$$X_1(2900)$$ as a $$\bar{D}_1 K$$ molecule

The analyses of the LHCb data on X(2900) in the $$D^- K^+$$ D - K + spectrum are performed. Both dynamically generated and explicitly introduced $$X_1(2900)$$ X 1 ( 2900 ) are considered. The results show that both these two approaches support the interpretation of $$X_1(2900)$$ X 1 ( 2900 ) as a $$\bar{D}_1 K$$ D ¯ 1 K molecular state, with $$J^{P}=1^-$$ J P = 1 - and an iso-singlet interpretation is much more favorable. The effect of triangle singularity on the production of $$X_1(2900)$$ X 1 ( 2900 ) is also discussed, and it is found that it cannot be interpreted as a pure triangle cusp.

Triangle relations for XY Z states

We propose novel triangle relations, not the well-known triangle singularity, for better understanding of the exotic [Formula: see text] states. Nine [Formula: see text] resonances, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] have been classified into triples to construct three triangles based on the assumption that they are all tetra-quark states. Here [Formula: see text] has not been observed experimentally yet, and we predict its mass and roughly the width. We also suggest some channels deserving search for with high priority based on this hypothesis, as well as predictions of a few production/decay rates of these channels. We hope further experimental studies of the [Formula: see text] states will benefit from our results.

Triangle singularity as the origin of $$X_0(2900)$$ and $$X_1(2900)$$ observed in $$B^+\rightarrow D^+ D^- K^+$$

The LHCb collaboration recently reported the observation of a narrow peak in the $$D^- K^+$$ D - K + invariant mass distributions from the $$B^+\rightarrow D^+ D^- K^+$$ B + → D + D - K + decay. The peak is parameterized in terms of two resonances $$X_0(2900)$$ X 0 ( 2900 ) and $$X_1(2900)$$ X 1 ( 2900 ) with the quark contents $${\bar{c}}{\bar{s}}ud$$ c ¯ s ¯ u d , and their spin-parity quantum numbers are $$0^+$$ 0 + and $$1^-$$ 1 - , respectively. We investigate the rescattering processes which may contribute to the $$B^+\rightarrow D^+ D^- K^+$$ B + → D + D - K + decays. It is shown that the $$D^{*-}K^{*+}$$ D ∗ - K ∗ + rescattering via the $$\chi _{c1}K^{*+}D^{*-}$$ χ c 1 K ∗ + D ∗ - loop and the $${\bar{D}}_{1}^{0}K^{0}$$ D ¯ 1 0 K 0 rescattering via the $$D_{sJ}^{+}{\bar{D}}_{1}^{0}K^{0}$$ D sJ + D ¯ 1 0 K 0 loop can simulate the $$X_0(2900)$$ X 0 ( 2900 ) and $$X_1(2900)$$ X 1 ( 2900 ) with consistent quantum numbers. Such phenomena are due to the analytical property of the scattering amplitudes with the triangle singularities located to the vicinity of the physical boundary.