We here discuss exotic Higgs decays that can arise by the addition of a light fermion to the SM. We focus on two possibilities,

*neutrino portal-mediated*and

*Higgs portal-mediated*Higgs decays. The leading interaction of a single Majorana fermion χ with the SM fields is given by the renormalizable but lepton-number violating "neutrino portal" operator,

(1) |

^{1},

(2) |

*M*

^{2})], where μ is some hidden sector mass scale. This is a consequence of chiral symmetry, and, as we frequently may have μ <<

*M*, may result in the Higgs portal interaction becoming effective dimension six. As an example of this kind of UV completion, consider a simple hidden sector consisting of a singlet scalar

*S*together with the fermion χ,

(3) |

*V*(

*S*) allow

*S*to develop a vacuum expectation value, 〈

*S*〉 ≡ μ.

^{2}Then integrating out the excitations of

*S*around this 〈

*S*〉, with mass

*m*

_{s}, we obtain the operator

(4) |

*m*

_{χ}=

*m*

_{0}+

*c*μ, so either there are large cancellations or

*c*μ ∼

*m*

_{0}∼

*m*

_{χ}<<

*m*

_{s}, and the operator is effective dimension-six.

**Neutrino portal-mediated Higgs decays**We first consider exotic Higgs decays mediated by the neutrino portal operator, Eq. (1). The renormalizable neutrino portal coupling occurs in the so-called νSM, the minimal model that can give mass to the SM neutrinos. Here the SM is extended by sterile neutrinos, allowing the SM neutrinos to get a mass from a see-saw type mechanism triggered by a Majorana mass term (

*M*/2) χχ. The operator of Eq. (1) mixes the sterile neutrino χ with the active SM neutrino ν arising from the

*SU*(2) doublet

*L*. In the absence of large cancellations in the neutrino mass matrix, sterile neutrinos must be extremely heavy,

*M*>>

*v*, or extremely decoupled,

*y*<<

*y*

_{e}<< 1. In this limit, the decay

*h*→χν is negligible, even if kinematically allowed. However, the authors of [1,2] show that active-sterile mixing angles as large as several percent are possible, with (accidental) cancellations among the Yukawa couplings still allowing for small active neutrino masses. Mixing angles of the order of a few percent may imply a sizable partial width for

*h*→νχ,

(5) |

*m*

_{χ}is the mass of the sterile neutrino χ. For

*m*

_{h}< 130 GeV, neutrino data and pion decay constraints on W-lepton coupling universality still allow the partial width into

*h*→νχ to exceed that into

*h*→

*b*

*b*, see [2] for a detailed discussion (see also [3]). The mass mixing between sterile (right-handed (RH)) neutrinos and active (left-handed (LH)) neutrinos introduces couplings of the RH neutrinos to

*W*and

*Z*gauge bosons. Therefore, in the region of parameter space for which the active-sterile mixing angle Θ is close to its phenomenological upper bound, the RH neutrinos decay promptly into χ→

*l*

*W*

^{*}→

*l*

*f*

*f*′ and χ→ ν

*Z*

^{*}→ ν

*f*

*f*, where

*f*and

*f*′ are either a lepton or a quark of the SM, and with all branching ratios fixed by the electroweak quantum numbers of the SM fermions. In general χ may have non-zero mixings with one, two, or all three SM neutrinos.

**Higgs portal-mediated Higgs decays**We next turn to the higher-dimension decays, mediated by the higher-dimension operator of Eq. (2). After electroweak symmetry breaking, this operator yields a coupling λ

*h*(χχ+ χ

^{†}χ

^{†}), with effective Yukawa coupling given by λ = κ

*v*/2

*M*. The resulting partial width into χ is then

(6) |

*b*-quark Yukawa, substantial branching fractions Br(

*h*→χχ) can be obtained even for Higgs portal scales

*M*significantly above a TeV, as shown in Fig. 1, where we fix κ = 1 for simplicity.

Figure 1: Higgs branching fraction into Majorana fermions χ resulting from the partial width of Eq. (6), as a function of the Higgs portal scale

*M*and the mass of the fermion*m*_{χ}. We fix the coupling κ to be equal to 1. Dotted lines indicate branching ratios of 0.1 and 0.01.*Z*

_{2}symmetry taking χ→−χ, then χ will remain stable. On the other hand, if the

*Z*

_{2}is violated by a dimension-six operator of the form

(7) |

*f*

_{1}

*f*

_{2}

*f*

_{3}is a gauge-invariant combination of quarks and leptons, then χ will undergo the three-body decay χ→

*f*

_{1}

*f*

_{2}

*f*

_{3}. Some of these decays are familiar from previous study of R-parity violating neutralino decays in the MSSM, namely those involving holomorphic combinations of SM fermion fields (we suppress spinor structures for simplicity),

(8) |

(9) |

(10) |

## References

- [1]J. Kersten and A. Y. Smirnov,
*Right-Handed Neutrinos at CERN LHC and the*Mechanism of Neutrino Mass Generation,*Phys.Rev.*D76 (2007) 073005, [`arXiv:0705.3221`]. - [2]A. de Gouvea,
*GeV seesaw, accidentally small neutrino masses, and Higgs*decays to neutrinos, [`arXiv:0706.1732`]. - [3]S. Chang and N. Weiner,
*Nonstandard Higgs decays with visible and missing*energy,*JHEP*0805 (2008) 074, [`arXiv:0710.4591`]. - [4]C. Csaki, E. Kuflik, and T. Volansky,
*Dynamical R-Parity Violation*, [`arXiv:1309.5957]`.

### Footnotes:

^{1}The dipole operator χ

^{†}σ

^{μν}χ

*F*

_{μν}is also dimension five, but vanishes for a Majorana χ.

^{2}For simplicity, we do not consider the possible interaction

*S*|

*H*|

^{2}. This operator could be forbidden in the presence of a global symmetry taking

*S*→ −

*S*, χ→

*i*χ, which would also forbid the mass term

*m*

_{0}(χχ+χ

^{†}χ

^{†}).

File translated from T

_{E}X by T

_{T}H, version 4.03. On 17 Dec 2013, 23:45.