We have systematically studied the strong and radiative decays of the low-lying $1P$-wave doubly charmed baryons. Some interesting observations are: (i) The states $\Xi_{cc}^*$ and $\Omega_{cc}^*$ with $J^P=3/2^+$ have a fairly large decay rate into the $\Xi_{cc}\gamma$ and $\Omega_{cc}\gamma$ channels with a width $\sim 15$ and $\sim7$ keV, respectively. (ii) The lowest lying excited doubly charmed baryons are dominated by the $1P$ $\rho$ mode excitations, which should be quite narrow states. They decay into the ground state with $J^P=1/2^+$ through the radiative transitions with a significant ratio. (iii) The total decay widths of the first orbital excitations of $\lambda$ mode ($1P_{\lambda}$ states with $J^P=1/2^-$, $3/2^-$, $5/2^-$) are about $\Gamma\sim100$ MeV, and the ratio between the radiative and hadronic decay widths is about $\mathcal{O}(10^{-3})$.Comment: 10 pages, 7 figure

Inspired by the newly observed Ξ 0 c states by the LHCb Collaboration, we investigate the OKubo-Zweig-Iizuka-allowed two-body strong decays of the λ-mode 1P wave Ξ 0 c states within the chiral quark model. Our results indicate that: (i) The newly observed states Ξ c ð2923Þ 0 and Ξ c ð2939Þ 0 are good candidates of the λmode 1P wave Ξ 0 c states with the spin-parity J P ¼ 3=2 − , namely j 4 P λ 3=2 − i and j 2 P λ 3=2 − i, respectively. (ii) The other newly observed state Ξ c ð2965Þ 0 mostly corresponds to the λ-mode 1P-wave Ξ 0 c state with the spin-parity J P ¼ 5=2 − , namely j 4 P λ 5=2 − i. (iii) For the two λ-mode J P ¼ 1=2 − mixed states, the jP λ 1=2 − i 1 is a narrow state with a width of Γ ∼ 15 MeV and mainly decays into Ξ 0 c π, while the jP λ 1=2 − i 2 state has a width of Γ ∼ 52 MeV and dominantly decays into Ξ c π and Λ c K channels. If the broad structure around 2880 MeVobserved at LHCb arises from the new Ξ 0 c state, this state is very likely to be the jP λ 1=2 − i 2 state.