**Dynamical chiral symmetry breaking by a magnetic field in an effective multi-quark Lagrangian**

**Abstract:**

Catalysis of dynamical symmetry breaking by a constant magnetic
field in (3+1) dimensions is considered. We use the three
flavour Nambu-Jona-Lasinio type model with 't Hooft and
eight-quark interaction terms (the latter are crucial for the stability of
the vacuum). It is shown that the multi-quark
interactions introduce new additional features to this phenomenon:
(a) the local minimum of the effective potential catalyzed by
the constant magnetic field is smoothed out with increasing
strength of the field at the characteristic scale *H* 10^{19}*G*, (b) the
multi-quark forces generate independently
another local minimum associated with a larger dynamical fermion mass.
This state may exist even for multi-quark interactions with a
subcritical set of couplings, and is globally stable with respect to a
further increase of the magnetic field.

Bibliography:

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2) A.A. Osipov, B. Hiller, A.H. Blin, J. da Providencia,
e-Print: hep-ph/0607066, Annals of Physics (N.Y.) (2007), in print.