Positronium oscillations to mirror world revisited

We present a calculation of the branching ratio of orthopositronium decay into an invisible mode, which is done in the context of mirror world models, where ordinary positronium can disappear from our world due to oscillation into its mirror twin. In this revision we clarify some formulas and approximations used previously, correct them at some places, add new effects relevant for a feasible experiment, and finally perform a combined analysis. We include into consideration various effects due to external magnetic and electric fields, collisions with cavity walls, and scattering off gas atoms in the cavity. Oscillations of the Rydberg positroniums are also considered. To perform a numerical estimate in a realistic case we wrote computer code, which can be adopted in any experimental setup. Its work is illustrated with an example of a planned positronium experiment within the AEgIS project.

Figure 1

The dependence of the branching ratio on the characteristic size of experiment cavity $L$ at different values of gas pressure. We chose $ϵ={10}^{-9}$, $k_B{T}_{\mathrm{oPs}}=0.025\mathrm{eV}$.

Figure 2

The dependence of the branching ratio of the positronium disappearance on gas (nitrogen) pressure (left panel) and gas temperature (right panel) with (points) and without [solid lines, Eq. (30)] wall collisions. The positronium temperature equals nitrogen temperature and we set $ϵ={10}^{-9}$. Note that $\mathrm{Br}(\mathrm{oPs}\to \mathrm{\text{invisible}})$ scales as ${ϵ}^2$.

Figure 3

The dependence of the branching ratio of the positronium disappearance on the external electric field $E$ at different values of gas pressure. We chose $ϵ={10}^{-9}$, $k_B{T}_{\mathrm{oPs}}=0.025\mathrm{eV}$ and the magnetic field $B=0$.

Figure 4

The dependence of the branching ratio of the positronium disappearance on the magnetic field $B$ at different values of gas pressure. We chose $ϵ={10}^{-9}$, $k_B{T}_{\mathrm{oPs}}=0.025\mathrm{eV}$ and the electric field $E=0$.