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 f 0 (1370), f 0 (1500) and f 0 (1710) mesons (the η (1760) meson) to be the lightest scalar (pseudoscalar) glueball. The present work predicts that the f 0 (2200) ( X (2370)) meson is the first excited scalar (pseudoscalar) glueball.