Dispersive Analysis of Excited Glueball States

Motivated by the determination for the spin-parity quantum numbers of the X(2370) meson at BESIII, we extend our dispersive analysis on hadronic ground states to excited states. The idea is to start with the dispersion relation which a correlation function obeys, and subtract the known ground-state contribution from the involved spectral density. Solving the resultant dispersion relation as an inverse problem with available operator-product-expansion inputs, we extract excited-state masses from the subtracted spectral density. This formalism is verified by means of the application to the series of ρ resonances, which establishes the ρ(770), ρ(1450) and ρ(1700) mesons one by one under the sequential subtraction procedure. Our previous study has suggested the admixture of the f₀(1370), f₀(1500) and f₀(1710) mesons (the η(1760) meson) to be the lightest scalar (pseudoscalar) glueball. The present work predicts that the f₀(2200) (X(2370)) meson is the first excited scalar (pseudoscalar) glueball.