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How does the $X (3872)$ show up in $e^{+} e^{-}$ collisions: Dip versus peak

Vadim Baru ^1,*, Feng-Kun Guo ^2,3,4,5,†, Christoph Hanhart ^6,‡, and Alexey Nefediev ^7,8,§

¹Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany
²CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
⁵Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
⁶Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
⁷Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
⁸CeFEMA, Center of Physics and Engineering of Advanced Materials, Instituto Superior Técnico, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal

^*vadim.baru@tp2.rub.de
^†fkguo@itp.ac.cn
^‡c.hanhart@fz-juelich.de
^§Alexey.Nefediev@ijs.si

Phys. Rev. D 109, L111501 – Published 12 June, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L111501

Abstract

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for $e^{+} e^{-} \to J / ψ π^{+} π^{-}$ admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong $S$ -wave $D {\bar{D}}^{*}$ attraction that generates the state $X (3872)$ . We anticipate the appearance of a similar dip in the $e^{+} e^{-} \to J / ψ π^{+} π^{-} π^{0}$ final state near the $D^{*} {\bar{D}}^{*}$ threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-2 partner of the $X (3872)$ .

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Phys. Rev. D 109, L111501– Published 12 June, 2024

Vol. 109, Iss. 11 — 1 June 2024

Received 22 April 2024
Accepted 16 May 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L111501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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How does the $X (3872)$ show up in $e^{+} e^{-}$ collisions: Dip versus peak

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How does the $X (3872)$ show up in $e^{+} e^{-}$ collisions: Dip versus peak