Production of $P_c$ states in $Λ_b$ decays

Abstract

We develop a model for the production of the P c states observed at LHCb in Λ b → J/ψ p K − decays. With fewer parameters than other approaches, we obtain excellent fits to the J/ψ p invariant mass spectrum, capturing both the prominent peaks, and broader features over the full range of invariant mass. A distinguishing feature of our model is that whereas P c ( 4312), P c (4380) and P c (4440) are resonances with Σ ( * ) c D( * ) constituents, the nature of P c (4457) is quite different, and can be understood either as a Σ c D * threshold cusp, a Λ c (2595) D enhancement due to the triangle singularity, or a Λ c (2595) D resonance. We propose experimental measurements that can discriminate among these possibilities. Unlike in other models, our production mechanism respects isospin symmetry and the empirical dominance of colour-enhanced processes in weak decays, and additionally gives a natural explanation for the overall shape of the data. Our model is consistent with experimental constraints from photoproduction and Λ b → Λ c D( * )0 K − decays and it does not imply the existence of partner states whose apparent absence in experiments is unexplained in other models.

The $P_{ψs}^Λ(4338)$ pentaquark and its partners in the molecular picture

“…if one of these systems binds the other is also likely to bind. In this regard there are previous phenomenological predictions of DΛ c [33,34] and DΛ c (2595) [35] bound states and arguments for the interpretation of the P N ψ (4457) as a DΛ c (2595) state [36] (instead of the more usual D * Σ c identification, which has been argued not to fully explain the P N ψ (4457) [37,38]). However, the existence of an unusually long-ranged, L = 1 one pion exchange force in the DΛ c (2595) system [39,40] has also been shown to make binding much more easy in this case [41].…”

The LHCb state PψsΛ(4338) as a triangle singularity

“…We notice that the J /ψ distribution [1] has exactly this shape, and we regard this as strong support for this proposed production mechanism. We also notice that, similar to the other exotic hadron systems [30,32], the tree-level diagrams for the J /ψ p final state are color-suppressed; hence it is natural to assume that the colorfavored triangle diagram is a dominant contribution.…”

“…We note that the exact locations of these thresholds (which can be defined with respect to pole Signals at (rather than below) threshold are more amenable to non-resonant interpretations, and we recently demonstrated that P c (4457) can be explained as a cusp or an enhancement due to the logarithmic triangle singularity [32]. In this paper we explore related possibilities for P ψ s (4338).…”

“…Moreover, the analogy relies on the assumption that P c (4440) and P c (4457) are both c D * molecules, and we recently argued that this assumption is not consistent with experimental constraints [30]. (Scenarios with different interpretations for P c (4457) [31,32] do not have the same problem. )…”

“…We assume, as in our previous work [32,33], that the distribution can be described by triangle diagrams which couple to the final state through interactions which respect heavy-quark symmetry, and that the dominant diagrams are those with color-favored weak vertices. Hence we consider B → D ( * )− s D( * ) transitions, noting that such branching fractions range from approximately 1-3%.…”