On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

162 Chapter 4. The Asymmetry in Top Pair Production
(cuL − cuR ), we find
S (0)
uū,RS
A (0)
uū,RS
∼ 2παs
M 2 KK
(1 + ctL + ctR ) , (4.61)
2παs
∼
M 2 L e
KK
L(1+cu L +cu R ) (1 + cuL + cuR ) (4.62)
��
× 2 + 1
�
�
1
L (ctL − ctR ) (cuL − cuR ) + (1 + ctL + ctR ) ,
3
3
where the symmetric function S (0)
uū,RS is entirely due to s channel KK gluon exchange,
while the contributions to the asymmetric coefficient A (0)
uū,RS that arise from the s
channel (t channel) correspond to the term(s) with coefficient 2 (1/3) in the curly
bracket.
The relations (4.58) exhibit some interesting features. We observe that S (0)
uū,RS , which
enters the RS prediction for σs in (4.28), is in our approximation independent of the
localization of the up-quark fields and strictly positive (as long as ctA > −1/2). This
in turn implies an enhancement of the inclusive t¯t production cross section which gets
more pronounced the stronger the right- and left-handed top-quark wave functions
are localized in the IR.
In contrast to S (0)
uū,RS , both terms in A(0)
uū,RS are exponentially suppressed for UVlocalized
up quarks, i.e. , cuA < −1/2. For typical values of the bulk mass parameters,
ctL = −0.34, ctR = 0.57, cuL = −0.63, and cuR = −0.68 [150], one finds numerically
that the first term in the curly bracket of (4.73), which is enhanced by a factor of
L but suppressed by the small difference (cuL − cuR ) of bulk mass parameters, is
larger in magnitude than the second one by almost a factor of 10. This implies that
to first order the charge asymmetry can be described by including only the effects
from s channel KK gluon exchange, which can already be inferred from the fact that
the coefficients C (V,1)
tū,�
and C(V,8)
tū,� in (4.55) are only generated by the tensor structures
(2.181), which include the zero mode profiles of all external fermions, compare (2.182).
Since generically (1+cuL +cuR )(cuL −cuR ) < 0, we furthermore observe that a positive
LO contribution to A (0)
uū,RS
requires (ctL − ctR ) to be negative, which can be achieved
by localizing the right-handed top quark sufficiently far in the IR. To leading powers
in hierarchies, one finds using the mass relation for the top quark (2.158) the condition
ctR
mt 1
� √ − , (4.63)
2v |Yt| 2
in which the top-quark mass is understood to be normalized at the KK scale. Numerically,
this means that for mt(1 TeV) = 144 GeV and |Yt| = 1 values for ctR bigger
than 0 lead to A (0)
uū,RS > 0 and thus to a positive shift in σa.
In conclusion, we can identify three independent aspects of the RS model which render
the contributions to the asymmetric kernel A (0)
uū,RS tiny. First, the fact that the KK
gluons only have a negligible axial vector coupling will generate a small Born level