# New Physics and Flavour Symmetries

**Principal Investigator:** Thorsten
Feldmann (Siegen)

**Participating Researchers:** Gudrun
Hiller (Dortmund), Thomas
Mannel (Siegen), Joachim
Brod (Dortmund)

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
10^{11-15} 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.