In this work, we revisit the isospin violating decays of $X(3872)$ in a coupled-channel effective field theory. In the molecular scheme, the $X(3872)$ is interpreted as the bound state of $bar{D}^{*0}D^0/bar{D}^0D^{*0}$ and $D^{*-}D^+/D^-D^{*+}$ chan
nels. In a cutoff-independent formalism, we relate the coupling constants of $X(3872)$ with the two channels to the molecular wave function. The isospin violating decays of $X(3872)$ are obtained by two equivalent approaches, which amend some deficiencies about this issue in literature. In the quantum field theory approach, the isospin violating decays arise from the coupling constants of $X(3872)$ to two di-meson channels. In the quantum mechanics approach, the isospin violating is attributed to wave functions at the origin. We illustrate that how to cure the insufficient results in literature. Within the comprehensive analysis, we bridge the isospin violating decays of $X(3872)$ to its inner structure. Our results show that the proportion of the neutral channel in $X(3872)$ is over $80%$. As a by-product, we calculate the strong decay width of $X(3872)to bar{D}^0 D^0pi^0$ and radiative one $X(3872)to bar{D}^0 D^0gamma$. The strong decay width and radiative decay width are about 30 keV and 10 keV, respectively, for the binding energy from $-300$ keV to $-50$ keV.
Very recently, the LHCb Collaboration reported the doubly charmed tetraquark state $T_{cc}^+$ below the $D^{*+}D^0$ threshold about $273$ keV. As a very near-threshold state, its long-distance structure is very important. In the molecular scheme, we
relate the coupling constants of $T_{cc}^+$ with $D^{*0}D^+$ and $D^{*+}D^0$ to its binding energy and mixing angle of two components with a coupled-channel effective field theory. With the coupling constants, we investigate the kinetically allowed strong decays $T_{cc}^+to D^0D^0pi^+$, $T_{cc}^+to D^+D^0pi^0$ and radiative decays $D^+D^0 gamma$. Our results show that the decay width of $T_{cc}^+to D^0D^0pi^+$ is the largest one, which is just the experimental observation channel. Our theoretical total strong and radiative widths are in favor of the $T_{cc}^+$ as a $|D^{*+}D^0rangle$ dominated bound state. The total strong and radiative width in the single channel limit and isospin singlet limit are given as $59.7^{+4.6}_{-4.4} text{ keV}$ and $46.7^{+2.7}_{-2.9} text{ keV}$, respectively. Our calculation is cutoff-independent and without prior isospin assignment. The absolute partial widths and ratios of the different decay channels can be used to test the structure of $T_{cc}^+$ state when the updated experimental results are available.
We systematically study the mass spectrum and strong decays of the S-wave $bar cbar s q q$ states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine int
eractions. The hyperfine potential leads to the mixing between different color configurations, as well as the large mass splitting between the two ground states with $I(J^P)=0(0^+)$ and $I(J^P)=1(0^+)$. We calculate their strong decay amplitudes into the $bar D^{(*)}K^{(*)}$ channels with the wave functions from the mass spectrum calculation and the quark interchange method. We examine the interpretation of the recently observed $X_0(2900)$ as a tetraquark state. The mass and decay width of the $I(J^P)=1(0^+)$ state are $M=2941$ MeV and $Gamma_X=26.6$ MeV, respectively, which indicates that it might be a good candidate for the $X_0(2900)$. Meanwhile, we also obtain an isospin partner state $I(J^P)=0(0^+)$ with $M=2649$ MeV and $Gamma_{Xrightarrow bar D K}=48.1$ MeV, respectively. Future experimental search for $X(2649)$ will be very helpful.
The chiral corrections to the magnetic moments of the spin-$frac{1}{2}$ doubly charmed baryons are systematically investigated up to next-to-next-to-leading order with heavy baryon chiral perturbation theory (HBChPT). The numerical results are calcul
ated up to next-to-leading order: $mu_{Xi^{++}_{cc}}=-0.25mu_{N}$, $mu_{Xi^{+}_{cc}}=0.85mu_{N}$, $mu_{Omega^{+}_{cc}}=0.78mu_{N}$. We also calculate the magnetic moments of the other doubly heavy baryons, including the doubly bottomed baryons (bbq) and the doubly heavy baryons containing a light quark, a charm quark and a bottom quark (${bc}q$ and $[bc]q$): $mu_{Xi^{0}_{bb}}=-0.84mu_{N}$, $mu_{Xi^{-}_{bb}}=0.26mu_{N}$, $mu_{Omega^{-}_{bb}}=0.19mu_{N}$, $mu_{Xi^{+}_{{bc}q}}=-0.54mu_{N}$, $mu_{Xi^{0}_{{bc}q}}=0.56mu_{N}$, $mu_{Omega^{0}_{{bc}q}}=0.49mu_{N}$, $mu_{Xi^{+}_{[bc]q}}=0.69mu_{N}$, $mu_{Xi^{0}_{[bc]q}}=-0.59mu_{N}$, $mu_{Omega^{0}_{[bc]q}}=0.24mu_{N}$.
