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We report a measurement of the ratio of the top-antitop to Z/gamma*production cross sections in sqrt(s) = 1.96 TeV proton-antiproton collisionsusing data corresponding to an integrated luminosity of up to 4.6 fb-1,collected by the CDF II detector. The top-antitop cross section ratio ismeasured using two complementary methods, a b-jet tagging measurement and atopological approach. By multiplying the ratios by the well-known theoreticalZ/gamma*->ll cross section, the extracted top-antitop cross sections areeffectively insensitive to the uncertainty on luminosity. A best linearunbiased estimate is used to combine both measurements with the resultsigma_(top-antitop) = 7.70 +/- 0.52 pb, for a top-quark mass of 172.5 GeV/c^2.

First Measurement of the Ratio sigma_(t-tbar) / sigma_(Z/\gamma*->ll) and Precise Extraction of the t-tbar Cross Section