The top quark pair production and decay into leptons with at least one being a tau lepton is studied in the framework of the CDF experiment at the Tevatron proton antiproton collider at Fermilab (USA). The selection requires an electron or a muon produced either by the tau lepton decay or by a W decay. The analysis uses the complete Run II data set i.e. 9.0 fb-1, selected by one trigger based on a low transverse momentum electron or muon plus one isolated charged track. The top quark pair production cross section at 1.96 TeV is measured at 8.2+-1.7(+1.2-1.1)+-0.5 pb, and the top branching ratio into tau lepton is measured at 0.120+-0.027(+0.022-0.019)+-0.007 with statistical, systematics and luminosity uncertainties. These are up to date the most accurate results in this top decay channel and are in good agreement with the results obtained using other decay channels of the top at the Tevatron. The branching ratio is also measured separating the single tau lepton from the two tau leptons events with a log likelihood method. This is the first time these two signatures are separately identified. With a fit to data along the log-likelihood variable an alternative measurement of the branching ratio is made: 0.098+-0.022(stat.)+-0.014(syst.); it is in good agreement with the expectations of the Standard Model (with lepton universality) within the experimental uncertainties. The branching ratio is constrained to be less than 0.159 at 95% confidence level. This limit translates into a limit of a top branching ratio into a potential charged Higgs boson.
