Scalar-isoscalar states in the large-NcRegge approach

Abstract

Scalar-isoscalar states (${J}^{\mathrm{PC}}={0}^{++}$) are investigated within the large-${N}_{c}$ Regge approach. We elaborate on the consequences of including the lightest ${f}_{0}(600)$ scalar-isoscalar state into such an analysis, where the position of ${f}_{0}(600)$ fits very well into the pattern of the radial Regge trajectory. Furthermore, we point out that the pion and nucleon spin-0 gravitational form factors, recently measured on the lattice, provide valuable information on the low-mass spectrum of the scalar-isoscalar states on the basis of the scalar-meson dominance in the spin-0 channel. Through the fits to these data we find ${m}_{\ensuremath{\sigma}}=450--600\text{ }\text{ }\mathrm{MeV}$. We compare the predictions of various fits and methods. An analysis of the QCD condensates in the two-point correlators provides further constraints on the parameters of the scalar-isoscalar sector. We find that a simple two-state model suggests a meson nature of ${f}_{0}(600)$, and a glueball nature of ${f}_{0}(980)$, which naturally explains the ratios of various coupling constants. Finally, we note that the fine-tuned condition of the vanishing dimension-two condensate in the Regge approach with infinitely many scalar-isoscalar states yields a reasonable value for the mass of the lightest glueball state.