Untwisting twisted NJL2 kinks by a bare fermion mass

Twisted kinks in the massless NJL2 model interpolate between two distinct vacua on the chiral circle. If one approaches the chiral limit from finite bare fermion masses m0, the vacuum is unique and twist cannot exist. This issue is studied analytically in the nonrelativistic 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 Nf