Precision Spectroscopy of the Pionic Helium-4

The transition frequency of (n,ℓ)=(17,16)→(16,15) in pionic helium-4 is calculated to an accuracy of 4 ppb (parts per billion), including relativistic and quantum electrodynamic corrections up to O(R_{∞}α^{5}). Our calculations significantly improve the recent theoretical values [Hori et al., Phys. Rev. A 89, 042515 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042515]. In addition, collisional effects between pionic helium and target helium on transition frequencies are estimated. Once measurements reach the ppb level, our Letter will improve the value of the π^{-} mass by 2-3 orders of magnitude.