The lightest QCD resonance, the $\sigma$, has been recently fixed in the $\pi \pi$ scattering amplitude. The nature of this state remains nowadays one of the most intriguing and difficult issues in particle physics. Its coupling to photons is crucial for discriminating its structure. We propose a new method that fixes this coupling using only available precise experimental data on the proton electromagnetic polarizabilities together with analyticity and unitarity. By taking into account the uncertainties in the analysis and in the parameter values, our result is ${\Gamma }_{\mathrm{pole}}(\sigma \to \gamma \gamma )=1.2\pm 0.4\mathrm{keV}$.

• Received 13 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.241804