Pii: S0146-6410(01)00152-1

1 I n t r o d u c t i o n Our understanding of physics in general and particle physics in particular has been mainly put forward by the discovery of symmetries. It is remarkable, that most of the symmetries discovered have, however, finally turned out to be only "almost-symmetries", i.e. to be more or less broken. Mirror symmetry (parity P) is broken by weak interaction, which makes a maximal distinction between fermions of left and right chirality. First ideas of this unexpected behaviour emerged as a solution of the "~9 r puzzle", the fact that the neutral kaon decays both to P = +1 and P = -1 eigenstates [1], and a direct observation as left-right-asymmetry in weak beta decays followed soon [2]. It is most pronounced in the massless neutrinos, which are produced in weak interactions only with lefthanded helicity, or righthanded in the case of anti-neutrinos, thus violating the charge-conjugation symmetry (C) at the same time. The product of both discrete symmetries, CP, is almost intact, and seemed to be conserved even in weak interaction processes. A small violation has first been observed in 1964 [3] in K ° decays, which are up to now the only system which is known not to respect CP symmetry completely. The explanation of this violation in the Standard Model will be briefly discussed in the next chapter. This is not the only possible description, but the one with no additional assumptions. At the same time, the Standard Model predicts CP violating effects [4] in the decay of beauty mesons (B °, Bs, B+), which should be even large in some rare decay channels. It should be stressed that the small CP violation observed in the sixties lead to the prejudice that CP asymmetries are always small. It has been demonstrated, however, that the CP violating asymmetry is about 60% for a certain lifetime interval in the K ° --~ 7r+rr decay [5], and asymmetries up to 100% can be expected for B, decays. These most spectacular effects occur in "mixing mesons", i.e. mesons which oscillate into their anti-particles. It is therefore natural to report on both phenomena at the same time. Chapter 2 will be devoted to this flavour oscillation, and chapter 3 is dedicated to CP violation. 0146-6410/01/$ see front matter © 2001 Elsevier Science BV. All rights reserved PII: S0146-6410(01)00152-1 2 R. Waldi/Prog. Part. Nuel. Phys. 47 (2001) 1-71 1.1 T h e E x p e r i m e n t s After the discovery of the T states, B meson properties have been investigated since the mid-80s at e+e storage rings operating at the T'(4S) resonance: DORIS II at DESY (Gemany), with the experiment ARGUS, and CESR at Cornell (USA) with the detector CLEO. ARGUS had collected 0.25 Million BB events when it stopped in 1992, CLEO has accumulated 10 Million B/3 events by the end of 2000. These experiments have the advantage to investigate events with nothing else but two B mesons, which are even almost at rest since the mass of the T(4S) is only 20MeV above the B/3 threshold. This source is also exploited by the asymmetric e+e eolliders PEP-II at SLAC (USA) and KEK-B at KEK (Japan), where the experiments BABAR and BELLE have started taking data in 1999. They both have reached record luminosities above 3. 1033/cm2/s, and have collected 23 and 11 Million BB pairs by the end of 2000, respectively. These B factories have different electron and positron energies to produce the T(4S) with a boost of/3~/= 0.55 (BABAR) and 0.42 (BELLE) in order to measure the difference of the lifetime of the two B mesons. This is an essential information for the observation of time-dependent CP asymmetries, as will be discussed in chapter 3. In the 1990s the four experiments ALEPH, DELPHI, L3 and OPAL at the LEP storage ring at CERN (Switzerland) started investigating bb jets from Z ° decays. They have each a sample of almost one Million bb events. They were joined by SLD which accumulated polarized Z ° events at the linear collider SLC at SLAC (USA). Hadronic production of bb jets in addition to the fragments of the original particles are the source of B mesons at the p~ storage ring Tevatron at Fermilab (USA). Hadronic production of bbX at high energies is orders magnitude higher than any other source, but the samples of triggered and detected events being only a small fraction. The exploitation of these vast amounts of data is a challenge, which has been met in the past by the CDF detector which was the first experiment to collect enough B ° ~ J/¢ K ° decays for a meaningful exclusive CP violation analysis. Both CDF and DO will start collecting new data this year. Hadronic production will also be the source of B mesons at the planned experiments ATLAS, CMS and the dedicated experiment LHCb at the LHC pp storage ring, and the BTeV experiment at the Tevatron. These experiments will ultimately deliver enough bbX events for high precision measurements of CP violation parameters that can be expected about ten years from n o w . 2 Quark Mix ing and Particle Anti-Part ic le Oscil lations Mesons are neither particles nor anti-particles in a strict sense, since they are composed of a quark and an anti-quark. This implies the existence of pairs of charge-conjugate mesons, which can be transformed into each other via flavour changing weak interaction transitions. These are K°/_K ° (~d/sd), D ° / D ° (c~/~u), B ° / B ° (bd/bd), and Bs /Bs (bs/b~). 2.1 T h e U n i t a r y C K M M a t r i x The charged current weak interactions responsible for flavour changes are described in the Standard Model by the couplings gWgJ~C of the W boson to the current () (i) ve I-9'5 e u I 7 5 V. ~v r,g,b (i) with a non-trivial transformation matrix V in the quark sector, the Cabibbo-Kobayashi-Maskawa R. Waldi / Prog. Part. Nucl. Phys. 47 (2001) 1-71 (CKM) Matrix [6,7]: 3 Local gauge invariance requires this matrix to be unitary, unless it is a sub-matrix of a larger unitary matrix involving more than three fermion families. However, this possibility is unlikely, given the limit on neutrino flavours from LEP experiments, who find nV = 2.994 f 0.012 [8] for neutrinos with mass much below the 2’ mass. From the 9 real parameters of a general unitary matrix, 5 can be absorbed in 1 global phase, 2 relative phases between,u, c, t and 2 relative phases between d, s, b which are all subject to convention and in principle unobservable. If two quarks within one of these two groups were degenerate in mass, even the sixth phase could be removed by redefining the basis in their two-dimensional subspace. Removing as much unphysical phases as possible, the CKM matrix is described by 4 real parameters, where only one is a phase parameter, while the other three are rotation angles in flavour space. The physical phase is not one unique number due to the arbitrary choice of the unphysical phases. Unambiguous representations of this phase as the angles of unitarity triangles will be discussed below. The standard parametrization [8] (first proposed in [9], notation follows [lo]) uses a choice of phases, that leave I&d and V,, real: with cij = cost'ij, sij = sin&j, and Sij > 0, cij > 0 (0 5 6’ij 5 r/2). The angle Bc = 812 is the Cabibbo-angle [6]. A convenient substitution’ is siz = X, ~23 = AX’, ~13 sin&s = AX3q, and srscos6rs = AX3p [ll], which reflects the apparent hierarchy in the size of mixing angles via orders of a parameter X. This leads to l_$_$ x AX3(p iv) v= ( -X A2X5(p + iv ;) 1 $ (5 + +)X4 AX2 +(7(X6) (3) AX3[1 (p + iq)(l $)] -AX2 AX4(p + iv +) 1 $A2X4 1 and agrees to (3(X3) with the Wolfenstein approximation [I2]. Equation (3) is more convenient [13] in higher orders than the original proposal of Wolfenstein, or an exact parametrization [14] using the Wolfenstein parameters. Unitarity of the CKM matrix implies twelve equations, among them rows 1 x 3, tu V;dVtd + V:,V,, + V:,v,, = 0 columns 1 x 3, bd V,,V:, + V,,V$, + V,,V,l, = 0 (4) Dividing (4) by AX3 E -V,,VA yields the unitarity triangles’ as shown in figure 1. In the Wolfenstein approximation, they correspond to (p + i7j) 1 + (1 p in) = 0 (5) ’ An equivalent choice is X = Sizers which leads to the same parametrization to 0(X5). 2 this geometric interpretation has been pointed out by Bjorken N 1986; its first documentation in printed form is in ref. 15 and more general in ref. 16.