On the analytic properties of chiral solitons in the presence of the ωmeson
Abstract
A thorough study is performed of the analytical properties of the fermion determinant for the case that the time components of (axial) vector fields do not vanish. For this purpose the nonhermitian euclidean Dirac hamiltonian is generalized to the whole complex plane. The Laurent series are proven to reduce to Taylor series for the corresponding eigenvalues and functions as long as field configurations are assumed for which level crossings do not occur. The condition that no level crossings appears determines the radius convergence. However, the need for regularization prohibits the derivation of an analytic energy functional because real and imaginary parts of the eigenvalues are treated differently. Consistency conditions for a Minkowski energy functional are extracted from global gauge invariance and the current field identity for the baryon current. Various treatments of the NambuJonaLasinio soliton are examined with respect to these conditions. Motivated by the studies of the Laurent series for the energy functional the euclidean action is expanded in terms of the ωfield. It is argued that the regularization scheme has to be imposed on the operator level rather than on an expression in terms of the oneparticle eigenenergies. The latter treatment is plagued by the inexact assumption that the euclidean Dirac hamiltonian and its hermitian conjugate can be diagonalized simultaneously. It is then evident that approaches relying on counting powers of the ωfield in the oneparticle eigenenergies are inappropriate. Expanding the action up to second order and employing a parametrical description of the soliton profiles the repulsive character of the ω meson is confirmed. In the presence of the ω meson the soliton mass is enhanced by a few hundred MeV.
 Publication:

Nuclear Physics A
 Pub Date:
 February 1995
 DOI:
 10.1016/03759474(94)00625W
 arXiv:
 arXiv:hepph/9407304
 Bibcode:
 1995NuPhA.585..513W
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 UNITUTHEP13/1994, 34 LaTeX pages, 5 figures appended as postscript file