A potential approach to the $X(3872)$ thermal behavior

Abstract

We study the potential of $X(3872)$ at finite temperature in the Born-Oppenheimer approximation under the assumption that it is a tetraquark. We argue that, at large number of colors, it is a good approximation to assume that the potential consists in a real part plus a constant imaginary term. The real part is then computed adapting an approach by Rothkopf and Lafferty and using as input lattice QCD determinations of the potential for hybrids. This model allows us to qualitatively estimate at which temperature range the formation of a heavy tetraquark is possible, and to propose a qualitative picture for the dissociation of the state in a medium. Our approach can be applied to other suggested internal structures for the $X(3872)$ and to other exotic states.

12 pages, 7 figures. Numerical mistakes affecting two plots corrected, text changed accordingly; main conclusions unchanged

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• Multiquark Resonances
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• Static quark anti-quark interactions at non-zero temperature from lattice QCD
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• Tetraquark-Jet Systems at the High-Luminosity LHC
• Fully-heavy tetraquarks in the vacuum and in a hot environment