CP Violation

CP Violation in Elementary Particle Physics
If we take the entire universe and move it over by 100 meters, we say it has undergone a spatial transformation of 100 meters. Now imagine inverting space, that is, reflecting every point to the opposite side of a fixed (but arbitrary) center. This is known as a parity transformation, and is designated by the symbol P. Another possible transformation of the physical world is to take every single particle and turn it into its antiparticle. This is known as the charge conjugation transformation, and we refer to it using the symbol C. If the universe would remain unchanged after being through a transformation, we say that it is symmetric, or invariant, under that transformation. In any physical model of the universe, the laws are represented by equations, and we can prove invariance under any given transformation by performing the transformation on the equations and seeing if the resulting equations are equivalent to the original ones. For example, the universe is invariant under spatial transformations - the laws are the same at any location, and it's impossible to tell whether the universe has undergone a spatial transformation. If we consider a universe with no particles or interactions, the physical laws are also invariant under both P and C transformations. What we find if we introduce interactions is that some that exist in our universe would not exist in a P-transformed universe, and vice versa, in other words, the universe is NOT invariant under P. In pretty much the same way, we find it is not invariant under C. Amazingly, invariance is regained (almost) if we consider not just P or C, but the combined transformation CP. The intriguing and maddening observation is that the laws are not-quite-invariant under CP transformations. In other words, we have CP violation. CP symmetry refers to the fact that physical processes in nature occur in precisely the same manner if all particles were converted to their antimatter opposites using the CP transformation. Explicitly, the C operation reverses all additive quantum numbers such as electric charge, hypercharge, strangeness, etc., while the P transformation "inverts" the coordinate system and the orientation of all objects in it: x -> -x, y-> -y, z-> -z. That is, a particle traveling to the right in the +x direction finds itself traveling to the left (still in the +x direction) after a P transformation. More significantly, P reverses the relationship between the intrinsic angular momentum (spin) of a particle and the direction of its velocity. If the spin is aligned with the velocity, the particle is referred to as having "positive helicity." If the spin is anti-parallel to the velocity direction, the particle has "negative helicity." Under a P transformation, the velocity direction is reversed but the spin direction is not (as spin is a purely internal quantum number); thus a positive helicity particle -> negative helicity and vice versa. So under a CP transformation, a negative helicity proton becomes a positive helicity antiproton. It was first predicted - and subsequently confirmed by experiment (in the 1950's) - that positive and negative helicity particles interact differently: a negative helicity electron will scatter off a nucleus and transform into a neutrino, but a positive helicity electron will not. However, a positive helicity positron will, just like the negative helicity electron. This is an example of CP symmetry. The symmetry was believed to be exact until 1964, when an experiment by Fitch et al. showed that for K⁰ mesons, CP symmetry breaks down 0.2% of the time.

If we take the entire universe and move it over by 100 meters, we say it has undergone a spatial transformation of 100 meters. Now imagine inverting space, that is, reflecting every point to the opposite side of a fixed (but arbitrary) center. This is known as a parity transformation, and is designated by the symbol P. Another possible transformation of the physical world is to take every single particle and turn it into its antiparticle. This is known as the charge conjugation transformation, and we refer to it using the symbol C. If the universe would remain unchanged after being through a transformation, we say that it is symmetric, or invariant, under that transformation. In any physical model of the universe, the laws are represented by equations, and we can prove invariance under any given transformation by performing the transformation on the equations and seeing if the resulting equations are equivalent to the original ones. For example, the universe is invariant under spatial transformations - the laws are the same at any location, and it's impossible to tell whether the universe has undergone a spatial transformation. If we consider a universe with no particles or interactions, the physical laws are also invariant under both P and C transformations. What we find if we introduce interactions is that some that exist in our universe would not exist in a P-transformed universe, and vice versa, in other words, the universe is NOT invariant under P. In pretty much the same way, we find it is not invariant under C. Amazingly, invariance is regained (almost) if we consider not just P or C, but the combined transformation CP. The intriguing and maddening observation is that the laws are not-quite-invariant under CP transformations. In other words, we have CP violation.

CP symmetry refers to the fact that physical processes in nature occur in precisely the same manner if all particles were converted to their antimatter opposites using the CP transformation. Explicitly, the C operation reverses all additive quantum numbers such as electric charge, hypercharge, strangeness, etc., while the P transformation "inverts" the coordinate system and the orientation of all objects in it: x -> -x, y-> -y, z-> -z. That is, a particle traveling to the right in the +x direction finds itself traveling to the left (still in the +x direction) after a P transformation. More significantly, P reverses the relationship between the intrinsic angular momentum (spin) of a particle and the direction of its velocity. If the spin is aligned with the velocity, the particle is referred to as having "positive helicity." If the spin is anti-parallel to the velocity direction, the particle has "negative helicity." Under a P transformation, the velocity direction is reversed but the spin direction is not (as spin is a purely internal quantum number); thus a positive helicity particle -> negative helicity and vice versa. So under a CP transformation, a negative helicity proton becomes a positive helicity antiproton.

It was first predicted - and subsequently confirmed by experiment (in the 1950's) - that positive and negative helicity particles interact differently: a negative helicity electron will scatter off a nucleus and transform into a neutrino, but a positive helicity electron will not. However, a positive helicity positron will, just like the negative helicity electron. This is an example of CP symmetry. The symmetry was believed to be exact until 1964, when an experiment by Fitch et al. showed that for K⁰ mesons, CP symmetry breaks down 0.2% of the time.