On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

3.7 Flavor Observables and LHC Bounds
3.7. Flavor Observables and LHC Bounds 137
As elaborated in the last section, the extension of the color gauge group in the bulk
makes it necessary to introduce an extended scalar sector and as a consequence changes
the localization of the quarks along the extra dimension. Therefore not only observables
in which the new axigluon resonances directly mediate FCNCs change in the
extended model, but also processes which involve only photon or Z exchange.
In this section we will therefore comment on the new contributions to observables discussed
in the earlier sections of this chapter and repeat the numerical analyses with
the axigluon contributions as well as the fermion localization implemented. .
We will also analyze the bounds from direct detection experiments for the color octet
and axigluon resonances at the LHC.
Electroweak Precision Observables
The modification of the strongly coupled sector will not give direct contributions to
the oblique parameters and the relocalization of the fermions does also not affect the
analysis in Section 3.1, because only flavor universal contributions have been considered
there.
In principle, a color octet, electroweak doublet scalar leads to modifications of the
electroweak gauge boson propagators via loop insertions. A model independent analysis
yields an upper bound on the mass splitting between charged and neutral color
octets of O(50) GeV in order to agree with the T parameter [198]. This splitting
depends on the parameters in the Higgs potential and can be used as a constraint for
generating the physical spectrum. Note also, that we have not considered loops of KK
fermions or gauge bosons in Section 3.1, which might change these conclusions.
Corrections to the Z → b ¯ b vertex depend sensitively on the localization of the bottom
quark. The extended color sector shifts all right-handed quarks closer to the IR
brane, so that effectively only modifications to the coupling of the Z to right-handed
b quarks gb R in (3.11) play a role.14 From (3.108) one can infer that the relocalization
amounts to a factor p2 d of the RS contribution δgb R . Since these corrections go in the
wrong direction and are already enhanced in the custodial model, the Z ¯ bb constraint
also prefers small tan β, which is in line with the parameter region favored by ɛK. The
resulting scatter plot in the extended model is shown for tan β = 1/2 and θ = 45 ◦ in
Figure 3.11, and despite the misleading scaling, still more than 95% do agree with the
measurements at 99% CL.
Flavor Violating Observables
Although the extended gauge sector leads to smaller values for ɛK, the contributions
to ∆B = 2 observables as discussed in Section 2.6 may be even larger in the RS model
with extended color gauge group. The reason is, that for K − ¯ K mixing the mixed
14 There is also a modification for the second term in (3.10), but this term is suppressed by m 2 b/m 2 Z.