Using 980 $fb^-1$ of data collected with the Belle detector operating at the KEKB asymmetric-energy e^+e^- collider, we report a study of the electromagnetic decays of excited {charmed baryons} $Xi_c(2790)$ and $Xi_c(2815)$. A clear signal (8.6 standard deviations) is observed for $Xi_c(2815)^0 to Xi_c^0gamma$, and we measure: $B[Xi_c(2815)^0 to Xi_c^0gamma]/B[Xi_c(2815)^0 to Xi_c(2645)^+pi^- to Xi_c^0pi^+pi^-] = 0.41 pm 0.05 pm 0.03$. We also present evidence (3.8 standard deviations) for the similar decay of the $Xi_c(2790)^0$ and measure: $B[Xi_c(2790)^{0}toXi_c^{0}gamma]/B[Xi_c(2790)^0toXi_c^{prime +}pi^{-}toXi_c^{+}gamma pi^-] = 0.13 pm 0.03 pm 0.02$. The first quoted uncertainties are statistical and the second systematic. We find no hint of the analogous decays of the $Xi_c(2815)^+$ and $Xi_c(2790)^+$ baryons and set upper limits at the 90% confidence level of: $B[Xi_c(2815)^{+}toXi_c^{+}gamma]/B[Xi_c(2815)^+toXi_c(2645)^0pi^+toXi_c^+pi^-pi^+] < 0.09,$ and $B[Xi_c(2790)^{+}toXi_c^{+}gamma]/B[Xi_c(2790)^+toXi_c^{prime 0}pi^{+}toXi_c^{0}gamma pi^+] < 0.06.$ Approximate values of the partial widths of the decays are extracted, which can be used to discriminate between models of the underlying quark structure of these excited states.
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