On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

4.1. Top-Antitop Pair Production and Observables at Tevatron and the LHC 147
We report therefore also the mass dependent asymmetry measured by CDF, which
could be interpreted as a hint at heavy new resonances, since it shows a linear slope
which is significantly larger than predicted in the SM,
A t FB(m t¯t < 450GeV) = � 7.8 ± 5.4 � % ,
A t FB(m t¯t > 450GeV) = � 29.6 ± 6.7 � % , (4.9)
although the SM prediction goes in the same direction [220]
A t FB(mt¯t < 450GeV) = � 6.2 +0.4�
−0.3 % , (4.10)
A t FB(mt¯t > 450GeV) = � 12.9 +0.8�
−0.6 % .
One can understand the observable (4.8) as the number of top quarks going in forward
direction minus the number of top quarks going in backwards direction relative to the
interaction point in the CM frame, normalized to the total number of tops,
A t FB = Nt(F ) − Nt(B)
. (4.11)
Nt(F ) + Nt(B)
Because of charge conjugation invariance, the antitops scattered forwards (backwards)
can be counted as tops scattered backwards (forwards), so that N¯t(F ) = Nt(B).
Analogous to (4.11), one can therefore define the asymmetry as the number of tops
scattered in forward direction minus the number of antitops scattered in forward
direction, which then corresponds to a charge asymmetry
A t C = Nt(F ) − N¯t(F )
. (4.12)
Nt(F ) + N¯t(F )
A charge asymmetric initial state is required in order to generate contributions to such
an asymmetry. This is the case at the Tevatron, as it is a proton antiproton collider,
but not at the LHC, which collides protons with each other. This is illustrated by a
sketch of the rapidity distributions for the Tevatron and LHC in Figure 4.1. Clearly,
counting the tops versus the antitops in forward direction (y > 0) will only in the case
of the Tevatron lead to a non-zero number. On a more fundamental level however, the
asymmetry can be traced back to the fact, that the top quark likes to go in the direction
of the initial state quark and the antitop in the direction of the initial state antiquark.
These directions are well defined at the Tevatron as the proton consists mainly of
quarks, which results in the shifts of the rapidity distributions in the left panel of
Figure 4.1. At the LHC, one can infer that the initial antiquark must be a sea quark.
Sea quarks carry less momentum fraction than valence quarks and consequentially the
rapidity distributions at the LHC are symmetric, but have a different width, as shown
in the right panel of Figure 4.1. On average, the top carries more momentum than
the antitop.
One can therefore define a charge asymmetry based on the difference in absolute
rapidity, ∆|y| = |yt| − |y¯t|,
A y N(∆|y| > 0) − N(∆|y| < 0)
C = . (4.13)
N(∆|y| > 0) + N(∆|y| < 0)