Limits on low energy photon-photon scattering from an experiment on magnetic vacuum birefringence

Experimental bounds on induced vacuum magnetic birefringence can be used to improve present photon-photon scattering limits in the electronvolt energy range. Measurements with the Polarizzazione del Vuoto con Laser apparatus [E. Zavattini , Phys. Rev. D 77, 032006 (2008)PRVDAQ0556-282110.1103/PhysRevD.77.032006] at both λ=1064 and 532 nm lead to bounds on the parameter A_e, describing nonlinear effects in QED, of A_e⁽¹⁰⁶⁴⁾<6.6×10^-21T^-2@1064nm and A_e⁽⁵³²⁾<6.3×10^-21T^-2@532nm, respectively, at 95% confidence level, compared to the predicted value of A_e=1.32×10^-24T^-2. The total photon-photon scattering cross section may also be expressed in terms of A_e, setting bounds for unpolarized light of σ_γγ⁽¹⁰⁶⁴⁾<4.6×10^-62m² and σ_γγ⁽⁵³²⁾<2.7×10^-60m². Compared to the expected QED scattering cross section these results are a factor of ≃2×10⁷ higher and represent an improvement of a factor about 500 on previous bounds based on ellipticity measurements and of a factor of about 10¹⁰ on bounds based on direct stimulated scattering measurements.