Abstract
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.
Highlights
INTRODUCTIONAs the values of angular coefficients depend on the choice of a reference frame, an adequate comparison between observables measured in different coordinate systems (and between theory and experiment) may be performed for frame-independent quantities
The Drell-Yan-type processes in which a lepton pair is produced in hadronic collisions are the sensitive tests of Standard Model and probes of New Physics
As the values of angular coefficients depend on the choice of a reference frame, an adequate comparison between observables measured in different coordinate systems may be performed for frame-independent quantities
Summary
As the values of angular coefficients depend on the choice of a reference frame, an adequate comparison between observables measured in different coordinate systems (and between theory and experiment) may be performed for frame-independent quantities. Method is to express the hadronic tensor corresponding to the process, which happens to be the initial state density matrix, in terms of coefficients of final state dilepton angular distribution. This procedure was proposed and realized for a case of parity-conserving angular distribution in [10]. For the later we consider a geometric model [10,11] interpretation, which later allowed, by including the additional concept of noncoplanarity angle, to describe the violation of Lam-Tung relations and classify the rotational invariants [12,13,14] for Drell-Yan and quarkonium production in both collider and fixed-target experiments
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