Determine the physical nature and pole positions of doubly heavy pseudo-bound states with P-wave dynamics

Determine the true physical nature and pole positions of the isoscalar pseudo-bound states predicted in the S-wave cc\bar{n}\bar{n} and bb\bar{n}\bar{n} sectors by explicitly incorporating the omitted P-wave decay channels and dynamics.

Background

The calculations are restricted to S-wave configurations. In the isoscalar ccnˉnˉcc\bar{n}\bar{n} 0(0+)0(0^+) and 0(2+)0(2^+) channels, Bose-symmetry constraints prohibit S-wave decays into the corresponding ground-state DDDD and D∗D∗D^*D^* channels, while the lowest allowed S-wave thresholds involve radially excited mesons. Because the lower-lying P-wave channels are omitted, the resulting deeply bound eigenvalues are interpreted as “pseudo-bound states” that may instead represent physical P-wave scattering states.

The unresolved issue is whether these states are genuine tetraquark bound states or artifacts of the restricted partial-wave treatment, and how their complex pole positions change once the relevant P-wave dynamics are included. The same qualification is stated for the analogous isoscalar pseudo-bound states in the bbnˉnˉbb\bar{n}\bar{n} sector.

References

Lacking these corresponding decay thresholds, they manifest as pseudo-bound states'', which are intrinsically physical $P$-wave scattering states. Notably, thesepseudo-bound states'' cannot be obtained within the H-only framework. The K-type configurations are indispensable, as they partially encapsulate the effects of higher partial waves. The explicit inclusion of $P$-wave dynamics in future studies could alter their positions and reveal their true physical nature.

— Investigation of S-wave tetraquark bound and resonant states with all Jacobi coordinates  (2608.28284 - Zheng et al., 28 Aug 2026) in Section “Numerical results,” subsection “$cc\bar{n}\bar{n}$” (discussion of the isoscalar $0(0^+)$ and $0(2^+)$ channels); reiterated in subsection “$bb\bar{n}\bar{n}$”