Abstract
In the effective field theory framework the interaction between two heavy hadrons can be decomposed into a long- and a short-range piece. The long-range piece corresponds to the one-pion-exchange potential and is relatively well-known. The short-range piece is given by a series of contact-range interactions with unknown couplings, which substitute the less well-known short-range dynamics. While the general structure of the short-range potential between heavy hadrons is heavily constrained from heavy-quark symmetry, the couplings are still free parameters. Here we argue that the relative strength and the sign of these couplings can be estimated from the hypothesis that they are saturated by the exchange of light mesons, in particular the vector mesons $\rho$ and $\omega$, i.e. from resonance saturation. However, we propose a novel saturation procedure that effectively removes form-factor artifacts. From this we can determine in which spin and isospin configurations the low-energy constants are most attractive for specific two-heavy-hadron systems. In general the molecular states with lower isospins and higher spins will be more attractive and thus more probable candidates to form heavy-hadron molecules. This pattern is compatible with the interpretation of the $X(3872)$ and $P_c(4312/4440/4457)$ as molecular states, but it is not applicable to states with maximum isospin like the $Z_c(3900/4020)$.
Highlights
Heavy-hadron molecules might very well be the most popular type of exotic hadron [1,2,3]
We argue that the relative strength and the sign of these couplings can be estimated from the hypothesis that they are saturated by the exchange of light mesons, in particular the vector mesons ρ and ω, i.e., from resonance saturation
In general the molecular states with lower isospins and higher spins will be more attractive and more probable candidates to form heavy-hadron molecules. This pattern is compatible with the interpretation of the Xð3872Þ and Pcð4312=4440=4457Þ as molecular states, but it is not applicable to states with maximum isospin like the Zcð3900=4020Þ
Summary
Heavy-hadron molecules might very well be the most popular type of exotic hadron [1,2,3]. The present manuscript attempts to address this limitation by proposing a potential pattern in the spectrum of two-heavy-hadron bound states: for configurations without maximum isospin, the states with higher (light-quark) spin are expected to be lighter (i.e., more bound).
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