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Abstract |
When pions are exchanged almost on-shell the range of hadron interactions
is unusually long, opening the possibility to interesting phenomena. One
example is the Lambda_c(2590) -> Sigma_c pi transition, which is mediated by
the emission of an S-wave pion near the mass-shell. Other more well-known
example is the D* -> D \pi transition, though in this case the pion is in
P-wave. When we combine both vertices to obtain the Lambda_c(2590) Dbar -> Sigma_c D*bar potential, the result is a long-range inverse square potential. With this potential the Lambda_c(2590) Dbar - Sigma_c D*bar system becomes scale invariant, i.e. it is symmetric under dilatations, a property which is also shared by two- and three-body systems with large scattering lengths. This symmetry is however anomalous and is broken by the spectrum, which can at most display a discrete form of it if the interaction is strong enough. We explore where this is the case in the Lambda_c(2590) Dbar - Sigma_c D*bar system, which is a candidate for a molecular explanation of the recently observed heavy pentaquark Pc(4450)+, or in other hadron molecules. In addition we consider what happens when we have a Lambda_c(2590) Sigma_c (or anti Sigma_c) molecule. In this latter case the potential is of the 1/r type, but which an unusual long-range, behaving as Coulomb for typical hadronic scales. The interesting point here is that this coulomb-like potential probably holds an S-wave shallow state, making for a nice prediction of a near-threshold hadron molecule. |
