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A direct measurement of the total decay width of the W boson G_W is presented using 350 pb-1 of data from ppbar collisions at sqrt(s) = 1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. The width is determined by normalizing predicted signal and background distributions to 230185 W candidates decaying to enu and munu in the transverse-mass region 50 < M_T < 90 GeV and then fitting the predicted shape to 6055 events in the high-M_T region, 90 < M_T < 200 GeV. The result is G_W = 2032 +/- 45 (stat.) +/- 57 (syst.) MeV, consistent with the standard model expectation.

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