The role of the pion in the lineshape of the X(3872)
Creators
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1.
Sapienza University of Rome
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2.
INFN Sezione di Roma I
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3.
French National Centre for Scientific Research
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4.
École Polytechnique Fédérale de Lausanne
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5.
California Institute of Technology
Abstract
We determine the contribution of long-range pion interactions to the X(3872) dynamics, assuming it is a loosely bound D⁰D¯⁰ molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the X(3872) a term associated with, but not precisely corresponding to, the D* width. Our approach can also be applied to the recently discovered T⁺_(cc) state.
Copyright and License
© 2023 The Author(s). Published by Elsevier B.V. Funded by SCOAP³.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Acknowledgement
R.R. is partially supported by the Swiss National Science Foundation under contract 200020-213104 and through the National Centres of Competence in Research SwissMAP. A.E. and A.D.P. thank Hans Werner Hammer for an informative discussion. A.D.P. wishes to thank Adam Szczepaniak and Kevin Ingles for useful clarifications. We also thank the anonymous referee for providing suggestions on how to compare our results with those of [26].
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. R.R. is partially supported by the Swiss National Science Foundation under contract 200020-213104 and through the National Centres of Competence in Research SwissMAP.
Data Availability
No data was used for the research described in the article.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2307.11400 (arXiv)
Funding
- Swiss National Science Foundation
- 200020-213104
- Swiss National Science Foundation
- National Centres of Competence in Research
- SCOAP3
Dates
- Accepted
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2023-10-25Accepted
- Available
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2023-10-29Available online
- Available
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2023-10-31Version of record