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Regeneration

The equation of motion inside some material can be written as:

 

By comparing eq. 53 with the eq. 2, we can immediately write down the solutions for the time evolution of a neutral kaon state inside some material:

The mass and lifetime eigenvalues of and change equally in first order of the forward scattering amplitudes.

And the time evolution of a or in matter becomes:

For an arbitrary inital neutral kaon state we can write following the formalism in section 1:

Consider the standard case of an initial pure : ( counts time after regenerator, time inside regenerator):

To get a more simple expression, assume conservation, i.e. :

where , , and . A similar calculation yields:

For evaluating and decays in vacuum, it is useful to rotate to the basis using the transformation matrix:

with

The decay rates for initial pure and into after the regenerator is then given by:

The decay rates for initial pure or after a regenerator where the neutral kaons travel first through vacuum before reaching the regenerator can be calculated similarly:

Moreover, the decay rate after different regenerators can be easily calculated by multiplying the corresponding matrices:



Thomas Ruf
Fri Aug 9 14:24:14 MET DST 1996