Complete QED Theory of Multiphoton Trident Pair Production in Strong Laser Fields

Electron-positron pair creation by multiphoton absorption in the collision of a relativistic electron with a strong laser beam is calculated within laser-dressed quantum electrodynamics. Total production rates, positron spectra, and relative contributions of different reaction channels are obtained in various interaction regimes. We study the process in a manifestly nonperturbative domain which is shown accessible to future experiments utilizing the electron beam lines at novel x-ray laser facilities or all-optical setups based on laser acceleration. Our theory moreover allows us to add further insights into the experimental data from SLAC [D. Burke et al., Phys. Rev. Lett. 79, 1626 (1997).].

Figure 1

Furry-Feynman diagrams of multiphoton trident pair production. The zigzag lines represent the exact lepton wave functions in the laser field (Dirac-Volkov states [15]) and are labeled by the laser-dressed particle momenta. On the left, the incoming electron scatters from a state of dressed momentum $q$ to $q^{\prime }$ by absorbing $n$ laser photons and emitting an intermediate photon, which afterwards decays into an $e^{+}{e}^{-}$ pair upon absorption of $n^{\prime }$ laser photons. The corresponding exchange diagram is shown on the right. In the weakfield limit ($\xi \ll 1$), the diagrams can be expanded in Feynman diagrams of field-free QED. For a total number of $N=n+n^{\prime }=1$ absorbed photons, eight leading-order diagrams arise this way [16]. The case $N=6$ corresponds to 168 such diagrams.

Figure 2

Positron rate dependence on $\xi$ in the head-on collision of a 46.6 GeV electron with a linearly polarized 527 nm laser wave. The blue dots denote our numerical results from Eq. (6). The green short-dashed and red solid lines, respectively, are ${\xi }^{10}$ and ${\xi }^8$ power-law fits to the data, and the black long-dashed line is an exponential fit of the form $\exp [-\theta \pi /\xi ]$ with $\theta =1.73$. $N_0=6,\dots ,17$ indicate the minimum numbers of laser photons in different $\xi$ regimes [see Eq. (5)]. The inset shows an enlargement of the nonperturbative $\xi \sim 1$ domain on a linear scale.

Figure 3

Positron energy spectra in electron collisions with a 527 nm laser beam. (a) $\xi =0.3$ and $p^0=46.6\mathrm{GeV}$; the dots with an error bar are the experimental data from [2]. The three calculated curves refer to different center-of-mass energies, corresponding to different beam crossing angles as indicated, and have been normalized to the same height to facilitate their comparison. (b) Nonperturbative domain at $\xi =1$ and $p^0=17.5\mathrm{GeV}$; the blue long-dashed (red short-dashed) line refers to the partial spectrum including up to 30 (35) absorbed photons. The black solid line shows the full spectrum.

Figure 4

Laser frequency dependence of the pair creation rate in the collision of an intense VUV pulse ($\xi ={10}^{-4}$) [23] with a 17.5 GeV electron [21]. Shown are the separate contributions from the direct (circles) and two-step (triangles) processes whose sum yields the total rate.

Figure 5

Relation of the optical (527 nm) laser intensity and the electron energy to give an observable lab-frame positron rate $\sim {10}^5{\mathrm{s}}^{-1}$. The pair creation mechanism is changing from the perturbative few-photon regime to the quasistatic (i.e. low-frequency, high-intensity) regime, as indicated.