On superconducting double transition in PrOs₄Sb₁₂

Superconducting double transition in PrOs₄Sb₁₂ is investigated by analyzing the anisotropy of the upper critical field H _c2 in the ab-plane, and the possible pairing state is discussed. When mixing due to gradient coupling is active, the twofold-symmetric component is necessarily induced in the fourfold symmetric phase, leading to the twofold oscillation of H_c2, contrary to the experimental result. To avoid the mixing effect, the weak spin-orbit coupling triplet pairing state is considered as a likely pairing function, where time-reversal symmetry is broken.