $^3$He Droplets

TL;DR

This paper analyzes the decay properties of near-threshold multiparticle resonances, deriving decay width scaling laws, and explores the statistical distributions of decay products, with implications for metastable helium droplets.

Contribution

It introduces a universal decay width formula for multiparticle resonances near threshold and examines the statistical behavior of decay products for large particle numbers.

Findings

Decay width scales as E^{Δ-5/2} near threshold.

Bosonic decay products follow Maxwell-Boltzmann distribution.

Fermionic decay products follow a semicircle-like distribution.

Abstract

We consider a system of $N$ nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles can form a bound state, the resonance can only decay through an "explosion" into $N$ particles. We show that the decay width of the resonance scales as $E^{\Delta-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $\Delta$ is the ground state energy of a system of $N$ particles in a spherical harmonic trap with unit frequency. The formula remains valid when some pairs of final particles have zero-energy $s$-wave resonance, but the Efimov effect is not present. In the limit of large $N$, we show that the final particles follow a Maxwell-Boltzmann distribution if they are bosons, and a semicircle-like law if they are fermions. We argue that metastable $^3$He droplets exist with the lifetime varying over many orders of magnitudes ranging from a fraction of a nanosecond to values greatly exceeding the age of the Universe.