Can a charged decaying particle serve as an ideal clock in the presence of a magnetic field?

We investigate a model of a supposedly ideal clock based on the decay rate of a charged particle in circular motion in a constant magnetic field. We show that the time measured by an ideal clock depends on the acceleration. However, the effect becomes visible at an order of magnitude of $10^{28}\mathrm{g}$, therefore confirming the validity of the ideal clock hypothesis for realistic accelerations.

Figure 1

Decay rate $\gamma \mathrm{\Gamma }(m)/{\mathrm{\Gamma }}_0^{\prime }$ vs Landau levels $m$ for different radial energy values of the initial particle. Here, $M_{\mu }=105.7\mathrm{MeV}$, $M_e=M_{\nu }=0$.

Figure 2

Decay rate $\gamma \mathrm{\Gamma }(m)/{\mathrm{\Gamma }}_0^{\prime }$ vs Landau levels $m$ for an initial radial energy squared $p_{\perp }^2=5\times {10}^4{\mathrm{MeV}}^2$. Here, $M_{\mu }=105.7\mathrm{MeV}$, $M_e=M_{\nu }=0$.

Figure 3

Decay rate $\gamma \mathrm{\Gamma }(m)/{\mathrm{\Gamma }}_0^{\prime }$ vs the magnetic field $B(m)$ for a fixed radius $R=0.1{\mathrm{MeV}}^{-1}=2\times {10}^{-14}\mathrm{m}$. Here, $M_{\mu }=105.7\mathrm{MeV}$, $M_e=M_{\nu }=0$.

Figure 4

Decay rate $\gamma \mathrm{\Gamma }(m)/{\mathrm{\Gamma }}_0^{\prime }$ vs radial energy $p_{\perp }$ for a fixed radius $R=0.1{\mathrm{MeV}}^{-1}=2\times {10}^{-14}\mathrm{m}$ and $m=0$. Here, $M_{\mu }=105.7\mathrm{MeV}$, $M_e=M_{\nu }=0$.