The role of the pion in the lineshape of the X(3872)

Creators: Esposito, Angelo^{1, 2}; Germani, Davide¹; Glioti, Alfredo³; Polosa, Antonio D.^{1, 2}; Rattazzi, Riccardo⁴; Tarquini, Michele⁵

1. Sapienza University of Rome
2. INFN Sezione di Roma I
3. French National Centre for Scientific Research
4. École Polytechnique Fédérale de Lausanne
5. California Institute of Technology

Abstract

We determine the contribution of long-range pion interactions to the dynamics, assuming it is a loosely bound 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 a term associated with, but not precisely corresponding to, the width. Our approach can also be applied to the recently discovered

Copyright and License

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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