On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

170 Chapter 4. The Asymmetry in Top Pair Production
4.6 Axigluon Contributions to the Cross Section and
the Asymmetry
The conclusions drawn in Section 4.3 and at the end of the last Section suggest that
a new resonance with mainly axial vector couplings can bring the measured value of
the forward backward asymmetry in agreement with the SM prediction.
The model introduced in Chapter 3, which features an extended strong interaction
gauge group SU(3)D ×SU(3)S in the bulk fulfills some of the criteria which we identi-
fied as essential for a solution of the A t FB
puzzle in Section 4.3. It provides a large axial
vector coupling with negligible vector coupling component for mixing angles θ ≈ 45 ◦
preferred by the flavor sector. Further, the couplings are large for the top, even larger
then in the minimal model, because the extended scalar sector implies extremely IR
localized top profiles. In addition, the extended model furnishes a hierarchy between
couplings to down and to up type quarks, which is rooted in the different scalar fields
which provide their masses. Such a hierarchy might explain why the measurements
point to a smaller asymmetry at a machine which collides protons that contain equal
shares of ū and ¯ d quarks, compared to a proton-antiproton collider which provides
3/2 more ū than ¯ d in the initial state.
From (3.63) and (3.108), one finds that in the model with extended color gauge group
the Wilson coefficients in (4.55) take the form
�
1
C (V,8)
q¯q,�
C (V,8)
q¯q,⊥
C (V,8)
tū,�
= − παs
2M 2 KK
= − παs
2M 2 KK
παs
= −
M 2 L
KK
L − (∆′ Q)11 − (∆ ′ Q)33 − p 2 q (∆ ′ q)11 − p 2 q (∆ ′ q)33
�
1
+ 2L
c 2 θ
( � ∆Q)11 ⊗ ( � ∆Q)33 + p4q s2 (
θ
� ∆q)11 ⊗ ( � ∆q)33
− vIR � 2
tθ (∆Q)11(∆Q)33 + p
4
4 qct 2 θ (∆q)11(∆q)33
� ��
, (4.72)
�
1
L − (∆′ Q)11 − (∆ ′ Q)33 − p 2 q (∆ ′ q)11 − p 2 q (∆ ′ q)33
�
1
c 2 θ
+ p2qvIR 2 L � �
(∆Q)11(∆q)33 + (∆Q)33(∆q)11
�
,
(∆Q)13 ⊗ ( � ∆Q)31 + p4q s2 (∆q)13 ⊗ (
θ
� ∆q)31
− vIR � 2
tθ (∆Q)13(∆Q)31 + p
4
4 qct 2 θ (∆q)13(∆q)31
� �
,
and C (V,1)
tū,� is not modified by the axigluon KK modes, but only by the relocalization
of the fermions and is therefore not repeated here. In the above expressions, only
O(v 2 /M 2 KK ) contributions are kept, except for terms ∼ vIR, that become significant if
the suppression from vIR is balanced by powers of pu, which parametrizes the effect