Among the physics goals of LHC experiments, precision tests of the Standard Model in the Strong and Electroweak sectors play an important role. Because of nature of the proton-proton processes, observables based on the measurement of the direction and energy of leptons provide the most precise signatures. In the present paper, we concentrate on the angular distribution of Drell-Yan process leptons, in the lepton-pair rest-frame. The vector nature of the intermediate state imposes that distributions are to a good precision described by spherical polynomials of at most second order. We show that with the proper choice of the coordinate frames, only one coefficient in this polynomial decomposition remains sizable, even in the presence of one or two high $p_T$ jets. The necessary stochastic choice of the frames relies on probabilities independent from any coupling constants. This remains true when one or two partons accompany the lepton pairs. In this way electroweak effects can be better separated from strong interaction ones for the benefit of the interpretation of the measurements. Our study exploits properties of single gluon emission matrix elements which are clearly visible if a conveniently chosen form of their representation is used. We rely also on distributions obtained from matrix element based Monte Carlo generated samples of events with two leptons and up to two additional partons in test samples. Incoming colliding protons partons are distributed accordingly to PDFs and are strictly collinear to the corresponding beams.
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