Val Fitch (1982) - Aspects of CP-Violation

Well it’s especially appropriate that a discussion of CP-violation and matter antimatter asymmetry take place at this time because it was just fifty years ago this summer that Carl Anderson identified, discovered the positron, this first example of antimatter. It was published in September of 1932. This first identification was made in cosmic rays in a cloud chamber that was immersed in a magnetic field and it’s interesting that the principle experimental problem that Anderson faced in convincing himself and the community that he had positrons and not simply electrons travelling in the reverse direction. In the intervening years we have become so used to the idea of simply turning vectors around and making E minuses E pluses that it’s hard to adjust to the fact that his principle experimental problem was what we now take for granted. Well somewhat earlier Dirac had proposed his famous equation in which anti-matter is intrinsic but it appears that the theoretical developments and the experimental discovery were entirely disconnected. It’s one of the many remarkable coincidences in physics that these experimental and theoretical developments should occur almost simultaneously. Of course it took a bit of time to completely adjust to the notion of antimatter, but we’re now all very sophisticated and recognize that antimatter completely symmetric with matter is just a natural consequence of joining special relativity and quantum mechanics. I trust Professor Dirac will not object if I go back and quote what he had to say about matter and antimatter on the occasion of his Nobel prize. And I quote here, “If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of nature, one must regard it rather as an accident that the earth, presumably the whole solar system contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about, the stars being built on mainly positrons and negative protons. In fact there may be half the stars of each kind. The two kinds of stars would both show exactly the same spectra and there would be no way of distinguishing them by the present astronomical methods.” Well, I will come back to this. We’ve had some economists in our midst. There were economists here yesterday and of course with economists present physicists always feel that they somehow have to justify themselves on economic grounds. And we all know the list of things that physicists have done. You could recite the lists of all the instruments in the hospital, concluding with the computerated tomography machines, the CAT Scans and return to transistors and computers. There is one spin-off that had not occurred to me before. I wrote this down and that is there is this whole industry of science fiction and surely that industry would not be nearly as prosperous as it is if it weren’t for the idea of antimatter. Well, during this period when the notion of complete symmetry between matter and antimatter was developing the idea that all interactions were invariant interspatial reflections. Or also being firmly imbedded and as you know, Wigner proposed a symmetry to explain spectroscopic rules in particular those of Lukbart and Russell. And then following that, Ning Yang proposed that series of tests to see if the puzzle created by the tau and theta particles was indeed a manifestation of the failure of parity symmetry and the weak interactions. And as you all know it was found that not only parity was violated but also matter antimatter asymmetry. But still the cat landed on its feet in the end because it appeared that the total failure of parity was totally compensated by a corresponding failure in the charge conjugation and that all interactions in the end appeared symmetric under spacious inversion and matter-antimatter interchange. Well it’s now been eighteen years since my colleagues Cronin, Thorley and Christensen discovered that the world is not completely symmetric under CP. It’s a small but nonetheless unmistakable violation of CP and the system of neutral K-mesons. But again it’s been found that the CP violation appears to be totally compensated by a failure of time reversal, preserving the general idea of CPT symmetry. So let me now turn to a discussion of the K-meson system. And for that I will use this machine. These famous particles first invented by Gilman and Pais, based on the observation that through the weak interactions the particle, the K^0 and the K^0bar were coupled through these common decay modes. And correspondingly one has this elegant two state system of quantum mechanics. The coefficients in these equations comprise the so called mass decay matrix. Under CPT symmetry the diagonal elements, the A’s and the B’s are equal, but under CP symmetry the off diagonal elements of the matrix are equal. Now assuming for the moment CPT symmetry, then the mass eigenstates are simply the long-lived neutral K which I can write as pi K^0- Q^0bar appropriately normalized and the short-lived are anymore. Now it’s clear that with CPT symmetry the amplitude for decay of the K^0 and K^0bar must be the same. So one cannot have a decay of KL -> pi^+ pi^- for example unless P was different from Q, with the amplitudes for decay the same. Well, what was observed as you all know was a finite decay of the KL -> pi^+ pi^-. In fact the ratio of the rate of the KL -> pi^+ pi^- and the KS pi -> pi^+ pi^- is a very small number, about one in 200,000. It looks like an enormously small effect indeed in amplitude terms, however it is about 2/10 of a percent, emphasize precision which some of these quantities have been measured by noting that the phase angle of this amplitude has been measured to slightly more than one degree. But whether one considers this number small or not depends on how you feel about the fine structure constant. Because the magnitude of the ratio of these amplitudes is just about equal to alpha/pi, which itself is 2.32 x 10^-3. Now this amplitude could have two contributions. One from the mass decay matrix that I have already discussed, and also as I have indicated, even if P was equal to Q, if those off-diagonal elements were identical, it would still be possible for there to be CP violation. Simply if the decay amplitudes of K^0 and K^0bar differed in phase and when it normally allows for the possibility of CP violation in the decay amplitude by adding this extra parameter here, epsilon prime. Well, it turns out that at the moment all of the evidence is that at least 98 or 99% of the effect is in the mass decay matrix, but as we will see later, it is of extreme interest now is to just much might be in this epsilon prime. Stating it another way, the CP violation is the difference of the two vectors, the amplitude of the K^0 going to K^0bar might be indicated like so, the reverse process, K^0bar back to K^0 differs by this small amount which is at an angle as I have indicated of about 45 degrees and in terms of the length of each of the vectors is about 0.9 x 10^-2. Another way of phrasing it is that the difference to the off-diagonal elements and the mass decay matrix is about 10^-8 electron volts. Another manifestation of the CP violation and the effect being in the mass decay matrix comes from looking at the lepton decay modes of the K^0 and K^0bar. The K^0 can decay to E^+ pi^- neutrino and the K^0 bar to E^- pi^+ neutrino. The fact that it’s just the K^0 that decays the positrons and the K^0bar that decays the negative electrons is a consequence of a so called delta S = delta Q rule which in turn is just a manifestation of the fact that the K^0 is composed of an anti-strange quark and a down quark. And there is only one way one can draw such a diagram involving the W’s and that is this one. You cannot get a negative electron coming out of such a diagram. But independent of any such argument that delta S = delta Q rule has been tested to about the 1% level. Because of this fact that the K^0 can decay only the positrons and the K^0bar only to negative electrons and the fact that P is different from Q leads then to a charge asymmetry. Difference of the number of positrons from the decay of the long-lived neutral K’s compared to the sum is obviously a magnitude of P^2-Q^2 over the sum which is just two times real part of epsilon to a high degree of approximation. Now this charge asymmetry experimentally as you see is about 3/10 of a percent, measured with an error of something of the order of 5% in the case of the electron and for the cases where the my is substituting for the electron somewhat larger error with the numbers being the same within the error. Well, what are the consequences? First of all, I said that the eigenstates that I have drawn out have, I assume, CPT invariance. What if one does not assume CPT invariance it turns out that if you make that assumption, the phase angle difference between P^2 and Q^2 or I should say the phase angle of beta plus/minus independent of P^2 and Q^2, that phase angle should be something of the order of 135 degrees instead of the 45 degrees that is observed. So clearly CPT to quite a high degree of accuracy is experimentally confirmed and therefore it must be CP and time-reversal invariance that is violated. But for, asking the question, these results, what limit does this put on the equality of masses of K^0 and K^0bar, we come up with the following. Namely, we’ve already seen the effect is about 10^-8 electron volts, if I say that because of other arguments that I set a limit of about 10^-9 electron volts on the difference of the off diagonal elements, that compared to the mass of the K^0 is about 2 x 10^-18. That is one knows the mass of the K^0 and the K^0bar are identical to about two parts and 10^-18. Now yesterday I seized on a statement of Professor Schuller which I have written down here and I am being a little unfair but I can only say here that he is looking at the wrong particle when he makes the statement that nobody measures anything to one part and 10^17. Of course he was referring absolute numbers and I will correct my unfairness. One of the very interesting aspects of neutral K system is what it can tell us about the gravitational interaction. Question is one of strong universality. And that is whether different objects, in this case particle and anti-particle behave the same in the gravitational field. And if they differ by kappa then what limits does this system place on kappa? Now if one is discussing the gravitational potential of just the earth, where the K has a potential on the surface of the earth of about 3/10 of an electron volt, then kappa must be less than about 10^-10. If we’re discussing the solar system is should be around 10^-kappa is less than 10^11, if it’s a galaxy we’re discussing then that limit is around 10^13. Now you can argue well, mesons are composites of particles, anti-particles, quarks and anti-quarks, but I remind you that the mass of the strange quark differs from that of the down quark by something of the order of 125 MeV. What are the principle ramifications and consequences then of this asymmetry between matter and antimatter, the fact as we’ve seen that the rate of K^0 going to K^0bar differs from the reverse. These two vectors not only differ in magnitude but phase, which as we’ve seen also says that interactions are not invariant. Fundamental interaction is not invariant under time reversal. Well, we all know that time reversal is badly violated, disorder is always increasing, entropy is always increasing. But we also know that that’s due to the boundary conditions. You start with a clean house so you end up with a dirty house. But here we have time reversal in non-invariance due to fundamental interactions not boundary conditions – that is what is new and different from anything we have known before. This then can lead to matter-antimatter asymmetry in the universe, and we can make a simple argument, the following kind. We have already seen experimentally that the decay of long-lived neutral K leads to an excess of positrons. And it turns out if one integrates proper equations governing the time dependence of the K^0 and K^0bar that equal numbers of K^0 and K^0bar at T = 0 will also produce an excess of positrons, more positrons than electrons. But we already know that there is good reason for, at some level, coupling positrons and protons. We have learned that from Professor Weinberg this morning, correspondingly electrons with anti-protons. So with CP violation, since we’ve seen that the K^0 and K^0bars produce the number that leads to an excess of positrons. And with this kind of coupling we would also be automatically lead to the CP violation of equal numbers of K^0 and K^0bars producing an excess of protons over antiprotons. Of course, the difficulty is that the neutral K is not heavy enough to decay the nucleons, so I’m arguing only in principle here. In fact, the fact is however that there are other mesons that have plenty of mass to decay to protons, in particular the D^0, the D^0bar, B^0, B^0bar are in the presumably in excess the T^0 and the T^0bar. All of these mesons produce neutral systems that are completely analogous to the K system and are expected to show a CP violation and in some cases rather large, for example, large effects are expected in the case of the B^0, B^0bar. So with this identity, and the fact that this existence of these objects means that independent of any particular model, one has a mechanism for producing an asymmetry of matter over antimatter. Now, most generally this is discussed in terms of a heavy particle, as Professor Weinberg did earlier today. Here we have equated proton and E^+ and proton is just two up quarks and a down quark of course. So this is just the same thing written with the, one of the up quarks on the other side of the equation, which is then made equivalent to a leptoquark. A leptoquark then can decay to a U^+, an up plus, a down quark or to a positron and an anti-up quark. And a corresponding anti-heavy particle can go to the charge conjugate state. Now back in 1967 Sakharov seized on CP violation right away. And this is pre-grand unified theories. And he drew it all out. He had the heavy leptoquark decaying appropriately, and for example the heavy leptoquark going to positron and My(bar) with an amplitude A -> D + U with an amplitude, relative amplitude of 1- A choosing these as the only two decay channels for the purposes of symbolic arguments. By CPT it’s necessary that the total rate of the heavy leptoquark, total rate of decay, be the same as that of the anti-heavy particle. On the other hand these partial rates, the A and the A-bar don’t necessarily have to be equal, by CP violation they can be different. The net results of all of this is that it can produce numbers of these heavy particles and in their decay end up with a total baryon number which is just the difference of A-bar and A, through CP violation in this particular channel. There is another essential ingredient to producing a baryon asymmetry in the universe which I have not mentioned yet and that is that you have to guarantee that back reactions are not going to cancel out everything you have accomplished in these forward reactions. So one has to have a non-equilibrium situation prevailing. Well, how does CP violation fit into any of the theoretical ideas that we have had described to us? First of all the non-perturbative quantum chromodynamics has intrinsically a strong CP violation. Characterizing that phenomenon by parameter theta, the most natural value for theta is 1. However to suppress the electric dipole moment of the neutron to an appropriate level it is necessary that theta<10^8. This is still an awkward problem. I don’t believe that anyone would agree that it has been satisfactorily resolved. And what is has to do with the weak interactions is anyone’s guess. Within the frame work of the gauge models, there are two independent, not completely independent ideas that have been put forward. First of all the Kobayashi-Maskawa six quark model which extends the four quarks of Glashow and company to six quarks and this model was actually proposed back in 1973 when we only knew of three quarks. Since then two more quarks have been discovered and as we have heard again and again now, a sixth quark is expected at any moment. So this particular model has established some popularity. The essential point here is that it has space in it, an extra phase which is CP violating. So it provides a very natural home for CP violation. There is also an independent suggestion that the CP effect could be due to the exchange of Higgs particles which were also mentioned by Professor Weinberg earlier, indeed he is one of the original proponents of this particular idea. One of the reasons for resurgence of interest in this problem is that it turns out that these become imminently testable and I will come back to that. Professor Schwinger has also proposed that the effect might lie in dyons, that is, electrically charged monopoles. One of the original suggestions seized on the fact that the effect that is measured in 8^+/- is very close to the fine structure constant divided by pi. It is a terribly suggest correlation that is that the effect is electromagnetic. That seems to be completely ruled out now by the very relatively tight limits, at least tight limits for this argument on the electric dipole moment of the neutron. So what are the consequences of these various theoretical models, what are they, what is really testable? Well with Higgs exchange, as proposed originally by Lee and Weinberg, the leading consequences are that one has milliweak effects throughout the weak interaction. The electric dipole moment of the neutron should be in the range of 10^-24, 10^-25 e-cm. At the present moment the accepted limit is 10^-24 e-cm. So a small improvement in this measurement will begin to have a telling effect on this idea. The experiments outside the neutral K system that have been done on the weak interactions have all been done essentially at the center-weak level. And another factor of ten is necessary in the accuracy of those experiments in order to begin to say something about whether there are milliweak effects everywhere. But there is apparently a big problem with this model already because it's been recently pointed out by Sanda and Deshpande and later by Donoghue, Hagelin and Holstein that in fact the ratio of epsilon prime over epsilon within the frame work of this model and some other assumptions that I won’t go into here, should be of the order of 0.05. Now in fact the present experimental limit on this number is something like 0.02. There are two ways one can get out of this immediately though, one of them is that the theoretical prediction is apparently not as hard as one would really like. So there is some softness here, and in view of the difficulty in measuring the epsilon prime component of the CP violation, there could be some softness in the present experimental number also. If one takes all that’s known about the phases and the KM model, Kobayashi-Maskowa model, then various people have made various predictions of what should be measured for epsilon prime over epsilon. And as I indicated the current experimental number has a limit of around 2%. New experiments could show something exceedingly interesting, and indeed my colleague Cronin has just concluded taking data devoted to this problem in the last week or so. On the other hand the effects within the framework of this model and other sectors are really very small indeed. For example the electric dipole moment of the neutron which I have already indicated has been limited to around 10^-24 e-cm is predicted to be something of the order of 10^-30. Let me remind you that the magnetic dipole moment of the neutron is around 10^-14 e-cm, so the present limit is already ten orders of magnitude less than this number, which is rather easily measured of course. Well, these new experiments then promise to be able to distinguish between these principal ideas involving gauge theories. But I think it’s fair to say that we still do not know what the real source is, even if it’s found to lie within the extra phase that’s available in the Kobayashi-Maskawa model, the source of the violation is still a great unknown. It might find a natural home there, but the real effect, the real cause has yet to be determined. I would like to conclude by making a few remarks directed to the students here, a few remarks of a semi-philosophical nature, about the process of doing physics. At any one time there are always plenty of people, fellow physicists who would tell you that everything is understood and anything that follows is just a mopping up operation. In a certain sense I feel that we are at a time like that now, but it just never happens that way. Every time we explore a new domain, we inevitably discover new phenomena which require a major reordering of the old ideas or completely new theories to accommodate them. Who could possibly have guessed that the discovery of strange particles in the late 1940’s would have lead in the following fifteen years to the discovery of parity and charge-conjugation violation? And then the failure of CP, or that we would now be calling strangeness just another flavour? I would hope that I have left you with the feeling that, just to say it again, that we still know very little about the details of CP violation, time-reversal violation is obviously touching on our knowledge of physics at the deepest level. What is the source, how does it operate? We have likely written down relations between quarks and leptons and then we can ask, why does the electron have a charge three? In terms of the quark of course. And when will the electrons start to show structure? Just what are particles anyway? These little concentrations of energy that travel like waves, then when are we going to be able to provide the experimental control or the sometimes rampant speculations about the nature of the gravitational interaction? These are questions for your generation and the answers you get will sometimes have nothing to do with the questions. But that’s what one does physics for. I have been doing experimental work for about 35 years and at each point in time proposed experiments, experiments that we have thought of, have always seemed impossible. That’s where you start from. We have always had to push the limit of the technology or exceed it and just to achieve what we set out to do. But surprisingly often then we have learned something that no one expected. It’s interesting that, starting from the position where it seemed impossible, when it’s all over and the data is understood, that which seemed impossible at the beginning now seems trivial. But that’s true of everything in physics: it’s either trivial or impossible. And before you try it’s impossible and after you’ve succeeded it’s trivial. You’re as students at sort of the impossible stage now, but keep at it, some parts of it will eventually seem trivial and good luck to you.

Val Fitch (1982)

Aspects of CP-Violation

Val Fitch (1982)

Aspects of CP-Violation

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