could also belong to the (0 , 0) representation. Admit- tedly, the heated debate on the nature of the σ meson is not completely over, with the tetraquark [15] (see also [16]) or glueball interpretations [17] considered (see, e.g, Ref. [1] and numerous references therein). liable determination of the asymptotic value of the σ mass at N$_{c}$ → ∞ . A fit to the $^{1}$S$_{0}$ leading- N$_{c}$ poten- tial yields m$_{σ}$ = 501(20) MeV [27]. Moreover, it was shown in Ref. [31] within the large- N$_{c}$ framework, that the correlated 2 π exchange corresponds to a Yukawa po- tential where the corresponding Yukawa mass differs by a 1 /N$_{c}$ correction to the pole mass or equivalently to the Breit-Wigner mass (the difference between both masses is O ( N − 2 c ) [32]). Finally, we should also note that using an alternative large- N$_{c}$ counting [33, 34], the scalar meson behaves as a ¯ qq ¯ qq state [35] and its width is O ( N − 2 c ). In the present work we take into account an infinite number of scalar-isoscalar states. In order to gather in- formation on their coupling to hadrons and the vacuum, we use a Regge model for the radial trajectories and study correlation functions between the energy-momentum ten- sor. Surprisingly, we find in Section II that quite natu- rally all the scalar-isoscalar states can be described by a single radial Regge trajectory with half the standard slope. The mass of the σ state can be deduced from this trajectory as the mass of the lowest state. As a conse- quence, there seems to be no obvious difference between mesons and glueballs, as far as the spectrum is concerned. Despite this surprising ordering with a sort of a radial quantum number, we should warn the reader that states of different nature may not necessarily be characterized by a single quantum number and other interpretations are considered in the literature. For example, f$_{0}$ (980) is often regarded as ¯ qq ¯ qq , f$_{0}$ (1370) as mainly ¯ uu + ¯ dd , f$_{0}$ (1500) as mainly a glueball, and f$_{0}$ (1710) dominantly as ¯ ss [1]. In such a case, there is no trajectory reveal- ing the sigma meson mass, and the observed regularity would be accidental. Our goal in the present paper is to point out that the large- N$_{c}$ Regge models may provide valuable insight into this problem. Clearly, the numbers in Eq. (1) represent the values for N$_{c}$ = 3. We recall that in the large- N$_{c}$ limit QCD can be mapped onto a theory of infinitely many stable and non-interacting mesons and glueballs [18, 19]. In the standard large- N$_{c}$ counting, meson and glueball masses are both O ( N 0 $_{c}$) whereas their widths are O ( N − 1 c ) and O ( N − 2 c ), respectively. However, there is also a large- N$_{c}$ -suppressed mass shift which makes a literal use of Eq. (1) somewhat questionable. Actually, lattice calcu- lations have shown that QCD$_{∞}$ is generally not too far from QCD at N$_{c}$ = 3 (see, e.g., Ref. [20] and references therein), at least for certain observables. The lightest scalar-isoscalar state (commonly denoted by σ ), due to its unusually large width, seems to be an exceptional case, and in this paper we try to address its nature and phe- nomenological consequences within the framework of the large- N$_{c}$ Regge models. Large- N$_{c}$ -motivated investigations for the ππ or NN interactions keep only the lowest 0 ++ state, and hence constitute the low-energy analyses (see e.g. Ref. [21] for an early investigation). The studies of the ππ scattering, based on a large- N$_{c}$ scaling of the N$_{c}$ = 3 parameters and unitarized via the Inverse Amplitude Method (IAM) ap- plied to the χ PT amplitudes, provide an N$_{c}$ dependence of resonances which, regarding the σ state, depends on the details of the scheme used. While the one-loop cou- pled channel approach [22] yields a very wide range of m$_{σ}$ and a large width (in an apparent contradiction with the standard large- N$_{c}$ counting [18, 19] when extrapolated to N$_{c}$ ≫ 10), the two-loop approach [23] produces a large shift (by a factor of 2) of m$_{σ}$ when going from N$_{c}$ = 3 to N$_{c}$ = ∞ (the corresponding mass shift is small in the case of the ρ meson). One should note the large uncertainties of the two-loop IAM, documented in Ref. [24]. Along similar large- N$_{c}$ counting, the K -matrix approach [25] gives m$_{σ}$ ∼ $_{2}$√$_{πf}$$_{π}$ = O $_{(}$√$_{N}$$_{c}$$_{). The Bethe-Salpeter ap-}$ proach [26] yields an estimate m$_{σ}$ ∼ 500 MeV [27] at N$_{c}$ → ∞ . A more refined analysis using the large- N$_{c}$ consistency conditions between the unitarization and res- onance saturation suggests m$_{ρ}$ − m$_{σ}$ = O ( N − 1 c ) [14]. Existing lattice studies of hadronic matrix elements of the energy-momentum tensor, the so-called gravitational form factors of the pion and nucleon, provide a very valuable complementary information on the σ properties, with the large- N$_{c}$ interpretation behind (Section IV). Unfortunately, the data are too noisy as to pin down the coupling of the excited scalar-isoscalar states to the energy-momentum tensor. Nevertheless, useful informa- tion confirming the mass estimates for the σ -meson can be extracted (Sect. IV). It is observed from the lattice data that the σ mass grows with the value of the light current quark mass in a natural way. It is interesting to discern the nature of the σ state from an analysis of a truncated spectrum. The minimum number of states, allowed by certain sum rules and low energy theorems, is just two. In Section V we undertake such an analysis, which suggests that f$_{0}$ (600) is a ¯ qq me- son, while f$_{0}$ (980) is a glueball. Finally, in Section VI we address the rather fundamental issue of the existence of dimension-2 condensates within the context of the Op- erator Product Expansion of QCD. Such objects appear naturally in the Regge approach and could not vanish if only a finite number of states were kept. Actually, we show that the dimension-2 condensate may vanish when infinitely many states are considered, in which case a The large- N$_{c}$ analysis of the NN force was carried out in Refs. [28, 29] at the quark level and in Ref. [30] at the hadronic level, providing a justification of the meson- exchange picture. Moreover, it indicates what mesons are the leading ones, namely the infinite tower of σ , π , ρ , ω , A$_{1}$ , etc. , states. Meson widths enter as relative 1 /N 2 c corrections to the potential, on equal footing with many other effects (the spin-orbit force, relativistic dy- namics, or the inclusion of other mesons), independently on how large the σ width is in the real N$_{c}$ = 3 world. In this regard the large- N$_{c}$ analysis may provide a re- 2