Our discussion of CP violation based on left–right models was driven by two complementary goals, namely to implement CPnon-invariance in a spontaneous fashion and to have the dynamics subjected to a higher degree of symmetry. The motivation for analysing non-minimal Higgs dynamics was much less profound: since no rationale more compelling than simplicity has emerged for limiting ourselves to minimal Higgs dynamics, we should be obliged to look beyond a minimalistic version – even if it served only as an imagination stretcher. The Higgs sector is quite commonly perceived as the product of some effective, yet ultimately unsatisfactory, theoretical engineering. Two types of scenario have been suggested to provide a more appealing framework.

(A): Higgs fields are composites rather than elementary and represent an effective description of some unknown underlying dynamics. Technicolour models are one implementation of this scenario that used to be quite popular. Few definite statements can be made in such models. Yet it would be miraculous if a minimal Higgs sector emerged, and extra sources of CP violation are likely to surface following the classification given in Chapter 17.

(B): There is one very elegant theoretical scheme that provides a natural habitat for scalars – namely supersymmetry (SUSY). Since we consider it so attractive, we will describe and analyse this scenario explicitly.

At the same time we note that over the last few years there have been two developments of great significance in this context.

As described before, CKM dynamics have passed their greatest challenge so far with flying colours. From a tiny CP asymmetry in K0 decays it had been inferred that certain decays of B mesons exhibit CP asymmetries larger by two orders of magnitude. This prediction has been validated experimentally. At least the bulk of the observed effects is fully consistent with CKM dynamics as embedded within the SM. With the ‘battle for supremacy’ decided in favour of CKM theory, what remains to be settled is the question whether additional layers of dynamics are needed to describe CP violation. There is no direct evidence for the presence of New Physics in the decays of K, B and D mesons. On the other hand we know there must be a new source of CP violation, if baryogenesis has occurred in our universe, i.e. if the observed baryon number is not merely an arbitrary initial value of our universe.

We will discuss two generic corrections to the KM ansatz in this chapter. The first class – models with right-handed currents – has intriguing theoretical features, whereas the second class – a non-minimal Higgs sector – might be seen as an exercise in theoretical engineering. Yet the latter's redeeming feature is that it can find a natural habitat in supersymmetric extensions of the SM. Both scenarios had originally been introduced as competitors for the CKM ansatz and therefore had been calibrated to reproduce ∈K. We will sketch this early history, since we view it as of theoretical interest. Furthermore, some of the technical considerations might become relevant again in the future. These possible corrections tend to leave a relatively small footprint in B decays.

The analysis of CP asymmetries in K and B decays – and likewise for charm – is clearly hampered by our failure to accurately evaluate hadronic matrix elements, since those are shaped by non-perturbative dynamics. There are, however, fermionic systems that are not subject to non-perturbative dynamics thus making our calculational tools more powerful. These are leptons – electrons, muons, τ leptons and neutrinos – and top quarks. The electron's EDM has been discussed in Section 3.6 and CP violation in neutrino oscillations in Section 16; the decays of charged leptons will be addressed here. As pointed out in Section 10.10.3 the aforementioned gain in calculational control comes with a price – namely at best small CP asymmetries. We will see that final state distributions rather than partial widths probably have the best chance to reveal CP violation.

Production and decay of top quarks

The existence of all members of three quark families has been established with the top quark being discovered last. Even before that time it had been realized that the top quark, once it becomes sufficiently massive, will decay (semi-)weakly – t → bW – before it can hadronize; i.e. top states decay as quarks rather than hadrons. This transition occurs around the 110–130 GeV region (for |V (tb)| ∼ 1), i.e. well below the mass value now observed. Non-perturbative dynamics thus plays hardly any role in top decays, and the strong forces can be treated perturbatively. While this is certainly good news for our ability to calculate observables, it carries also a negative message concerning the observability of CP asymmetries.

The sciences in general and physics in particular are full of fascinating phenomena; this is why they have attracted intense human interest early on and have kept it ever since. Yet even so we feel that the question to which degree nature is invariant under time reversal and CP transformations is so fundamental that it richly deserves its own comprehensive monograph. Two lines of reasoning – different, though not unrelated to each other – lead us to this conclusion. The first relies on multi-layered considerations, the second is based on a property inferred for the whole universe.

• The first line of reasoning centres on the important role symmetries have always played in physics. It has been recognized only last century, though, how central and crucial this role actually is, and this insight forms one of the lasting legacies of modern physics to human perception of nature and thus to human culture. The connection between continuous symmetries – like translational and rotational invariance – and conserved quantities – momentum and angular momentum for these examples – has been formulated through Noether's theorems. The pioneering work of Wigner and others revealed how atomic and nuclear spectra that appeared at first sight to be quite complicated could be understood through an analysis of underlying symmetry groups, even when they hold only in an approximate sense. This line of reasoning was successfully applied to nuclear and elementary particle physics through the introduction of isospin symmetry SU(2), which was later generalized to SU(3) symmetry in particle physics.

Some discoveries in the sciences profoundly change how we view nature. The discovery of parity violation in the weak interactions in 1956 certainly falls into this illustrious category. Yet it just started the shift to a new perspective; it was the discovery of CP violation in 1964 by Christenson, Cronin, Fitch and Turlay at Brookhaven National Lab – completely unexpected to almost all despite the experience of 8 years earlier – that established the new paradigm that even in the microscopic regime symmetries should not be assumed to hold a priori, but have to be subjected to determined experimental scrutiny.

It would seem that after the initial period of discoveries little progress has been achieved, since despite dedicated efforts CP violation has not been observed outside the decays of KL mesons, nor can we claim to have come to a real understanding of this fundamental phenomenon.

We have, however, ample reason to expect imminent dramatic changes. Firstly, direct CP violation has been observed in KL decays. Secondly, our phenomenological and theoretical descriptions have been refined to the point that we can predict with confidence that the known forces of nature will generate huge CP asymmetries, which could even be close to 100%, in the decays of so-called beauty mesons. Dedicated experiments are being set up to start taking data that would reveal such effects before the turn of the millennium. What they observe – or do not observe – will shape our knowledge of nature's fundamental forces.

We consider it thus an opportune time to take stock, to represent CP invariance and its limitations in its full multi-layered complexity.

A host of mostly theoretical arguments points to the presence of New Physics (beyond the SM Higgs state) at the 1TeV scale. This led to the expectation that experiments at the LHC will find direct evidence for new degrees of freedom. This confidence has been moderated recently for some people by the fact that neither precision measurements of electroweak observables (like the masses of the weak bosons) nor the detailed data on B decays have so far shown any evidence for such New Physics entering there through quantum corrections. One potential conclusion is that the mass scale of the New Physics states – like SUSY quanta – is significantly higher than the 1 TeV scale and might be beyond the reach of the LHC for direct production. In any case, we view it as a challenge to increase our efforts in B studies.

Alternatively one can search for a principle to suppress sufficiently the impact of New Physics on B and K decays, even when the New Physics quanta enter with masses below 1 TeV. In the SUSY framework described in Chapter 19, that amounts to requiring the mass insertion parameters Δij to satisfy the bounds listed in Table 19.2 (and potentially tighter ones in the future) while retaining squark and gluino masses below 1TeV or so. This might be feasible along the lines sketched in Section 19.4.4.

On minimal flavour violation

As discussed in the preceding Chapter minimal SUSY extensions of the SM can be constructed in such a way that no additional sources of CP violation arise.