^{1}

^{2}

^{,*}

^{2}

^{3}

^{2}

^{,†}

^{3}.

The

The existence of hadronic molecules was conjectured long ago

Though it is easy to conjecture the existence of hadronic molecules from theoretical principles, making concrete predictions is considerably harder. The reason is that in most cases hadronic molecules are generated as a consequence of unknown short-range physics. This is manifest from the necessity of cutoffs/form factors. If we consider the one pion exchange (OPE) potential, which is expected to be the longest range piece of the interaction between two hadrons (provided they contain at least one light quark), we will quickly realize that it requires regularization: the OPE potential contains a tensor piece that is singular at short distances. The tensor force, if attractive, will be able to hold an infinite number of bound states. This situation is circumvented by the introduction of a form factor, cutoff or other regulator that renders predictions possible at the price of the introduction of an unknown new parameter

Yet the tensor force is not present in every hadron molecule. The richness of the hadron spectrum gives rise to other possibilities even if we only consider the exchange of a pseudo–Nambu-Goldstone boson. If a pion or a kaon is exchanged in a vertex involving hadrons with different parities a series of interesting situations can arise. If in addition a vertex involves hadrons with different masses, this can lead to interactions with an unusual long range for strong interactions. A recent example is a Coulomb-like force in the

Here we consider the

This type of kaon exchange leads to a different spectrum than the one obtained from standard OPE

The

Now we calculate the one kaon exchange (OKE) potential in the

The heavy meson chiral lagrangian for the interaction between the S- and P-wave heavy mesons is

In the second scenario we deduce

The leading order (

This is a consequence of extended Bose-Einstein statistics. The potential exchanges the

Concrete calculations of the binding will be divided in two scenarios: a compact and a molecular

In the first scenario—

The importance of OKE can also be understood by reinterpreting the previous predictions as the leading order (LO) calculation in an effective field theory (EFT) with the heavy mesons and the pseudo–Nambu-Golstone bosons as the low energy degrees of freedom. Within this framework, the longest range correction to the OKE potential comes from two pion exchange (TPE),

Two kaon exchange does not benefit from the enhanced range of OKE and we do not further consider it.

in particular the football and triangle diagramsIn the second scenario—the

For instance, a monopolar form factor in each kaon vertex with

Yet the binding momenta of the

Other interesting aspect of the

Probably the most effective way to produce the

The previous ideas also apply to the bottom sector, where the

To summarize, the

M. P. V. thanks the Institut de Physique Nucléaire d’Orsay, where part of this work was done, for its hospitality, This work is partly supported by the National Natural Science Foundation of China under Grants No. 11375024, No. 11522539, No. 11735003, the Fundamental Research Funds for the Central Universities, the Thousand Talents Progam for Youth Professionals and by the JSPS KAKENHI Grant No. JP16K17694.