Rotation-invariant observables as density matrix invariants

It is shown that general dilepton angular distribution (with parity violating terms taking into account) in vector particle decays can be described through a set of five SO(3) rotational-invariant observables. These observables are derived as invariants of the spacial part of the hadronic tensor (density matrix) expressed in terms of angular coefficients. The restrictions on the invariants following from the positivity of the hadronic tensor are obtained. Special cases of SO(2) rotations are considered. Calculation of invariants for available data on Z and J/{\psi} decays is performed.