ElectroWeak precision data: the minimal set of parameters

Abstract

We show how precision electroweak data, assuming CP conservation and flavor universality, despite being sensitive to 20 dimension 6 operators, constrain severely only 9 combinations of them. We define a set of 7 oblique parameters $\hat S, \hat T, \hat U, V, X,W,Y$ which fully describe corrections to the leptonic observables. We add two additional parameters $\delta \epsilon_q, \delta C_q$ to take into account the most precise hadronic observables. Another parameter $\delta \epsilon_b$ is considered for the bottom quark if flavor universality is not assumed for the third generation of quarks. We show that the approximation is extremely satisfactory testing it on a set of random new physics models and on some famous $Z'$ gauge bosons.