Improved calculation of the hyperfine structure of muonic helium

Using perturbation theory for the fine-structure constant $\alpha$ and the electron-to-muon mass ratio, we calculated new contributions to the hyperfine structure of the ground state of the muon-electron helium atom. Compared to our previous results, we calculated new corrections in second-order perturbation theory. This calculation reduces the discrepancy between the theoretical value and the new experimental hyperfine structure measurement.