Neutral meson oscillations and equivalence principle for particles and antiparticles

Abstract

Oscillations of neutral meson (K ⁰-$\overline {K^0 }$, D ⁰-$\overline {D^0 }$, and B ⁰-$\overline {B^0 }$ are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$\overline {K^0 }$ oscillations:

$$ \left| {\left( {\frac{{m_g }} {{m_i }}} \right)_{K^0 } - \left( {\frac{{m_g }} {{m_i }}} \right)_{\overline {K^0 } } } \right| \leqslant 8 \times 10^{ - 13} , at C.L. = 90\% $$

. This estimate is model dependent; in particular, it depends on the method used to estimate the gravitational potential. An analysis of K ⁰-$\overline {K^0 }$, D ⁰-$\overline {D^0 }$, and B ⁰-$\overline {B^0 }$ oscillations provides weaker but model independent estimates which, in particular, eliminate the possibility of antigravity for antimatter.