Abstract
We examine whether the LHCb vector udc¯s¯ state X(2900) can be interpreted as a kinematical cusp effect arising from D¯⁎K⁎ and D¯1K(⁎) interactions. The production amplitude is modelled as a triangle diagram with hadronic final state interactions. A satisfactory fit to the Dalitz plot projection is obtained that leverages the singularities of the production diagram without the need for D¯K resonances. A somewhat better fit is obtained if the final state interactions are strong enough to generate resonances, although the evidence in favour of this scenario is not conclusive.
Highlights
We remark that we do not distinguish two-body threshold (Wigner) cusps from triangle singularities in the following as these are intertwined in the production mechanism; rather we refer to any enhancement that appears due to the production portion of the process as a kinematical cusp
We explore the implications of a triangle diagram coupling between an initial B+ meson and the final D D K state
The final state interactions were modelled with a separable potential with a structure motivated by one-pion-exchange phenomenology
Summary
The LHCb collaboration has announced the discovery of a D K enhancement in the reaction B → D D K that can be interpreted as. Liu et al use an effective Lagrangian that couples heavy quark fields and light mesons to compute binding energies of possible D K , D ∗ K , D K ∗ and D ∗ K ∗ molecules [27] They argue that X0 can be interpreted as an isoscalar D ∗ K ∗ molecule, but find no viable explanation for. We remark that we do not distinguish two-body threshold (Wigner) cusps from triangle singularities in the following as these are intertwined in the production mechanism; rather we refer to any enhancement that appears due to the production portion of the process as a kinematical cusp These concepts are usefully reviewed in Ref. It is natural for structures to appear near the D ∗ K ∗ threshold, since this is the lightest combination of hadrons with this flavour that can interact via elastic one-pion exchange. An even better fit is obtained when D 1 K ∗ and strong final state interactions are considered
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