Remarks on the Heavy-Quark Flavour Symmetry for doubly heavy hadronic molecules

TL;DR

The paper critically examines the applicability of a unified effective field theory for doubly heavy hadronic molecules across different heavy-quark flavors, highlighting limitations in relating binding energies between charm and bottom sectors.

Contribution

It clarifies that a common effective field theory cannot reliably connect heavy-quark sectors, emphasizing the need for phenomenological approaches with uncontrolled uncertainties.

Findings

Unified EFT does not allow precise relations between charm and bottom sectors.

Heavy-quark spin symmetry can be used within individual sectors.

Relations between sectors require phenomenological models with large uncertainties.

Abstract

The possibility for a common effective field theory for hadronic molecules with different heavy-quark flavours is examined critically. It is argued that such a theory does not allow one to draw definite conclusions for doubly heavy molecules. In particular, it does not allow one to relate binding energies for the molecules in the c-quark and b-quark sectors with controlled uncertainties. Therefore, while this kind of reasoning does not preclude from employing heavy-quark spin symmetry for charmonium- and bottomonium-like states separately within a well established effective field theory framework, relations between different heavy-quark sectors can only be obtained using phenomenological approaches with uncontrolled uncertainties.