On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

154 Chapter 4. The Asymmetry in Top Pair Production
and with the notation C± ≡ 1+β 2 cos2 θ ± 4m2t ˆs , one finds in addition to the SM kernel
(4.21) the hard-scattering kernels
K (0)
q¯q, SM×NP
πβρ
= αs
16NC
2ˆs(ˆs − m 2 A )
(ˆs − m 2 A )2 + m 2 A Γ2 A
� g q
V gt V C+ + 2g q
A gt A β cos θ � , (4.38)
K (0)
q¯q, NP2 πβρ ˆs
= αs
16NC
2
(ˆs − m2 A )2 + m2 AΓ2 (4.39)
A
��(gq V )2 + (g q
A )2�� (g t V ) 2 C+ + (g t A) 2 � q
C− + 8gV gq
Agt V g t �
A β cos θ ,
from the interference between SM and new physics amplitude and from the new physics
amplitude squared, respectively. Both expressions have terms linear in cos θ, which
contribute to the asymmetry, but not to the cross section. For the interference kernel
this term depends only on the axial couplings to top and light quarks, while in the
case of the new physics squared contribution it is sensitive to all couplings in (4.37).
For large masses of the resonance, the latter is suppressed by an additional 1/m 2 A and
for light resonances, assumed they are broad enough to be concealed in the invariant
t¯t mass spectrum, the vector couplings need to be large for 8g q
V gq
Agt V gt A to explain the
effect. Sizable vector couplings lead to an enlarged cross section, which does not only
induce a tension with the total cross section measurements, but in turn also decreases
the asymmetry, because the cross section appears in the denominator in (4.25). Since
the main contribution to the cross section comes from the interference term, it will
always dominate over the asymmetric contributions3 . It is therefore justified to concentrate
on the interference term in looking for a viable model which explains the
asymmetry.
In order for the interference kernel to generate a large asymmetric contribution to the
differential cross section, at the Born level only the axial vector couplings are relevant,
while sizable vector couplings are even dangerous for the reasons explained above.
Note, that at the one-loop level, the situation is reversed and the vector couplings
contribute to the asymmetry, because the corresponding diagrams 4.6 are already odd
under the exchange of t and ¯t (which is the original reason for the asymmetry being an
NLO effect in the SM). However, if NP contributions to the asymmetry are generated
at the one-loop level by vector couplings, one would expect that the same couplings
enhance the cross section at the Born level and thus partially cancel the effect in
(4.25). We will later confirm this assumption for KK gluon exchange in the minimal
RS model.
Besides a large axial vector and a small vector coupling, there are further requirements
> ˆs, the relevant term in (4.38)
on the couplings in (4.37). For large masses m2 A
comes with a minus sign, which will lead to a negative asymmetry (4.27). Therefore,
either the new resonance is light, m2 A < ˆs, or the couplings are flavor non-universal
3
If the effect is due to the new physics amplitude squared it is more likely that the new resonance
is a color singlet, for which the interference term vanishes, but K (0)
q ¯q, NP2 is larger by a factor of 9/2
[224].