Tests of the equivalence principle with neutral kaons

We test the Principle of Equivalence for particles and antiparticles, using CPLEAR data on tagged Pkao and Pkab decays into $pi^+ pi^-$. For the first time, we search for possible annual, monthly and diurnal modulations of the observables $|eta_{+-}|$ and $phi _{+-}$, that could be correlated with variations in astrophysical potentials. Within the accuracy of CPLEAR, the measured values of $|eta _{+-}|$ and $phi _{+-}$ are found not to be correlated with changes of the gravitational potential. We analyze data assuming effective scalar, vector and tensor interactions, and we conclude that the Principle of Equivalence between particles and antiparticles holds to a level of $6.5$, $4.3$ and $1.8 imes 10^{-9}$, respectively, for scalar, vector and tensor potentials originating from the Sun with a range much greater than the distance Earth-Sun. We also study energy-dependent effects that might arise from vector or tensor interactions. Finally, we compile upper limits on the gravitational coupling difference between Pkao and Pkab as a function of the scalar, vector and tensor interaction range.