A new mass relation among the hadron vector resonances

We show that the hadron vector resonances are described by fields transforming according to different inequivalent representations of the Lorentz group: (1/2, 1/2) and (1, 0) + (0, 1). The vector representation (1/2, 1/2) is well studied and corresponds to the gauge fields. On the other hand, the chiral representations (1, 0) and (0, 1) are described by the second rank antisymmetric tensor fields, for which interaction theory has not yet been constructed. In the framework of the phenomenological Nambu– Jona-Lasinio approach we have introduced and used all these fields for a description of the vector resonances. A new mass relation between low-lying hadron vector and axial-vector resonances is obtained. This relation is in agreement with the present experimental data.