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arXiv · 2307.11400

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

Angelo Esposito·Davide Germani·Alfredo Glioti·Antonio D. Polosa·Riccardo Rattazzi·Michele Tarquini
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Abstract

We determine the contribution of long-range pion interactions to the $X(3872)$ dynamics, assuming it is a loosely bound $D^0 \bar{D}^{*0}$ 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 $X(3872)$ with a term associated with, but not precisely corresponding to, the $D^*$ width. Our approach can also be applied to the recently discovered $T_{cc}^+$ states.

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Angelo Esposito, Davide Germani, Alfredo Glioti, Antonio D. Polosa, Riccardo Rattazzi, Michele Tarquini. 2023-07-21. The role of the pion in the lineshape of the $X(3872)$. https://doi.org/10.1016/j.physletb.2023.138285

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