Minimal models of loop-induced lepton flavor violation in Higgs boson decays

The LHC has recently reported a slight excess in the $h\to \tau \mu$ channel. If this lepton flavor violating (LFV) decay is confirmed, an extension of the standard model (SM) will be required to explain it. In this paper we investigate two different possibilities to accommodate such a LFV process: the first scenario is based on flavor off-diagonal $A$ terms in the minimal supersymmetric standard model, and the second is a model where the Higgs boson couples to new vectorlike fermions that couple to the SM leptons through a LFV four-fermion interaction. In the supersymmetric model, we find that the sizes of the $A$ terms needed to accommodate the $h\to \tau \mu$ excess are in conflict with charge- and color-breaking vacuum constraints. In the second model, the excess can be successfully explained while satisfying all other flavor constraints, with order-one couplings, vectorlike fermion masses as low as 15 TeV, and a UV scale higher than 35 TeV.

Figure 1

Lepton-violating Higgs decay driven by the $A$ term.

Figure 2

Left: Effective flavor off-diagonal Yukawa coupling for $h\to l_i{l}_j$ through exchange of vectorlike fermions $\psi$, $\chi$. Right: induced amplitude for $l_i\to l_j\gamma$ via an open fermion line.

Figure 3

The $2.6\sigma$ LFV Higgs decay best fit (green band) and the bound on the lepton radiative decay (dotted line) in the $\tau -\mu$ sector, with $y^{\prime }=y=0.25$ and the $\mu \tau$ couplings set to $({\lambda }_1{)}_{\tau \mu }=({\lambda }_2{)}_{\tau \mu }=({\lambda }_3{)}_{\tau \mu }=1$. Near the dip feature, $M_{\text{fermion}}/\mathrm{\Lambda }$ approaches the value that minimizes the loop function $\mathcal{G}$.

Figure 4

Left: Radiative decay $\tau \to \mu \gamma$ (dotted line) and contours of $\mu \to e\gamma$ with varying ${\lambda }_{\mu e}$ (dashed red lines) and fixed fermion mass splitting. For each ${\lambda }_{\mu e}$, the forbidden regions (shadowed) are to the left and below the contours. Right: Contours of $\mu \to e\gamma$ for various fermion mass splittings (red dashed lines) with fixed ${\lambda }_{\mu e}=0.0005$. In both panels $y^{\prime }=y=0.25$ and ${\lambda }_1={\lambda }_2={\lambda }_3=1$.

Figure 5

Left (right) panel: scenario for a low (high) $\mathrm{\Lambda }$ scale obtained by lowering (increasing) the Yukawa couplings. In both panels ${\lambda }_{\mu e}=0.0005$, $M_{\chi }/M_{\psi }=1$ and the $\tau -\mu$ couplings are fixed at ${\lambda }_1={\lambda }_2={\lambda }_3=1$.

Figure 6

Solid lines show the contours from the bound on $\mu \to e\gamma$ taking $({\lambda }_1{)}_{\mu e}=({\lambda }_1^{\mathrm{eff}}{)}_{\mu e}$, the value assuming ${\lambda }_1$ is solely generated by loops involving $({\lambda }_2{)}_{\mu e}=({\lambda }_3{)}_{\mu e}$. The excluded regions are shown in gray. Corresponding colored dashed lines display values of $\mathrm{\Lambda }$ and $M_{\text{fermion}}$ where $\mathcal{B}r(h\to \mu e)$ is satisfied right at its experimental bound.

Figure 7

Left: Leading-order amplitude for $l_i\to l_j{l}_j{l}_j$ through gauge bosons. Right: Amplitude $l_i\to l_j{l}_j{l}_j$ through a Higgs boson.

Figure 8

$\mu -e$ conversion amplitude from gauge boson exchange. Analog diagrams with a Higgs boson connecting the loop to the nucleon are suppressed by the first generation quark Yukawas.

Figure 9

Comparison of bounds on $\mu -e$ observables. Current limits are shown in thick dashed lines, and the thin dashed lines represent the corresponding sensitivity improvements in the future experiments of Table 1.