Determination of antiproton mass from the calculation of energy levels of antiprotonic helium atoms

We calculate the energy levels of the metastable states of an antiprotonic helium atom. The coupled rearrangement channel method is employed to describe a dual character of the atom effectively. Calculated transition frequencies between the metastable states are in good agreement with the observed values. The uncertainty of an antiproton mass is estimated by the calculated transition frequencies with the slightly shifted antiproton mass from the proton mass. When a more accurate value of the charge-to-mass ratio of antiproton is considered, the uncertainty of antiproton mass and charge is estimated at 54 ppb which improves the value recommended by the particle data by a factor of ten.