Search for $XYZ$ states in $\Lambda_b$ decays at the LHCb

We consider $X(3872)$ and $Y(4140)$ as the vector tetraquark states of $X_c^0\equiv c\bar c u\bar u(d\bar d)$ and $c\bar c s\bar s$, respectively. By connecting $\Lambda_b\to X_c^0\Lambda$ to $B^-\to X_c^0 K^-$, we predict that the branching ratios of $\Lambda_b\to \Lambda(X(3872)^0\to) J/\psi \pi^+\pi^-$ and $\Lambda_b\to \Lambda(Y(4140)\to) J/\psi \phi$ are $(5.2\pm 1.8)\times 10^{-6}$ and $(4.7\pm 2.6)\times 10^{-6}$, which are accessible to the experiments at the LHCb, respectively. The measurements of these $\Lambda_b$ modes would be the first experimental evidences for the $XYZ$ states in baryonic decays.


I. INTRODUCTION
With the quantum numbers of J P C = 1 ++ determined by the B − → X(3872) 0 K − decay [1], the state of X(3872) 0 has been established as one of the XY Z states [2], which are regarded to be exotic due to the non-pure cc components. However, it is still a puzzle whether X(3872) 0 is really a tetraquark state (four-quark bound state) with the quark content ccuū(dd) [3]. Note that, while there is no sign of its charged partner to be the ccud(dū) state, Y (4140) can be a tetraquark consisting of ccss [4], of which the quantum numbers of J P C are not experimentally assigned. As more investigations are apparently needed, the study of X(3872) has been restricted in the B decays of B → X(3872) 0 K ( * ) and B → X(3872) 0 Kπ with Kπ partly from K * [5,6], where the resonant X 0 (3872) decay channels can be X(3872) 0 → J/ψπ + π − , J/ψω, J/ψγ and DD * . At present, no other observation has been found beyond the B decays.
On the other hand, being identified as the exotic meson, which could be the tetraquark [3], DD * molecule [7], or hybrid ccg bound state [8], the X(3872) state causes the difficulty of the theoretical calculations. In this study, we will concentrate on the tetraquark scenario by denoting X 0 c to be composed of ccqq, where qq can be uū, dd, or ss. In particular, we take X(3872) 0 and Y (4140) as two of these exotic X 0 c states. Through the b → ccs transition at the quark level in Fig. 1, the decays of B → (X(3872) 0 , J/ψ)K correspond to the processes of the B → K transition with the recoiled charmed mesons of X(3872) 0 and J/ψ, respectively. Although the J/ψ formation from the cc currents can be calculated within the framework of QCD, the X(3872) one cannot be done at the moment.
However, it is interesting to see in Fig. 1 that all decays of (B, Λ b ) → (X 0 c , J/ψ)K are originated from the b → ccs transition at the quark level, and therefore connected.
As a result, despite the unknown matrix elements of the X 0 c hadronization through the cc currents, we can relate these decays. In particular, we can predict the branching ratios of The experimental searches of these Λ b decays at the LHCb will clearly improve our understanding of the XYZ states.
where G F is the Fermi constant, V ij are the CKM matrix elements, M c represents J/ψ of J P C = 1 −− or the exotic X 0 c state with its constituent being ccqq. For simplicity, we take that the quantum numbers of X 0 [11,12], is also assumed to be the J P C = 1 ++ state and treated as one of the X 0 c states with the tetraquark of ccss [4]. To calculate the processes in Fig. 1, we need to know the matrix elements of X 0 c |cγ µ (1 − γ 5 )c|0 , which is the most difficult part unless these can be related to the observed quantities. In Eq. (1), the parameters a 2 andâ 2 , involving the nonfactorizable effects, can be extracted from the observed branching ratios of B(Λ b → J/ψΛ) with t ≡ q 2 , where the momentum dependences of the form factors are given by [13] and [14] F BK Note that the other form factors f 2,3 (g 2,3 ) in Eq. (2) with C F to be extracted from the measured Λ b → p(K − , π − ) decays [13]. With X 0 c being J P C = 1 ++ , the matrix elements in Eq. (1) of the 0 → J/ψ and 0 → X 0 c productions can be parameterized as where m J/ψ(X 0 c ) , f J/ψ(X 0 c ) and ε * µ are the mass, decay constant and polarization for J/ψ(X 0 c ), respectively. Because of the exotic nature of the X 0 c state, which could be the DD * molecule, the hybrid ccg state, or the tetraquark state, no present QCD model can derive f X 0 c . Nonetheless, as we propose that Λ b → X 0 c Λ and B → X 0 c K are connected, we are able to eliminate the unknown f X 0 c and predict B( For the numerical analysis, the theoretical inputs of the CKM matrix parameters in terms of the Wolfenstein parameterization are taken to be (λ, A, ρ, η) = (0.225, 0.814, 0.120 ± 0.022, 0.362 ± 0.013) [5]. For the form factor in Eq. (5), we choose C F = 0.136 ± 0.009 [13], which is consistent with other QCD model calculations and used to explain the data in the Λ b decays [9,13]. In addition, from Ref. [14] we get F BK we take (a 2 ,â 2 ) = (0.154 ± 0.024, 0.268 ± 0.004), which are extracted from Λ b → J/ψΛ [9] and B − → J/ψK − [5], respectively. In terms of Eq. (1), we obtain where the unkown decay constant f X 0 c has been eliminated. The measurements for and [11,12] B where we have used B(B − → J/ψφK − ) = (5.2 ± 1.7) × 10 −5 [5]. By relating Eq. (7) to Eqs. (8) and (9), we find respectively, which can be reliable predictions to be compared with the future data. We remark that B(B 0 →K 0 (X(3872) 0 →)J/ψπ + π − ) = (4.3 ± 1.3) × 10 −6 [5] can also lead to similar results but with larger uncertainties than those in Eq. (10). It should be noted that the quantum numbers for Y (4140) have not been experimentally identified yet, although they are predicted to be J P C = 0 ++ (2 ++ ) in Ref. [15] and 1 −+ in Ref. [16] besides 1 ++ in Ref. [4]. We emphasize that, even it is finally measured to have J P C = 0 ++ [17] or 1 −+ , the decay of Λ b → Λ(Y (4140) →)J/ψφ can still be examined by our method. However, the factorization approach would not support the tensor (T) identification of the J = 2 state due to T |cγ µ (1 − γ 5 )c|0 = 0.
Finally, we note that unlike B − → X(3872) 0 K − , which receives the dominant contribution from the doubly charmful b → ccs transition, the decay of B − → X(3872) −K 0 is forbidden in Fig. 1 as supported by the experiment due to its non-observation [18], where X(3872) − is the charged counterpart of X(3872) 0 . However, this mode can proceed from the charmless b → dds transition, provided that the cc contents in X(3872) − come from the intrinsic charm within the B meson, which is similar to the pentaquark state productions in the Λ b decays [19,20]. As a result, in the charmless B decays, the branching ratios of the three possible exotic decays ofB 0 → X + c K − , X + c π − , and B − → X − cK 0 can be at the same level. In addition, the intrinsic charm mechanism would be used to the productions of the charged Y and Z particles asB 0 → Z(4430) + K − with Z(4430) + to consist of ccud [21,22].
Moreover, the analogous statements for the corresponding Λ b decays can also be drawn.

IV. CONCLUSIONS
We have explored the possibility to find the exotic meson states, such as the tetraquark four-quark bound states of X 0 c = ccuū(dd) and ccss in the Λ b decays. In particular, by concentrating on the scenarios with X(3872) 0 and Y (4140) being J P C = 1 ++ , we have studied the doubly charmful Λ b → X 0 c Λ decays. By connecting Λ b → ΛX 0 c to B − → K − X 0 c , we have found that B(Λ b → Λ(X(3872) 0 →)J/ψπ + π − ) and B(Λ b → Λ(Y (4140) →)J/ψφ) are (5.2 ± 1.8) × 10 −6 and (4.7 ± 2.6) × 10 −6 , respectively. As these predicted branching ratios are accessible to the experiments at the LHCb, a measurement will be the first clean experimental evidence for the XY Z states in baryonic decays.