$(g-2{)}_{e,\mu }$ in an extended inverse type-III seesaw model

There has been a longstanding discrepancy between the experimental measurements of the electron and muon anomalous magnetic moments and their predicted values in the Standard Model. This is particularly relevant in the case of the muon $g-2$, which has attracted a remarkable interest in the community after the long-awaited announcement of the first results by the Muon $g-2$ collaboration at Fermilab, which confirms a previous measurement by the E821 experiment at Brookhaven and enlarges the statistical significance of the discrepancy, now at $4.2\sigma$. In this paper we consider an extension of the inverse type-III seesaw with a pair of vectorlike leptons that induces masses for neutrinos at the electroweak scale and show that one can accommodate the electron and muon anomalous magnetic moments, while being compatible with all relevant experimental constraints.

Figure 1

Feynman diagrams that contribute to the charged lepton anomalous magnetic moment at the 1-loop level in the ISS3VL. Here ${\chi }_i$ and $N_j$ denote any of the charged and neutral lepton mass eigenstates, respectively. Momenta are shown in blue. (a) $W$. (b) $Z$. (c) $h$.

Figure 2

Dominant $W$ contribution in the ISS3. Mass insertions are represented by white blobs.

Figure 3

Dominant $W$ contribution in the ISS3VL. Mass insertions are represented by white blobs.

Figure 4

$\mathrm{\Delta }{a}_e$ (left) and $\mathrm{\Delta }{a}_{\mu }$ (right) as a function of the product ${(Y_{\mathrm{\Sigma }})}_{ii}{({\lambda }_L)}_i{({\lambda }_R)}_i$. Blue dots correspond to parameter points that pass all the experimental constraints, whereas gray points are experimentally excluded. The horizontal dashed lines represent the central values for $\mathrm{\Delta }{a}_e$ and $\mathrm{\Delta }{a}_{\mu }$, whereas $1\sigma$ ($3\sigma$) regions are displayed as yellow (green) bands.

Figure 5

$\mathrm{\Delta }{a}_{\mu }$ as a function of the combination ${(Y_{\mathrm{\Sigma }})}_{22}{({\lambda }_L)}_2{({\lambda }_R)}_2/[{(M_{\mathrm{\Sigma }})}_2{M}_L^2]$. Dashed line, horizontal bands and color code as in Fig. 4.

Figure 6

$\mathrm{\Delta }{a}_e$ (left) and $\mathrm{\Delta }{a}_{\mu }$ (right) as a function of ${(M_{\mathrm{\Sigma }})}_{11}$ and ${(M_{\mathrm{\Sigma }})}_{22}$, respectively. Dashed line, horizontal bands and color code as in Fig. 4.

Figure 7

$\mathrm{\Delta }{a}_{\mu }$ as a function of $M_L$. Dashed line, horizontal bands and color code as in Fig. 4.

Figure 8

$R_{hee}$ (left) and $R_{h\mu \mu }$ (right) as a function of $\mathrm{\Delta }{a}_e$ and $\mathrm{\Delta }{a}_{\mu }$, respectively. The vertical dashed lines represent the central values for $\mathrm{\Delta }{a}_e$ and $\mathrm{\Delta }{a}_{\mu }$, whereas $1\sigma$ ($3\sigma$) regions are displayed as yellow (green) bands.