On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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4.4. Cross Section and Asymmetry in the Minimal RS Model 163
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Figure 4.6: Cut diagrams which contribute to the charge asymmetry at O(α 2 s) in the
SM extended by the four quark operators (4.46). The cuts refer to the initial- and
final state interference and the box diagram- Born level interference respectively.
asymmetry, as discussed in Section 4.3. 6 Second, the localization of the up-quarks,
which suppresses all contributions to A (0)
uū,RS and finally, the fact that the leading s
channel contribution as well as part of the t channel contribution in (4.58) is sensitive
to the difference between the localization parameters of the 5D up doublet and singlet,
which is generically small. As we will see below in our numerical analysis, the inclusion
of electroweak corrections arising from the Born-level exchange of the Z boson, of KK
excitations of both the photon and the Z boson as well as of the Higgs boson, do not
change this picture qualitatively.
The Asymmetry in the RS Model at NLO in QCD
As explained in 4.3, in models with small axial-vector couplings to light quarks and
no significant FCNC effects in the t channel, the charge-asymmetric cross section
σa is suppressed at LO. As we will show in the following, this suppression can be
evaded by going to NLO, after paying the price of an additional factor of αs/(4π).
In order to understand how the LO suppression is lifted at the loop level, it is useful
to recall the way in which the charge asymmetry arises in the SM. As elaborated in
Section 4.2, following from the fact that QCD is a pure vector theory, the lowestorder
processes q¯q → t¯t and gg → t¯t, which are of O(α 2 s) do not contribute to A t FB .
However, starting at O(α 3 s), quark-antiquark annihilation q¯q → t¯t (g), as well as flavor
excitation qg → qt¯t receive charge-asymmetric contributions, see Figure 4.2, while
gluon fusion gg → t¯t (g), remains symmetric to all orders in perturbation theory.
Because of charge conjugation invariance the interference between the lowest-order
and the QCD box graphs are the only virtual corrections to q¯q → t¯t, which contribute
to the asymmetry at NLO. Similarly, for the bremsstrahlungs (or real) contributions,
only the interference between the amplitudes that are odd under the exchange of t and
¯t furnishes a correction. Since the axial-vector current is even under this exchange, the
NLO contribution to the asymmetry arises solely from vector-current contributions.
6 This effect concerning the mostly vector-like couplings of light quarks was emphasized in [235].
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