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Extracting sigma_effective from the CDF gamma+3jets measurement

In their 1997 paper, CDF measured sigma_effective, the normalization factor that relates the cross section for double parton scattering to the product of the inclusive cross sections of the two individual scatters, in a model in which they are assumed to be independent. In his 2007 paper, Treleani pointed out that CDF used a non-standard definition, in which the double parton scattering cross section corresponds to exactly two scatters, rather than the more conventional one in which it is the inclusive two-scatter cross section. He also estimated the correction from one definition to the other, to give a corrected value of sigma_effective. Treleani's form would be correct under the assumption that CDF were able to uniquely identify and count the number of scatters in an event, which is certainly not the case. In this publication we consider CDF's event definition in more detail to provide an improved correction.