The decay constant of the holographic techni-dilaton and the 125 GeV boson

TL;DR

This paper examines whether the 125 GeV boson could be the holographic techni-dilaton arising from strongly coupled, nearly conformal electroweak dynamics, using five-dimensional sigma-models coupled to gravity. A central result is the near-universal decay-constant relation $F/\Lambda_0 \simeq \sqrt{3/2}$ across diverse holographic constructions, implying a suppressed universal coupling $a=v_W/F \lesssim 0.22$ for most models, with the caveat that bulk-based electroweak breaking can lower this bound. The authors compute the spectrum in toy models and in the GPPZ two-scalar truncation, discuss the impact on precision electroweak constraints via the $S$ parameter (yielding $\Lambda_0 \gtrsim 900$ GeV and $M_\rho \gtrsim 2.4$ TeV in standard realizations), and perform a global fit to LHC/Tevatron data showing the holographic dilaton can fit as well as, or marginally better than, the SM Higgs depending on data selection. They find that while current data show an enhanced $\gamma\gamma$ rate compatible with a dilaton, tensions from certain channels prevent a decisive conclusion, highlighting directions for future work in non-AdS geometries, bulk EW breaking implementations, and more robust experimental constraints.

Abstract

We critically discuss the possibility that the 125 GeV boson recently discovered at the LHC is the holographic techni-dilaton, a composite state emerging from a strongly-coupled model of electroweak symmetry breaking. This composite state differs from the SM for three main reasons. Its decay constant is in general larger than the electroweak scale, hence suppressing all the couplings to standard model particles with respect to an elementary Higgs boson, with the exception of the coupling to photons and gluons, which is expected to be larger than the standard-model equivalent. We discuss three classes of questions. Is it possible to lower the decay constant, by changing the geometry of the holographic model? Is it possible to lower the overall scale of the strong dynamics, by modifying the way in which electroweak symmetry breaking is implemented in the holographic model? Is there a clear indication in the data that production mechanisms other than gluon-gluon fusion have been observed, disfavoring models in which the holographic techni-dilaton has a large decay constant? We show that all of these questions are still open, given the present status of theoretical as well as phenomenological studies, and that at present the techni-dilaton hypothesis yields a fit to the data which is either as good as the elementary Higgs hypothesis, or marginally better, depending on what sets of data are used in the fit. We identify clear strategies for future work aimed at addressing these three classes of open questions. In the process, we also compute the complete scalar spectrum of the two-scalar truncation describing the GPPZ model, as well as the decay constant of the holographic techni-dilaton in this model.

Figures (7)

• Figure 1: Numerical study of the mass $m$ of the four lightest scalar states and the decay constant $F$ (in units of $\Lambda_0$) of the lightest of them (the holographic pseudo-dilaton), for the model defined by Eq. (\ref{['Eq:sinh']}). The plots are obtained by varying $\Delta$, while keeping $r_1=0.01$ and $r_2=5$.
• Figure 2: $\hat{S}$ as a function of $\Delta$ for the model defined by Eq. (\ref{['Eq:sinh']}), and $\varepsilon=0.07$: the numerical result (blue), the approximation Eq. \ref{['eq:ShatGPPZapprox']} (black), and the experimental bound (dashed black).
• Figure 3: Numerical study of the mass $M$ (in units of $\Lambda_0$) for the first few spin-1 states of the model based on the background coming from Eq. (\ref{['Eq:sinh']}). The plots are obtained by varying $\Delta$, while keeping $\varepsilon=0.25$, $r_1=0.001$ and $r_2=10$. The axial-vector points are for $\Omega^2=550$, which is a very good approximation of $\Omega\rightarrow +\infty$. The blue dots are numerical results for the spectrum of vector states, while the red dots are the axial-vector states. The line is the approximation for $M_Z$ in the text.
• Figure 4: Numerical study of the mass spectrum of scalar composite states and the decay constant $F$ of the holographic techni-dilaton for the GPPZ model. The calculations have been performed for UV cutoff $r_2=10$. The three colors correspond to different choices of IR cutoff, defined through the condition $A(r_1) = -2.5$ (black), $A(r_1) = -2$ (blue), and $A(r_1) = -1$ (red). This means that the black points are obtained for values that are closest to the IR end-of-space. Shown in the left panel is the mass $M$ of the scalar states, as a function of $c_1-c_2$: when $c_1-c_2>0$ the end-of-space is due to the behavior of $\sigma$, and vice-versa due the behavior of $m$ when $c_1-c_2<0$. The right panel shows the decay constant $F$ (in units of $\Lambda_0$) as a function of $c_1-c_2$ with $c_1=0$.
• Figure 5: Profile of the integrand (in arbitrary units) appearing in Eq. \ref{['eq:bdgammaA1']} for $\Delta=3$ and $r_*=2$.