Abstract
The process of electron-positron annihilation into two photons in the presence of an intense classical plane wave of an arbitrary shape is investigated analytically by employing light-cone quantization and by taking into account the effects of the plane wave exactly. We introduce a general description of second-order 2-to-2 scattering processes in a plane-wave background field, indicating the necessity of considering the localization of the colliding particles and achieving that by means of wave packets. We define a local cross section in the background field, which generalizes the vacuum cross section and which, though not being directly an observable, allows for a comparison between the results in the plane wave and in vacuum without relying on the shape of the incoming wave packets. Two possible cascade or two-step channels have been identified in the annihilation process and an alternative way of representing the two-step and one-step contributions via a "virtuality" integral has been found. Finally, we compute the total local cross section to leading order in the coupling between the electron-positron field and the quantized photon field, excluding the interference between the two leading-order diagrams arising from the exchange of the two final photons, and express it in a relatively compact form. In contrast to processes in a background field initiated by a single particle, the pair annihilation into two photons, in fact, also occurs in vacuum. Our result naturally embeds the vacuum part and reduces to the vacuum expression, known in the literature, in the case of a vanishing laser field.
Highlights
With the development of high-power laser technology the verification of the nonlinear-QED predictions for various phenomena in an intense background field of a macroscopic extent is becoming attainable in laboratory experiments [1,2,3,4,5]
Among QED processes in an intense laser field, two first-order ones, nonlinear Compton scattering (e− ⇒ e−γ) [6,7,8,9,10,11,12,13,14,15,16,17,18] and nonlinear Breit-Wheeler pair production (γ ⇒ e−eþ) [8,19,20,21,22,23,24,25,26] have been extensively investigated theoretically, where by a double-line arrow we highlight the fact that a process happens in a background field, which in general has to be taken into account nonperturbatively
A general idea is that QED processes in a background field can be described locally as ones happening in a constant-crossed field (CCF) [8]
Summary
With the development of high-power laser technology the verification of the nonlinear-QED predictions for various phenomena in an intense background field of a macroscopic extent is becoming attainable in laboratory experiments [1,2,3,4,5]. If electron-positron annihilation and photon absorption are to be included into the consideration of the evolution of a many-particle system in an intense laser field, which may involve different geometries of particle collisions, it is necessary to assess the next-order processes, i.e., e−eþ ⇒ γγ and e−γ ⇒ e−γ, respectively. Using the Schwinger proper time representation for the electron propagator, we express the two-step and one-step contributions in a form, which has an advantage that it is concise and involves only integrals with fixed limits Another feature of 2-to-2 processes in a plane wave is the particular importance of taking into account the fact of the localization of the incoming particles, which we carry out by introducing normalized wave packets. Throughout the paper, Heaviside and natural units are used (ε0 1⁄4 ħ 1⁄4 c 1⁄4 1), m and e < 0 denote the electron mass and charge, respectively, α 1⁄4 e2=ð4πÞ ≈ 1=137 is the fine-structure constant
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