On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

3.4. A Solution in the Gauge Sector 115
mixing angle is tiny and the elementary mode has a mass of the order Planck scale,
see (2.39), so that the hierarchy problem is not reintroduced.
A related mechanism is provided in models with a soft wall [189]. Originally inspired
by the modeling of the Regge trajectories in AdS/QCD models (see the footnote
on page p.47), a soft wall model assumes in contrast to the RS model, that the
backreaction of the dilaton on the metric is not small, but large enough to distort the
metric in the IR, so that the action (2.11) is replaced by
�
S = d 5 x � |G|e −Φ L , (3.50)
in which Φ denotes the dilaton/radion field and L stands for the whole bulk Lagrangian.
As a consequence, the metric is no longer pure AdS, but changes in the IR,
and the bulk is not cut off by a delta-function potential (a brane), but by a smooth
potential wall, depending on the coordinate dependent vev of Φ. Because the bulk
coordinate runs between t ∈ [ɛ, ∞] in this setup, the IR boundary conditions are replaced
by integrals up to t = ∞, or by overlap integrals with a bulk Higgs respectively.
This bulk Higgs and the distorted metric both induce a shift of the fermion profiles
towards the UV brane and as a result further suppress FCNCs [188, 190]. The change
in the warp factor generated by the backreaction of the dilaton will however lead to
considerable fine-tuning in order to solve the gauge hierarchy problem in such models
[189].
3.4 A Solution in the Gauge Sector
A qualitatively different solution to the RS flavor problem is to consider an extension
of the strong interaction gauge group in the bulk. It is based on the idea, that the
contributions from the gluon KK excitations to the coefficients C4 and C5 of the
mixed chirality operators in (3.20) can be canceled by a KK tower of a strongly
interacting gauge boson, which couples with opposite sign to left- and right-handed
quarks, but with the same coupling strength as the gluon. The zero mode of this
new bulk field can be projected out by choosing the appropriate BCs. In contrast
to gauged flavor symmetries in the bulk, this model does neither affect the order one
Yukawa couplings nor does it impose a symmetry on the bulk masses which generate
the hierarchies in the quark masses and mixings. Therefore, instead of a widespread
implementation of the SM flavor structure with all its features and shortcomings, this
solution specifically targets the single operator which is not sufficiently suppressed by
the RS-GIM mechanism. Some of the results derived in the following sections have
been published in [191].
Extension of the Color Gauge Group
The goal is to find an extension of the strong interaction gauge group, which will be
able to accommodate the RS gluon as well as another gauge boson with couplings