We report on a measurement of the fraction of events with a W or Z boson which are produced diffractively in (p) over barp collisions at root s = 1.96 TeV, using data from 0.6 fb-1 of integrated luminosity collected with the CDF II detector equipped with a Roman- pot spectrometer that detects the (p) over bar from (p) over bar + p -> (p) over bar + [X + W/Z]. We find that (1.00 +/- 0.11)% of Ws and (0.88 +/- 0.22)% of Zs are produced diffractively in a region of antiproton or proton fractional momentum loss xi of 0.03 < xi < 0.10 and 4-momentum transferred squared t of -1 < t < 0 (GeV/c)(2), where we account for the events in which the proton scatters diffractively while the antiproton dissociates, (p) over bar + p -> [X + W/Z] + p, by doubling the measured proton dissociation fraction. We also report on searches for W and Z production in double Pomeron exchange, (p) over bar + p -> [X + W/Z] + p, and on exclusive Z production, (p) over bar + p -> (p) over bar + Z + p. No signal is seen above background for these processes, and comparisons are made with expectations.
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