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We use a new method to estimate with 5% accuracy the contribution of pion andkaon in-flight-decays to the dimuon data set acquired with the CDF detector.Based on this improved estimate, we show that the total number and theproperties of the collected dimuon events are not yet accounted for by ordinarysources of dimuons which also include the contributions, as measured in thedata, of heavy flavor, $\Upsilon$, and Drell-Yan production in addition tomuons mimicked by hadronic punchthrough.

Improved determination of the sample composition of dimuon events produced in {\boldmath $p\bar{p}$} collisions at {\boldmath $\sqrt{s}=1.96$} TeV