Stability of neutral Fermi balls with multiflavor fermions

Abstract

A Fermi ball is a kind of nontopological soliton which is thought to arise from the spontaneous breaking of an approximate ${Z}_{2}$ symmetry and to contribute to cold dark matter. We consider a simple model in which fermion fields with multiflavors are coupled to a scalar field through Yukawa coupling and examine how the number of the fermion flavors affects the stability of the Fermi ball against the fragmentation. (1) We find that the Fermi ball is stable against fragmentation in most cases even in the lowest-order thin-wall approximation. (2) We then find that in the other specific cases the stability is marginal in the lowest-order thin-wall approximation, and the next-to-leading order correction determines the stable region of the coupling constants; we examine the simplest case where the total fermion number ${N}_{i}$ and the Yukawa coupling constant ${G}_{i}$ of each flavor i are common to the flavors, and find that the Fermi ball is stable in a limited region of the parameters and has the broader region for the larger number of flavors.