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After the long investigations presented in Chapters 8–11, we will be able to collect various lessons and thereby gain a grand picture of how the SM faces the data in 2019. In particular it will be important to collect possible deviations from its predictions, which these days carry the name of anomalies. This will show us that indeed the SM has significant difficulties in describing all the flavor data simultaneously. Not all of these anomalies are still fully convincing because of theoretical and experimental uncertainties, but they give us strong motivations for making an important step toward the identification of N,P which could be responsible for them.
We will next go beyond the SM. It will be strategically useful to present first the general structure of effective Hamiltonians beyond the SM and identify new operators that are absent in the SM. This chapter will deal with physics at the electroweak scale and below it as we already encountered in previous chapters but now particular emphasis will be put on new operators generated by some NP at much higher scale that at the electroweak scale, and below it they will contribute to various processes. What will be discussed here is the low-energy effective theory that carries the name LEFT to distinguish it from the effective theory discussed in the next chapter. Here the basic symmetries for finding possible operators is simply the product SU(3)*U(1), that are the symmetries of QCD and QED. Simply the color and electric charges have to be conserved.
Finally, we will be able to present a grand summary of weak decays, list open questions, and present a shoping list for the coming years. energy observables that could be useful for the search for NP, in particular beyond the reach of the LHC. Subsequently, with the goal to distinguish various NP models we will discuss DNA charts proposed already in a number of papers.
Next we will discuss flavor-changing neutral current (FCNC) processes. In the SM such processes can only occur first at the one-loop level due to Glashow–liopoulos–Maiani (GIM) mechanism, a very important mechanism in the field of weak decays. We will first present the general structure of these processes, which will involve a set of basic master one-loop functions. We will calculate most of these functions explicitly without including first QCD corrections. Subsequently we will show how these functions enter the operator product expansion. Next we will include QCD and electroweak corrections to a number of FCNC processes. This will result in a number of effective Hamiltonians for most important processes that involve new operators not encountered in previous chapter: the so-called penguin operators. In this step we will study several properties of these Hamiltonians but we will postpone detailed phenomenology of these processes to later chapters.
We will next attempt a grand summary of NP models discussed by us comparing the different patterns of flavor violation present in these models. While they have been discussed already previously in some detail, it will be instructive to compare how different models face various anomalies listed in Chapter 12. This chapter is really a general view on the literature related to various anomalies and after being completed will hopefully motivate the readers to study numerous papers containing many ideas with the goal to construct their own models.
In order to describe properly the physics above the electroweak scale, we will discuss next the so-called gauge invariant Standard Model Effective Theory (SMEFT). This theory became very popular in view of the fact that the LHC until now did not discover directly any new particles. It offers a model independent formulation of NP beyond the SM in terms of operators that are invariant under the full SM gauge group. This is a very important framework, and many techniques developed in this decade in the context of SMEFT are crucial for a serious phenomenological applications in order to obtain model independent results. Moreover, SMEFT technology plays an important role in the derivation of predictions in concrete models as well. We will see this in this chapter and subsequent chapters of our book. But already in this chapter we will discuss implications of SMEFT in a number of general NP scenarios in which only a subset of operators is relevant. Moreover, we will present a few general formulas valid for any NP model, in particular the one for the ratio epsilon'/epsilon.
In order to illustrate what happens in specific models we will discuss three classes of models: the so-called 331 models, models with heavy vector-like quarks and models with leptoquarks, either of spin-0 or spin-1. We will concentrate on models with leptoquarks having sufficiently low masses so that they could be in principle discovered by the LHC. But even if the masses of new particles in the models considered will turn out to be beyond the reach of the LHC, their presence can still be identified in the rare processes discussed by us. These three classes of models are sufficiently simple so that we can present them here in some details. The new aspect of these models will be larger involvement of leptons than in previous sections. Yet, in this chapter we will confine the phenomenology to quark flavour observables postponing the discussion of lepton flavor violation to the next chapter. There are several more complicated models that we will only briefly mention providing list of references to papers investigating weak decays in these models.
This chapter deals with basic aspects of flavor physics in the charm sector. It is not as detailed as other ones. Yet, it contains many fundamentals related to CP violation and mixing in the charm sector.
In this chapter we present a detailed discussion of the particle-antiparticle mixing in the SM and perform the classification of various types of CP violation. We will discuss the determination of the CKM parameters in tree-level decays and also the determination of the so-called unitarity triangle from particle-antipartcle mixing both from B and K meson systems and tree-level decays in question. In this context we will present various methods for the determination of the angles in this triangle from certain leading decays. The considered decays are subject to only small contributions from NP so that the CKM parameters can be extracted without knowledge of what happens beyond the SM. This is useful as then the results of tree-level determinations of CKM parameters can be used to find SM predictions for particle-antiparticle mixing observables considered already in this chapter and for rare processes considered in the next two chapters. Both particle-antiparticle mixing and rare processes are subject to potential NP contributions and could help us to identify NP through the pattern of deviations of the data for them from SM predictions.
In this chapter we will discuss flavor physics of leptons, in particular charged lepton decays mediated by flavor changing neutral currents. While very strongly suppressed within the SM, lepton flavor violation (LFV) can be by many orders of magnitude larger in NP models. Therefore finding such transitions would be a clear signal of NP. The nice feature of most of these decays is the absence of QCD corrections, making the theoretical analysis much simpler than was the case of meson decays. Another important topic are electric dipole moments (EDMs) of various atoms, molecules, nuclei, and nucleons that all are very strongly suppressed in the SM. They test CP violation without flavor violation. Similar to LFV, a measurement of any nonvanishing EDM would be a clear signal of NP at work. But in contrast to LFV there are large nonperturbative uncertainties in this case. In this part we will also discuss anomalous magnetic moments of charged leptons. We will present a compendium of formulas for many observables. These formulas are quite general so that one can use them for various models. We will illustrate them on a few examples.
Chapter 14 will be rather general, and it will be strategically useful to look next at specific simple examples of NP. Having already all relevant SM formulas for flavor observables at hand, it will be of interest to see how they generalize beyond the SM. In this step we will first discuss the concept of minimal flavor violation (MFV), that is the most modest modification of the flavor-violating effects found in the SM. In these models a number of strict correlations between flavor observables are found. Next we will go go beyond MFV models considering the so-called simplified models in which NP contributions to flavor-violating processes are dominated by tree-level exchanges of neutral bosons, in particular the SM Z-boson, a heavy neutral gauge boson Z', and a heavy scalar or pseudoscalar. In these models FCNC processes appear already at tree-level modifying in a striking manner the pattern of flavor violation found in the SM and in MFV models. Moreover, right-handed currents will enter the scene. We will see that some of these simplified models will give us some insight into the origin of anomalies found in previous chapters.