On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

164 Chapter 4. The Asymmetry in Top Pair Production
The main lesson learned from the way the charge asymmetry arises in QCD is that
beyond LO vector couplings alone are sufficient to generate non-vanishing values of
At FB . In the case of the EFT (4.45) this means that cut diagrams like the ones shown in
Figure 4.6, can give a sizable contribution to the charge asymmetry if the combination
CV q¯q = � C (V,8) �
q¯q,� + C(V,8)
q¯q,⊥ of Wilson coefficients is large enough. In fact, from (4.50),
(4.52), and (4.73) it is not difficult to see that in the case of the RS model NLO
corrections to σa should dominate over the LO ones, if the condition 7
αs
4π (1 + ctL + ctR ) � L eL(1+cu L +cu R )
(4.64)
is fulfilled. For example, employing ctL = −0.34, cuL = −0.63, and cuR = −0.68, the
above formula tells us that for ctR = 0.57 the NLO contributions are bigger than the
LO corrections by a factor of roughly 25. This suggests that it might be possible to
generate values of At FB that can reach the percent level with typical and completely
natural choices of parameters. Notice that in contrast to QCD, in the RS framework
the Feynman graphs displayed in 4.6 are not the only sources of charge-asymmetric
contributions. Self-energy, vertex, and counterterm diagrams as well as box diagrams
involving the virtual exchange of one zero-mode and one KK gluon might also give a
contribution to At FB at NLO. As in Chapter 3, we will however not implement KK
modes in loops as it is technically involved to compute the nested sums over KK
modes in these diagrams. Also, those corrections are, like the Born-level contribution,
all exponentially suppressed by the UV localization of the light-quark fields (and the
small axial-vector coupling of the light quarks for what concerns the contributions from
the operators Q (V,8)
q¯q,AB ). Compared to the tree-level corrections, these contributions
are thus suppressed by an additional loop factor, so that they can be ignored for all
practical purposes in this particular observable.
The relevant contributions to At FB arising in the RS model beyond LO include the
graphs depicted in Figure 4.6. After integrating over cos θ, one obtains in the partonic
CM frame (q¯q = uū, d ¯ d)
A (1)
q¯q,RS =
ˆs
16παs
C V q¯q A (1)
q¯q , (4.65)
where A (1)
q¯q denotes the NLO asymmetric SM coefficient, given in (4.36), and C V q¯q the
Wilson coefficient including the vector couplings as defined below (4.52). Employing
an exemplary value of C q¯q
V = 10 TeV−2 , Figure 4.3 shows A (1)
q¯q,RS in the left panel and
A (1)
q¯q,RS
multiplied with the up-quark PDFs in the right panel, both plotted against the
CM energy √ s in dashed black. This has to be compared with the solid black plots in
Figure 4.3 , which shows the same plots for the SM expressions. Clearly, the peak at
the t¯t threshold is washed-out in the RS model, because the extra factor ˆs in (4.65)
prevents the function from dropping off for large CM energies. This is a consequence
of the fact that the new physics is considered heavy, which means that interference
terms scale as ˆs/m2 A , compare (4.38), and is symbolized by the propagators being
replaced by contact interactions in Figure 4.6.
7 This inequality should be considered only as a crude approximation valid up to a factor of O(1).