Abstract
We discuss how the angular distribution of lepton pairs from decays of vector mesons depends on the choice of reference frame, and provide a geometrical description of the transformations of the coefficients of the angular distribution. Invariant expressions involving all coefficients are discussed, together with bounds and consistency relations.
Highlights
The study of the angular distribution of lepton pairs in hadron collisions allowed the test of the Drell-Yan model [1, 2] and of its corrections in perturbative QCD [3], and verified the electro-weak couplings of W and Z bosons
Frame–independent characteristics of the angular distribution are those linked to properties of the ellipses, and not depending on the position of the point as it moves along the loops when the reference frame is rotated about the y–axis
7 Conclusions Understanding the implications of the choice of reference frame is relevant for the study of of qq resonances decaying to lepton pairs, and we have provided a geometrical interpretation of the transformations of the coefficients of the angular distribution
Summary
The study of the angular distribution of lepton pairs in hadron collisions allowed the test of the Drell-Yan model [1, 2] and of its corrections in perturbative QCD [3], and verified the electro-weak couplings of W and Z bosons. Recent studies [11, 12] have discussed the relevance of taking directly into account properties related to the description of the process in different frames, and have specified rotation-invariant quantities that provide information on intrinsic, frame independent properties of the polarization of the qq state. We provide a geometrical description of the transformation of the different terms of the angular distribution, and specify new invariant quantities that relate all the components. Equation (1) makes the assumption of parity conservation and symmetry for reflection on the production plane, and its validity covers both the case of elementary processes, where the coefficients λθ, λφ and λθφ are directly related to the helicity amplitudes of the vector meson, or the case of different, uncorrelated processes contributing to the angular distribution. 1) The limit on λφ could have been obtained from (2) and requiring that |λ′θ| ≤1 for any angle δ [12]
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