B PHYSICS AND CP VIOLATION

The Violation of Discrete Space-Time Symmetries, P and CP

IN CLASSICAL MECHANICS, Newton's laws of motion, $F=\; ma$, have two important symmetries. Under reflections of the co-ordinates, the vectors $F$ and $a$ both change sign, and the equation is unchanged. This is called a symmetry under parity (or $P$) transformat ion. If we change the direction of time, then velocities change sign --- if time is reversed particles move backwards --- but the acceleration is unchanged. Thus, unless the forces are velocity-dependent, Newton's laws are also unchanged when we reverse the direction of time. They are symmetric under the time reversal or $T$ transformation.

Time reversal symmetry is not familiar to us in our everyday world. You only have to run a movie backwards to see how unnatural the time reversed world is. This is because of frictional forces, which are velocity-dependent. At the level of atomic collisions however, these frictional effects are absent and Classical Mechanics is time reversal invariant.

$P$ and $T$ transformations exist also in the quantum world that describes the dynamics of the fundamental particles of Nature. Here, there is an additional transformation, the transformation of particles like electrons and protons into their antiparticles, positrons and antiprotons. This transformation, called the $C$ transformation (for charge conjugation), is linked to the $P$ and $T$ transformations by the famous $CPT$ theorem which states that it is almost impossible to write down a quantum theory that is consistent with Special Relativity which is not symmetric under the combined $CPT$ transformation.

Before 1956, everyone believed that the world was also symmetric under the individual transformations $P$, $C$ and $T$. Then experiments showed that this was not the case. One of the classic experiments considered the decay of the pi meson into a muon mu and a neutrino nu, $pi+->\; mu+nu$ . A possible configuration is that shown in the left half of Figure 1, where the muon and the neutrino are travelling "back to back", both the muon and the neutrino having "left-handed'' angular momentum about the direction of motion. Another possible state is illustrated in the right half of Figure 1, which is obtained by reflecting the left state in the "mirror" represented by the line AA'. In this second possible final state, the neutrino and the muon are both "right-handed". While this second state is theoretically possible if $P$ is conserved, it is not observed in Nature, clearly showing that the interaction responsible for the decay called the weak interaction is not invariant under parity transformation. Let us return to the pion decay reaction $pi+->\; mu+nu$ and replace each particle by its antiparticle so that the reaction becomes $pi-->\; mu-nu$. What happens in this new reaction? The situation is depicted in Figure 2. The initial reaction is in Figure 2(a), and the effect of replacing particles by their antiparticles is illustrated in Figure 2(b). However the latter is not observed. The experimentally observed reaction is shown in Figure 2(c), which may be obtained from Figure 2(b) by a mirror reflection. The weak interactions are not $P$ or $C$ invariant, but are invariant under the combined $CP$ transformation.

Then in 1964, it was discovered that even this symmetry is violated! It was found that the K meson, containing an s quark which is not a constituent of normal matter like ourselves, had decay processes in which $CP$ was violated.

Although $CP$ Violation was found 30 years ago, our understanding of it has not progressed very far. We are looking forward to the new experiments involving B particles, which should see $CP$ Violation and help us to understand it better. When we do that we may gain a better understanding of why the universe is made of matter and not of an equal mixture of matter and antimatter, a condition necessary for our existence. $CP$ Violation is a necessary feature of a theory which can produce a universe like ours (see The Early Universe article), a fact pointed out by Shakarov shortly after its original discovery.