Search

In this work, we study the weak decay between two heavy baryons $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$ B i ( 1 2 + ) → B f ( 3 2 + ) in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of $$ {\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$ B i ( 1 2 + ) → B f ( 3 2 + ) , and analyze two specific cases of transitions: the weak decays of single heavy baryon $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ and the decays of double-charmed baryon $$\Xi _{cc}\rightarrow \Sigma _{c}^*(\Xi _{c}^*)$$ Ξ cc → Σ c ∗ ( Ξ c ∗ ) . We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+) l\bar{\nu }_l$$ B i ( 1 2 + ) → B f ( 3 2 + ) l ν ¯ l and non-leptonic $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)M$$ B i ( 1 2 + ) → B f ( 3 2 + ) M . Previously we studied the transition $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ with the quark–diquark picture of baryon in the light-front quark model. Here we revisit this transition with three-quark picture of baryon. At the quark level, the transition $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ is induced by the $$b\rightarrow c$$ b → c transition.The subsystem of the two unchanged light quarks which possesses definite and same spin in initial and final state can be viewed as a spectator, so the spectator approximation can be applied directly. For the weak decay of doubly charmed baryon $$\Xi _{cc}$$ Ξ cc , a c quark decays to a light quark $$q_1$$ q 1 , so both the initial state cc and final state $$q_1q_2$$ q 1 q 2 ( $$q_1$$ q 1 and the original $$q_2$$ q 2 in initial state may be the same flavor quarks) which possess definite spin are no longer spectators. A rearrangement of quarks for initial and final states is adopted to isolate the unchanged subsystem $$cq_2$$ c q 2 which can be viewed as the spectator approximately. Future measurements on these channels will constrain the nonperturbative parameter in the wavefunctions and test the model predictions.

In this work, we propose to search for the exotic doubly charmed meson $$T_{cc}^+$$ T cc + and its analog $$T_{cc\bar{s}}^+$$ T c c s ¯ + in $$B_c^+$$ B c + decays, which provide a good environment for the formation of the exotic state containing double charm quarks. Within the molecular scheme, the production of $$T_{cc}^+$$ T cc + and $$T_{cc\bar{s}}^+$$ T c c s ¯ + through various rescattering processes with different intermediate states are investigated. For the moderate values of model parameters, the branching ratios of $$B_c^+$$ B c + decaying into $$T_{cc}^+ \bar{D}^{0}$$ T cc + D ¯ 0 , $$T_{cc}^+ \bar{D}^{*0}$$ T cc + D ¯ ∗ 0 , $$T_{cc\bar{s}}^+ \bar{D}^{0}$$ T c c s ¯ + D ¯ 0 and $$T_{cc\bar{s}}^+ \bar{D}^{*0}$$ T c c s ¯ + D ¯ ∗ 0 are estimated to be of the order of $$10^{-7}$$ 10 - 7 , $$10^{-5}$$ 10 - 5 , $$10^{-6}$$ 10 - 6 and $$10^{-4}$$ 10 - 4 , respectively, which may be tested by future experiments.

We investigate the process $$B\rightarrow \bar{D}D_s \pi $$ B → D ¯ D s π via several rescattering processes. It is shown that the triangle singularity (TS) peak around the $$D^*K^*$$ D ∗ K ∗ threshold generated from the $$\chi _{c1}K^* D^*$$ χ c 1 K ∗ D ∗ loop is relatively narrow, which may simulate the resonance-like structure $$T_{c\bar{s}}(2900)$$ T c s ¯ ( 2900 ) recently observed by LHCb in the $$D_s\pi $$ D s π spectrum. However, the TS peak around the $$D_s^*\rho $$ D s ∗ ρ threshold generated from the $$D^{**} D_s^* \rho $$ D ∗ ∗ D s ∗ ρ loop is smoothed by the broad width of $$\rho $$ ρ , which itself can hardly describe the $$T_{c\bar{s}}(2900)$$ T c s ¯ ( 2900 ) structure. A non-resonance TS signal around the DK threshold generated from the $$\chi _{c0}K D $$ χ c 0 K D loop is also predicted.

Recently the LHCb collaboration reported a new exotic state $$T^+_{cc}$$ T cc + which possesses $$cc\bar{u}\bar{d}$$ c c u ¯ d ¯ flavor structure. Since its mass is very close to the threshold of $$D^0D^{*+}$$ D 0 D ∗ + (or $$D^{*0}D^{+}$$ D ∗ 0 D + ) and its width is very narrow, it is inclined to conjecture that $$T^+_{cc}$$ T cc + is a molecular state of $$D^0D^{*+}$$ D 0 D ∗ + (or $$D^{*0}D^{+}$$ D ∗ 0 D + ). In this paper we study the possible molecular structures of $$D^{(*)}D^{(*)}$$ D ( ∗ ) D ( ∗ ) and $$B^{(*)}B^{(*)}$$ B ( ∗ ) B ( ∗ ) within the Bethe–Salpeter (B–S) framework. We employ one boson exchange model to stand the interaction kernels in the B–S equations. With reasonable input parameters we find the isospin eigenstate $$\frac{1}{\sqrt{2}}(D^0D^{*+}-D^{*0}D^{+})$$ 1 2 ( D 0 D ∗ + - D ∗ 0 D + ) ( $$J^P=1^+$$ J P = 1 + ) constitutes a solution, which supports the ansatz of $$T^+_{cc}$$ T cc + being a molecular state of $$D^0D^{*+}$$ D 0 D ∗ + (or $$D^{*0}D^{+}$$ D ∗ 0 D + ). With the same parameters we also find that the isospin-1 state $$\frac{1}{\sqrt{2}}(D^{*0}D^{*+}+D^{*0}D^{*+})$$ 1 2 ( D ∗ 0 D ∗ + + D ∗ 0 D ∗ + ) ( $$J^P=0^+$$ J P = 0 + ) can exist. Moreover, we also study the systems of $$B^{(*)}B^{(*)}$$ B ( ∗ ) B ( ∗ ) and their counterparts exist as possible molecular states. Consistency of theoretical computations based on such states with the data of the future experiments may consolidate the molecular structure of the exotic state $$T^+_{cc}$$ T cc + .

We investigate the $$B^+\rightarrow J/\psi \phi K^+$$ B + → J / ψ ϕ K + decay via various rescattering diagrams. Without introducing genuine exotic resonances, it is shown that the $$Z_{cs}(4000)$$ Z cs ( 4000 ) , $$Z_{cs}(4220)$$ Z cs ( 4220 ) and X(4700) reported by the LHCb collaboration can be simulated by the $$J/\psi K^{*+}$$ J / ψ K ∗ + , $$\psi ^\prime K^+$$ ψ ′ K + and $$\psi ^\prime \phi $$ ψ ′ ϕ threshold cusps, respectively. These cusps are enhanced by some nearby triangle singularities. The X(4685) with $$J^P=1^+$$ 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 recently reported the observation of a narrow peak in the $$D^- K^+$$ D - K + invariant mass distributions from the $$B^+\rightarrow D^+ D^- K^+$$ B + → D + D - K + decay. The peak is parameterized in terms of two resonances $$X_0(2900)$$ X 0 ( 2900 ) and $$X_1(2900)$$ X 1 ( 2900 ) with the quark contents $${\bar{c}}{\bar{s}}ud$$ c ¯ s ¯ u d , and their spin-parity quantum numbers are $$0^+$$ 0 + and $$1^-$$ 1 - , respectively. We investigate the rescattering processes which may contribute to the $$B^+\rightarrow D^+ D^- K^+$$ B + → D + D - K + decays. It is shown that the $$D^{*-}K^{*+}$$ D ∗ - K ∗ + rescattering via the $$\chi _{c1}K^{*+}D^{*-}$$ χ c 1 K ∗ + D ∗ - loop and the $${\bar{D}}_{1}^{0}K^{0}$$ D ¯ 1 0 K 0 rescattering via the $$D_{sJ}^{+}{\bar{D}}_{1}^{0}K^{0}$$ D sJ + D ¯ 1 0 K 0 loop can simulate the $$X_0(2900)$$ X 0 ( 2900 ) and $$X_1(2900)$$ X 1 ( 2900 ) with consistent quantum numbers. Such phenomena are due to the analytical property of the scattering amplitudes with the triangle singularities located to the vicinity of the physical boundary.

In this work we study the weak decays of $$\Xi _{cc}\rightarrow \Xi _c$$ Ξcc→Ξc and $$\Xi _{cc}\rightarrow \Xi '_c$$ Ξcc→Ξc′ in the light-front quark model. Generally, a naive, but reasonable conjecture suggests that the cc subsystem in $$\Xi _{cc}$$ Ξcc ( us pair in $$\Xi ^{(')}_c$$ Ξc(′) ) stands as a diquark with definite spin and color assignments. During the concerned processes, the diquark of the initial state is not a spectator, namely 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.