Heavy-hadron molecular spectrum from light-meson exchange saturation

Abstract

If known, the spectrum of heavy-hadron molecules will be a key tool to disentangle the nature of the exotic states that are being discovered in experiments. Here we argue that the general features of the molecular spectrum can be deduced from the idea that the short-range interaction between the heavy hadrons is effectively described by scalar and vector meson exchange, i.e. the $\sigma$, $\omega$ and $\rho$ mesons. By means of a contact-range theory where the couplings are saturated by the aforementioned light mesons we are indeed able to postdict the $X(3872)$ (as a $D^{\ast }\bar{D}$ molecule) from the three $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks (as $\bar{D}{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c$ molecules). We predict a $J^{PC}=1^{--}$ $D{\bar{D}}_1$ molecule at $4240-4260\mathrm{MeV}$ which might support the hypothesis that the $Y(4260)$ is at least partly molecular. The extension of these ideas to the light baryons requires minor modifications, after which we recover approximate SU(4)-Wigner symmetry in the two-nucleon system and approximately reproduce the masses of the deuteron and the virtual state.

13 pages, 1 table; corresponds to the published version

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Cited by in corpus (10)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Revisiting the $D{D}^{\ast }$ chiral interactions with the local momentum-space regularization up to the third order and the nature of $T_{cc}^{+}$
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• Heavy- and light-flavor symmetry partners of the $T_{cc}^{+}(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation
• Production rates of $D_s^{+}{D}_s^{-}$ and $D\bar{D}$ molecules in $B$ decays
• Molecular charmed baryons and pentaquarks from light-meson exchange saturation
• Molecular $P_{\psi }$ pentaquarks from light-meson exchange saturation
• Insights into the nature of the $P_{cs}(4459)$
• Hadronic molecules and multiquark states
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram