Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I = 0 mesons sigma(600) and f(0)(980) to the operators (q) over barq, alpha(s)G(2) and to two photons. The Roy dispersive representation for the pi pi amplitude t(0)(0)(s) is used to determine the pole positions as well as the residues in the complex plane. On the real axis, t(0)(0) is constrained to solve the Roy equation together with elastic unitarity up to the K (K) over bar threshold leading to an improved description of the f(0)(980). The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator j(S) and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omnes dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the (q) over barq couplings with earlier determinations of the analogous couplings of the lightest I = 1 and I = 1/2 scalar mesons are compatible with an assignment of the sigma, kappa, a(0)(980), f(0)(980) into a nonet. Concerning the gluonic operator alpha(s)G(2) we find a significant coupling to both the sigma and the f(0)(980).