On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

100 Chapter 3. Solving the Flavor Problem in Strongly Coupled Theories
negative, so that one finds to leading order (see [114] for details and the derivation)
g b �
L = − 1
2 + s2 � �
w
1 +
3
m2 Z
2M 2 F
KK
2 (cbL ) 5 + 2cbL
3 + 2cbL 2(3 + 2cbL )
�
+ m2 b
2M 2 �
1 F 2 (cbR
KK 1 − 2cbR
)
3 + 2cbR
g b R = s2 w
3
− m2 b
2M 2 KK
Here, δg b R /δgb L
�
− 1 ,
(3.15)
�
1 − m2 Z
2M 2 F
KK
2 (cbR )
�
3c2 w
3 + 2cbR s2 5 + 2cbR
L −
w 2(3 + 2cbR )
��
(3.16)
⎡
�
⎣
1 1
1 − 2cbL F 2 (cbL ) − 1 + F 2 (cbL )
�
+
3 + 2cbL
� |(Yd)i3| 2
|(Yd)33| 2
1 1
1 − 2cQi F 2 (cbL )
⎤
⎦ .
> 1, and the right-handed corrections will lead to a worse then 3σ
discrepancy for some parameter points. Despite the misleading scatterplot however,
more than 99% of the parameter points are in the 3σ CL ellipsis in Figure 3.3.
tend to slightly improve the sit-
Interestingly, with the new fit, the corrections to gb L
uation compared to the SM. Both is evident from the plot on the right hand side
of Figure 3.3, which shows the same set of parameter points as the left plot for the
couplings in the custodially protected RS model (3.15) and (3.16). Note, that an
improvement can be achieved for small MKK, which should be contrasted with the
model without custodial symmetry discussed above, in which a large new physics scale
is preferred in order to not spoil the fit. Also, the reparametrization invariance can
be used in favor of an IR shift of the left-handed profiles for even better agreement
with the measurements. 2
i=1,2
This shows that the custodial protection is sufficient to protect the T parameter and
allows for an even slight attenuation of the tension from the fit to R 0 b , , Ab and A 0,b
FB .
Even though other solutions exist, we will assume that the custodial protection in the
SM is not broken by the underlying theory, in order not to be pushed to a corner
of parameter space or having to resort to a large MKK scale for agreement with
electroweak precision tests.
3.2 RS GIM Working
The present status of flavor physics is characterized by a large number of precision
results on B, D and K decays which are in tantalizing agreement with the SM picture
of flavor and CP violation. In the RS model, the KK modes generate tree-level
FCNCs, which are ultimatively caused by the flavor non-universal couplings in (1.34),
and are suppressed by the mixing angles in (1.34) or equivalently by the zero-mode
profiles (2.150) in the context of the RS-GIM mechanism.
In the following it will be demonstrated how the RS-GIM mechanism successfully suppresses
FCNCs by using observables involving b quarks, which have a large composite
2 It should be pointed out, that in the custodial model without the PLR symmetry, many parameter
points end up in the 2σ ellipsis in Figure 3.3. Since this is not a consequence of a physically motivated
parameter choice, but depends on the random relative size of the right-handed localization parameters
and Yukawa matrices, we will not discuss this scenario.