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The role of the pion in the lineshape of the $X(3872)$
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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.
Forward citations
Cited by 2 Pith papers
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High-energy dynamics of QCD: Theoretical and phenomenological results
Real NLO corrections to the BFKL Higgs impact factor are derived with a physical top-quark mass, and updated tetraquark fragmentation functions are applied to predict rates at 14 and 100 TeV.
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A short review on the compositeness of the $X(3872)$
Radiative decays and the LHCb line-shape data are incompatible with a purely molecular X(3872) and favor a compact or partially composite state, with a proposed molecular-amplitude fit for a decisive test.
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