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The Results and Their Interpretation 178 Part C the postulate of quarks as the fundamental building blocks The results and their of matter. interpretation Strangeness, parity violation, and charm Chapter 16 The decays of the strange particles, in particular of the kaons, paved the way for the further development of our The CKM matrix and the understanding. Before 1954, the three discrete symmetries Kobayashi-Maskawa mechanism C (charge conjugation), P (parity) and T (time rever- sal) were believed to be conserved individually, a conclu- Editors: sion drawn from the well known electromagnetic interac- Adrian Bevan and Soeren Prell (BABAR) tion. Based on this assumption, the so called θ-τ puzzle Boˇstjan Golob and Bruce Yabsley (Belle) emerged: Two particles (at that time called θ and τ, where Thomas Mannel (theory) the latter is not to be confused with the third generation lepton) were observed, which had identical masses and lifetimes. However, they obviously had different parities, since the θ particle decayed into two pions (a state with 16.1 Historical background even parity), and the τ particle decays into three pions (a state with odd parity). Fundamentals The resolution was provided by the bold assumption by Lee and Yang (1956) that parity is not conserved in In the early twentieth century the “elementary” particles weak interactions, and θ and τ are in fact the same par- known were the proton, the electron and the photon. The ticle, which we now call the charged kaon. Subsequently first extension of this set of particles occurred with the the parity violating V A structure of the weak interac- neutrino hypothesis, first formulated by W. Pauli in his tion was established and,− on the experimental side, par- famous letter to his “radioactive friends” in 1924. From ity violation was confirmed directly in β decays (Garwin, the theoretical side, the formulation of a theory of weak Lederman, and Weinrich, 1957; Wu, Ambler, Hayward, interactions by Fermi in 1934 marked another milestone Hoppes, and Hudson, 1957). However, the combination of in the development of our understanding. This set up for two discrete transformations, namely CP , still seemed to the first time a framework, in which some of the funda- be conserved. mental questions on the role of hadrons versus leptons and on the properties of particles and their interactions could Another puzzle related to kaon decays was the relative be formulated. This also resulted in a clear formulation of coupling strength. It tuned out that the coupling strength “weak” versus “strong” interactions and the understand- of strangeness-changing processes is much smaller than ing of interactions as an exchange of mediating particles. that of strangeness-conserving transitions. This finding In particular, Yukawa postulated the existence of such a eventually led to the parameterization of quark mixing particle and triggered the search for what we now know by Cabibbo (1963). In modern language, the up quark u couples to a combination d cos θC + s sin θC of the down as the pion. At about the same time the muon was dis- ◦ quark d and the strange quark s. The value θC 13 covered, and initially called the “µ meson”, however this ∼ soon turned out to be distinct from the pion. for the Cabibbo angle explained the observed pattern of Although the the term “flavor” came much later, one branching ratios in baryon decays. may mark the beginning of (quark) flavor physics by the Experiments at that time only probed the three light- discovery of strange particles (Rochester and Butler, 1947). est quarks, and there was no known reason for the extreme Their decays into non-strange particles had lifetimes too suppression of the flavor changing neutral current (FCNC) + + + − long to be classified as strong decays: this led to the intro- decay K π ℓ ℓ with respect to the charged cur- →+ 0 + + + + − + duction of the strangeness quantum number (Gell-Mann, rent decay K π ℓ ν, Γ (K π ℓ ℓ )/Γ (K π0ℓ+ν) 10−6.→ The resolution of→ this puzzle was found→ 1953), which is conserved in strong decays but may change ∼ in a weak decay. by Glashow, Iliopoulos, and Maiani (1970): one includes The subsequent proliferation of new particles could the charm quark, with the same quantum numbers as the nicely be classified and ordered by Gell Mann’s “eight- up quark, and coupling to the orthogonal combination d sin θC + s cos θC . fold way” (Gell-Mann, 1962), which was an extension of − the isospin symmetry to a symmetry based on the group FCNC processes are suppressed by this “GIM mecha- SU(3). However, none of the particles fitted into the fun- nism”. In fact, FCNC’s in the kaon system involve a tran- damental representation of this group, although there were sition of an s quark into a d quark. This can be achieved various attempts such as Sakata’s model, in which the pro- by two successive charged current processes involving (in ton, the neutron and the Λ baryon formed the fundamen- the two-family picture) either the up or the charm quark tal representation. Eventually this puzzle was resolved by as an intermediate state. Taking Cabibbo mixing into ac- 179 ′ −3 count, these amplitudes are KL ππ decays, Re(εK /εK ) = (1.65 0.26) 10 (Alavi-Harati→ et al., 1999; Burkhardt et± al., 1988;× Fanti (s d)= (s u d)+ (s c d) et al., 1999). Nonetheless, convincing evidence for the KM A → A → → A → → = sin θC cos θC [f(mu) f(mc)],(16.1.1) mechanism required the measurement of sin(2φ1) at the − B Factories. where f(m) is some smooth function of the mass m. Hence, With the discovery of the τ lepton in 1975 (Perl et al., 0 if the up and charm quark masses were degenerate, K 1975) and of the bottom quark in 1977 (Herb et al., 1977) 0 − K mixing and other kaon FCNC processes would not oc- it became clear that there is a third generation of quarks cur. and leptons. Furthermore, the bottom quark turned out However, the up and charm masses are not degenerate to be quite long-lived, indicating a small mixing angle be- and thus K0 K0 mixing can occur. Neglecting the small − tween the first and second generation. This fact is the up-quark mass, the mixing amplitude turns out to be experimental foundation of using B decays to study CP 2 violation, as well as for b tagging in high-pt physics. 2 2 mc (K K) sin θC cos θC 2 . (16.1.2) The third generation remained incomplete for many A → ∝ MW decades, since the top quark turned out to be quite heavy, and a direct discovery had to wait until 1995, when it was This implies that a mass difference ∆m appears in the K discovered at the Tevatron at Fermilab (Abachi et al., neutral kaon system. From this mass difference (an expres- 1995a; Abe et al., 1994). However, the first hint of the sion analogous to Eq. 10.1.17) Gaillard and Lee (1974b) 0 0 could extract the prediction that the charm-quark mass large top-quark mass was the discovery of B B oscil- lations (also known as mixing) by ARGUS (Albrecht− et al., should be about mc 1.5 GeV, and it was one of the great triumphs of particle∼ physics when narrow resonances 1987b). The measured ∆md implied a heavy top with a mass mt above 50 70 GeV, if the standard six quark with masses of about 3 GeV were discovered a few months − later (Aubert et al., 1974; Augustin et al., 1974): these model was assumed (Bigi and Sanda, 1987; Ellis, Hagelin, were identified as cc bound states. Around this time the and Rudaz, 1987). The phenomenon of neutral meson mix- term “particle family” was coined, and the discovery of ing is discussed in Chapter 10, while Section 17.5 discusses the charm quark completed the second particle family; it results on B mixing from the B Factories. also introduced a 2 2 quark mixing matrix into the phe- In fact, if the top mass had been significantly smaller, nomenology of weak× interactions. ARGUS could not have observed B0 B0 oscillations. The GIM mechanism for down-type quarks− leads generally to suppression factors of the form CP violation and the Kobayashi-Maskawa mechanism 2 2 1 mt mu Almost ten years before the discovery of charm, CP vio- CKM Factor − (16.1.3) × 16π2 M 2 lation was observed in the study of rare kaon decays by W Christenson, Cronin, Fitch, and Turlay (1964). This ef- fect is difficult to accommodate for two families, but an and hence the GIM suppression for the bottom quark is extension to three families allows it to be taken into ac- much weaker than in the up-quark sector, where the cor- count naturally. The “six-quark model” was proposed by responding factor is Kobayashi and Maskawa (1973), extending Cabibbo’s 2 2 × quark mixing matrix into the 3 3 Cabibbo-Kobayashi- 1 m2 m2 × CKM Factor b − d . (16.1.4) Maskawa (CKM) matrix. The GIM mechanism for the six × 16π2 M 2 quark model is implemented by the unitarity of the CKM W matrix. 0 Hence FCNC decays of B-mesons have branching ratios While the observation of decays KL 2π meant that CP was violated, the data at that time→ only required in the measurable region, while FCNC processes for D- CP violation in mixing (see Section 16.6 for the classi- mesons are heavily suppressed. fication of CP -violating effects). The observed strength The third particle family was completed by the dis- −3 of CP violation in mixing, εK 2.3 10 , was consis- covery of the τ neutrino as a particle distinct from the tent with the Kobayashi-Maskawa≃ (KM)× mechanism (El- electron and the muon neutrino by the DONUT collabora- lis, Gaillard, and Nanopoulos, 1976; Pakvasa and Sug- tion (Kodama et al., 2001).
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