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$T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})\pi$ three-body effect

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arxiv 2205.14628 v2 pith:2G3MSN7T submitted 2022-05-29 hep-ph

Zi-Yang Lin , Jian-Bo Cheng , Shi-Lin Zhu This is my paper · ORCID
classification hep-ph
keywords effectthree-bodychannelscomplexfindwidthapplyaround
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DD\pi$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DD\pi$ three-body threshold. By solving the complex scaled Schr\"odinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}\pi$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole

    hep-ph 2024-12 conditional novelty 6.0 of 10

    A model-dependent study showing that the existence of a DDD* bound state is tied to the virtual-state pole position of Zc(3900), with binding occurring only for near-threshold Zc poles.

  2. Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states

    hep-ph 2025-01 conditional novelty 5.0 of 10

    S-wave calculations predict bound and resonant states in trilepton and tetralepton systems made of electrons and muons, including the first muon-containing tetralepton resonances.

  3. Investigating the two-pion exchange of the double charm $DD^*$ chiral interactions and $T_{cc}$

    hep-ph 2025-09 conditional novelty 4.0 of 10

    In this chiral EFT calculation the I=0 DD* two-pion-exchange potential is repulsive, and its near-cancellation with attractive contact and one-pion terms provides the weak binding of Tcc.

  4. Composite nature of the $T_{cc}$ state

    hep-ph 2024-12 conditional novelty 4.0 of 10

    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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