Untwisting twisted NJL$_2$-kinks by a bare fermion mass

TL;DR

This paper revises the understanding of twisted kinks in the NJL$_2$ model by analyzing the effects of a bare fermion mass, revealing that fermion number is distributed over space and proposing a composite picture of the kink.

Contribution

It introduces a new interpretation of twisted kinks in the NJL$_2$ model with finite fermion mass, resolving the missing baryon puzzle and clarifying fermion number distribution.

Findings

Fermion number is spread out due to the massless pion field.

Twisted kinks can be viewed as composites of a fermion-number-carrying winding and an energy-carrying kink.

The interpretation of twisted kinks must be revised in the presence of a bare fermion mass.

Abstract

Twisted kinks in the massless NJL$_2$ model interpolate between two distinct vacua on the chiral circle. If one approaches the chiral limit from finite bare fermion masses $m_0$, the vacuum is unique and twist cannot exist. This issue is studied analytically in the non-relativistic limit, using a no-sea effective theory. We conclude that even in the massless limit, the interpretation of the twisted kink has to be revised. One has to attribute the fermion number of the valence state to the twisted kink. Fermion density is spread out over the whole space due to the massless pion field. The result can be pictured as a composite of a twisted kink (carrying energy, but no fermion number) and a partial winding of the chiral spiral (carrying fermion number, but no energy). This solves at the same time the puzzle of missing baryons with fermion number $N_f<N$ in the massless NJL$_2$ model.