We investigate quarkonium mass spectra in external constant magnetic fields by using QCD sum rules. We first discuss a general framework of QCD sum rules necessary for properly extracting meson spectra from current correlators computed in the presence of strong magnetic fields, that is, a consistent treatment of mixing effects caused in the mesonic degrees of freedom. We then implement operator product expansions for pseudoscalar and vector heavy-quark current correlators by taking into account external constant magnetic fields as operators and obtain mass shifts of the lowest-lying bound states ${\eta }_c$ and $J/\psi$ in the static limit with their vanishing spatial momenta. Comparing results from QCD sum rules with those from hadronic effective theories, we find that the dominant origin of mass shifts comes from a mixing between ${\eta }_c$ and $J/\psi$ with a longitudinal spin polarization, accompanied by other subdominant effects such as mixing with higher excited states and continua.

We investigate the mass spectra of open heavy flavor mesons in an external constant magnetic field within QCD sum rules. Spectral Ansätze on the phenomenological side are proposed in order to properly take into account mixing effects between the pseudoscalar and vector channels, and the Landau levels of charged mesons. The operator product expansion is implemented up to dimension-5 operators. As a result, we find for neutral $D$ mesons a significant positive mass shift that goes beyond simple mixing effects. In contrast, charged $D$ mesons are further subject to Landau level effects, which together with the mixing effects almost completely saturate the mass shifts obtained in our sum rule analysis.

We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between ${\eta }_c$ and $J/\psi$ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.

We improve our previous variational method based nonrelativistic quark model by introducing a complete set of three-dimensional harmonic oscillator bases as the spatial part of the total wave function. To assess the validity of our approach, we compare the binding energy thus calculated with the exact value for the hydrogen model. After fitting to the masses of the ground state hadrons, we apply our new method to analyzing the doubly heavy tetraquark states $q{q}^{\prime }\overline{Q}\overline{Q^{\prime }}$ and compare the results for the binding energies to results in other works. We also calculate the ground state masses of $T_{sc}(ud\overline{s}\overline{c})$ and $T_{sb}(ud\overline{s}\overline{b})$ with $(I,S)=(0,1),(0,2)$. We find that $T_{bb}(ud\overline{b}\overline{b})$ and $us\overline{b}\overline{b}$, both with $(I,S)=(0,1)$, are stable against the two lowest threshold meson states with binding energies $-145$ and $-42\mathrm{MeV}$, respectively. We further find that $T_{cb}(ud\overline{c}\overline{b})$ is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.

The constituent quark model with color-spin hyperfine potential is used to investigate the property of a compact pentaquark configuration with $J^p=3/2^{-}$ and $\text{isospin}=1/2$, which is the most likely quantum number of one of the recently observed exotic baryon states at LHCb. Starting from the characterization of the isospin, color, and spin states for the pentaquark configuration, we construct the total wave function composed of the spatial wave function, which we take to be symmetric and in S wave, and the four orthogonal $\text{isospin}\otimes \text{color}\otimes \text{spin}$ states that satisfy the Pauli principle. We then use the variational method to find a compact stable configuration. While there are compact configurations where the hyperfine potential is more attractive than the sum of $p$ and $J/\psi$ hyperfine potentials, we find that the ground state is the isolated $p$ and $J/\psi$ state. Furthermore, the mass of the excited state lies far above the observed pentaquark state leading us to conclude that the observed states cannot be a compact configuration with $J^p=3/2^{-}$, generated by the conventional two-body quark interactions.