## Final Report Summary - FLAVOUR (Towards the Construction of the Fundamental Theory of Flavour)

The theoretical research at the high-intensity frontier of particle physics, that is flavour physics, and its interplay with the dynamics of electroweak symmetry breaking being explored by the LHC was the main goal of this research project. While LHC did not give until now clear evidence for new physics (NP) beyond the Standard Model (SM) a number of experimental results that were presented during the duration of our project stimulated our research leading to 95 publications in leading journals and 17 contributions in conference proceedings. The most important achievements are summarized below. They have been presented at various workshops and conferences. One of the highlights in quark flavour physics was the improved measurement of the branching ratio for the very rare decay B_s-> mu^+mu^- at the LHC that turned out to be within 30% of the SM prediction and having thereby important impact on the parameter space of various extensions of the SM. In view of relatively small room for NP contributions left in this decay we have performed an improved estimate of the branching ratio for this decay in the SM. Moreover a number of detailed analyses of flavour observables have been performed in several concrete NP models. This includes in particular models with tree-level flavour changing neutral currents mediated by a new heavy gauge boson Z' and by heavy scalars. The study of correlations between various observables like branching ratios and asymmetries in these and more specific models, like 331 models, left-right symmetric models and models with extended gauge symmetries allowed to identify certain patterns of flavour violations characteristic for these models which in the future should allow to select successful NP scenarios. These studies have been summarized in a very long review published in Reports on Progress in Physics. Another highlight was the identification of the significant departure of SM prediction for CP Violation in K-> pi pi decays which was only possible through the improved calculations using large N approach to QCD.

We have extended this strategy to the leptonic sector and analysed the signatures in the charged lepton and Higgs sectors of a simple and predictive neutrino mass model consisting in adding to the SM two right-handed neutrinos with electroweak scale masses and sizable charged current interactions. In this model, the flavour structure of the charged current interactions is determined by the low energy neutrino data thus allowing to set correlations between various flavour observables, such as mu->e gamma, mu->3 e, mu-e conversion in nuclei or Higgs decays into one heavy and one light neutrino. Motivated by the significant improvement in precision measurements of CP asymmetries in charm decays by the LHCb experiment, we have analysed under which condition such asymmetries can be identified as signals of physics behind the SM. We have demonstrated that CP asymmetries as large as few % in radiative D-meson decays would be unambiguous signals of physics beyond the SM and could be generated in motivated supersymmetric extensions of the SM. In view of the discovery of the Higgs particle at the LHC, we have analysed in full generality the bounds on possible flavour-violating interactions of such new particle, taking into account the existing constraints from low-energy observables. We have found that lepton-flavour-changing decays of the Higgs particle are very weakly constrained, such that the processes h->tau mu and h-> tau e could occur with relative rates as large as 10% and be within the reach of the LHC experiments.

The work on effective field theories of electroweak symmetry breaking is complementary to the detailed study of explicit models. The results obtained include the clarification of the systematics of the electroweak chiral Lagrangian including a light Higgs particle and the construction of the complete basis of operators at next-to-leading order. This effective theory allows for the possibility of new strong dynamics in the few TeV range and is more general than the usual formulations. The framework has been applied to investigate new physics effects in e+e- -> W^+W^-, h -> Zl^+l^-, and in particular to the analysis of anomalous Higgs couplings. An important achievement is the result that the phenomenological kappa parametrization of Higgs couplings has a firm quantum-field theory basis in terms of the leading order electroweak chiral Lagrangian.

It was commonly believed that the maximal R symmetry of N=1 supersymmetry is a U(1). We have shown that this is not true; rather, one can also have non--Abelian discrete R symmetries, under which the superspace coordinate theta furnishes a non--trivial one--dimensional representation. Such a symmetry allows us to simultaneously solve the mu, proton decay and flavor problems of the supersymmetric extensions of the standard model.

We have extended this strategy to the leptonic sector and analysed the signatures in the charged lepton and Higgs sectors of a simple and predictive neutrino mass model consisting in adding to the SM two right-handed neutrinos with electroweak scale masses and sizable charged current interactions. In this model, the flavour structure of the charged current interactions is determined by the low energy neutrino data thus allowing to set correlations between various flavour observables, such as mu->e gamma, mu->3 e, mu-e conversion in nuclei or Higgs decays into one heavy and one light neutrino. Motivated by the significant improvement in precision measurements of CP asymmetries in charm decays by the LHCb experiment, we have analysed under which condition such asymmetries can be identified as signals of physics behind the SM. We have demonstrated that CP asymmetries as large as few % in radiative D-meson decays would be unambiguous signals of physics beyond the SM and could be generated in motivated supersymmetric extensions of the SM. In view of the discovery of the Higgs particle at the LHC, we have analysed in full generality the bounds on possible flavour-violating interactions of such new particle, taking into account the existing constraints from low-energy observables. We have found that lepton-flavour-changing decays of the Higgs particle are very weakly constrained, such that the processes h->tau mu and h-> tau e could occur with relative rates as large as 10% and be within the reach of the LHC experiments.

The work on effective field theories of electroweak symmetry breaking is complementary to the detailed study of explicit models. The results obtained include the clarification of the systematics of the electroweak chiral Lagrangian including a light Higgs particle and the construction of the complete basis of operators at next-to-leading order. This effective theory allows for the possibility of new strong dynamics in the few TeV range and is more general than the usual formulations. The framework has been applied to investigate new physics effects in e+e- -> W^+W^-, h -> Zl^+l^-, and in particular to the analysis of anomalous Higgs couplings. An important achievement is the result that the phenomenological kappa parametrization of Higgs couplings has a firm quantum-field theory basis in terms of the leading order electroweak chiral Lagrangian.

It was commonly believed that the maximal R symmetry of N=1 supersymmetry is a U(1). We have shown that this is not true; rather, one can also have non--Abelian discrete R symmetries, under which the superspace coordinate theta furnishes a non--trivial one--dimensional representation. Such a symmetry allows us to simultaneously solve the mu, proton decay and flavor problems of the supersymmetric extensions of the standard model.