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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62 Chapter 2. The Randall Sundrum Model and its Holographic Interpretation<br />
(DD) When a Higgs vev is turned on on <strong>the</strong> IR brane, <strong>the</strong> higgs<strong>in</strong>g generates<br />
mass correction to <strong>the</strong> bosonic composites. We expect <strong>the</strong>refore <strong>the</strong><br />
same contributions as <strong>in</strong> <strong>the</strong> (DN) scenario, however additional ∆F = 2<br />
contributions should appear. The situation <strong>in</strong> <strong>the</strong> UV is unchanged (still<br />
Dirichlet BCs) and s<strong>in</strong>ce <strong>the</strong>re is no mix<strong>in</strong>g, no extra flavor diagonal or<br />
∆F = 1 terms should appear. Accord<strong>in</strong>gly, we f<strong>in</strong>d,<br />
D ξ=1<br />
µν (q, t; t ′ ) = ηµν L<br />
4πrc M 2 KK<br />
which perfectly agrees with <strong>the</strong> expectations.<br />
� t 2 < − t 2 t ′2� , (2.85)<br />
(NN) If one allows for Neumann BCs on both branes, <strong>the</strong> situation changes<br />
significantly. There is still <strong>the</strong> exclusively composite exchange like <strong>in</strong><br />
<strong>the</strong> (DN) scenario, however as Neumann BCs <strong>in</strong> <strong>the</strong> UV correspond<br />
to gauge fields <strong>in</strong> <strong>the</strong> elementary sector <strong>the</strong> mix<strong>in</strong>g term <strong>in</strong> (2.41)<br />
becomes active and allows for all <strong>the</strong> additional diagrams shown on<br />
<strong>the</strong> left hand side. We cannot reproduce a one-to-one correspondence<br />
for each diagram here, because <strong>the</strong>re exist many diagrams<br />
contribut<strong>in</strong>g to <strong>the</strong> same terms. However, one can <strong>in</strong>fer that <strong>in</strong><br />
contrast to <strong>the</strong> (DD) scenario no additional ∆F = 2 contributions<br />
should appear. Also, <strong>the</strong> existence of a pure gauge boson diagram will<br />
lead to a flavor diagonal term <strong>in</strong>dependent of <strong>the</strong> KK scale. There<br />
should be additional flavor-diagonal contributions as well, from <strong>the</strong><br />
diagram with mix<strong>in</strong>g <strong>in</strong>to <strong>the</strong> composite boson and back. We f<strong>in</strong>d<br />
D ξ=1<br />
µν (q, t; t ′ ) =− ηµν<br />
2πrcp 2<br />
+<br />
ηµν<br />
4πrc M 2 KK<br />
�<br />
Lt 2