On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

δg b R /δgb L ∼ F (cbR )2 /F (cbL )2 for δg b = (g b RS −gb SM )/gb SM
3.1. Electroweak Precision Observables 99
, which is typically of the order
of a few percent, because cbL is more IR localized in order to help realizing the large
top mass in (2.158). The scaling on the plot in the left panel of Figure 3.3 however
makes the gb R corrections completely invisible. As a consequence, our set of parameter
points, which is chosen so that the correct quark masses and mixings are reproduced
(see Appendix A for details), lies entirely in the red band shown in the left panel of
Figure 3.3 and therefore fails to agree with the experiment within 3σ for the majority
of points.
Note, that the scaling of Figure 3.3 distorts the fact that there are still 10% of the
parameter points in the 3σ ellipse. Translating this into a constraint for MKK would
yield a very strong bound. One can invoke the reparametrization invariance introduced
in section 2.5 in order to examine the characteristics of the parameter corner
which is in agreement with this constraint. By reshuffling between F (cbL ) and F (cbR )
using (2.169), for η < 1, one increases δgb R /δgb L . For η = 1/2(1/3), about 35(45)%
of the parameter points do at least not aggravate the already large discrepancy between
the SM and the experiment. Thus, parameter points with strongly IR localized
right-handed bottom quarks tend to give less dangerous corrections to the global fit
in (3.14).
It is interesting to discuss the implications for the dual theory of such a considerable
reparametrization. Scaling down F (cbL ) will not only enlarge F (cbR ), but also F (ctR ),
the zero mode of the right-handed top, which is already strongly IR localized. In a
generalization of this shift to all generations, one can assume that all doublets are extremely
UV localized and all singlets shifted towards the IR. The dual theory of such
a model would have, to a good approximation, only right-handed quarks composites,
while the left-handed quarks are elementaries. This right-handed compositeness was
found to be a very attractive idea in [149], in which the relevance for the Z¯bb vertex
was however not pointed out. In the later sections we will get back to this scenario
and check the compatibility with other observables.
This situation is also ameliorated by the mixing between the Z zero mode and the
additional neutral composite vector bosons of the SU(2)R present in the custodially
protected RS model [148]. This is especially intriguing, because as discussed in the
previous section, the scalar sector of any extension of the SM should respect the cus-
todial symmetry in order to not get into conflict with the oblique parameters. The
mixing eliminates completely the L enhanced term in gb L and increases the L enhanced
term in g b R by L → 3c2 w
s 2 w
L ≈ 10L. Therefore, corrections to g b L
are dominated by the
terms in the second line of (3.10), which can now account for both negative and
positive modifications, controlled by the interplay of the singlet down quark localization
parameters of all generations. Choosing the correct quark representations under
the enlarged symmetry group and assuming the bulk symmetric under the exchange
and make them purely
SU(2)L ↔ SU(2)R, will further reduce the correction to g b L