Elementarteilchenphysik

Elementarteilchenphysik Antonio Ereditato LHEP University of Bern Lesson on: Weak interaction (6) Exercises: K and CP violation A.Ereditato SS 2008

The establishment of parity violation in Weak Interactions (1943-1957) In 1848 Pasteur discovered the property of optical isomerism. Two forms of the same chemical compound, isomers, were found to rotate polarized light in two different directions, one to the left, the other to the right. Isomers are essentially identical chemical compounds. They have the same number and type of atoms and the same structure, almost. The difference in the two isomers of a compound is that one is the mirror image of the other. This is the same symmetry that exists between the left and right hands. Pasteur observed as well that living organisms were able to synthesize and use only one isomer and never the other. But nature itself appeared to have no preference over which form it produced. In reactions the isomers were produced in equal quantities. That is, nature appears to exhibit complete symmetry between the left and right. Until 1957 physicists believed this symmetry to hold for all physical processes. A mirror image of any reaction should be identical in every way to the actual reaction. This idea was intuitive to physicists: what could it mean if nature preferred left over right or vice-versa? To describe more precisely the symmetry between left and right, physicists used the concept of parity, originated with the development of quantum mechanics. In 1924 Laporte classified the wave functions of an atom as either even or odd, depending upon the symmetry of the wave function. Laporte discovered that when an atom transitions from one state to another and a photon is emitted, the wave function changes from even to odd or vice-versa, but never remains the same. Even functions were defined to have parity of +1 and odd functions a parity of -1. In addition, the emitted photon was defined to have parity of -1. Laporte's rule could then be stated as a conservation law, the conservation of parity. A.Ereditato SS 2008

The parity of any system is the product of the parities of the individual components. Parity is conserved in atomic transitions. If the initial wave function was odd (-1 parity), Laporte's rule asserts the final wave function must be even (+1 parity). Since the initial system has -1 parity and the final system has as its parity the product of parities of the final wave function and the parity of the emitted photon, (+1)(-1) = -1, parity is conserved in the transition. The parities of the initial and final wave functions can be interchanged; conservation of parity will still hold. The importance of parity conservation was discovered in 1927 by Wigner who proved that Laporte'srule was a consequence of right-left symmetry (or mirror image symmetry) of the electromagnetic force. Conservation of parity rested upon Maxwell's equations describing electromagnetism, but more important, the intuitive idea that nature should be left-right symmetric had been established on the quantum level. Thus, the weak force was postulated to explain disintegration of elementary particles, physicists could not conceive that parity conservation would not hold for reactions involving the weak force. It was a minor oversight however that there was no direct evidence for the extension of this law to the fourth force of nature. A.Ereditato SS 2008

Within the cosmic rays in which Powell discovered the pion there were other new particles. In 1949 Powell identified a cosmic-ray particle which disintegrated into three pions. He named this new particle the tau-meson. Another particle called the theta-meson was also discovered. It disintegrated into two pions. Both particles disintegrated via the weak force. Now, a problem arose when the masses and the lifetimes of the tau and theta particles were considered. The two particles turned out to be indistinguishable other than their mode of decay. Their masses and lifetimes were identical within the experimental uncertainties. Were they indeed the same particle? The problem itself was not that the tau and theta, if they were the same particle, decayed in two different modes, one by two pions, the other by three pions. The problem dealt with the more fundamental parity conservation law. In 1953 Dalitz argued that since the pion has parity of -1, two pions would combine to produce a net parity of (-1)(-1) = +1, and three pions would combine to have total parity of (-1)(-1)(-1) = -1. Hence, if conservation of parity holds, the theta should have parity of +1, and the tau of -1. Hence, they could not be the same particle. Thus the theta-tau puzzle was born. Its resolution would involve an almost unacceptable proposition to the physicists of the time... (Today we know that the tau and the theta are the same particle, the kaon, which can decay by weak interaction in two or three charged pions) A.Ereditato SS 2008

The events which led to the publication of Lee and Yang's historic paper, Question of Parity Conservation in Weak Interactions, began at the International Conference on High Energy Physics at the University of Rochester in April 1956. Lee and Yang attended the conference with a proposal for ending the theta-tau puzzle. Their idea was that certain kinds of elementary particles occur in two forms with different parities. The idea was called parity doubling. Feynman was also attending the conference. He was famous for his development of quantum electrodynamics. Feynman's room mate at the conference was the experimentalist Block. He suggested to Feynman on the first night of the conference that parity just may not be conserved in certain interactions. The next day, following Yang's presentation of the parity doubling idea, Feynman brought up the question of non-conservation of parity. Feynman himself later said, "I thought the idea (of parity violation) unlikely, but possible, and a very exciting possibility." Indeed Feynman later made a fifty-dollar bet with a friend that parity would not be violated. Yang's reply was that he and Lee had considered the idea but had arrived at no conclusions. During the discussion, Wigner, who had formulated the law of conservation of parity in the first place, also suggested that perhaps it did not hold in weak interactions. A.Ereditato SS 2008

Lee and Yang pursued the question further after the conference making a careful study of all known experiments involving weak interactions. After several weeks of reviewing they had come to two conclusions: 1) Past experiments on weak interactions had actually no bearing on the question of parity conservation.  2) In strong interactions, ... there were indeed many experiments that established parity conservation to a high degree of accuracy... As Yang commented in his Nobel lecture, "The fact that parity conservation in the weak interactions was believed for so long without experimental support was very startling. But what was more startling was the prospect that a space-time symmetry law which the physicists have learned so well may be violated. This prospect did not appeal to use.” A.Ereditato SS 2008

When Lee and Yang's paper appeared in the October 1, 1956 issue of The Physical Review, physicists were not immediately prompted into action. The proposal of parity non conservation was not unequivocally denied; rather, the possibility appeared so unlikely that experimental proof did not warrant immediate attention. Dyson wrote of his reaction to the paper: "A copy of it was sent to me and I read it. I read it twice. I said, “This is very interesting,” but I had not the imagination to say, `By golly, if this is true it opens up a whole new branch of physics.' And I think other physicists, with very few exceptions, at that time were as unimaginative as I". Hence, the initial reaction among most physicists to verifying parity conservation was not enthusiastic. In their paper, Lee and Yang stated, "To decide unequivocally whether parity is conserved in weak interactions, one must perform an experiment to determine whether weak interactions differentiate right from left." They proposed several experiments. One of the (conceptually) simplest involved measurements of Cobalt-60 beta-decay. The idea was to orient Cobalt nuclei with a strong magnetic field so that their spins are aligned in the same direction. Beta electrons are emitted at the poles of the nuclei. A mirror image of the system would also show electrons being emitted from the poles of the mirror Cobalt nuclei, the only difference being that the north and south poles of the mirror nuclei would be reversed since they spin in opposite direction of their real counterparts. Hence parity conservation demands that the emitted beta rays be equally distributed between the two poles. If more electrons emerged from one pole than the other, it would be possible to distinguish the mirror image nuclei from their counterparts. A.Ereditato SS 2008

At the time Lee and Yang considered the question of parity, Mrs Wu was a professor at Columbia and a long time friend of both men. She was the first to act on the proposed experiment involving beta decay in Cobalt 60. Even before Lee and Yang's paper had been submitted to The Physical Review, Lee had discussed the experiment with Wu. However, the experiment could not be performed with only her expertise. Reaching the low temperatures necessary to be able to orient the Cobalt nuclei spins required equipment few laboratories possessed. Nevertheless, one such laboratory existed in the United States, the Cryogenics Physics Laboratory at the National Bureau of Standards in Washington. Early in June of 1956, Wu sought the help of Ambler at NBS. He accepted enthusiastically. Indeed his doctoral thesis dealt with the orientation of Cobalt-60 nuclei. In addition, Hudson, with expertise in cryogenics, and Hayward and Hoppes, with experience in radiation detection, joined the team. By early October they began to assemble and test their equipment. The same month saw the publication of Lee and Yang's paper. The experimental problems were enormous. Temperatures as low as one hundredth of a Kelvin were necessary to attain a high degree of spin orientations for the Cobalt nuclei. While such temperatures could be reached through the so-called adiabatic demagnetization, maintaining the super coldness posed quite a problem for the group. Another problem was leaks in the apparatus since the experiment required the detectors and Cobalt sample to be placed in a vacuum. Nevertheless, after reconstructing their equipment and after several trials, the experiment finally succeeded. The day was December 27, 1956. A.Ereditato SS 2008

News of the success reached Lee and Yang at Columbia. When Lee announced that positive results to parity violation were being given by Wu's group, Lederman was present and realized that he could perform an independent test of parity with the cyclotron in Columbia. His experiment, which involved the decay of pions and muons had also been proposed by Lee and Yang in their paper. Soon, Lederman, along with his graduate students Weinrich, and Garwin began their experiments. Results from Lederman's group at the cyclotron came quickly. They obtained distinct evidence for parity violation, too. Both groups submitted their papers together to The Physical Review on January 15, 1957. On that day, Columbia called for a press conference. As newspaper headlines told of a physics principle demolished, reactions emerged from other physicists. Feynmanhad lost his bet. From Zurich, Pauli wrote to Weisskopf at MIT, "Now after the first shock is over, I begin to collect myself. Yes, it was very dramatic." At the Columbia's press conference, Rabi said, "A rather complete theoretical structure has been shattered at the base and we are not sure how the pieces will be put together". Credulity of parity non-conservation had taken hold among physicists. The failure of the physicists' intuition had been enormous. Nature, as it had done with relativity, did not oblige itself to follow the rules of "common sense". The results of the Columbia experiments generate the question: why did nature distinguish between the left and the right? Though the question remains unanswered, the physicists had set themselves up for the shock. Violation of the law of conservation of parity, then, should lead one to search for an even more fundamental symmetry to the Universe. A.Ereditato SS 2008

Parity (P) operation: x, y, z go into -x, -y, -z • 1956: Yang and Lee suggested that weak interaction could violate P • in this case a spin 1/2 particle may not exist in both helicity states • soon after: Wu reported on the Cobalt-60 experiment • electrons mostly emitted opposite to the (nuclear) spin direction: if P is conserved no correlation is expected between s and p • this correlation is measured by <s•p> a quantity that changes sign under P operation. If <s•p> = 0 P is conserved. That is not the case • 1957 Yang & Lee:theory of 2-component neutrino (-1/2 helicity , +1/2 helicity anti-) • 1958 Gell-Mann & Feynman: V-A structure of the weak force (maximally P violating) • Weak force selects (and acts on) LH components of particles and RH of anti-particles A.Ereditato SS 2008

Helicity:  = s • p / | p | = ± 1/2 s is a axial-vector: does not change for spatial inversion The mirror changes (e.g.) a left handed neutrino (existing in nature) into a right handed neutrino, that does not exist in nature. One is then able to distinguish our world from its mirror image: parity is not conserved in weak interactions. However, if we also apply C operation, we get a right handed antineutrino (that exists!). This implies that CP is conserved in weak interactions A.Ereditato SS 2008

Electron distribution (Wu experiment): With E and p, energy and momentum of the electron,  = -1, and  is the spin unit vector along the J axis. Parity is violated: 1 scalar, does not change under reflection EVEN parity  axial-vector, does not change either EVEN parity p polar vector, changes under reflection ODD parity The final product is a pseudo-scalar (ODD parity) Experimentally we then have:  = -1 for positrons with polarization P = +v/c  = +1 for electrons with polarization P = -v/c While for neutrinos P = -1 antineutrinos P = +1 A.Ereditato SS 2008

Pion decay Why the pion decays into a muon and not into an electron ? The fraction of left-helicity in the RH anti-lepton (proportional to m/E) is larger for the muon than for the electron A.Ereditato SS 2008

e+ u p (uud) W- g g d e e+ () d (u) p (uud) Z0 d (u) e-() g g W and Z bosons • Indirect evidence for Z (neutral currents) from the CERN Gargamelle experiment (1973) • The W and Z bosons were directly observed for the first time at CERN (UA1 and UA2 experiments) in 1983 • They were found thanks to the the SPS proton collider (270 GeV protons  270 GeV antiprotons) • Nobel Prize to Rubbia and Van der Meer: UA1 and antiproton cooling • V-A theory: only LH fermions and RH anti-fermions involved • Color factor 1/3 to match quark-antiquark of color-anticolor • Quark density functions to be taken into account A.Ereditato SS 2008

(d cosc +s sinc) u Mass- and weak- quark eigenstates Experimental indication of a difference in the weak coupling strength between muon and neutron decay (by 4% lower in the case of neutron decay), and in the decay rate of S=1 and S=0 weak reactions (factor ~20 !), such as neutron decay vs  decay. This is in apparent contrast with the principle of universality of the weak interaction. The problem was solved by Cabibbo assuming that the states actually involved in the weak interaction processes are a linear combination (mixing) of the quark mass-eigenstates u, d, s with a mixing angle c (experimentally ~120, sinc = 0.208, cosc =0.98) Mass- and weak-eigenstates do not coincide for quarks A.Ereditato SS 2008

Comparison of n and  weak decay Proportional to cos2c = 0.96 Proportional to sin2c = 0.04 Good agreement with the experiments, but another problem arises… A.Ereditato SS 2008

u + u d K+ s  Z0  u 0 u d cosc + s sinc u u K+ s +  W+  Z0 Z0 S=1 neutral current ! u d cosc + s sinc GIM mechanism and CKM matrix Experimentally, weak neutral currents follow the selection rule S=0 (no flavor changing neutral currents S=1): NC/CC: However, the Cabibbo theory, although successful, allows for S=1 transitions: How to “cancel” the unwanted flavor changing neutral currents ?? GIM mechanism, i.e. introducing a new up-like quark, the charm A.Ereditato SS 2008

(d cosc +s sinc) (s cosc - d sinc) u c 1970: Glashow, Iliopoulos and Maiani (GIM) postulated the charm quark (discovered in1974) arranged with the strange quark in a second doublet, in addition to the up and down doublet A.Ereditato SS 2008

d cosc + s sinc d cosc + s sinc u c + + d cosc + s sinc d cosc - s sinc Z0 Z0 Z0 Z0 c u + S = 0 S = 1 The discovery of the other quark bottom led to a natural extension of the 2x2 matrix and to the prediction of the 6th up-like quark (top). Cabibbo-Kobayashi-Maskawa 3x3 unitary matrix • Rotation matrix in 3D space • 3 angles and one phase • The phase can introduce CP violation • Elements determined by experiments, e.g. studying the decay of heavy quarks (Vub from bu decays, etc.) • Exploit unitarity condition: • Diagonal terms close to 1: tb, cs and ud A.Ereditato SS 2008

Elementarteilchenphysik