Observing light-by-light scattering in vacuum with an asymmetric photon collider

The elastic scattering of two real photons in vacuum is one of the most elusive of the fundamentally new processes predicted by quantum electrodynamics. This explains why, although it was first predicted more than eighty years ago, it has so far remained undetected. Here we show that in present-day facilities, the elastic scattering of two real photons can become detectable far off axis in an asymmetric photon-photon collider setup. This may be obtained within one day of operation time by colliding 1 mJ extreme ultraviolet pulses with the broadband gamma-ray radiation generated in nonlinear Compton scattering of ultrarelativistic electron beams with terawatt-class optical laser pulses operating at a 10 Hz repetition rate. In addition to the investigation of elastic photon-photon scattering, this technique allows us to unveil or constrain new physics that could arise from the coupling of photons to yet undetected particles, therefore opening new avenues for searches of physics beyond the standard model.

Figure 1

Schematic setup. A collimated ultrarelativistic electron beam propagating along $x$ collides with an intense linearly polarized optical laser pulse, therefore generating a collimated gamma-ray beam. The laser pulse polarization axis and propagation direction are in the $xy$ plane. The electron beam and possible positrons generated in the collision with the laser pulse are deflected by a magnetic field along $z$. The gamma-ray beam passes through a collimator, which selects photons with small angle with respect to the $xy$ plane. The collimated gamma-ray beam collides with an XUV pulse propagating in the $xz$ plane. Elastic photon-photon scattering events can result in large-angle ${\psi }_s≔\arctan (p_{s,z}/p_{s,x})$ photon deflection, where ${\mathbf{p}}_s$ is the photon momentum after scattering.

Figure 2

Normalized exact differential elastic photon-photon scattering cross section ${\sigma }^{-1}d\sigma /d\mathrm{\Omega }$ in the CM frame for ${ϵ}_{\mathrm{CM}}=0.9m_e{c}^2$ (orange line), ${ϵ}_{\mathrm{CM}}=0.5m_e{c}^2$ (blue line), ${ϵ}_{\mathrm{CM}}=0.1m_e{c}^2$ (red line), and the ${ϵ}_{\mathrm{CM}}\ll m_e{c}^2$ approximation (black dashed line). The inset plots the exact total elastic photon-photon cross section $\sigma$ (orange line) and its ${ϵ}_{\mathrm{CM}}\ll m_e{c}^2$ approximation (black dashed line).

Figure 3

Fraction of photons elastically scattered to angles greater than ${\theta }_s$ from Eq. (1) as a function of ${\theta }_s$ for ${\gamma }_{\mathrm{CM}}={10}^4$ (orange line), ${\gamma }_{\mathrm{CM}}=5\times {10}^3$ (black line), and ${\gamma }_{\mathrm{CM}}={10}^3$ (blue line).

Figure 4

Normalized gamma-ray beam distributions after the collimator. (a) ${\log }_{10}[N_{\gamma }({\psi }_{\gamma },{ϵ}_{\gamma })/\max (N_{\gamma }({\psi }_{\gamma },{ϵ}_{\gamma }))]$, (b) ${\log }_{10}[N_{\gamma }({\psi }_{\gamma },{\eta }_{\gamma })/\max (N_{\gamma }({\psi }_{\gamma },{\eta }_{\gamma }))]$. $N_{\gamma }$ is the photon number, ${ϵ}_{\gamma }$ the photon energy, ${\psi }_{\gamma }≔\arctan (p_{\gamma ,z}/p_{\gamma ,x})$, and ${\eta }_{\gamma }≔\arctan (p_{\gamma ,y}/p_{\gamma ,x})$, where ${\mathbf{p}}_{\gamma }$ is the photon momentum. Note the different scales for ${\psi }_{\gamma }$ and ${\eta }_{\gamma }$.

Figure 5

Number of elastically scattered photons for one-week operation time as a function of the scattered photon energy ${ϵ}_s$ and of the photon scattering angle ${\psi }_s≔\arctan (p_{s,z}/p_{s,x})$. The inset displays the number of events as a function of ${\psi }_s$ and of ${\eta }_s≔\arctan (p_{s,y}/p_{s,x})$. Photons scattered in the region outside the two black horizontal lines provide a detectable signal of scattering.