On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

152 Chapter 4. The Asymmetry in Top Pair Production
(b) are related by
� �
dσa
� = −dσa
� , (4.34)
(a) (b)
one can infer that the overall contribution must be proportional to
A (1)
q¯q ∼ 1
16N 2 αsd
C
2 abc . (4.35)
Note, that one factor αs is factored out in (4.28) and another one in (4.20), so that
the A (n)
ij will always be linear in αs although the overall contributions are ∼ α3 s.
One can conclude, that the Born-Box diagram interference in Figure 4.2 gives a positive
overall contribution, while the contributions from interference of initial- with final
state radiation diagrams enter with the opposite sign. The exact computation reveals,
that the latter are smaller, so that one ends up with a net positive asymmetry. The
exact formulas are compiled in [215, App. A] and will not be repeated here. The final
result can however be described by the parametrization
A (1)
q¯q = αs d 2 abc
16N 2 c
�
5.994 βρ 1 + 17.948 β − 20.391 β 2 + 6.291 β 3 �
+ 0.253 ln (1 − β) ,
(4.36)
which approximates the exact result with permille level accuracy. It has been obtained
by integrating the expressions for the charge-asymmetric contributions to the
differential t¯t production cross section over the relevant phase space. 2
Employing Nc = 3, d2 abc = � N 2 c − 1 � � N 2 c − 4 � /Nc = 40/3, mt = 173.1 GeV, and
αs(mt) = 0.126, one can plot (4.36) as a function of the square root of the CM energy
√
s. This is shown by the solid black plot in the left panel of Figure 4.3, while in the
right panel A (1)
q¯q is multiplied with the up-quark PDFs ffuū(ˆs/s, µf ) and also plotted
in solid black. In both cases the function peaks at √ s ≈ 420 GeV, i.e. around the
t¯t threshold. The right panel shows also, that the integrated asymmetry (4.29) will
be saturated long before the upper integration limit s is reached, which is rooted in
the fact that the quark luminosities behave roughly like 1/ˆs 2 . These results can be
compared with the plots of the exact calculation, which can be found in [215, Fig. 7].
4.3 New Physics and the Forward-Backward
Asymmetry
Since it is the only observable dealt with in this thesis, which shows significant deviations
from the SM and because top physics are largely unaffected by hadronic
uncertainties, it makes sense to categorize what kind of new physics would be able to
explain the observed deviation. Severely constrained by the requirement to achieve
agreement with the SM regarding the other observables introduced in Section 4.1, the
vast space of new physics models can be reduced to two different classes, new physics
2 The numerical integration has been performed using the Vegas Monte Carlo algorithm imple-
mented in the CUBA library [223]