Molecular interpretation of the XYZ states

We study the vector vector system including all the possible channels with quantum numbers charm= 0, strangeness= 0 around the energy region of 4000 MeV. New states with hidden charm around 4000 MeV have been discovered by the B factories. They are intriguingly close to theD∗D̄∗ andDsD̄ ∗ s thresholds and do not have the properties of the charmonium states. We study the possible formation of D∗D̄∗ andDsD̄ ∗ s bound states in the framework of the Hidden Gauge formalism and discuss some of the models that favor the molecular assumption of some XYZ states: The hidden gauge formalism, Heavy baryon Chiral Perturbation Theory and the compositeness condition of Weinberg.

A summary of the properties of the candidate XYZ mesons discussed in the text. For simplicity, the quoted errors are quadratic sums of statistical and systematic uncertainties.

The XYZ particles
Some of the properties of the X(3872), X(3940), Y(3940), Z(3940) and X(4160) are They are just below of the DD ⇤ , D ⇤ (s)D ⇤ (s) thresholds They are relatively narrow The XYZ⇠3940 MeV and X(4160) have C-parity= + Some of them have estimated partial widths to !J/ or J/ above 1 MeV, quite larger than the measured partial decay widths for hadronic transitions between charmonium states The hidden gauge formalism Formalisms for heavy -heavy meson molecules
In the heavy -heavy sector we have ⇢, ! ( ) exchange The heavy -heavy sector is conected to the light -light sector through D ⇤ -exchange In PRD76 D. Gamermann, E. Oset, D. Strottman and M. J. Vacas, the chiral model and the phenomenological one lead to qualitatively the same results and small quantitative discrepancies Introduction Formalisms for heavy -heavy meson molecules The hidden charm sector   Table: Residues for the pole at (3866 0.003i) MeV in the C = 0; S = 0; I = 0 sector and positive C-parity The X(3872) "Essentially the couplings are proportional to the value of the wave function at the origin in coordinate space or the averaged value within the range of the interaction. They are not sensitive to the wave function at long distances and the averaged value of the wave function at the origin is the only information that is needed when dealing with short range processes," The fields H (Q) a transform as a (2,2) representation under the heavy quark spin ⌦SU (2) At leading order in the EFT expansion, the potential is the sum of a contact + pion exchange term (OPE) To have bound states compatible with power counting, J. Nieves and M. P. Valderrama, arXiv:1204.2790 (2012) molecules with 0 ++ or 2 ++ "molecular content of the deuteron" Weinberg (1963) 2 gives the probability of finding the molecular states in the physical state Can be generalized to unstables particles if the width is narrow and for resonances very near to threshold (Varu'04): 1429 i216 889 + i196 215 i107 Table: Couplings g i in units of MeV for I = 0, J = 0.
int. pseu.&anomal. int. pseu.&anomal. For Same interaction for DD, DD ⇤ , D ⇤ D ⇤ in the diagonal elements in the vector exchange terms

Heavy-heavy meson molecules
For the most important channel, DD: X (3700) ) " = m D + mD m X (3700) = 30 MeV Weinberg's formula for the deuteron: We can compare with our couplings (units of MeV): Weinberg formula hidden gauge X(3700) 13300 10400 X(3875) 8760 7270 X(3940) 18000 18800 Differences of the 10 20% or less. For diagram (4), we obtain:  HHChPT and hidden gauge theory leads to some "compatible" predictions on the existence of DD, DD ⇤ , D ⇤D⇤ meson molecules Coupled channel (DD, DD ⇤ , D ⇤D⇤ ) and pion exchange have small effects ⇢, !, exchange plays an important role in the heavy meson -heavy meson "molecules "