Laser measurements of the density shifts of resonance lines in antiprotonic helium atoms and stringent constraint on the antiproton charge and mass

We have performed laser spectroscopy of metastable antiprotonic helium atoms $\left(\overline{p}{\mathrm{He}}^{+}\right)$ formed in helium media of 0.2–8.0 bars at 5.8–6.3 K and have observed a density dependence of the resonance vacuum wavelengths for the known transitions $\mathrm{}(n,l)=(39,35)\mathrm{}\to \mathrm{}(38,34)\mathrm{}$ and $\mathrm{}(37,34)\mathrm{}\to \mathrm{}(36,33).$ They showed linear redshifts of $0.61\pm 0.01$ GHz and $0.22\pm 0.02$ GHz per 1 g/l, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding ${\lambda }_0=597.2570\mathrm{}\pm 0.0003$ nm and ${\lambda }_0=470.7220\mathrm{}\pm 0.0006$ nm, respectively. These values, with a 0.5-ppm precision, were compared with the result of recent theoretical calculations on the energy of the Coulombic three-body system, including relativistic corrections and the Lamb shift. The agreement between our experimental values and the calculations has become as good as $2\times {10}^{-6}.$ This excellent agreement in turn provides a precise value of the antiproton Rydberg constant that surpasses the currently known precision and sets a severe constraint on the antiproton charge $\left(-Q_{\overline{p}}\right)$ and the mass ${(M}_{\overline{p}})$ that both $|Q_{\mathit{p}}-Q_{\overline{p}}|/e$ and $|M_{\mathit{p}}-M_{\overline{p}}|{/M}_p$ be less than $5\times {10}^{-7},$ when a more precisely known constraint on the charge-to-mass ratio is combined. Thus we have opened a possibility of determining fundamental constants of the antiproton.