Estimated accuracies of pure XH⁺ (X: Even isotopes of group II atoms) vibrational transition frequencies: Towards the test of the variance in m_p/m_e

This paper gives a proposal for the precise measurement of the |X ¹ Σ, n_ν = 0, J = 0, F = 1/2,M = ±1/2} → |X¹ Σ, n_ν = 1,J = 0, F = 1/2,M = ±1/2} transition frequencies of a XH⁺ molecular ion (X: ²⁴Mg, ⁴⁰Ca, ⁸⁸Sr, ¹³⁸Ba, ⁶⁴Zn, ¹¹⁴Cd, ¹⁷⁴Yb and ²⁰²Hg), trapped inside a linear rf-trap. The frequency uncertainty can be reduced down to the order of 10^-16 because the energy shifts induced by the trapping electric field (Stark shift and quadrupole shift) and magnetic field (Zeeman shift) for the upper and lower states of the transition almost cancel each other. Measuring the variances in these vibrational transition frequencies in comparison with atomic transitions (for example ¹S ₀-³P₀ transitions of Al⁺ ion or Sr atoms) can be utilized for the variance test in the proton-to-electron mass ratio. Among XH⁺ molecular ions, ¹⁷⁴YbH⁺ seems most advantageous for this purpose.