CP, T AND CPT VIOLATIONS IN THE $K^0-\overline{K^0}$ SYSTEM: PRESENT STATUS

Abstract

Possible violation of CP , T and CP T symmetries in the K 0 −K 0 system is studied in a way as phenomenological and comprehensive as possible. For this purpose, we first introduce parameters which represent violation of these symmetries in mixing parameters and decay amplitudes in a convenient and well-defined way and, treating these parameters as small, derive formulas which relate them to the experimentally measured quantities. We then perform numerical analyses to derive constraints to these symmetry-violating parameters, with the latest data reported by KTeV Collaboration, NA48 Collaboration and CPLEAR Collaboration, along with those compiled by Particle Data Group, used as inputs. The result obtained by CPLEAR Collaboration from an unconstrained fit to a time-dependent leptonic asymmetry, aided by the Bell-Steinberger relation, enables us to determine or constrain most of the parameters separately. It is shown among the other things that (1) CP and T symmetries are violated definitively at least at the level of 10 −4 in 2π decays, (2) CP and T symmetries are violated at least at the level of 10 −3 in the K 0 − K 0 mixing, and (3) CP T symmetry is at present tested to the level of 10

Effective action and the quantum equation of motion

“…In discussing CP violation, care should be taken in considering which parameters are unphysical because their value depends on the arbitrary choice of the phase for the state vectors representing the different particles; indeed, there is a considerable amount of literature concerning the proper definition of rephasing-invariant parameters in the kaon system (see e.g. [11] [12] [13]). …”

CPT invariance and neutrino physics

“…The constraint that is usually quoted is the stringent upper limit of the CPT violation in the difference ∆(K 0 , K 0 ) of K 0 and K 0 masses: [96]. However, since this difference caused by the transition K 0 → K 0 is small from the very beginning, this constraint is not exclusively characteristic of the CPT-odd interaction: the true parameters of the CPT nonconservation in the K 0 -K 0 system [91] can only be bounded at the level 10 −3 -10 −4 (see the review [97] and also [98]) 8 . The general constraints imposed by analyticity and discrete symmetries Р, С, СР, TCP on the description of binary systems of neutral mesons of the type (K 0 , K 0 ) were obtained in the framework of quantum field theory in [99].…”

Particle Physics Aspects of Antihydrogen Studies with ALPHA at CERN

“…Furthermore the interpretation of the 0 0 K K − results as a test of CPT is controversial. The impressive quoted precision is derived with some theoretical assumptions, and Kobayashi and Sanda [17] have put forward an argument that the CPT violating interaction is tested only at much reduced level (currently ~10 -5 [18]). Bigi has also questioned the quoted relative precision of 10 -18 for similar reasons [19].…”