Large invisible decay of a Higgs boson to neutrinos

# Large invisible decay of a Higgs boson to neutrinos

Osamu Seto Department of Life Science and Technology, Hokkai-Gakuen University, Sapporo 062-8605, Japan
###### Abstract

We show that the standard model (SM)-like Higgs boson may decay into neutrinos with a sizable decay branching ratio in one well-known two Higgs doublet model, so-called neutrinophilic Higgs model. This could happen if the mass of the lighter extra neutral Higgs boson is smaller than one half of the SM-like Higgs boson mass. The definite prediction of this scenario is that the rate of the SM-like Higgs boson decay into diphoton normalized by the SM value is about . In the case that a neutrino is Majorana particle, a displaced vertex of right-handed neutrino decay would be additionally observed. This example indicates that a large invisible Higgs boson decay could be irrelevant to dark matter.

preprint: HGU-CAP-038

## I Introduction

The newly discovered particle at the Large Hadron Collider (LHC) is now identified as a Higgs boson Aad:2012tfa (); Chatrchyan:2012ufa (). Its measured properties such as spin, parity, and couplings are consistent with the Higgs boson in the standard model (SM) of particle physics Aad:2013wqa (); Aad:2013xqa (); Chatrchyan:2013iaa (); Chatrchyan:2013mxa () within uncertainties, which are not very small yet. Possible deviations from the SM prediction on the Higgs boson also have been examined.

One of those is an invisible Higgs boson decay. Actually, an invisible Higgs boson decay occurs even in the SM through an off-shell boson pair into four neutrinos , as . Its branching ratio in the SM is of the order of . If once it is found with a larger branching ratio than that due to SM processes, this must be a sign of a beyond the SM (BSM). Such BSM models include, for instance, a light neutralino in supersymmetric models Griest:1987qv (), a Majoron Joshipura:1992ua (), graviscalars Giudice:2000av (), fourth generation neutrino Belotsky:2002ym () and Higgs portal dark matter InvisibleDecayByDM (). Searches of invisible decays of the Higgs boson have been carried out and to date only an upper bound on the branching ratio of the invisible decay has been obtained Aad:2014iia (); Chatrchyan:2014tja ().

In this paper, we show that the Higgs boson would decay into four neutrinos through an extra Higgs boson, which can be seen as the invisible decay, in a class of the two Higgs doublet model (THDM). The remarkable feature in this scenario is that the invisible final states are a SM particle, neutrinos, compared with other BSM models mentioned above where final invisible states are new hypothetical particles, such as a supersymmetric particle or dark matter. We consider the so-called neutrinophilic THDM Ma (); Wang (); Nandi (), where one Higgs doublet provides the mass of the SM fermions, while the other generates neutrino Dirac masses with its small vacuum expectation value (VEV). Phenomenology of the charged Higgs boson was studied in Refs. Davidson:2009ha (); Haba:2011nb (). In this paper, we will study a possible phenomenology of neutral Higgs bosons in those models. Because of these Yukawa couplings, both extra -even and extra -odd neutral Higgs bosons, and , respectively, couple mostly with neutrinos. Thus, through interactions between the SM-like Higgs boson and the extra Higgs bosons , as the boson makes new decay processes

 h→H(∗)H(∗)orA(∗)A(∗)→2ν2¯ν (1)

arise. 111 This possibility was briefly mentioned in Ref. Davidson:2009ha () for a very heavy SM-like Higgs boson in a different type of neutrinophilic Higgs model. If the intermediate or is off shell, the resultant contribution is comparable to the SM contribution by the boson and is not so large. However, if either or is on shell, the resultant invisible decay width is large.

## Ii Neutrinophilic two Higgs doublet model

The Higgs sector is of the so-called neutrinophilic THDM, where one Higgs doublet with its VEV generates the mass of the SM fermions, while the other generates neutrino Dirac masses through its VEV . Such a Yukawa coupling is realized by introducing the softly broken -parity charge assigned as in Table 1.

The Yukawa interaction is given by

 LY=−yℓα¯¯¯¯LαΦ1ℓRα−yuα¯¯¯¯Qα~Φ1uRα−ydα¯¯¯¯QαΦ1dRα−yαi¯¯¯¯¯¯Lα~Φ2νRi+H.c., (2)

where , () is the left-handed doublet quark (lepton), and , , , and are the right-handed (RH) singlet fermions, respectively. denotes flavor where we neglect mixing in quarks and represents the generation index of RH neutrinos. If we admit lepton number violation in theory, the lepton number violating Majorana mass term

 LM=−12¯¯¯¯¯¯¯νcRiMiνRi (3)

also can be introduced Ma (). The scalar potential is given by

 V = μ21|Φ1|2+μ22|Φ2|2−(μ212Φ†1Φ2+H.c.) (4) +λ1|Φ1|4+λ2|Φ2|4+λ3|Φ1|2|Φ2|2+λ4|Φ†1Φ2|2 +{λ52(Φ†1Φ2)2+H.c.},

where is the soft breaking parameter of the parity, as introduced above. Conditions that the potential(4) is bounded from below and a stable vacuum are given by Kanemura:2000bq ()

 λ1>0,λ2>0,2√λ1λ2+λ3+min[0,λ4−|λ5|]>0. (5)

Components in two Higgs doublets, each with a VEV, are parameterized as

 Φ1=⎛⎝ϕ+1v1+h1+ia1√2⎞⎠,Φ2=⎛⎝ϕ+2v2+h2+ia2√2⎞⎠. (6)

Following the concept of neutrinophilic Higgs model, we take GeV and . The smallness of is due to the small  Ma (). We define as usual; this corresponds to . The states and are diagonalized to the mass eigenstates ( and ) as

 (h1h2)=(cosα−sinαsinαcosα)(hH). (7)

Because of , and are mostly eaten by the and bosons, while we can identify the physical states as , , , and . Then, the mixing angle is found to be

 sinα≃v2v1. (8)

Automatically almost, the so-called SM limit is realized. Because of , is realized. The Higgs boson with the mass of GeV is also composed as . From Eq. (2), the Yukawa interactions of extra neutral Higgs bosons are written as

 LY ⊃ −∑f=ui,di,ℓimfvsinαsinβ¯¯¯fHf−imuiv(−cotβ)¯¯¯uiAγ5ui−i∑f=di,ℓimfvcotβ¯¯¯fAγ5f (9) −yαi√2cosα¯¯¯¯¯ναHPRνi+iyαi√2sinβ¯¯¯¯¯ναAPRνi+H.c.

We find that or decays into mostly neutrinos for

 yαi≫√2mfvtanβ. (10)

Masses of extra Higgs bosons are given by

 m2H = μ22+λ3+λ4+λ52v2, (11) m2A = μ22+λ3+λ4−λ52v2, (12) m2H± = μ22+λ32v2. (13)

To be consistent with the electroweak precision test, one neutral Higgs boson mass should be close to the charged Higgs boson mass as

 mH+≃mAormH+≃mH. (14)

Interactions of extra Higgs bosons with is

 L⊃−v(12(λ3+λ4−λ5)A2+12(λ3+λ4+λ5)H2+λ3|H+|2)h. (15)

## Iii Exotic SM-like Higgs boson decay

Now we consider a case where either or is light enough to be produced on shell by the decay. There are two mass spectra of Higgs bosons that are as consistent with the electroweak precision test:

 mH

and

 mA

From the mass formulas(11), (12), and (13), we find that mass spectra (16) and (17) can be realized for

 0>λ4≃λ5and0>λ4≃−λ5, (18)

respectively.

With couplings (9) and (15), if decays into or , which decays into neutrinos, then this fraction is measured as its invisible decay.

The decay width of is given by

 Γ(h→HH)=λ2Hv232πmh(1−4m2Hm2h)1/2, (19)

with . For the case of , we obtain the same result just by replacing and with and , respectively. The LHC constraints on exotic decay modes, or , indicate that is allowed. We define

 Br(h→HH)=Γ(h→HH)Γ(h→all), (20)

which is shown in Fig. 1. By combining the constraint on and Eq. (18), we find that, for the light (),

 λ3≃−λ4−(+)λ5 (21)

should be positive and of , which leads to the deviation in the diphoton decay rate of from the SM value HHG (), as shown in Fig. 2. Here, the brown and magenta shaded regions correspond to the region where the extra light Higgs boson is tachyonic and its on shell production is kinematically forbidden, respectively. One can find that this scenario predicts . The signal strength of has been reported as by ATLAS Aad:2014eha () and by CMS Khachatryan:2014ira ().

In the following sections, we discuss more detailed phenomenology which depends on neutrino mass nature.

## Iv Dirac neutrino case

The condition (10) is satisfied by a large for the Dirac neutrino case. Thus, the light is, in practice, invisible and we have (shown in Fig. 1). The same is true for a light as well.

The constraint on the charged Higgs boson, which decays into a lepton and a neutrino, is, in fact, stringent. This decay mode is similar to that of a slepton in supersymmetric models Davidson:2009ha () and masses of the first and the second generation slepton is constrained as GeV by ATLAS Aad:2014vma () or GeV by CMS Khachatryan:2014qwa (). Although some differences due to its decay branching ratio exist Davidson:2009ha (), roughly speaking, there is a similar bound on . Referring to Fig. 2, we find that a rather large coupling for the ATLAS (CMS) bound is required.

## V Majorana neutrino case

With the presence of the Majorana mass term (3), the neutrino mass matrix is given as

 M=⎛⎜⎝m(loop)νy√2v2y√2v2Mk⎞⎟⎠, (22)

with the radiative generated mass  Ma:2006km (),

 m(loop)ν=∑kyαkyTkβMk16π2(m2Hm2H−M2klnm2HM2k−m2Am2A−M2klnm2AM2k). (23)

We obtain a light neutrino mass

 (mν)αβ=m(loop)ν−∑kyαkyTkβv22/2Mk, (24)

the mass of a heavier RH-like neutrino and the left-right mixing angle  Type1seesaw ()

 sinθ≃yv2√2Mk. (25)

could be indeed dominant —– or at least comparable with tree level seesaw mass —– because of from Eqs. (18) and (21).

The charged Higgs boson decays into or , depending on the mass in the neutrinophilic Higgs model Haba:2011nb (). The results for the mode with a normalizing production cross section of pb can be found in Ref. CMS:2014pea (). However, this constraint is not so stringent because the actual production cross section is not so large. The LHC data constrains the mass of decaying into between and GeV Aad:2013hla () and decaying into  Aad:2014kga ().

We note here one cosmological argument on the Majorana neutrino case. The lepton number violation by the Majorana nature of neutrino plays an important role in cosmology. Several cosmological discussions on neutrinophilic Higgs model were held in Refs. HabaSeto (); Haba:2013pca (); Choi:2012ap (). One of them is an enhancement washout process by large Yukawa couplings and relatively light RH neutrinos in a neutrinophilic Higgs model HabaSeto (). Although a discussion of baryogenesis is beyond the scope and purpose of this paper, as a necessary condition to have nonvanishing baryon asymmetry in our Universe, we roughly evaluate the condition of no strong washout of lepton asymmetry, 222 This is because lepton asymmetry is a potential source of the baryon asymmetry in our Universe in the large class of baryogenesis scenario FukugitaYanagida (). provided a nonvanishing lepton asymmetry has been generated by any means of a higher energy physics process. If this condition were violated, it would be difficult to explain nonvanishing baryon asymmetry in our Universe, because any generated lepton asymmetry is washed out. The washout rate is given by . The condition at GeV, with being the cosmic expansion rate, is rewritten as

 y≲10−4, (26)

which would be regarded as a cosmologically favored region. 333 One known mechanism of baryogenesis which works without any lepton asymmetry is “baryogenesis via neutrino oscillation” Akhmedov:1998qx (); Asaka:2005pn ().

Now we discuss the decay of or . For , an extra neutral Higgs boson decay produces one light left-handed-like neutrino and the other heavy RH-like neutrino . The amplitude is calculated as

 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯|M(H/A→νNR)|2=2|y|2(p1⋅p2)=|y|2((p1+p2)2−m2NR), (27)

where and are outgoing momentum of and , respectively. In addition, is neglected and indexes of are omitted. The decay width is given by

 Γ(H/A→νNR) = 116πmH/A3∑|y|2(mH/A2−m2NR)2. (28)

Here, the summation is taken for all kinematically possible modes. An extra Higgs boson decays into SM fermions, mostly the bottom quark, through a tiny mixing . Thus, its decay width is strongly suppressed by a large as

 Γ(H/A→b¯b)≃38π(mbvtanβ)2mH/A. (29)

Here, we define

 Br(H/A→inv)=Γ(H/A→νNR)Γ(H/A→b¯b)+Γ(H/A→νNR), (30)

and

 Br(h→2H/2A→2ν2NR)=Br(h→HH/AA)Br(H/A→inv). (31)

Figure 3 shows the contour plot of the invisible decay branching ratio with thick black lines as well as the contour of Eq. (25) with thin blue thin lines of and , respectively. In both cases, the invisible decay branching ratio is large for GeV. The dashed green (thick) lines are contours of the typical size of Yukawa coupling estimated from Eq. (24) with the atmospheric neutrino mass. As discussed above, would be critical when we consider nonvanishing baryon asymmetry in our Universe. In both panels, neutrino masses dominantly come from the tree level seesaw at the upper left region, and do from at the lower right region. In the light case shown in the right panel of Fig. 3, the destructive cancellation between and the seesaw term takes place. This cancellation makes cuspy curves of the invisible branching ratio and Yukawa couplings in contours. For the decay, GeV and GeV are taken. For the decay, GeV and GeV are taken.

Figure 4 is the contour plot of the invisible decay branching ratio of . Here, GeV and GeV are taken.

The produced RH neutrino decays as or through a tiny left-right mixing of . Here, a sign of inequality becomes more appropriate as becomes sizable. For such a left-right mixing of the order of or less, the displaced vertex of decay could be generated, and the decay length of the RH neutrino becomes cm for GeV Displaced (). For a further lighter or a much smaller , would not decay inside the detector. One can see that such a small mixing is realized in Fig. 3.

On the other hand, for , or decays into SM fermions through a tiny mixing of a Higgs boson (8) as in the usual type-I THDM.

## Vi Summary

We have shown that the SM-like Higgs boson could have a sizable invisible decay branching ratio such as with four neutrinos final states, for a Dirac neutrino and for a Majorana neutrino, in neutrinophilic Higgs doublet models, if one of the extra Higgs bosons is light enough to be produced by the SM-like Higgs boson decay. For the Majorana neutrino, this becomes a case in the parameter region GeV. Because of this mass spectrum of Higgs bosons, the SM normalized decay rate of is predicted to be . In the Majorana neutrino case, the displaced vertex of a decay also would be observed. Although the invisible decay of the Higgs boson was recently widely discussed in InvisibleDecayByDM () or applied to dark matter physics Aad:2014iia (); Chatrchyan:2014tja (), we emphasis that such a size of invisible decay can be realized just within simple THDM without a dark matter candidate.

## Acknowledgments

We would like to thank Koji Tsumura and Shigeki Matsumoto for the valuable comments. This work is supported in part by Grant-in-Aid for Scientific Research No. 2610551401 from the Ministry of Education, Culture, Sports, Science and Technology in Japan.

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