Muon magnetic moment and the pseudo-Goldstone Higgs boson

We compute the correction to the muon magnetic moment in theories where the Higgs is a pseudo-Goldstone boson and leptons are partially composite. Using a general effective Lagrangian we show that in some regions of parameters a sizable new physics contribution to the magnetic moment can be obtained from composite fermions that could explain the $3.5\sigma$ experimental discrepancy from the standard model prediction. This effect depends on the derivative interactions of the Higgs that do not modify the coupling of the Higgs to leptons and it does not require extremely light fermions, allowing us to easily avoid LHC bounds. Our derivations can be in general applied to dipole operators in theories with Goldstone boson Higgs.

Figure 1

Diagrams contributing to $\mathrm{\Delta }{a}_{\mu }$. On the first line the diagrams with gauge and Yukawa interactions are shown while on the second line the ones with Higgs derivative interactions.

Figure 2

New physics contribution to $\mathrm{\Delta }{a}_{\mu }$ for $c_L=c_R=c$ (real) and $f=800\mathrm{GeV}$. The scan is performed by choosing $y\subset [-0.1,0.1]$ and $m_{1,4}\subset [300,3000]\mathrm{GeV}$. Blue points corresponds to fermionic contribution to the $S$ parameter $\mathrm{\Delta }S<0.5$ assuming 3 degenerate generation partners (we use the formulas with finite terms of Ref. [15]). The green band represents the experimental value for $\mathrm{\Delta }{a}_{\mu }$ within $2\sigma$.

Figure 3

Contribution to $\mathrm{\Delta }{a}_{\mu }$ in the scenario with $y_{L_1}=y_{L_4}$ and $y_{R_1}=y_{R_4}$ for $f=800\mathrm{GeV}$. The $2\sigma$ experimental value is reproduced in the region between the dashes lines. The white horizontal strip corresponds to $y_{L,R}>0.1$. Some of the allowed regions are not sampled in the scan corresponding to Fig. 2 due to the finite number of points.