On the Flavor Problem in Strongly Coupled Theories - THEP Mainz
On the Flavor Problem in Strongly Coupled Theories - THEP Mainz
On the Flavor Problem in Strongly Coupled Theories - THEP Mainz
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4.4. Cross Section and Asymmetry <strong>in</strong> <strong>the</strong> M<strong>in</strong>imal RS Model 157<br />
<strong>in</strong>teraction terms for different color representations <strong>in</strong> <strong>the</strong> Lagrangian read [234]<br />
Lφ ∋ ¯t(g φ<br />
V<br />
+ gφ<br />
Aγ5)φ a 1,8 ˜ T a 1,8u + ¯t c (g φ<br />
V + gφ<br />
Aγ5)φ a 3,6 ˜ T a 3,6u , (4.44)<br />
<strong>in</strong> which <strong>the</strong> subscript identifies <strong>the</strong> color representation of <strong>the</strong> scalar as s<strong>in</strong>glet, triplet,<br />
sextet or octet, ˜ T a denotes <strong>the</strong> correspond<strong>in</strong>g SU(3)C Clebsch Gordon coefficient<br />
which connects it to <strong>the</strong> two quarks and t c = iγ 0 γ 2 t. The correspond<strong>in</strong>g contribution<br />
to <strong>the</strong> cross section can be found <strong>in</strong> [234, Sec. III] and we content ourselves with quot<strong>in</strong>g<br />
<strong>the</strong> result, that <strong>the</strong> sextet and triplet color representation can accommodate <strong>the</strong><br />
asymmetry while <strong>the</strong> color s<strong>in</strong>glet and octet runs <strong>in</strong>to trouble with o<strong>the</strong>r observables.<br />
Tak<strong>in</strong>g <strong>in</strong>to account <strong>the</strong> LHC measurements does require similar adaptations as <strong>in</strong><br />
<strong>the</strong> case of s channel models and leads to a modification of <strong>the</strong> already very tuned<br />
flavor-chang<strong>in</strong>g coupl<strong>in</strong>gs.<br />
4.4 Cross Section and Asymmetry <strong>in</strong> <strong>the</strong> M<strong>in</strong>imal RS<br />
Model<br />
In <strong>the</strong> RS model, many of <strong>the</strong> contributions described <strong>in</strong> Section 4.3 are generated.<br />
S<strong>in</strong>ce left- and right-handed fermions are localized at different po<strong>in</strong>ts <strong>in</strong> <strong>the</strong> bulk, <strong>the</strong><br />
KK gluon coupl<strong>in</strong>gs to quarks are <strong>in</strong> general not purely vector-like, but receive nonvanish<strong>in</strong>g<br />
axial-vector components. These coupl<strong>in</strong>gs generate a charge asymmetry <strong>in</strong><br />
top-quark pair production at <strong>the</strong> Born level, which is associated to quark-antiquark<br />
annihilation q¯q → t¯t and proceeds through tree-level exchange of KK gluons <strong>in</strong> <strong>the</strong><br />
s channel. Fur<strong>the</strong>r corrections to A t FB<br />
arise from <strong>the</strong> fact that <strong>the</strong> coupl<strong>in</strong>gs of KK<br />
gluons and photons, <strong>the</strong> Z boson and its KK excitations, as well as <strong>the</strong> Higgs boson<br />
are flavor non-diagonal, lead<strong>in</strong>g to <strong>the</strong> flavor-chang<strong>in</strong>g uū → t¯t transition which affects<br />
<strong>the</strong> t channel. 5 The correspond<strong>in</strong>g diagrams are shown <strong>in</strong> Figure 4.5. <strong>On</strong> <strong>the</strong> o<strong>the</strong>r<br />
hand, <strong>the</strong> gluon-fusion channel gg → t¯t does not receive a correction at Born level,<br />
s<strong>in</strong>ce ow<strong>in</strong>g to <strong>the</strong> orthonormality of gauge-boson wave functions <strong>the</strong> coupl<strong>in</strong>g of two<br />
gluons to a KK gluon is zero.<br />
Lead<strong>in</strong>g Order Contributions of <strong>the</strong> RS Model with and without<br />
Custodial Protection<br />
The effective Lagrangian needed to account for <strong>the</strong> effects of <strong>in</strong>termediate vector and<br />
scalar states reads<br />
Leff = � � �<br />
C (V,8)<br />
q¯q,AB Q(V,8)<br />
q¯q,AB + C(V,8)<br />
tū,AB Q(V,8)<br />
tū,AB + C(V,1)<br />
tū,AB Q(V,1)<br />
tū,AB + C(S,1)<br />
tū,AB Q(S,1)<br />
�<br />
tū,AB ,<br />
q,u A,B=L,R<br />
(4.45)<br />
5 In pr<strong>in</strong>ciple, also <strong>the</strong> d ¯ d → t¯t transition receives corrections due to <strong>the</strong> t channel exchange of <strong>the</strong><br />
W boson and its KK partners. However, <strong>the</strong>se effects are negligibly small for viable values of MKK<br />
and will <strong>the</strong>refore be ignored <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g.