New Era for CP Asymmetries

The following sections are included:

• Dedication
• Foreword
• Contents

This volume is not a textbook where the reader may get a first glimpse at the subject of CP symmetry and its rich and complex dynamics. Although all concepts that are necessary to understand or follow the arguments are usually recalled and summarised, a previous knowledge of the fundamentals of quantum mechanics, quantum field theory, and particle and nuclear physics is required. This volume is not as well a traditional review about CP asymmetries (including axion dynamics) and rare decays. Instead, we try to update the progress that our community has achieved and focus particularly on new ‘directions’ and possible future developments, often using the past as a guide…

The era of non-relativistic quantum mechanics (QM) started in the 1920’s, in particular with the Schrödinger equation [9]:

based on the Hamiltonian:

It was also the era of obvious love of symmetries. However, it had changed by the 1950’s in subtle ways, heading towards the era of quantum field theories (QFT).

In this chapter we discuss the dynamics of hadron weak transitions and the relevant tools used to describe them. There are many theoretical tools we can use; some are obvious, some others are not.

It is said that the king Ptolemy once approached the resident 'sage' (Euclid) with the request to be educated in 'geometry', but in a 'royal way'', since he was busy with many obligations. Whereupon Euclid replied with admirable candor: "There is no 'royal way' to 'geometry'." One can say the same for QFT.

In this chapter, we first mention quark models, which are still used in the 21^st century; they have systematic uncertainties, whose value is usually determined by hand-waving arguments. Then we brie y discuss renormalized QFTs, where one can better control uncertainties in systematic ways. Lastly, we follow the tradition and analyze effective field theories in different 'dimensions'; sometimes they were not labelled effective field theories, although they are.

We focus both on CP asymmetries and rare decays-what was found in the past and what we expect for the future. As stated in the Prologue, the SM is incomplete. The available experimental data, however, do not suggest any clear path to follow and our community, rightly so, is seeking for new dynamics along diverse directions.

In Chapter 3 we have discussed ‘strategies’ for understanding the impact of the SM and its possible existence of new dynamics, while in this Chapter we talk about ‘tactics’…

While the main title of this book is “New Era for CP Asymmetries”, we have also a sub-title “… and Rare Decays of Hadrons and Leptons”. The goal is to find hints of new dynamics (ND) and possibly even its features there…

Here we mostly discuss neutral mesons and anti-mesons that are distinguished by an internal quantum number F. In these systems we can observe oscillations, namely transitions with ΔF = 2 units…

Indirect CP violation can happen only for neutral mesons which undergo oscillations, namely K⁰, B⁰, $B_s^0$ and D⁰; it depends on the initial state of the transitions. Direct CP asymmetries depend on the FS of flavor hadrons, in different ways and at different levels. The landscapes are quite different, with strange and beauty mesons on one side, and charm mesons on the other one:

• Indirect CP violation has been established first in K⁰ (or K_L) decays, then in B⁰ ones (but not in $B_s^0$ decays); direct CP asymmetries (mostly with smaller values) have been observed later.
• While indirect CP violation has not been found yet in $D^0\to K^{+}{K}^{-}$ or in $D^0\to {\pi }^{+}{\pi }^{-}$, direct CP asymmetry $\Delta A_{\mathbf{\text{CP}}}^{\text{charm}}\equiv A_{\mathbf{\text{CP}}}\left(D^0\to K^{+}{K}^{-}\right)-A_{\mathbf{\text{CP}}}\left(D^0\to {\pi }^{+}{\pi }^{-}\right)\ne 0$ has been established in 2019

The top quark, unsuccessfully searched for by means of electron-positron colliders (TRISTAN in Japan in the 80s and LEP at CERN in the early 90s) and by means of the $p\overline{p}$ collider SPS at CERN, was finally discovered at the Fermilab Tevatron by the CDF and D0 collaborations in 1995. It was a remarkable achievement at that time, because of the relatively poor signal and the large top quark mass. Though unsuccessful because of the very large top quark mass, the efforts made at electron-positron colliders, TRISTAN and LEP in particular, played two key roles: the first one was to develop the technology and the analysis tools, paving the way to the asymmetric colliders, which have been the key for the great successes of BaBar and Belle in the first decade of this new millennium; the second one was the precise prediction of the top quark mass made by means of the careful calculation of forward-background production asymmetries of fermion-anti fermion pairs from Z⁰ decay at LEP…

The SM had been constructed under the assumption that the three known neutrinos are massless; therefore they cannot undergo flavor oscillations. This assumption was very well supported by experiments in the early days, in particular by the measurement of neutrino fixed helicity made by Goldhaber, Grodzhins and Sunyar [146] and by the failed attempts to measure the neutrino mass, particularly by studying the ³H β spectrum near the end-point (for a review of the early attempts see [287]; for a recent review see [288]). However, it was quite clear from the beginning that no fundamental symmetry prevented neutrino masses and speculations about flavor oscillations [148] in the neutrino sector date back to the late 60’s. Now we know that neutrinos do oscillate among the three known flavors and likewise for anti-neutrinos – i.e., ΔL = 0. No evidence for neutrino - antineutrino oscillations nor for neutrino-less double beta decay has been found yet – i.e., ΔL = 2. We will come back to this in Sect. 9.5.1…

The only known candidate among local QFTs capable to describe the strong forces is QCD, based on the unbroken non-abelian gauge group SU(3)_C. CP is ‘naturally’ conserved in the Lagrangian of QCD, given in Eq. (3.1): a very attractive feature. QCD is in agreement with experimental observations, in particular “confinement” and “asymptotic freedom”, and it is very well tested in high energy collisions…

In Chapter 10, as previously in Chapter 9, we have shown a significant ‘chink’ in the SM’s armor. The tiny limit of $\overline{\theta }<{10}^{-9}$ could hardly come by accident, and it ‘begs’ for an explanation. In QFTs one finds challenges all the time while producing finite results and comparing them with present data and possible future one. In case of unexpected small values, one needs an ‘organizing’ principle to arrange various contributions from amplitudes in a way as to render the required cancellations. To use a different word: “symmetries”. The well-known and successful chiral symmetry fails to solve the “Strong CP violation” in presence of quark masses $m_q\ne 0$. Is it possible to invoke some other variance of chiral symmetry for this purpose, even if it is spontaneously broken? One particularly intriguing idea: an observable that is conventionally taken to be a constant could be re-interpreted as a dynamic degree of freedom; it would adjust itself to a desired value in response to forces acting upon it. One early example is provided by the original Kaluza-Klein theory invoking a six-dimensional space-time manifold: two of those could be compactified dynamically and thus led to the quantization of electric and magnetic charges…

The dynamics for charged leptons e and μ is simple: they are truly elementary, and there is no experimental hint that one needs to go beyond the SM. No CP violation is expected in μ decays. A more intriguing case is represented by the τ leptons, where the SM basically gives zero CP asymmetries except for ${\tau }^{+}\to \overline{\nu }{K}_S\pi$ decays. In this case the CP asymmetry is predicted to be O(10⁻³) due to ${\overline{K}}^0-K^0$ oscillations, as explained in Sect. 9.7…

In Sect. 2.6 we have discussed the impact of Quantum Mechanics on EDMs, while in Sect. 12.2 we developed the tools one gets from QFT and discussed how to apply them to leptons. The SM gives basically zero contributions to the EDMs of leptons and the same is true for baryons. Yet the description of EDMs for baryons is quite different from the case of leptons. It is much more ‘complex’, and in our opinion there are therefore more chances to find non-zero EDM values from ND. It should be pointed out, however, that even if a non-zero value for a baryon EDM is found, it would not automatically lead to a clear understanding of the underlying dynamics. To establish EDM ≠ 0 is, of course, a ‘golden goal’, but it would probably be just the beginning of a novel journey toward the ND and its features…

The SM is based on the non-abelian gauge dynamics SU(3)_C × SU(2)_L × U(1). As a first step, the symmetry provides gauge bosons, quarks and leptons that are massless; then one adds Higgs dynamics that couples with SU(2)_L × U(1) gauge bosons, but also with quarks and charged leptons to produce their masses. Higgs dynamics can do the ‘job’, never mind whether it is a piece of art or not. No rationale more ‘compelling’ than simplicity has emerged for limiting to minimal Higgs dynamics or close to it; thus one has to look beyond that, although no experimental hint, so far, suggests that this is indeed necessary…

In this book, we have mostly focused on CP asymmetries and rare decays in the SM, the theory of the fundamental structure of the known matter. Still, nowadays more than ever, astronomical discoveries are driving the frontiers of elementary particle physics beyond the SM, and, conversely, our knowledge of elementary particles is driving progress in understanding the Universe and its contents. In the “Prologue” we already stated that in the standard cosmological framework known matter gives us ∼ 4.5% of our Universe, while Dark Matter (DM) ∼ 26.5% and Dark Energy provide the rest. As discussed in Sect. 4.6, the SM assumes that neutrinos are massless; yet due to their oscillations we have learnt that they are not massless. Thus the SM is incomplete even for known matter.

The goal of this Chapter is not to find solutions to the numerous challenges that the modern Cosmology is facing, but, more realistically, to give some suggestions and explain their strengths and weakness. Or to use different words: to 'paint' the 'landscape'. Indeed, it is quite possible that we are still completely missing what our Universe is telling 'us'.

The following sections are included:

• Looking back
• Present ‘landscape’
  • Two neutral kaons
  • Truly rare decays of kaons
  • Transitions of beauty mesons
  • A new era for charmed mesons
• Better understanding of flavor forces
  • CP asymmetries in beauty, charm and strange baryons
  • Dynamics of top quarks in a complex ‘landscape’
  • Status of neutrino dynamics
  • Future neutrino oscillations
• Search for ND in EDMs
• The cathedral builder’s paradigm leading to ‘Novel SM’
• Somewhat final words

Discussions are crucial to make decisions: let us mention two very famous examples from the history:

• In the summer of 1519 in Germany there was a ‘disputation’ (= discussion) between J. Eck, A. Karlstadt, and M. Luther in person. In the series of events that led to the Diet of Worms, marking the definitive breach of Luther from Catholicism, few were more significant than this public theological debate.
• In 1632 Galileo had written the “Dialogue Concerning the Two Chief World Systems”. He compared the Copernican system with the Ptolemaic one with discussions between three ‘actors’ Salviati, Sagredo and Simplicio. The first two names were connected with real persons: Salviati was a scientist and Sagredo a mathematician. Both were close friends of Galileo; on the other hand, they had passed away by 1621. The third one – Simplicio – who defends the Ptolemy position, was not a real person, as the name shows; it is obvious that he was not an intelligent scientist – actually worse. In this dialogue new interpretative paradigms of reality (the scientific method) emerge, which are at the basis of modern science

The following sections are included:

• Bibliography
• Index