We show that a new Regge trajectory with alpha(f1)(0) approximate to 1 and
a slope alpha'(f1)(0) approximate to 0 explains the features of hadron-hadr
on scattering and photoproduction of the rho and phi mesons at large energy
and momentum transfer. This trajectory with quantum numbers P = C = +1 and
an odd signature can be considered as a natural partner of the Pomeron whi
ch has an even signature. The odd signature of the new exchange leads to co
ntributions to the spin-dependent cross sections, which do not vanish at la
rge energy. The links between the anomalous properties of this trajectory,
the axial anomaly, and the flavor singlet axial vector f(1)(1285) meson are
discussed.