Reciprocal of the CPT theorem
The CPT theorem originally proven by Lüders and Pauli ensures the equality of masses, lifetimes, magnetic moments and cross sections of any particle and its antiparticle. We show that in a Lorentz invariant quantum field theory described by its Lagrangian, CPT-violating interaction alone does not split the masses of an elementary particle and its antiparticle but breaks only the equality of lifetimes, magnetic moments and cross sections. However, CPT violation in the mass term of a field in the Lagrangian, which can be attributed to be due to the size of the particle described by a form factor, breaks only the equality of masses. Also it is shown that the two separate effects of CPT violation in the interaction terms or in the mass term do not mix due to higher quantum corrections and remain distinguishable. Thus, we urge the experimentalists to search for such observable effects concerning differences in the masses, magnetic moments, lifetimes and cross sections between the elementary or bound state particles and their antiparticles. In the case of CPT violation only in the mass term, besides the difference in the masses of elementary bound state particles and their antiparticles, there will be also an extremely tiny difference in the lifetimes of bound states due to the difference in their phase spaces. From the details of calculations, it appears that the separate effects of the CPT violation described above are quite general, neither depending on how the nonlocality is achieved, nor depending on what this violation is due to: due to T violation, as considered in the present work, which can be attributed to a cosmological direction of time; to CP or to both T and CP violations. The latter two cases satisfy the Sakharov's conditions for explaining the baryon asymmetry in the Universe.