Muon pair creation from positronium in a linearly polarized laser field

Positronium decay into a muon-antimuon pair by virtue of the interaction with a superintense laser field of linear polarization is considered. The minimum laser intensity required amounts to a few ${10}^{22}\mathrm{W}∕{\mathrm{cm}}^2$ in the near-infrared frequency range. Within the framework of laser-dressed quantum electrodynamics, the total reaction rate is calculated and related to the cross section for field-free electron-positron annihilation into muons. The muons are created with ultrarelativistic energies and emitted under narrow angles along the laser propagation direction. The dynamical properties of the muons are interpreted in terms of a classical simple man’s model for the production process. We show that the most promising setup for an experimental investigation of the process in the near future is based on the combination of upcoming superintense laser sources with envisaged positron accumulation techniques: It employs two counterpropagating laser beams impinging on a positronium target, where the advantage of the coherent electron-positron collisions becomes evident.

Figure 1

Feynman graph for muon pair creation from electron-positron annihilation in a background laser field. The arrows are labeled by the particle’s free momenta $(p_{\pm },P_{\pm })$ outside and the effective momenta $(q_{\pm },Q_{\pm })$ inside the laser field. The virtual photon has four-momentum $q$. The electron and positron are assumed to form a Ps atom initially.

Figure 2

Total rates for the process $\mathrm{Ps}\to {\mu }^{+}{\mu }^{-}$ induced by an intense near-infrared laser field $(\omega =1\mathrm{eV})$, as a function of the laser peak field strength. The black squares and the solid line refer to a linearly polarized laser field and show the results of numerical calculations based on Eq. (22) and the analytical estimate in Eq. (54), respectively. The black circles and the dashed line show the corresponding results for a laser field of circular polarization.

Figure 3

Partial rates for the laser-driven decay $\mathrm{Ps}\to {\mu }^{+}{\mu }^{-}$, as a function of the number of absorbed laser photons $r$. The linearly polarized laser field has a frequency of $\omega =1\mathrm{eV}$ and an intensity parameter of $\xi =170$ (solid line), 200 (dashed line, enhanced by a factor of 2), and 250 (dash-dotted line, enhanced by a factor of 5), respectively. For comparison, the dotted line shows the corresponding result for a circularly polarized field with ${\xi }_c=250$; it is enhanced by a factor of ${10}^8$. The photon number is given in units of $r_0=m{\xi }^2∕\left(2\omega \right)$.

Figure 4

Illustration of the applicability range of the asymptotic expansion in Eq. (30) for the generalized Bessel function. (a) $J_{50}(U,15)$ in the range $0⩽U⩽90$; the thick dashed line shows the exact value resulting from the series expansion in Eq. (8); the thin dotted line shows the asymptotic formula. (b) The condition (C5) for the example of the figure in (a), with the thick dashed and thin dotted lines showing the left- and right-hand sides of Eq. (C5), respectively. (c) Same as (a), but for $J_{50}(80,V)$ in the range $-40⩽V⩽20$.