In this paper I will try to give some general information about symmetries and charge parity violation (CP-violation). I will also mention the BaBar experiment at the B-Factory of the Stanford Linear Accelerator Collider(SLAC) going on in order to complete the explanation of CP-violation. As this subject is one of the most complicated issues of modern physics my paper will only aim at giving some general idea about the issue and why it is important. By being a member of University of Pennsylvania group working on the experiment in BaBar factory, I found it worthwhile to mention about that experiment, which is the most complex experiment going on it research about CP-violations in B Meson decays.
CP-violation arises as a point to be discussed as it is a violation of symmetries that our Universe posseses. A symmetry is an operation you can perform (at least conceptually) on a system that leaves it invariant. The set of symmetry operations on any system must have the following properties: (they are defining properties of a group):
The most trivial symmetries are translations in space, translation in time and rotation through a fixed angle. For example if we build a certain apparatus and start it at a certain time, and then build the same apparatus and start it some time later, the apparatuses will go through the same motions in exactly the same way as a function of time no matter what the starting time, (provided that the relevant features of the environment are also modified appropriately in time). The nature presents lots of symmetries but of course it also involves asymmetries like rotation at a uniform angular velocity.
The symmetries of physical laws is most interesting in the case of quantum mechanics, as for each rules of symmetry there is a corresponding conservation law (Noether's Theorem). The most interesting case about the symmetries is the symmetry of reflections in space and just by intuition about laws of physics we can say that they have such a symmetry. If we assume such a symmetry it would mean that if we change everything from "right" to "left" and leave it otherwise the same , we cannot tell the difference. This would mean that there is no absolute "right" or "left" and we cannot distinguish "right" and "left" by any physical phenomenon. It has been found that the laws of gravitation , the laws of electricity and magnetism, nuclear foces all satisfy the principle of reflection symmetry.
A phenomenon called beta decay, or weak decay which showed itself in connection with a particle discovered in about 1954 ended up posing a strange puzzle to physicists. A particle which used to be called t-meson which disintegrated into three p-mesons was found. Another particle which used to be called q-meson was found to disintegrate into two p-mesons; one of which need to be neutral from the conservation of charge. The process of disintegration can be shown schematically as follows:
Later on it was discovered that t and q had almost the equal mass, actually equal within the experimental errors. The length of time it took for them to disintegrate into three p's and two p's was also found to be almost exactly the same which meant that they lived the same length of time. The third interesting feature showed by these particles was that whenever they were made, they were made in the same proportions, for example 14% t's to 86% q's , and this led to the realisation of the fact that they must be the same particle, meaning that we have an object which has two different ways of disintegrating. This was impossible according to the principle of reflection symmetry in quantum mechanics. The same particle could not simply disintegrate in both of these ways. This was a violation of the conservation of parity law which is the name given to the conservation law corresponding to the principle of reflection symmetry. From the symmetry of the quantum-mechanical equations of weak decay under reflection , it was possible to show that this decay was impossible. Therefore, a possibility of that symmetry of nature being false arose. (this was actually an example for parity violation in the weak interactions, I will talk about this later).
Next thing to do was to test if similar asymmetries arose in other cases. The first of those experiments was done by using a strong magnet at very low temperature. It turned out that a certain isotope of cobalt , which disintegrates by emitting an electron, is magnetic and if the temperature is low enough that the thermal oscillations do not jiggle the atomic magnets too much, they line up in the magnetic field. The cobalt atoms would end up lining up in this strong field. Then , they would disintegrate, emit an electron and it was discovered that when atoms were lined up in a field whose B vector points upward, most of the electrons were emitted in a somewhat downward direction. This meant that when we put cobalt atoms in an extremely strong magnetic field, more disintegration electrons go down than up, which in turn meant that if we were to put it in a corresponding experiment in a "mirror" in which the cobalt atoms would be lined up in the opposite direction , they would send out electrons up, not down; an unsymmetrical action. This was a violation of symmetries. After similar other experiments it was found that the disintegration of the p into m and u; m into an electron and two neutrinos; the L into proton and p; disintegration of S's; and many others did not obbey the symmetry of reflection. All the cases where it was expected turned out to violate it which meant that that symmetry was incorrect.
The problem to be solved was to find the law of the failure of parity conservation. It turned out to be that it occurs only in very slow reactions called weak decay, and when it occurs, the rule is that the particles which carry spin, like the electron, neutrino, and so on, come out with a spin tending to the left. That is a lopsided rule as it connects a polar vector velocity and an axial vector angular momentum, and says that the angular momentum is more likely to be opposite to the velocity than along it.
Now that some symmetries lost, the thing to be done is to check if any other symmetries known to be or assumed to be were also lost. One other thing to mention there is the relation between matter and antimatter.Dirac (in 1927) predicted that for ordinary matter to be stable, there should be a particle called the positron which is the anti-particle of the electron, and all properties of these particles obey certain rules of correspondence; equal energies, equal masses, charges are reversed and when two of them come together they can annihilate each other and liberate their entire mass in the form of energy, for example as g-rays. All the rest of the particles in the world should also have corresponding anti-paricles and lots of them have been found experimentally. This also meant that as we have anti-electrons, anti-proton and anti-neutrons , we should be able to create antiatoms, in principle. Then an immediate suggestion that we can built tow different clocks one which is "left-hand" and the other which is "right-hand" arises. We can built one say, with cobalt, magnets and electron detectors which detect the presence of b-decay electrons and count them. Then we will have a mirror clock which counts less and so different time. What if we build two more clock with antimatter? After experiments with b-decays it was found out that a antimatter clock that we would have built in the shape of "left-hand" matter clock would have behaved as "right-hand" matter clock. The interconnection of matter to the "right" works the same way as antimatter to the "left". This meant that some parts of right and left symmetry were still maintained but it was interconnected to matter , antimatter relationship and matter to the right was symmetrical with matter to the left.
From the presence of the antimatter some other questions arose; why do we rarely see any "natural" antimatter? and how come we did not have all matter in the universe annihilated by antimatter? There are no antiplanets, antistars or any antigalaxies as if there were any, the flood of g-rays that result from the catastrophic annihilation between matter and antimatter at the boundaries where their two domains meet would have been clearly visible; but the flux of g-rays in the universe is extremely weak which testifies the scarcity of antimatter in the universe. This implies a cosmic favoritism for matter over antimatter. A certain number called the baryon number was introduced as a conservation law. Baryon number is and has been constant throughout the life of the universe. The baryon number in our universe is very large; there are at least 104 particles (+1) for every antiparticle (-1) in space. This value has an awkward meaning; today we observe about two billion photons for every proton on the average which meant that "big bang" had about a billion and one protons emerging from it for every billion antiprotons, which in turn annihilated with their billion anti-partners to cerate about two billion photons for every leftover proton. The special assumptions about the begining of the universe tells an equality of particles to antiparticles. The problem with this assumption in this assumption is that it meant that we should be seeing 1018 photons for every proton or antiproton today which is not the case.
Now, that we have basic knowledge about symmetries, we can approach where CP-violation arises from. In high energy physics the three most fundamentals symmetries are; parity, charge conjugation and time reversal. These can be represented schematically as follows:
Specifically these symmetries apply to the interactions between particles. Combinations of these symmetries also take place. The strong, EM, and gravitational interactions preserve all three symmetries , but, the weak interaction violates C,P and CP. Weak interaction is done by the weak force which is one of the four fundamental force of the universe; strong force (mediated by gluons, binds quarks into hadrons causes nuclear fusion and fission), electromagnetic force (mediated by photons, responsible for atoms, molecules, chemical reactions, light waves, electronics), gravitation (possibly mediated by gravitons, determines the large-scale structure of space-time), weak force (mediated by W and Z bosons, responsible for netron decay, beta radioactivity, muon and tau decay, u interactions). At present, it is believed that all matter can be broken down into fundamental constituents called quarks and leptons, grouped into doublets;
There are three successful theories explaining much about three of the four fundamental force acting on quarks and leptons:
QED: Describes the interaction of charged particles through the electromagnetic force.
QFD: Also called the Standard Model , describes the interaction of particles through the electromagnetic and weak nuclear force.
QCD: Describes the interaction of particles through the strong nuclear foce.
It is commonly believed that all the four fundamental forces are all different manifestations of a single, universal interaction and the vast difference in strength and behaviour of the forces we see is due to the breaking of a fundamental symmetry which is evident only at stupenduously high energies. Such Grand Unified theories uniting weak, strong, and EM interactions often predict a baryon number violation through the interactions of very massive (1014GeV) bosons, X and Y, which transform quarks to leptons and quarks to anti-quarks. As, weak interaction violate CP symmetry, grand unified fields must also do so. Therefore, CP-violation saves the universe by causing the unequal number of matter and antimatter by providing a "natural" mechanism by which X and bosons, which must have identical total decay rates, can have some decays which violate CP in second order, in analogy to an observed CP-violating decay of kaons:
Once the universe is cool enough, the CP-violating decays can produce a preponderance of baryons over antibaryons (about 1 in 109), leading to the observed baryon number. In the context of the Standard Model at least two quark families are needed to do that. Three quark families are needed to get an appreciable amount of violation and that is what has been observed so far.
Now, that I have given information about symmetries and some examples of charge parity violation , I will give some information about experiments about CP-violation. As this subject is far beyond my knowledge of physics and mathematics , I will try to be brief and limit myself to simple equations. Unfortunately, most of the equations are still past beyond my knowledge, therefore I will just state them and some facts about them without commenting.
So far, CP-violations has only been observed in neutral Kaons(schematically shown above). CP-violation here arises form the matrix transformation which takes us from the mass eigenstates of the lower doublet quarks to their appropriate weak eigenstates. This can be represented as:
V is a unitary 3 x 3 matrix specified by four parameter, 3 mixing angles and 1 arbitrary phase. It is called the Cabibbo-Kobayashi-Maskawa(CKM) matrix:
Any non-zero value for the phase incudes CP-violation and this can account for CP-violation neutral K system, and predicts very small CP-violation in all other quark systems except those involving bottom quraks, where CP asymmetries are large (about 50%).Therefore, a clever way to learn more about CP-violation is to study B-meson decays.This would unambiguously rule out the only model of CP-violation other than the Standard Model, and overconstrain the Standard Model prediction and thereby unambiguously show the existence of physics beyond the Standard Model. The primary means of study will be determining asymmetries in decay rates for
The goal of BaBar (mentioned in the introduction) is to do precision measurements of the CKM matrix elements. From the unitarity condition of CKM matrix , we can see the following equation:
which can also be expressed pictorally with the unitarity triangle. In BaBar experiment the overdetermination of this triangle through direct measurement of its sides and angles, looking particularly at Vub and measuring the angles a and b is the main goal. The unitarity triangle is:
I tried to explain very briefly and generally symmetries and CP-violation and the experiment going on about CP-violation decays. This is a popular area of high energy physics where there are still a lot of important information to be searched. I believe that the issue of symmetries is specifically important one and hope to be participating in further research about that topic. As my main aim of the paper was not to comment or derive anything about this advanced topic I limited myself to low level explanations.
REFERENCES: The Feynman Lectures on Phyiscs , Richard P. Feynmann, 1964, Caltech, USA The Left Hand of Creation, J.D Barrow, J.Silk, 1983, Oxford Uni. Press, USA Introduction to Elementary Particle Physics, D. Griffiths, 1987, John Willey & Sons, USA. CP-Violation Physics at BaBar, DOE site Review, L. Gladney, 1994 Letter of Intent for the Study of CP violation and Heavy Flavor Physics at PEP-II, BaBar Collaboration, 1994, USA