Unitarity of Neutral Kaon System : Particles and Fields

概要

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In a neutral kaon system, where we always use a non-hermitian Hamiltonian for convenience of treating decay processes, unitarity seems to be lost. If we take decay channels (ππ, πππ, πlν, …, etc.) into account, however, the Hamiltonian of the entire system must be hermitian. We attempt to derive an effective Hamiltonian with respect to only K^0 and K^^-^0 states, starting from a hermitian Hamiltonian. For brevity, we take only a ππ state into account as the decay channel in this paper. We cannot avoid an oscillation between K^0, K^^-^0 and ππ states if we start from a hermitian Hamiltonian whose states all have discrete energy levels. We therefore treat the ππ state more appropriately as to have a continuous energy spectrum to achieve the decay of K^0 and K^^-^0 into ππ. As a consequence, we find a time evolution which differs from what we expect in the conventional method immediately after the decay starts, though it recovers Fermi's golden rule for a sufficiently long time scale.
理論物理学刊行会の論文
1997-08-25