New Dynamics (?) of $J/ψJ/ψ$ and $ΥΥ$ families from QCD Laplace sum rules at NLO

Abstract

Motivated by the recent CMS data on a family of $2^{++}$ states from $J/ψJ/ψ$ mass spectrum, we determine the masses of the $2^{++}$ $J/ψJ/ψ$ molecule and $cc\bar c\bar c$ states, by using (for the first time) the two lowest QCD Laplace Sum Rules (LSR) moment-ratios within the standard optimization criteria with respect to the LSR variable $τ$ and to the QCD continuum threshold $t_c$ implemented by the $R_{P/C}$ requirement that the lowest ground state (Pole) contribution to the LSR is larger than the QCD continuum one. Including factorized NLO perturbative and LO $G^4$ gluon condensates in the OPE, we obtain the the lowest ground state masses: $M^{2^{++}}_{J/ψJ/ψ}=6521(69)$ MeV and $M^{2^{++}}_{cc\bar c \bar c}=6347(99)$ MeV with the couplings\,: $f^{2^{++}}_{J/ψJ/ψ}=96(14)$ keV and $f^{2^{++}}_{cc\bar c \bar c}= 151(29)$ keV normalized as $f_π=93$ MeV. The masses of the first radial excitations are :$M^{2^{++}{rad}}_{J/ψJ/ψ}=7987(251 )$ MeV and $M^{2^{++}{rad}}_{cc\bar c \bar c}=7739(221)$ MeV indicating a mass-splitting about $2.5 (M_{ψ(2S)}-M_{J/ψ})$. The decay constants are $f^{2^{++}{rad}}_{J/ψJ/ψ}=248(70)$ keV and: $f^{2^{++}{\rm rad}}_{cc\bar c\bar c}=453(96) $ keV which are (unexpectedly) larger than the lowest ground state ones. These features may indicate some new dynamics compared to ordinary $\bar cc$ states. We extend the analysis to the $0^{++}$ states and to the $ΥΥ$ family where the results are compiled in Tables 2 and 3. We critically review some other QCD spectral sum rules (QSSR) results. We suggest that the X(6600) might be a molecule ground state. Using a two-component mass mixing scheme, the X(6900) and X(7100) might be interpreted as a mixture of the $cc\bar c\bar c$ lowest ground state with its 1st radial excitation via an angle $θ=5^0$.