Evidence for t(t)over-bar gamma production and measurement of sigma(t(t)over-bar gamma)/sigma(t(t)over-bar)

Using data corresponding to 6.0 fb(-1) of p (p) over bar collisions at root s = 1.96 TeV collected by the CDF II detector, we present a cross section measurement of top-quark pair production with an additional radiated photon in the central region with 10 GeV or more of transverse energy t (t) over bar gamma. The events are selected by looking for a lepton (l or mu), a photon (gamma), significant transverse momentum imbalance (is not an element of(T)), large total transverse energy, and three or more jets, with at least one identified as containing a b quark (b). Using an event selection optimized for the t (t) over bar gamma candidate sample, we also measure the cross section of t (t) over bar (sigma(t (t) over bar)). We measure the t (t) over bar gamma cross section (sigma(t (t) over bar gamma)) to be 0.18 +/- 0.08 pb, and the ratio of sigma(t (t) over bar gamma) to sigma(t (t) over bar) to be 0.024 +/- 0.009. We observe a probability of 0.0015 (3.0 standard deviations) of the background (non-t (t) over bar gamma events alone producing 30 events or more.