W boson polarization in vector boson scattering at the LHC

Measuring the scattering of longitudinally-polarized vector bosons represents a fundamental test of the mechanism of Electroweak Symmetry Breaking. In addition to the challenges provided by low rates and large backgrounds, there are conceptual issues which need to be clarified for the definition of a suitable signal. Since vector bosons are unstable and can only be observed through their decay products, the polarization states interfere among themselves. Moreover, already at tree level, there are diagrams which cannot be interpreted as production times decay of EW bosons but are necessary for gauge invariance. We discuss a possible way to define a cross section for polarized W’s, dropping all non resonant diagram, and projecting on shell the resonant ones, thus, preserving gauge invariance. In most cases, the sum of polarized distributions reproduces accurately the exact results. In the absence of cuts, the polarization fractions obtained with this procedure agree with the results of a standard projection on Legendre polynomials. While the latter cannot be employed in the presence of selection cuts on the charged leptons, a comparison of the data with singly polarized templates allows the extraction of the polarization fractions in a realistic environment. For this work, the possibility of generating Vector Boson Scattering events with singly polarized W’s has been introduced into Phantom.