Ever thought why the world is full of matter and lacking antimatter? If yes, you have thought of CP violation and you've just found the right Web page!
Charge conjugation (C) is what we need to transform a particle into its antiparticle. The name of this transformation is actually quite tricky, because in fact it involves not just electric charge, but a change of all additive quantum numbers to their opposites, with charge being just one of them (and may well be irrelevant in the case of neutral particles).
A C invariant world is one fully symmetric with respect to charge conjugation. In such world, matter and antimatter should behave in exactly the same way, hence a simple exchange of all particles by their antiparticles should end up in an identical world. Most processes observed in particle physics indeed make no distinction between matter and antimatter, in paticular all electromagnetic and strong nuclear interactions are C invariant, let alone gravity. Nevertheless, it is clear that we are not living in a C invariant world after all: the Universe as a whole is made up of matter, hardly of antimatter. Why this is so, is a mystery of particle physics and cosmology.
We know also at the particle level processes that violate C. In fact, C is not at all a good symmetry of one of the four known basic forces acting between particles, called the weak interactions (in the Standard Model, it is perfectly correct to define a weak interaction as one mediated by any of W^+, W^- and Z^0 bosons). It is plain to see it in the case of neutrinos, particles which can only interact weakly. As shown in a classic experiment by M.Goldhaber, L.Grodzins and A.Snyder, neutrinos have a peculiar feature called left-handedness: their spin is always directed opposite to their momentum. Similarly, antineutrinos are always right-handed (I am neglecting here the tiny effect of non-zero neutrino mass, as recently discovered). Obviously, a C transformation would not produce an identical world. It would in fact produce a 100% different world: left-handed antineutrinos and right-handed neutrinos. Neutrinos maximally violate C.
Having in mind that the C symmetry alone is violated in particle physics, we can still hope to preserve strict balance between matter and antimatter. Indeed, sometime in the 60's there was a widespread belief that C violation is equivalent to violation of space parity. The latter is denoted by P and corresponds to an exchange of all space coordinates to their opposites. It is often said that P is the mirror reflection, which, strictly speaking, is not. A mirror inverts left-right and front-back; the P transformation inverts all coordinates: left-right, front-back and bottom-top.
As P inverts the sign of momentum, but leaves spin intact (remember angular momentum is a pseudo-vector!), it is immediate to notice that P cannot be a good symmetry of weak interactions, either. A P transformation on left-handed neutrinos and right-handed antineutrinos produces right-handed neutrinos and left-handed antineutrinos - again states which don't exist in real world. P violation has been known experimentally since the 50's.
Consider, however, the symmetry under CP: a C transformation followed by a P transformation. We go then from left-handed neutrinos and right-handed antineutinos to right-handed antineutrinos and left-handed neutrinos - a certainly plausible state! Once we include handedness in the picture, it is generally the right-handed antiparticles which are thought to correspond to left-handed particles; it is often more convenient to define explicitly CP, rather than C alone, as the relation between the world and the antiworld. For quite some time, the world was thought to be CP invariant. Thus, by complementing simple charge conjugation by space reflection, symmetry between matter and antimatter could hold. But is this really the case? The answer came in 1964, from another classic experiment by Cronin, Fitch, Christenson and Turlay. To their own surprise, the answer was no. Not even CP is conserved in particle physics! And, in fact that's good for us, since the observed asymmetry between matter and antimatter in the Universe requires a violation of both C and CP. Let me just stress here, that the Cronin et al. experiment discovered CP violation only in the quark sector. Whether or not neutrinos violate CP (as in the given example), is still a completely open question.
Another key transformation in particle physics is T, the time reversal. It is perhaps not very intuitive, but is generally believed to be equivalent to CP. Therefore, the symmetry with respect to time reversal is violated wherever CP is, but the combination of both, CPT, is conserved. Experimentally, though, T violation can often be studied independently of CP violation. An explicitly T violating effect has been observed by CPLEAR at CERN.
CPT invariance is, most of all, a theoretical assumption rather than an empirical observation. The world is bound to be CPT invariant because CPT invariance holds for any single particle separately: a particle is believed equivalent to its antiparticle moving backwards is both space and time. Once we allow both space and time inversions, matter and antimatter become the same thing.
It is hard to imagine a decent field theory without CPT invariance. On the other hand, some theoretical developments predict violation of CPT at a very low level, due to quantum effects. Experimental tests of CPT include the equality of masses, lifetimes, magnetic moments, etc., between particles and antiparticles. So far, no CPT violation has been observed.
Neutral kaons have long been known to be an extremely interesting system. Particles K^0 and anti-K^0 decay due to weak interactions. Their decays are observed, however, in two distinct components, called short-lived (K_S) and long-lived (K_L), differing in preferred decay channels, but otherwise similar to each other. K_S decays into two-body final states, chiefly two pions, either charged or neutral.
Meanwhile, K_L prefers three-body final states: either three pions or a charged pion, oppositely charged lepton (electron or muon) and a neutrino or antineutrino (the latter decay modes are often referred to as semileptonic).
Not for the first time, though, nature proved much more interesting than anyone could think of. The unexpected experimental signature of Cronin et al. was the decay K_L --> pi^+ pi^-, occurring at approximately 0.2% of all K_L decays. Easy to guess, there are in general two possible explanations of this. Either K_L is not a strict eigenstate with CP=-1, but contains a 0.2% addition of a CP=1 state, or a clean CP=-1 state can decay to a clean CP=1 state. These two possibilities are called indirect and direct CP violation, respectively; the formal meaning of it will be discussed in more detail in the appendix. For the moment it is clear, however, that regardless the underlying physical mechanism, neutral kaons violate CP, which is manifest by the decay K_L --> pi^+ pi^-.
More evidence of CP violation has been found in K_L semileptonic decays. An observed asymmetry between the corresponding semileptonic modes with a positive and a negative lepton proved that it is indirect CP violation which is dominant. This is described by the complex number eps (epsilon), hence shown to be non-zero. It is customary to say here that the semileptonic asymmetry provides a unambiguous definition of matter and antimatter, but in reality any CP violating effect could fulfill this job - it may just require a bit more work...
Meanwhile, direct CP violation is denoted by another complex number, called eps' (epsilon prime). For many years it was not clear whether eps' differs from zero. This question is in fact the main aim of the currently working large scale experiments, KTeV at Fermilab and NA48 at CERN.
Up to this date, various decays of K_L provide the only significant proof of CP violation in particle physics.
CP violation occurs in weak interactions. While this is today common knowledge for all particle physicists, the actual reason for it is a common lack of knowledge. There is nothing in the sole structure of the theory which generates CP violation and there is not even a way of describing CP violation, other than introducing by hand some mysterious empirical facts. One of them is that there are actually three generations of quarks. In particular, the existence of the third, heaviest generation of quarks is absolutely required to have CP violation in the Standard Model, but for essentially nothing else. The second empirical fact is the strange property of weak interactions of mixing the down-type quarks. Weak interactions do not see the same d, s and b quarks as electromagnetic and strong interactions, but some fancy combinations of them. More technically, the probabilities of various quark transitions due to weak interactions are parameterized by the 3x3 Cabbibo-Kobayashi-Maskawa matrix, which we know from experiment to be non-diagonal. Well, it has been shown that only a non-diagonal 3x3 (or larger) mixing matrix can have complex coefficients, which is a necessary condition to have CP violation in the theory. A miracle!
In the Standard Model, CP violation can reside in a single parameter, called the delta phase. Moreover, in the simplest Standard Model (with one Higgs doublet and no other extensions), this is the only possible source of CP violation. On the other hand, any possible extension of the model will usually produce new sources of CP violation, e.g. the Minimal Supersymmetric Standard Model (MSSM) has even too many of them. Since delta is a free parameter, it does not provide any direct predictions independent of experiment. It is predictive, however, in the sense of relating a huge number of different phenomenological effects to just one parameter. Although there is no purely theoretical value for eps (indirect CP violation), or eps' (direct CP violation), predictions can be drawn by measuring other processes related to the Cabbibo-Kobayashi-Maskawa matrix coefficients. Therefore, experimental studies of CP violation are important tests of the Standard Model on one hand, and searches for possible links to new physics on the other.
There is plenty of possible consistency tests that may reveal either the correctness or incompleteness of the Standard Model description. The most current one is the actual value of eps'. Our present knowledge of other Standard Model parameters, plus additional uncertainties due to the approximative character of some theoretical computations (as usual in this field, related to the fact that quarks can only exist confined within hadrons) restricts the possible range of the eps'/eps ratio to 0.0001-0.001. It has been found a real experimental challenge to measure such tiny effects, this is however the main research topic of KTeV at Fermilab, NA48 at CERN and the developing project KLOE at Frascati.
Several other ways are being presently considered of finding out if delta is in reality the sole source of CP violation. A promising path is to study the phenomenology of B mesons, short lived particles containing the b quark. CP violating effects, often much larger than those observed in kaon physics, are generally expected in the B sector. This is one of the main research topics of many presently running and developing experimental projects: CLEO at Cornell, Ba-Bar at SLAC, Belle at KEK, Hera-B at DESY, CDF and D0 at Fermilab and LHC-b at CERN. Consistency of the Standard Model requires all this phenomenology be described by means of the same Cabbibo-Kobayashi-Maskawa coefficients. The same coefficients should lead to the observed CP violating effects in kaon physics, too. In fact, some theorists hope the results won't be consistent...
A formally equivalent way of saying that K^0 and anti-K^0 decay via two mixed states called K_S and K_L is that a free K^0 (or anti-K^0 for that matter) evolves in time. This is often referred to as "strangeness oscillation" and is well known from observation. The time evolution of such system is given by a Schrodinger equation of the form
| M_1 i*m | | G_1 i*g |
M = | |, Gamma = | |.
| -i*m M_2 | | -i*g G_2 |
and
and same in case of two charged, as well as two neutral pions.
In Quantum Mechanics, we can nonetheless expect also K_2 to have a non-zero probablity of decaying into a CP=1 state. We then talk of direct CP violation, i.e., CP violation in the decay amplitude. This happens with a probability described by the number eps'; a generally non-zero value of this number arises from the interference between amplitudes for final states of two pions with total isospin 0 and 2.
with A0, A2 being the amplitudes and d0, d2 the phases for K^0 decaying into two pions of isospin 0 and 2, respectively. It just takes a bit of algebra to convince oneself that with eps' being different from zero, the relative amplitudes for a decay into pi^+pi^- and pi^0pi^0 are no longer equal.
It is an experimental fact, above all, that the indirect mechanism is dominant. We know this from both the approximate equality of |eta_+-|^2 and |eta_00|^2, and from the asymmetry in K_L semileptonic decays. The K^0-based decay K_L --> pi^- l^+ nu has been shown slightly favored over the anti-K^0-based K_L --> pi^+ l^- anti-nu, the difference being around 3 per mille. Given that the definition of K_L may be rewritten in means of K^0 and anti-K^0 in the form:
it is obvious that the observed semileptonic asymmetry is a direct measure of twice the value of eps (and C is a normalization constant, numerically close to 1/sqrt(2)).
The search for direct CP violation can be performed by a precise measurement of the ratio |eta_+-|^2/|eta_00|^2, which in the end is nothing but the double probability ratio of four decay modes. A departure of this ratio from unity is the sought signature.
All the above holds regardless of whether the Standard Model is correct.
Okay, my friend. Now that you've read and understood everything, you are ready to join us! Good luck!