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 PVLAS apparatus (E. Zavattini {\it et al.}, Phys. Rev. D {\bf77} (2008) 032006) at both $\lambda =1064$ nm and 532 nm lead to bounds on the parameter {\it A${}_e$}, describing non linear effects in QED, of $A_e^{(1064)}<6.6\cdot {10}^{-21}$ T${}^{-2}$ @ 1064 nm and $A_{e}^{(532)} < 6.3\cdot10^{-21}$T$^{-2}$ @ 532 nm, respectively, at 95% confidence level, compared to the predicted value of $A_e=1.32\cdot {10}^{-24}$ T${}^{-2}$. The total photon-photon scattering cross section may also be expressed in terms of $A_e$, setting bounds for unpolarized light of $\sigma_{\gamma\gamma}^{(1064)} < 4.6\cdot10^{-62}$m$^{2}$and$\sigma_{\gamma\gamma}^{(532)} < 2.7\cdot10^{-60}$m$^{2}$. Compared to the expected QED scattering cross section these results are a factor of $\simeq 2\cdot {10}^7$ higher and represent an improvement of a factor about 500 on previous bounds based on ellipticity measurements and of a factor of about ${10}^{10}$ on bounds based on direct stimulated scattering measurements.