Testing the equivalence principle with unstable particles

We develop a framework to test the equivalence principle under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the nonrelativistic quantum equation that describes the evolution of the wave function of unstable particles under the assumption of the validity of the equivalence principle and when small deviations are assumed to occur. As an example, we study the propagation of unstable particles in a COW experiment, and we briefly discuss the experimental implications of our formalism.

Figure 1

The probability $P(L)$ as a function of $\theta$ for particles with initial velocity $v_0=300\mathrm{m}/\mathrm{s}$, mass $m=939.6\mathrm{MeV}$ and decay constant $\Gamma =1.5\times {10}^4{\mathrm{s}}^{-1}$ in a COW configuration with length and height $L=h=3.5\times {10}^{-2}\mathrm{m}$. In all the plots, the solid (black) line corresponds to the case where $\Gamma =0$. In the top plots ${\xi }^I=0$ and the (blue) continuous, (magenta) dashed, (yellow) dotted and (green) dot-dashed lines correspond to ${\xi }^R=0$, ${10}^{16}$, $5\times {10}^{16}$ and ${10}^{17}$, respectively. In the bottom plots the phenomenological parameters we use are ${\xi }^R=0$ and ${\xi }^I=0$, ${10}^{17}$, $5\times {10}^{17}$ and ${10}^{18}$ which are, respectively, used for the (blue) continuous, (magenta) dashed, (yellow) dotted and (green) dot-dashed lines. The plots on the right show, in greater detail, a portion of the corresponding plots on the left.

Figure 2

The COW setting under consideration where the coordinate system and the labels for the different segments are shown.

Figure 3

The interference term contribution to the probability $P_{\mathrm{int}}$ as a function of $\Omega$ with $\Gamma =0$. It can be observed that for $\Omega \ge 10$ the probability of interference tends to zero.