Muon pair creation from positronium in a circularly polarized laser field

We study elementary particle reactions that result from the interaction of an atomic system with a very intense laser wave of circular polarization. As a specific example, we calculate the rate for the laser-driven reaction $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, where the electron and positron originate from a positronium atom or, alternatively, from a nonrelativistic $e^{+}{e}^{-}$ plasma. We distinguish accordingly between the coherent and incoherent channels of the process. Apart from numerical calculations, we derive by analytical means compact formulas for the corresponding reaction rates. The rate for the coherent channel in a laser field of circular polarization is shown to be damped because of the destructive interference of the partial waves that constitute the positronium ground-state wave packet. Conditions for the observation of the process via the dominant incoherent channel in a circularly polarized field are pointed out.

Figure 1

Feynman diagram for the process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in a laser field. The arrows are labeled by the free and effective momenta of the corresponding particle cf. Eq. (6).

Figure 2

Total rates for the laser-driven reaction $\mathrm{Ps}\to {\mu }^{+}{\mu }^{-}$ as a function of the intensity parameter $\xi$ of the applied laser field. The black squares show the results of our numerical calculations based on Eq. (22); the solid line shows the analytical estimate via Eq. (51).

Figure 3

Partial rates for the laser-driven reaction $\mathrm{Ps}\to {\mu }^{+}{\mu }^{-}$ as a function of the number of absorbed laser photons $r$ for an intensity parameter of $\xi =250$ (solid line), 500 (dashed line), and 1000 (dotted line). The latter two curves are enhanced by factors of ${10}^2$ and $5\times {10}^3$, respectively.

Figure 4

Angular spectrum with respect to the polar angle of the effective momentum for one of the produced muons at $\xi =250$.

Figure 5

Partial rates for the reaction $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ from a laser-driven nonrelativistic plasma. It is assumed that $N_{\pm }={10}^7$ particles are contained in the interaction volume $V_{\mathrm{int}}={10}^{-9}{\mathrm{cm}}^3$. The laser intensity parameter is $\xi =250$ (solid line), 500 (dashed line), and 1000 (dotted line). The latter two curves are enhanced by factors of $2\times {10}^2$ and $2\times {10}^4$, respectively.