High-precision comparison of the antiproton-to-proton charge-to-mass ratio

Invariance under the charge, parity, time-reversal (CPT) transformation$^{1}$ is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry—that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime—although it is model dependent$^{2}$. A number of high-precision CPT and Lorentz invariance tests—using a co-magnetometer, a torsion pendulum and a maser, among others—have been performed$^{3}$, but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available$^{4, 5, 6, 7, 8}$. Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H$^−$) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton $(q/m)_{\bar{p}}$ to that for the proton $(q/m)_{p}$ and obtain $(q/m)_{\bar{p}} / (q/m)_{p} - 1 = 1(69) \times 10^{-12}$. The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-to-proton mass comparisons$^{7, 9}$ as well as the respective figure of merit of the standard model extension$^{10}$ by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of < 720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of $|\alpha_g - 1| < 8.7 × 10^{−7}$