New $X_{0,1}(2900)$-like exotic states in $b$-baryon decays

In the $B^+\to D^+ D^-K^+$ decay, LHCb has reported the observation of the open-charm exotic states $X_{0,1}^0\equiv X_{0,1}(2900)^0$ with four different quark flavors~$(ud\bar s \bar c)$, where the subscripts (0,1) denote the spins. To confirm the discovery, we propose $\Lambda_b\to \Sigma_c^{0(++)} X_{0,1}^{\prime\,0(--)}$ in the final state interaction, where $X_{0,1}^{\prime\,0(--)}$ with $s u\bar d \bar c$ ($ds\bar u \bar c$) are the new $X_{0,1}$-like exotic states. More specifically, $\Lambda_c^+D_s^-$ in $\Lambda_b\to \Lambda_c^+D_s^-$ are transformed as $\Sigma_c^{0(++)} X_{0,1}^{\prime\,0(--)}$, by exchanging $\pi^{+(-)}$. As the order of magnitude estimates, we calculate ${\cal B}(\Lambda_b\to \Sigma_c^{0(++)} X_{0,1}^{\prime\,0(--)}) =(2.3\pm 0.6,4.3\pm 0.8^{+3.3}_{-2.5})\times 10^{-4}$. In addition, we estimate other $b$-baryon decays with the $X_{0,1}$-like states, such as ${\cal B}(\Xi_{b}^{0(-)}\to \Xi_{c}^{0(+)}(2645)X_{0}^{\prime\,0(--)}, \Lambda_{b}\to \Xi_{c}^{\prime\,0}X_{0,1}^{0})\sim 10^{-5}$. While one needs $\Lambda_b\to \Sigma_c^{0(++)}M_c M$ to observe $X_{0,1}^{\prime\,0(--)}\to M_c M$ with $M_c M=D_s^-\pi^+$, $\bar D^0 \bar K^0$ $(D_s^-\pi^-$, $D^-K^-)$, ${\cal B}(\Lambda_b\to \Sigma_c^{0(++)} X_{0,1}^{\prime\,0(--)}, X_{0,1}^{\prime\,0(--)}\to M_c M)\sim 10^{-4}$ are accessible to the LHCb experiment.


I. INTRODUCTION
The LHCb Collaboration has recently observed X 0 0,1 ≡ X 0,1 (2900) 0 from the B + → D + D − K + decay [1,2], where the subscript 0(1) denotes the spin. With the resonant strong decays X 0 0,1 → D − K + in the D − K + invariant mass spectrum, one concludes that X 0 0,1 are the first open-charm exotic states, which consist of four quarks with different flavorscdsu.
, the couplings in the triangle loop should be crucial. One [19], indicating the sizeable weak and strong couplings of the baryon decays. In addition, the coupling of is not small, due to the SU(3) flavor (SU(3) f ) symmetry that has been enabled to relate X ′ 0,1 and X 0 0,1 decays [10]. Hence, ) are anticipated to be as accessible as B(B + → D + X 0 0,1 ) to the LHCb experiment. In this paper, will be demonstrated as the promising decay channels to confirm the existence of the X 0 0,1 -like exotic states.

II. FORMALISM
The open-charm exotic states X 0 0,1 observed in B + → D + D − K + need to be confirmed by different decays. We think Λ b → Σ 0(++) c X ′ 0(−−) 0,1 may be promising. Like X 0 0,1 (cdsu), X ′ 0 0,1 (csdu) and X ′ −− 0,1 (csūd) also consist of four different quark flavors. See Fig. 1, Λ b → Σ c X ′ 0,1 are the triangle-rescattering decays, separated into two parts. The first part is the weak decay production. By following Refs. [20][21][22], we derive the amplitude of where In the above, we define 3 ) are the Fermi constant, CKM matrix element, decay constant, and Λ b → Λ + c transition form factors [23], respectively, while a 1 results from the factorization [24,25]. The second part as the rescattering effect proceeds through the strong decays, such that Λ + c D − s are turned into Σ c X ′ 0,1 by emitting or receiving a pion. Accordingly, the amplitudes are given by [10,26,27] with g c,0,1 the strong coupling constants and ǫ µ the polarization four vector, where M c (Σ c → Λ + c π) is presented as that used in the quark model and lattice QCD.
The exotic X 0 0,1 are observed in B + → D + D − K + . Likewise, we expect X Approximately, we present the resonant branching fractions as with B(Λ b → Σ c X ′ 0,1 ) in Eq. (13). In the SU(3) f symmetry, B(X ′ 0,1 → M c M) are given by [10] where B * stands for the higher-wave baryon state, and Ξ c (2645) is able to decay into Ξ c π.
These decays are worthy of the future explorations; particularly, we estimate that ) ∼ 10 −5 and B(Λ b → Ξ ′ 0 c X 0 0,1 ) ∼ 10 −5 , which suggest interesting measurements. As the final remark, we emphasize that our estimations rely on the observed weak decays in the triangle loop, such as the color-allowed However, there should be other triangle rescatterings to be discovered in the future work. For example, those proceed through the similar color-allowed Λ b decay processes but with Λ + c D − s or Λ + c D − (π − ) replaced by other particles of the same quark contents, or those through the color-suppressed ones, which are not necessarily suppressed in the final state interaction. Moreover, when the opencharm exotic particles are interpreted as the bound states [8], it allows for the rescatterings with the exchanges of the vector mesons, which also deserve future investigation.

IV. CONCLUSIONS
In summary, we have proposed the rescattering decays