New Physics and Flavour Symmetries
In the Standard Model (SM) different quark and lepton flavours are only distinguished by their Yukawa couplings to the Higgs field. The misalignment between the Yukawa matrices of up- and down-type quarks leads to the Cabibbo-Kobayashi-Maskawa (CKM) mechanism which mixes quarks of different species in weak transitions. The successful search for the Higgs particle at the Large Hadron Collider (LHC), and the abundance of experimental data on quark flavour observables from the B-factories confirm this particular feature of the SM. On the other hand, the observed neutrino oscillations are not explained in the (minimal) SM and already require new physics (NP), i.e. particles and interactions beyond the SM framework. In the latter case the NP scale is typically associated with grand unified theories (GUTs), as high as, say, of the order of 1011-15 GeV. The see-saw mechanism, which explains the tiny values for the neutrino masses, is then realized in a natural way. In contrast, the paradigm before the start of the LHC has been that NP around the TeV scale is to be expected in order to stabilize the Higgs mass (or more generally, the mechanism of electroweak symmetry breaking). At present, however, no compelling direct evidence for new particles has been observed at the LHC or other collider experiments.
In this situation, precision flavour physics provides an alternative strategy to search for indirect effects of physics beyond the SM, and to constrain the masses and couplings of specific NP models. Here, the strong hierarchies observed in the SM quark Yukawa couplings and mixings play an important role: Namely, if the energy scale for NP is relatively low (i.e. still in the reach of the future LHC searches), the associated flavour structure must be tuned to some degree in order to mimic the CKM mechanism in the SM. In the past, this has been formalized as the principle of minimal flavour violation (MFV). On the other hand, if it turns out that NP effects are generated at sufficiently higher scales, at least some of the MFV assumptions could be relaxed. In this context, flavour symmetries can play an important role. First, they can be used as a guiding principle in the construction of interesting NP benchmark models. Second, they provide a systematic classification scheme of NP flavour scenarios within an effective field-theory approach. Finally, discrete flavour symmetries have been proven useful to explain the particular mixing pattern in the lepton sector.
Considering the SM as a low-energy effective theory, the global flavour symmetry to consider is defined by the independent rotations of the chiral fermion multiplets which leave the SM gauge sector invariant. NP effects can then be encoded in higher-dimensional operators which are invariant under SM gauge transformations but, in general, transform non-trivially under flavour rotations. The relative orientation between the SM Yukawa matrices and the coupling constants in front of these operators is crucial for the resulting flavour phenomenology. While the MFV paradigm essentially assumes the new couplings to be aligned with the SM Yukawa matrices (in a technical sense that will be clarified further below), the non-observation of direct NP signals also allows for less constrained scenarios. Here, the SM flavour symmetries can be used as a book-keeping device to achieve systematic classification of NP flavour effects beyond MFV.
This concept has to be modified, if one wants to study the underlying flavour structure in extensions of the SM with new fermionic matter content or new gauge symmetries. For example, GUT scenarios combine different SM fermion multiplets into a smaller number of gauge-group representations. Interestingly, within such an approach, the quark and lepton flavour sector are inevitably connected. In the simplest version this leads to relations between masses and mixing in the quark and lepton sector, while the flavour symmetry group of the corresponding gauge-kinetic terms is smaller than in the SM. In the context of possible explanations for the flavour puzzle, an appealing scenario builds on models where the flavour symmetry is promoted to a local gauge symmetry. Spontaneous breaking of this symmetry is achieved by vacuum expectation values (VEVs) of appropriate scalar fields which generate the flavour structures observed at low-energies. For an anomaly-free realization of the gauged flavour symmetry, such models also generically require new fermionic degrees of freedom with flavour-specific couplings to the SM particles. Another interesting feature of GUTs is the presence of heavy leptoquarks which induce new transitions between quarks and leptons of different families.
The aim of this project is to scrutinize different viable avenues that connect the particular pattern of quark and lepton masses in the SM with the underlying flavour structure of physics beyond the SM. To this end, we are going to systematically analyze the various flavour couplings in the low-energy effective theory. This includes model-independent benchmark scenarios characterized by means of flavour-symmetry considerations (bottom-up approach), as well as representatives for different types of specific NP models (top-down approach). Concerning the latter, we are particularly interested in models that combine traditional concepts for the extension of the electroweak sector (e.g. GUTs, extra-dimensional models, ...) with the recently revived ideas about dynamical flavour-symmetry breaking. From the theoretical perspective, we will investigate the relations between NP flavour couplings and the SM Yukawa matrices, and study under which conditions one can generate realistic VEVs for flavoured scalar fields by an appropriate effective potential. From the phenomenological point of view, we shall identify appropriate precision observables that are sensitive to non-standard flavour effects, including right-handed flavour-changing currents, lepton-flavour, lepton-number and baryon-number violating decays.