  We propose a generalization of the upgraded Karl- Sehgal formula which
relates baryon magnetic moments to the spin structure of constituent quarks, by
adding anomalous magnetic moments of quarks. We first argue that relativistic
nature of quarks inside baryons requires introduction of two kinds of
magnetisms, one axial and the other tensoriel. The first one is associated with
integrated quark helicity distributions (standard) and the second with
integrated transversity distributions . The weight of each contribution is
controlled by the combination of two parameters, xi the ratio of the quark mass
to the average kinetic energy Ei and ai the quark anomalous magnetic moment.
The quark anomalous magnetic moment is correlated to transversity and both are
necessary ingredients in describing relativistic quarks. The proposed formula,
then when confronted with baryon magnetic moments data with reasonable inputs,
yields beside quark magnetic densities, anomalous magnetic moments enough large
to not be ignored.
