PHY304 |
Particle Physics |
Dr C N Booth |

##
The K^{0} System and Strangeness Regeneration

We have seen that the strong and weak eigenstates, when expressed in terms of quarks, are different.
We now look at evidence for different eigenstates in the observed, free particles themselves.
This is seen in the neutral kaon system.

The K^{0}(d)
has strangeness 1, and can be produced in π p collisions by the strong interaction in
association with a Λ hyperon (i.e. strange baryon).
In contrast, the
(s)
has strangeness −1, and as there are no baryons of positive strangeness, this can only be
formed in higher energy collisions.
A pure sample of K^{0} can therefore be produced.

The weak interaction does not conserve strangeness.
It therefore does not distinguish between K^{0} and
.
The eigenstates of the weak interaction are not those of strangeness but (approximately)
those of CP.
It will be shown in the lecture that these can be written as

| K_{1} = ^{1}/_{√2} (|K^{0}› −
|›) |
| with CP e-value +1 |

| K_{2} = ^{1}/_{√2} (|K^{0}›
+ |›) |
| with CP e-value −1 |

The K_{1} decays into two pions, while the K_{2} must decay to a 3-pion final state.
As there is much more phase space available for the K_{1} decay, its rate is about 600
times greater than that for the K_{2}.

Consider a beam of pions striking a thin solid target, mounted in a vacuum.
Strong interactions will occur, reulting in the production of K^{0} (with no
).
These then travel on and decay through the weak interaction.
The K^{0} is equivalent to an equal mixture of K_{1} and K_{2},
and the K_{1} component rapidly decays away.
If a further solid target (known as a regenerator) is introduced some distance downstream,
the remaining kaons will interact with it via the strong interaction.
Here the surviving K_{2} component must be seen as an equal mixture of K^{0}
and , so *S* = +1
and −1 states will be produced, even though only K^{0} (with *S* = +1)
was present initially!
In fact, the will be preferentially
absorbed, with only some of the K^{0} emerging from the regenerator.
Here, weak decays will again occur, and an equal mixture of K_{1} and K_{2}
will again be observed, even though previously the entire K_{1} component
had decayed away!

Quantum mechanically, the situation is exactly equivalent to a series of Stern-Gerlach
experiments, with crossed magnetic field gradients.
If an unpolarised beam of neutral, spin-½ atoms travelling along the
*z*-axis encounters a field gradient in the *x*-direction, it will split
into two equal divergent beams with *s*_{x} = ±½.
If one of these is blocked and the other allowed into a second region where the field
gradient is in the *y*-direction, it will split again into equal divergent beams with
*s*_{y} = ±½.
If now one of these is selected and encounters a region with a field gradient
again in the *x*-direction, it will split into two equal beans with
*s*_{x} = ±½ even though one of these components
had previously been eliminated.

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