Radion Dynamics and Electroweak Physics

TL;DR

The paper tackles radion stabilization in the RS framework with Goldberger–Wise mechanisms by solving the fully coupled 5D radion–bulk-scalar system, including backreaction. It shows that backreaction induces a TeV-scale radion mass and that the TeV-brane SM fields couple to the radion and to the bulk-scalar KK tower, enabling direct collider probes of stabilization physics. Using an effective field theory with a cutoff Λ, the authors compute radion contributions to electroweak oblique parameters S and T, finding small corrections for vanishing curvature–scalar mixing and potentially sizable effects if curvature–scalar mixing is present, with the latter allowing larger Higgs–radion mass combinations at the price of fine-tuning. They also demonstrate that late-time cosmology and the 4D effective theory shifts agree with prior results, and they explore implications for collider phenomenology, including anomalous couplings and the role of nonrenormalizable operators in renormalization. Overall, the work provides a coherent, testable framework connecting radion dynamics, backreaction, cosmology, and precision electroweak constraints in RS scenarios with GW stabilization.

Abstract

The dynamics of a stabilized radion in the Randall-Sundrum model (RS) with two branes is investigated, and the effects of the radion on electroweak precision observables are evaluated. The radius is assumed to be stabilized using a bulk scalar field as suggested by Goldberger and Wise. First the mass and the wavefunction of the radion is determined including the backreaction of the bulk stabilization field on the metric, giving a typical radion mass of order the weak scale. This is demonstrated by a perturbative computation of the radion wavefunction. A consequence of the background configuration for the scalar field is that after including the backreaction the Kaluza-Klein (KK) states of the bulk scalars couple directly to the Standard Model fields on the TeV brane. Some cosmological implications are discussed, and in particular it is found that the shift in the radion at late times is in agreement with the four-dimensional effective theory result. The effect of the radion on the oblique parameters is evaluated using an effective theory approach. In the absence of a curvature-scalar Higgs mixing operator, these corrections are small and give a negative contribution to S. In the presence of such a mixing operator, however, the corrections can be sizable due to the modified Higgs and radion couplings.

Figures (7)

• Figure 1: The lowest mass eigenvalues for the coupled radion-scalar system for $u/k=1$ are given by the zeroes of the function $b(m)$ defined in (\ref{['bm']}). On this plot $m$ is given in units $k e^{-k r_0}$, therefore the mass spacings are given by the TeV scale. Note, that in the approximation leading to this equation the lowest lying state is still massless.
• Figure 2: The dependence of the mass of the first KK mode on $\alpha$. Here $m_1$ is again given in units $k e^{-k r_0}$ and is therefore of the order of the TeV scale.
• Figure 3: The contributions to $S$, $T$ as a function of the "gauge" masses $m_h = m_r$. Each line is a contour for a fixed curvature scalar mixing $\xi$. The cutoff scale was chosen to be $1$ TeV ($\gamma = 0.1$). The shaded regions are excluded by the PDG measurements to one sigma.
• Figure 4: Same as Fig. \ref{['S-ex-fig']} except that $m_h$ is fixed to 300 GeV. Notice that the contributions to $S$ and $T$ are nearly independent of the radion mass if the curvature mixing is small since the radion contribution is suppressed by $\sim \gamma$.
• Figure 5: The allowed region of $m_h^{\rm phys}$ and $\xi$ as a function of the inverse of the cutoff scale $\gamma = v/\Lambda$ by requiring $S,T,U$ do not exceed the one sigma (dark region) or two sigma (light region) measurements from the PDG. The dashed lines correspond to the theoretical bound requiring the kinetic term is non-negative [see Eq. (9.14)]. The black sliver corresponds to the region where $m_h^{\rm phys} \approx 300$ GeV.