W production at LHC: lepton angular distributions and reference frames for probing hard QCD

Precision tests of the Standard Model in the Strong and Electroweak sectors play a crucial role, among the physics program of LHC experiments. Because of the nature of proton–proton processes, observables based on the measurement of the direction and energy of final state leptons provide the most precise probes of such processes. In the present paper, we concentrate on the angular distribution of leptons from W → ℓ ν decays in the lepton-pair rest-frame. The vector nature of the intermediate state imposes that distributions are to a good precision described by spherical harmonics of at most second order. We argue, that contrary to general belief often expressed in the literature, the full set of angular coefficients can be measured experimentally, despite the presence of escaping detection neutrino in the final state. There is thus no principle difference with respect to the phenomenology of the Z / γ → ℓ + ℓ - Drell–Yan process. We show also, that with the proper choice of the reference frames, only one coefficient in this polynomial decomposition remains sizable, even in the presence of one or more high p T jets. The necessary stochastic choice of the frames relies on probabilities independent from any coupling constants. In this way, electroweak effects (dominated by the V - A nature of W couplings to fermions), can be better separated from the ones of strong interactions. The separation is convenient for the measurements interpretation.