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This chapter of the report of the ``Flavour in the era of the LHC Workshop discusses the theoretical, phenomenological and experimental issues related to flavour phenomena in the charged lepton sector and in flavour-conserving CP-violating processes. We review the current experimental limits and the main theoretical models for the flavour structure of fundamental particles. We analyze the phenomenological consequences of the available data, setting constraints on explicit models beyond the Standard Model, presenting benchmarks for the discovery potential of forthcoming measurements both at the LHC and at low energy, and exploring options for possible future experiments.
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Electric dipole moments and charged-lepton flavour-violating processes are extremely sensitive probes for new physics, complementary to direct searches as well as flavour-changing processes in the quark sector. Beyond the smoking-gun feature of a potential significant measurement, however, it is crucial to understand their implications for new physics models quantitatively. The corresponding multi-scale problem of relating the existing high-precision measurements to fundamental parameters can be approached model-independently to a large extent; however, care must be taken to include the uncertainties from especially nuclear and QCD calculations properly.
Several experiments observed deviations from the Standard Model (SM) in the flavour sector: LHCb found a $4-5,sigma$ discrepancy compared to the SM in $bto smu^+mu^-$ transitions (recently supported by an Belle analysis) and CMS reported a non-zero measurement of $htomutau$ with a significance of $2.4,sigma$. Furthermore, BELLE, BABAR and LHCb founds hints for the violation of flavour universality in $Bto D^{(*)}tau u$. In addition, there is the long-standing discrepancy in the anomalous magnetic moment of the muon. Interestingly, all these anomalies are related to muons and taus, while the corresponding electron channels seem to be SM like. This suggests that these deviations from the SM might be correlated and we briefly review some selected models providing simultaneous explanations.
Searches for permanent electric dipole moments of fundamental particles and systems with spin are the experiments most sensitive to new CP violating physics and a top priority of a growing international community. We briefly review the current status of the field emphasizing on the charged leptons and lightest baryons.
We give a brief introduction to flavour physics. The first part covers the flavour structure of the Standard Model, how the Kobayashi-Maskawa mechanism is tested and provides examples of searches for new physics using flavour observables, such as meson mixing and rare decays. In the second part we give a brief overview of the recent flavour anomalies and how the Higgs can act as a new flavour probe.
Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in $K_Ltopipi$ decays represented by $varepsilon_K$ and the ratio $varepsilon/varepsilon$. In this millennium this role has been taken over by $B_{s,d}$ and $D$ mesons. However there is no doubt that in the coming years we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays $K^+rightarrow pi^+ ubar u$ and $K_{L}rightarrowpi^0 ubar u$ and the improved SM predictions for the ratio $varepsilon/varepsilon$, for $varepsilon_K$ and the $K^0-bar K^0$ mixing mass difference $Delta M_K$. Theoretical progress on the decays $K_{L,S}tomu^+mu^-$ and $K_Ltopi^0ell^+ell^-$ is also expected. They all are very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the $Ktopipi$ isospin amplitudes ${rm Re} A_0$ and ${rm Re} A_2$ improves. This talk summarizes several aspects of this exciting field. In particular we emphasize the role of the Dual QCD approach in getting the insight into the numerical Lattice QCD results on $K^0-bar K^0$ mixing and $Ktopipi$ decays.
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