Pair annihilation in laser pulses: optical vs. XFEL regimes
Introduction. Prospects for probing the quantum vacuum using laser light at facilities such as ELI and the European XFEL currently attract a great deal of attention. Taking into account both the finite duration and spatial extent of modern laser pulses is challenging, but good analytic progress can be made if one assumes the laser is not too tightly focussed; it may then be modelled by a time dependent electric field, or a plane wave. Scattering in such backgrounds is very well understood, especially when the pulse is treated as having an effectively infinite duration [1–3]. These results have recently been re-evaluated, following the advent of ultra-short laser pulses, in order to expose the effects of finite pulse geometry on laser-particle scattering [4–8]. One may therefore still ask if, within this well known topic, there are unique experimental signatures from which one could easily identify strong-field effects. We discuss such a signal here, based on electron-positron annihilation. Unlike in vacuum, pair annihilation in a laser pulse may produce a single photon, both the energy and momentum of which are fixed. Photons from each annihilation event are emitted in the same direction and with the same energy. In other words, repeated (idealised) events would themselves produce a laser-like beam of photons. Since the produced photons carry half the energy of the incoming, accelerated, particles, they have energies well above the electron rest mass: our annihilation process would produce a gamma ray beam! Even if gamma-ray lasers are still a pipe dream, we note that the most promising route to their developement is via the annihilation of molecular positronium, as has been demonstrated in the lab [9]. The process we investigate here is essentially an ‘accelerator based’ version of that idea. We begin by summarising the properties of our process, before giving its exact cross section in a laser pulse of finite duration, using strong-field QED. This is then investigated for a variety of realistic optical and XFEL beam parameters. For related recent investigations see [10, 11]. Kinematics. In vacuum, momentum conservation implies that an electron-positron pair must annihilate to (at least) two photons [12]. In a laser field, though, the one-photon channel opens. This process is rather novel since there is only one allowed final state, modulo polarisations: momentum conservation alone determines the scattering products, as we now describe. We model the laser by a plane wave function of k.x, with the laser momentum kμ lightlike. A pair with momenta pμ and pμ (mass m) annihilate, using up some quantity l kμ of momentum from the laser fields, and produce a sinFIG. 1: Left: annihilation to two photons in vacuum. Right: the one-photon channel in a laser pulse. Double lines indicate dressing of the fermions by the laser field.