The strong and radiative decays of the low-lying $S$- and $P$-wave ${\mathrm{\Lambda }}_{c(b)}$, ${\mathrm{\Sigma }}_{c(b)}$, ${\mathrm{\Xi }}_{c(b)}$, ${{\mathrm{\Xi }}_{c(b)}}^{\prime }$, and ${\mathrm{\Omega }}_{c(b)}$ baryons are systematically studied in a constituent quark model. We find that the radiative decay mode ${\mathrm{\Lambda }}_b^0\gamma$ could be very useful for us to establish the missing neutral states ${\mathrm{\Sigma }}_b^0$ and ${\mathrm{\Sigma }}_b^{*0}$. Our calculation shows that most of those missing $\lambda$-mode $P$-wave singly heavy baryons have a relatively narrow decay width of less than 30 MeV. Their dominant strong and radiative decay channels can be ideal for searching for their signals in future experiments. The ${\mathrm{\Sigma }}_c(2800)$ resonance may be assigned to $|{\mathrm{\Sigma }}_c{{}^{2}P}_{\lambda }{\frac{3}{2}}^{-}⟩$ with $J^P=3/2^{-}$ or $|{\mathrm{\Sigma }}_c{{}^{4}P}_{\lambda }{\frac{5}{2}}^{-}⟩$ with $J^P=5/2^{-}$. In general, the excitations of $|{{}^{2}P}_{\lambda }{\frac{3}{2}}^{-}⟩$ and $|{{}^{4}P}_{\lambda }{\frac{5}{2}}^{-}⟩$ of the ${\mathbf{6}}_F$ multiplet have similar strong decay properties. In order to identify them, angular distributions of their decays in either strong decay modes or radiative transitions should be needed.

The charmonium spectrum is calculated with two nonrelativistic quark models, the linear potential model, and the screened potential model. Using the obtained wave functions, we evaluate the electromagnetic transitions of charmonium states up to $4S$ multiplet. The higher multipole contributions are included by a multipole expansion of the electromagnetic interactions. Our results are in reasonable agreement with the measurements. As conventional charmonium states, the radiative decay properties of the newly observed charmoniumlike states, such as $X(3823)$, $X(3872)$, and $X(4140/4274)$, are discussed. The $X(3823)$ as ${\psi }_2(1D)$, its radiative decay properties well agree with the observations. From the radiative decay properties of $X(3872)$, one cannot exclude it as a ${\chi }_{c1}(2P)$ dominant state. We also give discussions of possibly observing the missing charmonium states in radiative transitions, which might provide some useful references to look for them in forthcoming experiments. The higher multipole contributions to the electromagnetic transitions are analyzed as well. It is found that the higher contribution from the magnetic part could give notable corrections to some E1 dominant processes by interfering with the E1 amplitudes. Our predictions for the normalized magnetic quadrupole amplitudes $M_2$ of the ${\chi }_{c1,2}(1P)\to J/\psi \gamma$ processes are in good agreement with the recent CLEO measurements.

In this work, we study the mass spectra of the all-heavy tetraquark systems, i.e., $cc\overline{c}\overline{c}$, $bb\overline{b}\overline{b}$, $bb\overline{c}\overline{c}/cc\overline{b}\overline{b}$, $bc\overline{c}\overline{c}/cc\overline{b}\overline{c}$, $bc\overline{b}\overline{b}/bb\overline{b}\overline{c}$, and $bc\overline{b}\overline{c}$, within a potential model by including the linear confining potential, Coulomb potential, and spin-spin interactions. It shows that the linear confining potential has important contributions to the masses and is crucial for our understanding of the mass spectra of the all-heavy tetraquark systems. For the all-heavy tetraquarks $Q_1{Q}_2{\overline{Q}}_3{\overline{Q}}_4$, our explicit calculations suggest that no bound states can be formed below the thresholds of any meson pairs $(Q_1{\overline{Q}}_3)-(Q_2{\overline{Q}}_4)$ or $(Q_1{\overline{Q}}_4)-(Q_2{\overline{Q}}_3)$. Thus, we do not expect narrow all-heavy tetraquark states to be existing in experiments.

We study the mass spectra and radiative decays of doubly heavy baryons within the diquark picture in a relativized quark model. The mass of the $J^P=1/2^{+}$ ${\mathrm{\Xi }}_{cc}$ ground state is predicted to be 3606 MeV, which is consistent with the mass of ${\mathrm{\Xi }}_{cc}^{++}(3621)$ newly observed by the LHCb Collaboration. The predicted mass gap between two $S$-wave states, ${\mathrm{\Xi }}_{cc}^{*}$ ($J^P=3/2^{+}$) and ${\mathrm{\Xi }}_{cc}$ ($J^P=1/2^{+}$), is 69 MeV. Furthermore, the radiative transitions of doubly heavy baryons are also estimated by using the realistic wave functions obtained from relativized quark model. The radiative decay widths of ${\mathrm{\Xi }}_{cc}^{*++}\to {\mathrm{\Xi }}_{cc}^{++}\gamma$ and ${\mathrm{\Xi }}_{cc}^{*+}\to {\mathrm{\Xi }}_{cc}^{+}\gamma$ are predicted to be about 7 and 4 keV, respectively. These predictions of doubly heavy baryons can provide helpful information for future experimental searches.

The strong and radiative decay properties of the low-lying ${\mathrm{\Omega }}_c$ states are studied in a constituent quark model. We find that the newly observed ${\mathrm{\Omega }}_c$ states by the LHCb Collaboration can fit well in the decay patterns. Thus, their spin parity can possibly be assigned as the following: (i) ${\mathrm{\Omega }}_c(3000)$ has $J^P=1/2^{-}$ and corresponds to the narrow $1P$ mixed state $|1{{}^{2}P}_{\lambda }{\frac{1}{2}}^{-}{⟩}_1$; its partner $|1{{}^{2}P}_{\lambda }{\frac{1}{2}}^{-}{⟩}_2$ should be a broad state with a width of $\sim 100\mathrm{MeV}$. (ii) ${\mathrm{\Omega }}_c(3050)$ and ${\mathrm{\Omega }}_c(3066)$ can be assigned to be two $J^P=3/2^{-}$ states, $|1{{}^{4}P}_{\lambda }{\frac{3}{2}}^{-}⟩$ and $|1{{}^{2}P}_{\lambda }{\frac{3}{2}}^{-}⟩$, respectively. (iii) ${\mathrm{\Omega }}_c(3090)$ can be assigned as the $|1{{}^{4}P}_{\lambda }{\frac{5}{2}}^{-}⟩$ state with $J^P=5/2^{-}$. (iv) ${\mathrm{\Omega }}_c(3119)$ might correspond to one of the two $2S$ states of the first radial excitations, i.e., $|2{{}^{2}S}_{\lambda \lambda }{\frac{1}{2}}^{+}⟩$ or $|2{{}^{4}S}_{\lambda \lambda }{\frac{3}{2}}^{+}⟩$.

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 ${\mathrm{\Xi }}_{cc}^{*}$ and ${\mathrm{\Omega }}_{cc}^{*}$ with $J^P=3/2^{+}$ have a fairly large decay rate into the ${\mathrm{\Xi }}_{cc}\gamma$ and ${\mathrm{\Omega }}_{cc}\gamma$ channels with a width $\sim 15$ and $\sim 7\mathrm{keV}$, 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 $\mathrm{\Gamma }\sim 100\mathrm{MeV}$, and the ratio between the radiative and hadronic decay widths is about $\mathcal{O}({10}^{-3})$.