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

Abstract

We determine the contribution of long-range pion interactions to the $X(3872)$ dynamics, assuming it is a loosely bound $D^0{\bar{D}}^{\ast 0}$ 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 $D^{\ast }$ width. Our approach can also be applied to the recently discovered $T_{cc}^{+}$ states.

9 pages, 1 figure. v2: minor changes. Comparison with ref. [26] improved

References in corpus (6)

• Multiquark Resonances
• The Z(4430) and a New Paradigm for Spin Interactions in Tetraquarks
• Pion Interactions in the X(3872)
• A Theory of X and Z Multiquark Resonances
• Galilean-Invariant XEFT
• The interplay between compact and molecular structures in tetraquarks

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• Tetraquark-Jet Systems at the High-Luminosity LHC
• Probing the structure of $X(3872)$ in photoproduction
• A short review on the compositeness of the $X(3872)$
• Multimodal Fragmentation of All-Heavy Pentaquarks: Uncertainty-Aware Predictions for Hadron Colliders
• The general propagator for S-wave threshold states
• Heavy-flavor multimodal fragmentation to $S$-wave pentacharms at next-generation hadron colliders
• The Compact X and Z and their Invisible Molecular Partners