## Contact Person(s)

David Curtin, Rouven Essig, Zhen Liu, and Ze'ev Surujon More details on this mode may be found in Section 10 of*Survey of Exotic Higgs Decays*(

`arXiv:1312.4992`).

## Theoretical Motivation

*h*→

*ZZ*

_{D}As discussed in SM+V, many theories feature a hidden

*U*(1) sector with small kinetic or mass mixing the the SM photon and

*Z*-boson. This possibility often arises in connection to dark matter, but similar phenomenology can also arise in hidden valley models, see Hidden Valley. The minimal setup to generate

*h*→

*Z*

*Z*

_{D}decay involves a kinetic mixing term between the hypercharge gauge boson and the dark

*U*(1) gauge boson

(1) |

*B*

_{μ}. In the canonical basis, SM matter has dark milli-charge and there is mass mixing between the SM

*Z*-boson and

*Z*

_{D}. The dominantly dark vector mass eigenstate has photon-like couplings to SM fermions (proportional to the small mixing ϵ) up to

*O*(

*m*

_{ZD}

^{2}/

*m*

_{Z}

^{2}) corrections. It is also possible to have pure mass mixing after EWSB via operators of the form

*h*

*Z*

^{μ}

*Z*′

_{μ}, but in this case additional constraints from parity violating interactions and rare meson decays apply, see [1,2,3]. Generically, new physics similar to that which generates kinetic mixing may also generate dimension-6 terms of the form

*H*

^{†}

*HB*

^{μν}

*Z*

_{Dμν}/Λ

^{2}. Once the Higgs acquires a VEV, this term yields the coupling in Eq. (1).

*h*→

*Za*Next we consider the decay

*h*→

*Z*

*a*. This is motivated by, for example, by the 2HDM+S or the NMSSM, where one of the CP-odd Higgs masses can be small. The relevant interaction Lagrangian in terms of mass eigenstates

*h*and

*a*is with an Yukawa term:

(2) |

*g*= √{(

*g*

^{2}+

*g*′

^{2})/2} sin(α− β) sinθ

_{a}. α is the mixing angle between the doublet scalars, tanβ =

*v*

_{u}/

*v*

_{d}and θ

_{a}is the mixing angle between the uneaten doublet pseudoscalar

*A*and the singlet pseudoscalar. Since the higgs coupling to

*ZZ*and

*W*

^{+}

*W*

^{−}is also proportional to sin(α− β), the SM-like rates in those channels (as well as the diphoton mode) favor the decoupling limit α = π/2 − β. θ

_{a}can be constrained by direct LEP and Tevatron searches for the CP-odd Higgs, but the SM-like higgs could still have large branching fractions to

*Za*[4].

(3) |

_{a}does not affect its branching ratios. For the length of the LHC program it will likely be safe to take Br(h→ Za)=10% as a benchmark point. In the next section, we discuss the experimental constraints on this mode. Depending on the mass of this pseudoscalar, the dominant decay mode could be

*b*

*b*, τ

^{+}τ

^{−}or μ

^{+}μ

^{−}(

*s*

*s*). We consider all of these cases when proposing searching strategies.

## Existing Collider Studies

Up to different branching ratios and some angular correlations the final states for*h*→

*Z*

*Z*

_{D}and

*h*→

*Z*

*a*are identical. As such, collider studies and experimental searches for one channel generally apply to both. The two relevant parameters to define a simplified model for this channel are

(4) |

*X*=

*a*,

*Z*

_{D}and

*y*= some SM particle, where the different

*a*,

*Z*

_{D}branching ratios lend different importance to different choices of

*y*. There have not been many collider studies specifically performed for the

*h*→

*Za*mode. Ref. [4] pointed out that this channel may be very large in the context of the NMSSM. Ref [5,6,7] discussed heavy non-SM-like Higgs decaying into

*Za*. More searches have been inspired by looking for a

*Z*

_{D}. The phenomenology of a

*Z*

_{D}with mass mixing to the

*Z*has recently been discussed in [8,1,2,3] (see also, e.g., [9,10,11,12] for earlier work), including collider phenomenology of

*h*→

*ZZ*

_{D},

*h*→ γ

*Z*

_{D}and

*h*→

*Z*

_{D}

*Z*

_{D}decays, as well as low energy constraints from dark photon experiments,

*g*−2 of the muon, meson physics and electroweak precision observables. In [3], the authors designed a search for

*pp*→

*h*→

*ZZ*

_{D}→

*e*

^{+}

*e*

^{−}μ

^{+}μ

^{−}. The backgrounds considered are

*Z*(→

*l*

^{+}

*l*

^{−})

*jj*,

*j*faking

*l*(probability ∼ 0.1%) and leptonic

*t*

*t*(reducible), as well as

*h*→

*ZZ*

^{*},

*Z*γ

^{*},

*ZZ*and

*Z*→ 4

*l*(irreducible). The authors of [3] assumed only mass mixing of the form ε

_{Z}

*m*

_{Z}

^{2}

*Z*

^{μ}

*Z*

_{Dμ}. For

*m*

_{ZD}=10 GeV and ε = 10

^{−6}, they find that the luminosity at 14 TeV LHC needed to exclude (2σ), observe (3σ) and discover (5σ) the

*Z*

_{D}is 42, 95 and 260 fb

^{−1}, respectively. For half of those values of

*m*

_{ZD}and mixing ε

_{Z}the numbers are slightly smaller: (33,75,210) fb

^{−1}.

## Existing Searches & Limits

Our focus is the*hZX*vertex (

*X*=

*a*,

*Z*

_{D}). No direct search for

*h*→

*Za*or

*ZZ*

_{D}has been performed to be best of our knowledge, but there are several channels and other searches at LEP, Tevatron and LHC that are sensitive to this interaction term.

*****

**LEP**The

*hZX*vertex not only give rise to the

*h*→

*ZX*decay, but also opens the channel

*e*

^{+}

*e*

^{−}→

*Z*

^{*}→

*h*

*X*at LEP. Related searches include

*e*

^{+}

*e*

^{−}→

*h*

*a*,

*ZZ*′→ 4

*b*[13], 4τ [13] and 2

*b*2τ [13]. For Br(h→ Za)=10%, these searches are not constraining because the cross section for

*e*

^{+}

*e*

^{−}→

*Z*

^{*}→

*h*

*a*is at the sub-fb level.

*****

**Tevatron and LHC**

Figure 1: 95% C.L. exclusion limit on Br(

The most relevant existing search sensitive to *h*→*Z**X*)×Br(*X*→*l**l*) for*X*=*Z*_{D},*a*, extracted from the SM*h*→ 4*l*searches (*l*=*e*, μ) assuming SM higgs production rate and Γ_{X}<< 1 GeV. (The lighter dashed lines indicate the expected limit. The large fluctuations in the observed limit are a consequence of low statistics in each bin.)*h*→

*ZZ*

_{D}and

*h*→

*Za*is

*h*→

*ZZ*

^{*}→ 4

*l*by CMS [14] and ATLAS [15], where 4

*l*stands for electrons and muons. The cleanliness of the 4

*l*decay makes these existing searches very sensitive to

*ZZ*

_{D}or

*Za*decaying into leptons. The leptonic

*h*→

*ZZ*

^{*}searches divide the four leptons of each event into two pairs, the "leading" pair (likely to have come from an on-shell

*Z*) and the "subleading" pair (from the off-shell

*Z*

^{*}). With The subleading dilepton mass distributions from ATLAS and CMS using 20 + 5 fb

^{−1}data set it is easy to estimate limits on

*h*→

*Z*

*X*decay. We show our translated 95% CL bounds on this exotic branching fraction for different

*m*

_{X}> 12 GeV in Fig. 1, see

`arXiv:1312.4992`for more details. The bound on Br(h → ZX) ×Br(X →

*l*

*l*) is <~10

^{−4}− 10

^{−3}for 12 GeV <~

*m*

_{X}<~34 GeV and

*l*=

*e*, μ. The situation is more ambiguous for pseudoscalars. Their branching ratios are more model-dependent in general, and their Yukawa couplings usually imply that

*a*→ ττ is enormously preferred over

*e*, μ. Bounds for

*X*→ ττ could also be derived from the leptonic

*h*→

*Z*

*Z*

^{*}searches but would be much weaker. Nevertheless this may be the preferred discovery channel for 2HDM+S and NMSSM type models, where Br(h → Z a) could easily be 10% and Br(a → ττ) is generally

*O*(0.05-1), see 2HDM+S.

## Proposals for New Searches at the LHC

For*m*

_{a, ZD}> 12 GeV it seems likely that LHC14 searches inspired by

*h*→

*ZZ*

^{*}will constrain

*h*→

*Za*in the

*a*→ 2τ modes, while LHC7+8 already gives significant

*direct*bounds to

*h*→

*Z*

*Z*

_{D}→ 4

*l*. A

*Z*+ lepton jet search would be able to set strong limits in particular for very light

*Z*

_{D}. Care must be taken to correctly account for challenging quarkonium backgrounds. Identifying promising search strategies will be the subject of future work.

## Updates

*Here we list new experimental and theory results pertinent to this exotic higgs decay channel.*

- Adam Falkowski, Roberto Vega-Morales, Exotic Higgs decays in the golden channel,
`arxiv:1405.1095`

## References

- [1]H. Davoudiasl, H.-S. Lee, and W. J. Marciano,
*'Dark' Z implications for*Parity Violation, Rare Meson Decays, and Higgs Physics,*Phys.Rev.***D85**(2012) 115019, [`arXiv:1203.2947`]. - [2]H. Davoudiasl, H.-S. Lee, and W. J. Marciano,
*Dark Side of Higgs Diphoton*Decays and Muon g-2,*Phys.Rev.***D86**(2012) 095009, [`arXiv:1208.2973`]. - [3]H. Davoudiasl, H.-S. Lee, I. Lewis, and W. J. Marciano,
*Higgs Decays as a*Window into the Dark Sector, [`arXiv:1304.4935].` - [4]N. D. Christensen, T. Han, Z. Liu, and S. Su,
*Low-Mass Higgs Bosons in*the NMSSM and Their LHC Implications, [`arXiv:1303.2113`]. - [5]G. Mahlon and S. J. Parke,
*Using Spin Correlations to Distinguish Zh from*ZA at the International Linear Collider,*Phys.Rev.***D74**(2006) 073001, [`hep-ph/0606052`]. - [6]S. Chang and A. Menon,
*Discovering Nonstandard Higgs bosons in the*H→ZA Channel Decay to Multileptons,*JHEP***1302**(2013) 152, [`arXiv:1211.4869`]. - [7]M. M. Almarashi and S. Moretti,
*LHC Signals of a Heavy CP-even Higgs*Boson in the NMSSM via Decays into a*Z*and a Light CP-odd Higgs State,*Phys.Rev.***D85**(2012) 017701, [`arXiv:1109.1735`]. - [8]H. Davoudiasl, H.-S. Lee, and W. J. Marciano,
*Muon Anomaly and Dark*Parity Violation,*Phys.Rev.Lett.***109**(2012) 031802, [`arXiv:1205.2709`]. - [9]A. Hook, E. Izaguirre, and J. G. Wacker,
*Model Independent Bounds on*Kinetic Mixing,*Adv.High Energy Phys.***2011**(2011) 859762, [`arXiv:1006.0973`]. - [10]S. Gopalakrishna, S. Jung, and J. D. Wells,
*Higgs boson decays to four*fermions through an abelian hidden sector,*Phys.Rev.***D78**(2008) 055002, [`arXiv:0801.3456`]. - [11]R. Schabinger and J. D. Wells,
*A Minimal spontaneously broken hidden*sector and its impact on Higgs boson physics at the large hadron collider,*Phys.Rev.***D72**(2005) 093007, [`hep-ph/0509209`]. - [12]K. Babu, C. F. Kolda, and J. March-Russell,
*Implications of generalized Z*- Z-prime mixing,*Phys.Rev.***D57**(1998) 6788-6792, [`hep-ph/9710441`]. **[13]ALEPH, DELPHI, L3, OPAL, LEP Working Group for Higgs Boson Searches**Collaboration, S. Schael*et. al.*,*Search for neutral MSSM Higgs*bosons at LEP,*Eur.Phys.J.***C47**(2006) 547-587, [`hep-ex/0602042`].*[14]Properties of the Higgs-like boson in the decay H to ZZ to 4l in pp*collisions at sqrt s =7 and 8 TeV, Tech. Rep. CMS-PAS-HIG-13-002, CERN, Geneva, 2013.**[15]ATLAS**Collaboration,*Measurements of the properties of the*Higgs-like boson in the four lepton decay channel with the ATLAS detector using 25 fb^{-1}of proton-proton collision data, ATLAS-CONF-2013-013

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