On the possibility of « kinematic » (unitarity) origin ofCP-violation in the K L → 2π decay

Abstract

The problem of adding ray corepresentations of pari ty (P) and t ime reversal (T) to the physically relevant uni tary irreducible representations of the connected Poincar~ group ~?+ (UIRP) was discussed by WIGNV.R (1). I t is noteworthy tha t P is interpreted in ref. (1) not as space inversion, but as the product of space inversion and charge conjugation. A reason for this interpretat ion may be posed as follows. Space inversion alone yields neutrinos of both negative and positive helicities. Since a positive-helicity (electronic or muonie) neutrino does not exist in nature, the Hilbert space ~f~---[(v]] spanned by the states of the neutrino does not (( aeeomodate , space inversion. This implies tha t any process involving one neutrino must violate space inversion invariance. If one insists on having par i ty as a symmetry operator, one has to , correct ~) the s i tuat ion; and this one can achieve by the aforementioned interpretat ion: ~f~ contains both the states of the negative-helicity neutrino and the positiveheliei ty antineutrino. In view of the discovery of processes violat ing par i ty in this new interpretation, the above mot ivat ion seems to lose its grounds. One is tempted therefore to resume the original interpretat ion of P as the space inversion operation, implying thereby the violation of par i ty in all processes involving one neutrino or antineutrino. Moreover, the relevant uni tar i ty sum rule induces/n pr inc ip le -v io la t ion of par i ty for nonleptonic processes as well. As an example, consider the process A°-->~-p. Wri t ing S ~-1 "4iB , uni tar i ty implies i(R* R) ~ BR*, or