# CPT and effective Hamiltonians for neutral kaon and similar complexes Source: [CPT and effective Hamiltonians for neutral kaon and similar complexes]() Collection index: [llms.txt]() Data updated: 2025-10-23T16:27:16.070Z Authors: K. Urbanowski Published: 2002-08-03T17:12:27.000Z ## Abstract We begin with a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next, the properties of the exact effective Hamiltonian for this complex are discussed. Using the Khalfin Theorem we show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t \> t\_0 (t\_0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for t \>\> t\_0 in the case of preserved CPT and violated CP symmetries. We also show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses properties consistent with the conclusions for the exact effective Hamiltonian described above. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()