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

الأصل · EN

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons σ(600) and f₀(980) to the operators qq, αₛ G² and to two photons. The Roy dispersive representation for the ππ amplitude t₀⁰(s) is used to determine the pole positions as well as the residues in the complex plane. On the real axis, t₀⁰ is constrained to solve the Roy equation together with elastic unitarity up to the K threshold leading to an improved description of the f₀(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 jₛ 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 Omnès dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the qq 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 σ, κ, a₀(980), f₀(980) into a nonet. Concerning the gluonic operator αₛ G² we find a significant coupling to both the σ and the f₀(980).