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 et al., Phys. Rev. D 77, 032006 (2008)] at both $\lambda =1064$ and 532 nm lead to bounds on the parameter $A_e$, describing nonlinear effects in QED, of $A_e^{(1064)}<6.6\times {10}^{-21}{\mathrm{T}}^{-2}@1064\mathrm{nm}$ and $A_e^{(532)}<6.3\times {10}^{-21}{\mathrm{T}}^{-2}@532\mathrm{nm}$, respectively, at 95% confidence level, compared to the predicted value of $A_e=1.32\times {10}^{-24}{\mathrm{T}}^{-2}$. The total photon-photon scattering cross section may also be expressed in terms of $A_e$, setting bounds for unpolarized light of ${\sigma }_{\gamma \gamma }^{(1064)}<4.6\times {10}^{-62}{\mathrm{m}}^2$ and ${\sigma }_{\gamma \gamma }^{(532)}<2.7\times {10}^{-60}{\mathrm{m}}^2$. Compared to the expected QED scattering cross section these results are a factor of $\simeq 2\times {10}^7$ 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.

Figure 1

First-order Feynman diagrams for both photon-photon scattering and magnetically (electrically) induced vacuum birefringence.

Figure 2

Schematic layout of a sensitive ellipsometer. See text for description.

Figure 3

Reference frame for the calculations using the Jones matrix formalism.

Figure 4

Schematic layout of the PVLAS apparatus. See text for description.

Figure 5

Calculated and measured noise contributions for the infrared and green configurations of the PVLAS apparatus. See text and Table 2 for the parameters of each configuration.

Figure 6

Polar plot for the ellipticity signal generated with a 2.3 T magnetic field intensity when helium gas is present in the vacuum chamber. The figure shows the signal for four different gas pressures: 5, 10, 15 and 20 mbar. Each data point represents the amplitude and phase of the signal peak observed in a 100 s long time record. This figure was already published as Fig. 3 in our previous paper cited in Ref. [16].

Figure 7

Noise distributions in the magnet rotation frequency band $1.92{\Omega }_{\mathrm{Mag}}-{2.08}_{\mathrm{Mag}}$ for the 2.3 T ellipticity measurements with the IR (left) laser and the green (right) laser. The vertical line indicates the value in the Fourier spectrum corresponding to $2{\Omega }_{\mathrm{Mag}}$. Indicated in the legend is the value of $\sigma$ for the two wavelengths. The figure on the left was already published as Fig. 7 (left) in our previous paper cited in Ref. [16].