Limits on Anomalous Trilinear Gauge Couplings in Zgamma Events from ppbar Collisions at sqrt{s} = 1.96 TeV

Using \Zg\ candidate events collected by the CDF detector at the Tevatron Colli\der, we search for potential anomalous (non-standard-model) couplings between t\he $Z$ boson and the photon. \Zg\ couplings vanish at tree level and are heavil\y suppressed at higher orders; hence any evidence of couplings indicates new ph\ysics. Measurements are performed using data corresponding to an integrated lum\inosity of 4.9 \invfb\ in the $Z\to \nu \bar{\nu }$ decay channel and 5.\1 \invfb\ in the \Zll\ ($l=\mu ,e$) decay channels. The combination of these me\asurements provides the most stringent limits to date on \Zg\ trilinear gauge c\ouplings. Using an energy scale of $\mathrm{\Lambda }=1.5$
TeV to allow for a direct c\omparison with previous measurements, we find limits on the CP-conserving param\eters that describe \Zg\ couplings to be $\mathrm{\mid }{h}_3^{\gamma ,Z}\mathrm{\mid }<0.022$ and |h_4^\{\gamma,Z}| < 0.0009. These results are consistent with standard model predict\ions.