Electron $g-2$ foreshadowing discoveries at FCC-ee

A future $e^{+}{e}^{-}$ circular collider (FCC-ee) may provide a unique probe of the electron Yukawa coupling through Higgs boson production on resonance. Motivated by this exciting possibility, we examine a simple model which can result in $\mathcal{O}(10)$ modifications of the Higgs coupling to electrons. The model can also lead to deviations in the electron anomalous magnetic moment, $g_e-2$, which at present shows a $+2.2\sigma$ or $-3.7\sigma$ deviation, implied by differing precision determinations of the electromagnetic fine structure constant. The electron $g_e-2$ can be a forerunner for FCC-ee discoveries which, as we elucidate, may not be accessible to the high-luminosity LHC measurements. A simple extension of our model can also account for the current deviation in the muon $g_{\mu }-2$.

Figure 1

Feynman diagram that can generate the operator in Eq. (11) if we assume $S_e$ and $\varphi$ to be heavy. Notice that we have ignored the numerical factors.

Figure 2

Contribution to the $g-2$ of a lepton $l$ induced by its coupling to the scalar $\varphi$.

Figure 3

The “Barr-Zee” contribution to the $g-2$ of a lepton $l$.

Figure 4

Enhancement of the electron Yukawa $K_e$ [see Eq. (20)] and $\mathrm{\Delta }{a}_e$ in terms of the Lagrangian paramenters $y_e$ and $g_{S_e}$, for $m_{\varphi }=150\mathrm{GeV}$.

Figure 5

Enhancement of the electron Yukawa $K_e$ [see Eq. (20)] and $\mathrm{\Delta }{a}_e$ in terms of the Lagrangian paramenters $y_e$ and $g_{S_e}$, for $m_{\varphi }=250\mathrm{GeV}$.