New strange pentaquarks

The new strange pentaquarks observed by LHCb are very likely hadronic molecules consisting of $\Xi_c \bar D$ and $\Xi_c \bar D^{*}.$ We discuss the experimental evidence supporting this conclusion, pointing out the similarities and differences with the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks in the non-strange sector. The latter clearly are hadronic molecules consisting of $\Sigma_c \bar D$ and $\Sigma_c \bar D^{*}.$ Following this line of thought, we predict three additional strange pentaquarks, consisting of $\Xi_c^{\prime} \bar D$ and $\Xi_c^{\prime} \bar D^{*}.$ The masses of these states are expected to be shifted upwards by $M(\Xi_c^{\prime})-M(\Xi_c) \approx 110$ MeV with respect to the corresponding known strange pentaquarks.

Very recently the LHCb Collaboration announced observation of a new strange pentaquark P Λ ψs (4338) § with minimal quark content ccuds, mass M = 4338.2 ± 0.7 MeV and width Γ = 7.0 ± 1.2 MeV. This new state has been observed in the decay B − → J/ψΛp as a resonance in the J/ψΛ invariant mass with statistical significance > 10 σ. Amplitude analysis yields spin-parity J P = 1/2 − with the alternative J P = 1/2 + rejected @90% confidence level [1].
Several features of the new state are strongly suggestive [2] of a Ξ cD hadronic molecule: (a) Vicinity to the relevant baryon-meson threshold. The central value of P Λ ψs (4338) mass is only 0.8 MeV above Ξ + c D − threshold and 2.9 MeV above Ξ 0 c D 0 threshold (cf. Appendix A).
(b) Spin and parity. The spin and parity of an S-wave hadronic molecule are necessarily inherited from its constituents. In this case the latter are a positive parity spin-1/2 baryon and a negative parity spin-0 meson. J P = 1/2 − is exactly what is expected.
(c) Narrow width, compared with the phase space available for decay. P Λ ψs (4338) decays into J/ψΛ, whose threshold is 4212.6 MeV, so the Q-value is 126 MeV. The 7 MeV width of P Λ ψs (4338) is unnaturally small for such a Q-value, so there must be a suitable decay-suppressing mechanism at work. Decay into J/ψΛ requires the charmed and anti-charmed quarks getting close to each other, but in a Ξ cD molecular configuration the average distance between Ξ c andD is much larger than 1 fermi, automatically providing an efficient decay-suppressing mechanism.
Additional (although less statistically significant) support for the molecular interpretation is provided by earlier LHCb data on the P Λ ψs (4459) pentaquark [3], [4]. In that case LHCb observed a strange pentaquark as a peak in J/ψΛ invariant mass in the decay Ξ − b → J/ψΛK − , with mass M = 4458.8 ± 2.9 +4.7 −1.1 MeV, width Γ = 17.3 ± 6.5 +8.0 −5.7 MeV and statistical significance of 3.1 σ. The central value of the P Λ ψs (4459) mass is approximately 20 MeV below the Ξ cD * threshold. Remarkably, LHCb observed [3] that this resonance can equally well be described by a two peak structure, with the two peaks split by 13 MeV: This pattern is consistent with general expectations (see, e.g., Refs. [7][8][9][10]). For a recent review and additional references, see Ref. [11]. The above structure is highly reminiscent of the two-peak pentaquark structure discovered by LHCb [5] in the non-strange sector, following the original discovery of hidden-charm pentaquarks [6], (a.k.a. P c (4440) + and P c (4457) + ) These two resonances are most likely the two possible spin states of an S-wave hadronic molecule consisting of a spin-1/2 Σ c and spin-1D * 0 . Clearly, in that case the expected J P values are 1/2 − and 3/2 − . Analogous reasoning leads to the expectation that the spin and parity of P Λ ψs (4455) and P Λ ψs (4468) are the two possible values for an S-wave hadronic molecule consisting of a spin-1/2 Ξ c and spin-1D * 0 , i.e., 1/2 − and 3/2 − .
One remaining issue is the specific mechanism which provides attraction betweenD and Ξ c . Binding betweenD * and Σ c or Ξ c can be provided by one-pion exchange. But sinceD is a pseudoscalar, its binding to another hadron cannot be provided by one-pion exchange, because that would require a vertex involving three pseudoscalars which is forbidden in QCD, since such a vertex cannot simultaneously conserve parity and angular momentum.
In the case of a Σ cD hadronic molecule a two-pion exchange can provide binding, because the intermediate Λ cD * state is relatively close in mass to the initial state [12]. Twopion exchange is expected to be weaker than one-pion exchange and as a result P N ψ (4312) + might be a virtual state, rather than a fully-fledged bound state.
For Ξ cD two-pion exchange is unlikely to work, since in this case the intermediate state is too heavy. One relatively simple possibility is ρ-mediated t-channel charge exchange, The Ξ cD state decays into ΛJ/ψ, so it has isospin zero. In such a state t-channel ρ exchange is attractive [13]. Clearly, more quantitative statements require a specific model-dependent calculation.
At this point it is important to stress that the analogy between Σ cD ( * ) and Ξ cD ( * ) hadronic molecules goes only so far. As discussed in Ref. [4], P Λ ψs (4455) and P Λ ψs (4468) do not correspond to an SU (3) F rotation q → s (q = u, d) of P N ψ (4440) + and P N ψ (4457) + . Neither does P Λ ψs (4338) correspond to an SU (3) F rotation of P N ψ (4312) + . The point is that in the non-strange pentaquark hadronic molecules the charmed baryon is Σ c , in which the two light quarks form a "bad diquark" (ud), with spin-1 and isospin-1. An SU (3) F rotation q → s then takes the Σ c baryon to Ξ c , rather than to Ξ c . The latter is approximately 110 MeV lighter than Ξ , ¶ because in Ξ c the light quarks form a spin-0 [qs] "good diquark" which is significantly lighter than the spin-1 qs "bad diquark" in Ξ c .
Moreover, Ξ c cannot decay via the strong interaction, because M (Ξ c ) − M (Ξ c ) < m π . It can only decay radiatively, M (Ξ c ) → M (Ξ c ) γ. Thus from the point of view of strong interactions Ξ c is as stable as Ξ c .
The upshot of the above observations is that, if -as strongly hinted by the data -P Λ ψs (4338) P Λ ψs (4455) and P Λ ψs (4468) indeed are Ξ cD and Ξ cD * hadronic molecules, then one should expect analogously three additional narrow strange pentaquarks, corresponding to Ξ cD and Ξ cD * hadronic molecules. Their masses are expected to be shifted by M (Ξ c ) − M (Ξ c ) ≈ 110 MeV with respect to the corresponding known strange pentaquarks, putting them approximately at 4448, 4564 and 4577 MeV, as shown in Fig. 1. Their spin-parity quantum numbers are expected to be the same as those of their counterparts. Their widths are expected to be rather small, similar to those of P Λ ψs (4338), P Λ ψs (4455) and P Λ ψs (4468). A potentially challenging point is that the Ξ cD state at 4448 MeV, analogous to P Λ ψs (4338), is expected just 7 MeV below P Λ ψs (4455). This is becauseD * −D splitting plus the Ξ cD * binding energy is close to Ξ c − Ξ c splitting. Ξ cD state is expected to have spin-1/2, so if P Λ ψs (4455) turns out to also have spin-1/2, the two states will likely mix.

Summary
Recently LHCb has reported several new narrow strange pentaquarks decaying into ΛJ/ψ, with minimal quark content ccuds. We have reviewed the experimental evidence and theoretical arguments strongly suggesting that they are Ξ cD  points are their proximity to the relevant baryon-meson thresholds, spin-parity and unnaturally narrow widths, given the phase space available for decay. We have discussed their similarities and differences with the three nonstrange narrow pentaquarks decaying into pJ/ψ, with minimal quark content ccuud, reported by LHCb in 2019.
On the basis of this discussion, we predict three additional narrow strange pentaquarks, corresponding to Ξ cD ( * ) hadronic molecules, with masses shifted upwards by approximately 110 MeV with respect to the known Ξ cD ( * ) states, i.e., approximately at 4448, 4564 and 4557 MeV and with narrow widths.

ACKNOWLEDGMENTS
The research of M.K. was supported in part by NSFC-ISF grant No. 3423/19.