The Effective Lagrangian in the Randall-Sundrum Model and Electroweak Physics
Csaba Csaki, Joshua Erlich, John Terning
TL;DR
The paper derives a 4D effective Lagrangian for the Randall-Sundrum model with bulk gauge fields by integrating the 5D theory and identifies tree-level, log-enhanced corrections to electroweak observables. The main finding is a large negative contribution to the oblique parameters, $S$ and $T$, dominated by $S$, arising from distorted $W$ and $Z$ wavefunctions due to a TeV-brane Higgs, along with a KK-induced four-fermion operator $V$. A global fit to precision data yields a bound $1/R' > 11$ TeV (for $\log(R'/R)=32$), implying gauge KK resonances near $27$ TeV and making LHC detection unlikely; heavier Higgs masses do not substantially alleviate the bound. The results show that warped extra dimensions with bulk gauge fields can be compatible with EW data but predict very heavy resonances, highlighting a distinctive negative $S$ feature in such holographic-like models.
Abstract
We consider the two-brane Randall-Sundrum (RS) model with bulk gauge fields. We carefully match the bulk theory to a 4D low-energy effective Lagrangian. In addition to the four-fermion operators induced by KK exchange we find that large negative S and T parameters are induced in the effective theory. This is a tree-level effect and is a consequence of the shapes of the W and Z wave functions in the bulk. Such effects are generic in extra dimensional theories where the standard model (SM) gauge bosons have non-uniform wave functions along the extra dimension. The corrections to precision electroweak observables in the RS model are mostly dominated by S. We fit the parameters of the RS model to the experimental data and find somewhat stronger bounds than previously obtained; however, the standard model bound on the Higgs mass from precision measurements can only be slightly relaxed in this theory.