First Measurement of the Ratio sigma_tt-bar/sigma_Z/gamma* --> ell ell and Precise Extraction of the tt-bar Cross Section

We report a measurement of the ratio of the tt-bar to Z/gamma* production cross section in s**(1/2) 1.96 TeV p anti-p collisions using data corresponding to an integrated luminosity of up to 4.6 fb-1, collected by the CDF II detector. The tt-bar cross section ratio is measured using two complementary methods, a b-jet tagging measurement and a topological approach. By multiplying the ratios by the well-known theoretical Z/gamma* -> ell ell cross section predicted by the standard model, the extracted tt-bar cross sections are effectively insensitive to the uncertainty on luminosity. A best linear unbiased estimate is used to combine both measurements with the result sigma_tt-bar 7.70 +/- 0.52 pb, for a top-quark mass of 172.5 GeV/c2.