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KK Gravitons and Unitarity Violation in the Randall-Sundrum Model
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UCD-2006-15
IFT-06-19
KK Gravitons and Unitarity Violation in the Randall-Sundrum Model
Bohdan Grzadkowski
Institute of Theoretical Physics
Warsaw University, 00-681 Warsaw, Poland
John F. Gunion
Davis Institute for High Energy Physics
University of California, Davis, CA 95616, U.S.A.
We show that perturbative unitarity for W+L W
?
L → W+L W?L scattering places significant con-
straints on the Randall-Sundrum theory with two 3-branes, with matter confined to the TeV brane.
The exchange of massive 4D Kaluza-Klein gravitons leads to amplitudes growing linearly with the
CM energy squared. Summing over KK gravitons up to a scale Λ and testing unitarity at
√
s = Λ,
one finds that unitarity is violated for Λ below the ’naive dimensional analysis’ scale, ΛNDA. We
evaluate Λ as a function of the curvature ratio m0/mPl for the pure gravity theory. We then demon-
strate that unitarity need not be violated at Λ in the presence of a heavy Higgs boson. In fact, much
larger Higgs masses are consistent with unitarity than if no KK gravitons are present. Observation
of the mass and width (or cross section) of one or more KK gravitons at the LHC will directly
determine m0/mPl and the scale bΛW specifying the couplings of matter to the KK gravitons. With
this information in hand and a measurement of the Higgs boson mass, one can determine the precise
scale Λ below which unitarity will remain valid.
I. INTRODUCTION
The Standard Model (SM) of electroweak interactions is confirmed by all existing experimental data. However the
model suffers from certain theoretical drawbacks. One of these is the hierarchy problem: namely, the SM can not
consistently accommodate the weak energy scale O(1 TeV) and a much higher scale such as the Planck mass scale
O(1019 GeV). Therefore, it is commonly believed that the SM is only an effective theory emerging as the low-energy
limit of some more fundamental high-scale theory that presumably
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