Heavy-hadron molecules from light-meson-exchange saturation

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 $Z_c(3900/4020)$.

arXiv comment8 pages, 1 figure, 1 table, corresponds to published version

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• The $P_{cs}(4459)$ pentaquark from a combined effective field theory and phenomenological perspective
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• Spin-parities of the $P_c(4440)$ and $P_c(4457)$ in the One-Boson-Exchange Model
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• The LHCb state $P_{\psi s}^{\Lambda }(4338)$ as a triangle singularity
• Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature
• Heavy-hadron molecular spectrum from light-meson exchange saturation
• Photoproduction of strange hidden-charm and hidden-bottom states
• Experimental constraints on the properties of $P_c$ states
• Production of $P_c$ states in ${\Lambda }_b$ decays
• Heavy- and light-flavor symmetry partners of the $T_{cc}^{+}(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation
• Peaks within peaks and the possible two-peak structure of the Pc(4457): the effective field theory perspective
• Molecular charmed baryons and pentaquarks from light-meson exchange saturation
• Prompt production of the hidden charm pentaquarks in the LHC
• Unravelling Pentaquarks with Born--Oppenheimer effective theory
• Molecular $P_{\psi }$ pentaquarks from light-meson exchange saturation
• Possible ${\Sigma }_c^{\ast }\bar{\Sigma }$ molecular states
• Hadronic molecules and multiquark states
• Decoding the near-threshold $X_{0,1}(4140)$ and $X_1(4685)$ states via OZI-suppressed coupled-channel scattering