Loop induced decays of the Little Higgs: H --> gg, gamma gamma

TL;DR

This paper analyzes loop-induced Higgs decays $H\rightarrow gg$ and $H\rightarrow \gamma\gamma$ in the Littlest Higgs model, where heavy states at scale $f$ affect the amplitudes. It shows that deviations from the Standard Model scale like $1/f^2$ and quantifies them for $f=1~\mathrm{TeV}$, finding $\Gamma(H\rightarrow gg)$ suppressed by about $6$–$10\%$ and $\Gamma(H\rightarrow \gamma\gamma)$ by about $5$–$7\%$. It compares collider sensitivities, showing that the LHC and $e^+e^-$ colliders probe only relatively light $f$ (roughly $0.6$–$0.65$ TeV), while a photon collider can test up to about $1.5$ TeV at $1\sigma$ (and $\sim 0.7$–$1.1$ TeV at higher significances). The results rely on the finite one-loop nature of these decays and the decoupling of heavy states, providing robust, testable predictions for a single-Higgs Little Higgs framework. The authors also remark that in two-Higgs-doublet variants, deviations can be larger, highlighting the sensitivity of loop-induced Higgs decays to extended Higgs sectors.

Abstract

We analyze the loop induced decays of the Higgs boson into pairs of gluons and photons in the Littlest Higgs model. We find that the deviation of the partial widths for these decays relative to their Standard Model values scales with 1/f^2, where f ~ TeV is the mass scale of the new heavy particles in the model. For f = 1 TeV, Gamma(H -> gg) is reduced by 6-10% and Gamma(H -> gamma gamma) is reduced by 5-7% compared to their Standard Model values. While the LHC and a linear e+e- collider would be sensitive to these deviations only for relatively low values of f <~ 650 GeV, a photon collider could probe the deviation in Gamma(H -> gamma gamma) up to f <~ 1.1 (0.7) TeV at the 2 (5) sigma level.

Figures (7)

• Figure 1: (left) $M_{W_H}/f$ as a function of $c^2$ and $M_T / f$ as a function of $c_t^2$; (right) $M_\Phi/f$ as a function of $x$ for various values of the $H$ mass.
• Figure 2: (a) The loop functions $F_1(\tau_{W_L})$ and $F_{1/2}(\tau_t)$ as a function of $m_H^{}$; (b) The loop functions as a function of the heavy mass $M_i$, for $m_H^{} = 120$ GeV. Both figures are normalized to their asymptotic values given in Eq. (\ref{['Fasympt']}).
• Figure 3: (a) Dependence of $\Gamma(H \to gg)$ on the parameters $x$ and $c_t$ for $f = 1$ TeV and $m_H^{} = 120$ GeV, normalized to the SM partial width. The solid lines show $\Gamma(H \to gg)/{\rm SM}$ as a function of $x$ for $c_t = 1$ or 0 and $1/\sqrt{2}$ (top to bottom). The dashed lines indicate the minimum ($c_t = 0$ or 1, $x = 0$) and maximum ($c_t = 1/\sqrt{2}$, $x = 1$) values of $\Gamma(H \to gg)/{\rm SM}$ obtainable in the LH model for $f=1$ TeV. (b) Accessible range of $\Gamma(H \to gg)/{\rm SM}$ in the LH model versus $f$ for various values of $m_H^{}$ as indicated.
• Figure 4: Dependence of $\Gamma(H \to \gamma\gamma)$ on the model parameters for $f = 1$ TeV and $m_H = 120$ GeV, normalized to the SM partial width. The solid and short-dashed lines show $\Gamma(H \to \gamma\gamma)$ relative to its SM value as a function of $x^2$ for several values of $c^2$ (a) and as a function of $c^2$ for several values of $x$ (b). The solid lines are for $c_t = 0$ and the short dashed lines are for $c_t = 1$. The long dashed lines show the minimum ($c=1/\sqrt{2}$, $c_t=x=1$) and maximum ($c=0$ or 1, $c_t=x=0$) values of $\Gamma(H \to \gamma\gamma)$ obtainable in the LH model for this value of $f$. Doubling $f$ reduces the deviation from 1 by a factor of four.
• Figure 5: Range of values of $\Gamma(H \to \gamma\gamma)$ accessible in the LH model as a function of $f$, normalized to the SM value, for $m_H = 120$, 150 and 180 GeV.