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International Journal of Modern Physics A

ANOTHER LOOK AT THE CP VIOLATION PROBLEM

K. Urbanowski

Published Oct 10, 1992• 7 citations
Publisher

Abstract

We show that the interpretation of neutral kaon decay (and [Formula: see text] and other decay) experiments is based on a not-too-correct theoretical description of such decays. This description does not take into account the specific early time properties of temporal evolution in the two-component subspace of a state space. The particle interpretation of vectors in such a subspace is shown to be proper for other states in an early time period and other states in a long time period.

DOI
10.1142/s0217751x92002854

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We show that the interpretation of neutral kaon decay (and [Formula: see text] and other decay) experiments is based on a not-too-correct theoretical description of such decays. This description does not take into account the specific early time properties of temporal evolution in the two-component subspace of a state space. The particle interpretation of vectors in such a subspace is shown to be proper for other states in an early time period and other states in a long time period.
It is easy to construct classical 2-state systems illustrating the behavior of the short-lived and long-lived neutral KKK mesons in the limit of CP conservation. The emulation of CP violation is more tricky, but is provided by the two-dimensional motion of a Foucault pendulum. Analogies are drawn between the pendulum and observables in neutral kaon decays. An emulation of CP- and CPT-violation using electric circuits is also discussed.
The well-known fact that the existing quantum mechanical formalism is inconsistent with the energy-time uncertainty-relation postulate is shown to play a crucial role in the logical deduction leading to the conclusion that CP\mathrm{CP}CP invariance is violated in some neutral kaon decays. It is therefore argued that if one believes in the existence of the energy-time uncertainty relation, then one has to accept that none of the existing experimental facts can unambiguously be interpreted as evidence against the universal validity of CP\mathrm{CP}CP invariance.
The time evolution of the KK system as a two-qubit system is given. The effect which is interpreted as CP violation in neutral kaon decays is explained via violation of quantum correlations during time evolution of the KK system as two-kaons system and description is via Yang-Baxterization and unitary time dependent R-matrices to con- struct Hamiltonian, determining the time evolution of two-kaons sys- tem. The nonseparability ideas and criterion can be extended on all mixing state-antistate system and all CP violation cases in particle physics.
Approximate formulas are given for the effective Hamiltonian ${\mathit{H}}_{\mathrm{\ensuremath{\parallel}}}$(t) governing the time evolution in a subspace ${\mathit{scrH}}_{\mathrm{\ensuremath{\parallel}}}$ of the state space scrH. It is proved that this approximation is correct for any Hamiltonian H of the system under consideration at the early-time period. The approximate form of the survival amplitude for a given state improving Fleming's estimation in the short-time region is found and the properties of a decay rate for small, intermediate, and long times are discussed.