Doctor of Philosophy / Department of Physics / Tim Bolton / This thesis represents the first study of the helicity distributions of Z[gamma] di-boson production at hadron colliders. I use 5 fb⁻¹ of [radical]s = 7 TeV center of mass energy proton-proton collision data, collected by the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC), to look at the angular distribution of the Z[gamma] [right arrow] e⁺e⁻[gamma] / [mu]⁺ [mu]⁻ [gamma] process and measure the helicity amplitudes that govern it. This study provides sensitivity to the interference terms between different quantum states and through the interference terms to the possible new physics. The final state is comprised of leptons (muon-antimuon or electron-positron pairs) with transverse momentum over 20 GeV and a photon with transverse energy over 30 GeV. Helicty amplitudes are measured for the total angular momentum of the quark-antiquark system up to J[subscript]q[subscript bar]q = 2. Four-dimensional multivariate analysis of the 2011 CMS data shows no significant deviations from the standard model prediction for the measured amplitudes.