|PHY304||Particle Physics||Dr C N Booth|
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 K0(ds̅) 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 K0 (sd̅) has strangeness −1, and as there are no baryons of positive strangeness, this can only be formed in higher energy collisions. At low energies, a pure sample of K0 can therefore be produced.
The weak interaction does not conserve strangeness. It therefore does not distinguish between K0 and K0. 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
|K1 = 1/√2 (|K0› − |K0›)||with CP e-value +1|
|K2 = 1/√2 (|K0› + |K0›)||with CP e-value −1|
Consider a beam of pions striking a thin solid target, mounted in a vacuum. Strong interactions will occur, reulting in the production of K0 (with no K0). These then travel on and decay through the weak interaction. The K0 is equivalent to an equal mixture of K1 and K2, and the K1 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 K2 component must be seen as an equal mixture of K0 and K0, so S = +1 and −1 states will be produced, even though only K0 (with S = +1) was present initially! In fact, the K0 will be preferentially absorbed, with only some of the K0 emerging from the regenerator. Here, weak decays will again occur, and an equal mixture of K1 and K2 will again be observed, even though previously the entire K1 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 sx = ±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 sy = ±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 sx = ±½ even though one of these components had previously been eliminated.
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