Limits on Low Energy Photon-Photon Scattering from an Experiment on Magnetic Vacuum Birefringence

Abstract

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 $\hat{I}»=1064$ 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 $A_e^{(532)}<6.3\cdot 10^{-21}$ 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 $\ddot{I}{ƒ}_{{\hat{I}}^3{\hat{I}}^3}^{(1064)}<4.6\cdot 10^{-62}$ m${}^2$ and $\ddot{I}{ƒ}_{{\hat{I}}^3{\hat{I}}^3}^{(532)}<2.7\cdot 10^{-60}$ 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.