On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

which are given by the overlap integrals
(g A L )qi
� 1 2π
=
Lɛ
ɛ
dt
t χ(1)
A
�
× tan θ a (Q)†
i
(g A � 1 2π dt
R)qi =
Lɛ ɛ t χ(1)
A
�
×
tan θ a (q)†
i
3.7. Flavor Observables and LHC Bounds 143
C(Q)
i (t) C (Q)
i (t) a (Q)
i
C(q)
i
− cot θ a(q)†
i
S(q)
i
(3.118)
�
(t) S(q) (t) a(q) ,
(3.119)
(t) C(q)
i (t) a(q)
i − cot θ a(Q)†
i S (Q)
i (t) S (Q)
i (t) a (Q)
�
i ,
with q, Q = {u, d} and i = 1, 2, 3 denoting the ith flavor. The left panel of Figure
3.14 shows the 95% CL upper bound on σ B A obtained by ATLAS (black line) to
our theory predictions for resonant axigluon production for the parameter set used
throughout this chapter. Scatter points above the black curve would be disfavored by
the data. Points below mA 1 ≈ 2.5 TeV are generated, because the parameter set has a
lower limit on the KK scale of MKK > 1 TeV, and the mass of the first axigluon resonance
is given by (3.103). The width of the “band” quantifies the effect of a different
localization of the electroweak singlet top quark, which is flatly distributed between
∈ [−0.5, 2] because we chose cu3 as the free parameter in generating the parameter
cu3
points, see Appendix A for details. Parameter points with an extreme IR localized tR
are colored blue and the color changes to red the more the tR is shifted towards the
UV. Since the top is not reconstructed in the analysis, a further IR localized tR lowers
the value of the branching fraction in (3.114), so that the dijet bound becomes even
weaker. Note, that no relocalization has been implemented in Figure 3.14, because
we can already infer, that the dijet bounds are weaker then the ones from the flavor
sector for all parameter points.
In the right panel of Figure 3.14, the mean values of our dataset for the branching
ratios to the different quark flavors is listed. The dominance of the top branching
ratio is clearly visible. Numerically, doing the same analysis for the gluon, which
corresponds to replacing the profile χA by χG and tan θ → 1, cot θ → −1 in (3.118),
will change the resulting branching fractions only at the permille level.
This allows to adopt the bounds from the most recent ATLAS analysis on t¯t final
states on the mass of a gluon KK mode for the axigluon KK modes [204]. The effect
from the relocalization of the fermions will enhance the couplings to right handed
tops of both gluon and axigluon resonances by a factor p2 u(tan β = 1/2) = 15, but the
predicted rate for a resonance mass in the ballpark of mA 1 ≈ 2.5MKK is several orders
of magnitude below the measured cross section, as shown in Figure 3.15, and can
therefore not compete with the bounds from the flavor sector. However, this concerns
the new physics amplitude squared, while the interference with SM amplitudes may
lead to an overall enhanced cross section into top pairs. These effects will be discussed
in detail in the next chapter.
One can draw the conclusion, that direct detection bounds on KK modes of gluons and
axigluons are generally weaker than the strongest bounds from flavor physics, given
the prejudice, that not a fine-tuned set of parameters is the reason for an unexpected
agreement with experiments.
i
i