On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

With this definition,
� |G|Lint ∋ e −3σ gs5
�
¯Q γ µ G a µ T a Q + ¯q c γ µ G a µ T a q c
3.4. A Solution in the Gauge Sector 117
− tan θ ¯ Q γ µ A a µ T a Q + cot θ ¯q c γ µ A a µ T a q c
(3.57)
�
.
It is obvious, that the linear combination Aµ will couple with opposite signs to 5D
doublets and singlets. These will in the case of the zero modes decompose into lefthanded
and right-handed 4D fields respectively, apart from small admixtures from
the other chirality. This is due to the fact, that the other chirality enters with the
S-profiles in (2.123), which for the zero modes are suppressed by x0 ≈ v/MKK, see
(2.149). The magnitude of the couplings depends on the form of the propagator and
the mixing angle θ. For θ = π/4, the couplings become purely axial and one could
speak of a 5D axigluon. In a slight abuse of language, in the following, this notation
will also be used for differing mixing angles. Interestingly, however, in contributions
to the diagrams responsible for C4, the dependence on the mixing angle cancels, while
the contributions to the purely left- and right-handed operators show the proportionality
C1 ∼ tan 2 θ and � C1 ∼ cot 2 θ.
Whether or not the contributions to C4 from the axigluon KK tower will lead to a
cancellation of the contribution from the gluon KK tower will therefore only depend
on the terms of the corresponding propagators which can induce flavor changes at
both vertices. These terms are fixed by the boundary conditions of Gµ and Aµ. As
discussed in Section 2.3, the gluon must have Neumann BCs on both branes, with the
corresponding propagator (2.86). The only contribution to ∆F = 2 processes arise
therefore from overlap integrals with the fermion profiles and the first term in the
second line of (2.86), which is ∼ t 2