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Different pole structures in line shapes of the $X(3872)$
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abstract
We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective-range because it can also handle with a near-threshold zero in the $D^0\bar{D}^{*0}$ $S$-wave. In terms of it we analyze the CDF data on inclusive $p\bar{p}$ scattering to $J/\psi \pi^+\pi^-$, and the Belle and BaBar data on $B$ decays to $K\, J/\psi \pi^+\pi^-$ and $K D\bar{D}^{*0}$ around the $D^0\bar{D}^{*0}$ threshold. It is shown that data can be reproduced with similar quality for the $X(3872)$ being a bound {\it and/or} a virtual state. We also find that the $X(3872)$ might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small $D^{*0}$ width vanishes. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the $D^{*0}$ width itself. The $X(3872)$ compositeness coefficient in $D^0\bar{D}^{*0}$ ranges from nearly 0 up to 1 in the different scenarios.
Forward citations
Cited by 5 Pith papers
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Two-pion exchange for coupled-channel scattering of two heavy mesons
The authors derive the next-to-leading-order two-pion-exchange potentials for heavy meson and heavy antimeson scattering and show the results are close to simple momentum-dependent contact terms.
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Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
X(3872) is best described as a shallow D D* molecule in which one-pion exchange and a small charmonium core provide comparable attraction.
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Branching Fractions of the $X(3872)$
If the X(3872) is a weakly bound charm-meson molecule, its J/psi pi+ pi- branching fraction lies between roughly 4% and 33%, and is likely several times larger than the measured resonance-feature fraction.
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Composite nature of the $T_{cc}$ state
A CDD-pole fit to the LHCb Tcc line shape yields a compositeness of 0.23, suggesting the Tcc is mostly compact tetraquark rather than a D*D molecule.
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Composite nature of exotic states from data analysis
Compositeness values for X(3872), Zb(10610), Zb(10650), and Tcc are extracted from CDD-pole fits to published spectra; X(3872) is unconstrained (0 to 1), Tcc is found at 0.23 with large errors.
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