Heavy ion collisions provide a unique opportunity to study the nature of X(3872) compared with electron-positron and proton-proton (antiproton) collisions. With the abundant charm pairs produced in heavy-ion collisions, the production of multicharm h
adrons and molecules can be enhanced by the combination of charm and anticharm quarks in the medium. We investigate the centrality and momentum dependence of X(3872) in heavy-ion collisions via the Langevin equation and instant coalescence model (LICM). When X(3872) is treated as a compact tetraquark state, the tetraquarks are produced via the coalescence of heavy and light quarks near the quantum chromodynamic (QCD) phase transition due to the restoration of the heavy quark potential at $Trightarrow T_c$. In the molecular scenario, loosely bound X(3872) is produced via the coalescence of $D^0$-$bar D^{*0}$ mesons in a hadronic medium after kinetic freeze-out. The phase space distributions of the charm quarks and D mesons in a bulk medium are studied with the Langevin equation, while the coalescence probability between constituent particles is controlled by the Wigner function, which encodes the internal structure of the formed particle. First, we employ the LICM to explain both $D^0$ and $J/psi$ production as a benchmark. Then, we give predictions regarding X(3872) production. We find that the total yield of tetraquark is several times larger than the molecular production in Pb-Pb collisions. Although the geometric size of the molecule is huge, the coalescence probability is small due to strict constraints on the relative momentum between $D^0$ and $bar D^{*0}$ in the molecular Wigner function, which significantly suppresses the molecular yield.
Without contamination from the final state interactions, the calculation of the branching ratios of semileptonic decays $Xi^{()}_{c}toXi+e^+ u_e$ may provide us more information about the inner structure of charmed baryons. Moreover, by studying thos
e processes, one can better determine the form factors of $Xi_ctoXi$ which can be further applied to relevant estimates. In this work, we use the light-front quark model to carry out the computations where the three-body vertex functions for $Xi_c$ and $Xi$ are employed. To fit the new data of the Belle II, we re-adjust the model parameters and obtain $beta_{s[sq]}=1.07$ GeV which is 2.9 times larger than $beta_{sbar s}=0.366$ GeV. This value may imply that the $ss$ pair in $Xi$ constitutes a more compact subsystem. Furthermore, we also investigate the non-leptonic decays of $Xi^{()}_cto Xi$ which will be experimentally measured soon, so our model would be tested by consistency with the new data.
Recently LHCb declared a new structure $X(6900)$ in the final state di-$J/psi$ which is popularly regarded as a $cc$-$bar cbar c$ tetraquark state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible $cc$-$bar cbar c$ bound states
and the interaction between diquark ($cc$) and antidiquark ($bar cbar c$). In this work $cc$ ($bar cbar c$) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of $cc$-$bar cbar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of $X(6900)$ when we assign appropriate values for parameter $kappa$ introduced in the interaction (kernel).We also briefly calculate the spectra of $bb$-$bar bbar b$ bound states. Future measurement of $bb$-$bar bbar b$ state will help us to determine the exact form of effective interaction.
We investigate the $B^+to J/psi phi K^+$ decay via various rescattering diagrams. Without introducing genuine exotic resonances, it is shown that the $Z_{cs}(4000)$, $Z_{cs}(4220)$ and $X(4700)$ reported by the LHCb collaboration can be simulated by
the $J/psi K^{*+}$, $psi^prime K^+$ and $psi^prime phi$ threshold cusps, respectively. These cusps are enhanced by some nearby triangle singularities. The $X(4685)$ with $J^P=1^+$ cannot be well simulated by the threshold effects in our model, which implies that it may be a genuine resonance.
The LHCb collaboration reported the observation of a narrow peak in the $D^- K^+$ invariant mass distributions from the $B^+to D^+ D^- K^+$ decay. The peak is parameterized in terms of two resonances $X_0(2900)$ and $X_1(2900)$ with the quark content
s $bar{c}bar{s}ud$, and their spin-parity quantum numbers are $0^+$ and $1^-$, respectively. We investigate the rescattering processes which may contribute to the $B^+to D^+ D^- K^+$ decays. It is shown that the $D^{*-}K^{*+}$ rescattering via the $chi_{c1}K^{*+}D^{*-}$ loop or the $bar{D}_{1}^{0}K^{0}$ rescattering via the $D_{sJ}^{+}bar{D}_{1}^{0}K^{0}$ loop simulate the $X_0(2900)$ and $X_1(2900)$ structures. Such phenomena are due to the analytical property of the scattering amplitudes with the triangle singularities located to the vicinity of the physical boundary.
Recently a vector charmonium-like state $Y(4626)$ was observed in the portal of $D^+_sD_{s1}(2536)^-$. It intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its h
adronic structure with suitable inner constituents. It indeed concerns the general theoretical framework about possible structures of exotic states. Since the mass of $Y(4626)$ is slightly above the production threshold of $D^+_sbar D_{s1}(2536)^-$ whereas below that of $D^*_sbar D_{s1}(2536)$ with the same quark contents as that of $D^+_sbar D_{s1}(2536)^-$, it is natural to conjecture $Y(4626)$ to be a molecular state of $D^{*}_sbar D_{s1}(2536)$, as suggested in literature. Confirming or negating this allegation would shed light on the goal we concern. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e. $D^*_sbar D_{s1}(2536)$ within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter $lambda$ in the form factor which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing an even very small binding energy $Delta E$. It implies that the $D^*_sbar D_{s1}(2536)$ system cannot exist in the nature as a hadronic molecule in this model, so that we may not think the resonance $Y(4626)$ to be a bound state of $D^*_sbar D_{s1}(2536)$, but something else, for example a tetraquark and etc.
The spectrum of hadrons is the manifestation of color confinement of quantum chromodynamics. Hadronic resonances correspond to poles of the S-matrix. Since 2003, lots of new hadron resonant structures were discovered in the mass regions from light me
sons to hadrons containing a pair of a heavy quark and an antiquark. Many of them are candidates of exotic hadrons, and they are usually observed as peaks in invariant mass distributions. However, the S-matrix also has kinematical singularities due to the on-shellness of intermediate particles for a process, such as two-body thresholds and triangle singularities, and they can produce peaks as well. On the one hand, such singularities may be misidentified as resonances; on the other hand, they can be used as tools for precision measurements. In this paper, we review the threshold cusps and various triangle singularities in hadronic reactions, paying attention to their manifestations in phenomena related to exotic hadron candidates.
In this work we study the weak decays of $Xi_{cc}toXi_c$ and $Xi_{cc}toXi_c$ in the light-front quark model. Generally, a naive, but reasonable conjecture suggests that the $cc$ subsystem in $Xi_{cc}$ ( $us$ pair in $Xi^{()}_c$) stands as a diquark w
ith definite spin and color assignments. During the concerned processes, the diquark of the initial state is not a spectator, and must be broken. A Racah transformation would decompose the original $(cc)q$ into a combination of $c(cq)$ components. Thus we may deal with the decaying $c$ quark alone while keeping the $(cq)$ subsystem as a spectator. With the re-arrangement of the inner structure we calculate the form factors numerically and then obtain the rates of semi-leptonic decays and non-leptonic decays, which will be measured in the future.
$P_c(4312)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of $Sigma_c$ and $bar D$ m
asses, it is naturally tempted to be considered as a molecular state composed of $Sigma_c$ and $bar D$. Moreover, $P_c(4312)$ is observed in the channel with $J/psi p$ final state, requiring that isospin conservation $P_c(4312)$ is an isospin-1/2 eigenstate. In literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.
A resonance-like structure as narrow as 10 MeV is observed in the $K^-p$ invariant mass distributions in $Lambda_c^+to p K^- pi^+$ at Belle. Based on the large data sample of about 1.5 million events and the small bin width of just 1 MeV for the $K^-
p$ invariant mass spectrum, the narrow peak is found precisely lying at the $Lambdaeta$ threshold. While lacking evidence for a quark model state with such a narrow width at this mass region, we find that this narrow structure can be naturally identified as a threshold cusp but enhanced by the nearby triangle singularity via the $Lambda$-$a_0(980)^+$ or $eta$-$Sigma(1660)^+$ rescatterings.
