On null tests of CP symmetry in scattering and reactions

It has often been stated that a T-odd reaction observable, which is the expectation value of a T-odd operator (e.g., σ·(kj - kf)), vanishes from T symmetry. Since this would provide a null test of T symmetry, this statement is in direct conflict with a theorem that proves the nonexistence of such a null test in reactions. A similar conception is that a CP-odd reaction observable vanishes from CP symmetry. However, the interconnection between CP and T, via the CPT theorem, suggests the feasibility of a comparable nonexistence theorem for CP null tests. Thus, the author extends the theorem to show the nonexistence of null tests of CP symmetry in reactions