Heavy Neutrino Search via the Higgs boson at the LHC

# Heavy Neutrino Search via the Higgs boson at the LHC

Arindam Das School of Physics, KIAS, Seoul 130-722, Korea Department of Physics & Astronomy, Seoul National University 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea Korea Neutrino Research Center, Bldg 23-312, Seoul National University, Sillim-dong, Gwanak-gu, Seoul 08826, Korea    Yu Gao Department of Physics and Astronomy, Wayne State University, Detroit, 48201, USA    Teruki Kamon Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA
###### Abstract

In inverse see-saw the effective neutrino Yukawa couplings can be sizable due to a large mixing angle. When the right-handed neutrino is lighter than the Higgs boson , it can be produced via the on-shell decay of an Higgs boson at the LHC. The Standard Model (SM) Higgs boson offers an opportunity to probe the neutrino mixing. In this paper we adopt below the Higgs mass, and found the QCD dominated channel can lead to a signal by singly producing at the LHC. In such a process, the SM Higgs boson can decay via at a significant branching fraction, and the mass can be reconstructed in its dominant semilpetonic decays. We perform an analysis on this channel and its relevant backgrounds, among which the jets background is the largest. Considering the existing mixing constraints from Higgs and electroweak precision data, the best sensitivity of the heavy neutrino search is found to be in the 100- 110 GeV range at the upcoming high luminosity runs.

Heavy Neutrino Search, Higgs boson Data, New Production Channel, Collider Phenomenology
preprint: July 14, 2019

WSU-HEP-1706, MI-TH-1748

## I Introduction

The existence of the tiny neutrino mass and the flavor mixing have been observed by the recent neutrino oscillation experiments Neut1 (); Neut2 (); Neut3 (); Neut4 (); Neut5 (); Neut6 () which requires us to extend the Standard Model (SM). Among the different extensions of the SM, the seesaw or type-I seesaw mechanism seesaw0 (); seesaw1 (); seesaw2 (); seesaw3 (); seesaw4 (); seesaw5 (); seesaw6 () is the probably the simplest idea to naturally explain the tiny neutrino mass. Due to the variation of the seesaw scale form the intermediate scale to the electroweak scale, the neutrino Dirac Yukawa coupling varies from scale of the electron Yukawa coupling to the top quark Yukawa coupling. Being SM gauge singlets, the right handed (RH) heavy Majorana neutrinos interact with the SM gauge bosons through the Dirac Yukawa coupling. The heavy neutrinos in the TeV or GeV scale, employed by the seesaw mechanism, have too small Dirac Yukawa coupling to produce the observable signatures at the high energy colliders such as Large Hadron Collider (LHC) and Linear Collider (LC).

There is another type of seesaw mechanism, commonly known as the inverse seesaw mechanism inverse-seesaw1 (); inverse-seesaw2 (); inverse-seesaw3 () where a small neutrino mass is generated by a tiny lepton number violating parameter. Where in case of seesaw mechanism a large lepton number violating mass term is introduced as a suppression factor to produce the tiny neutrino mass. In case of inverse seesaw, the heavy neutrinos are pseudo-Dirac particles with so that such RH neutrinos could be produced at the LHC and LC while having masses in the TeV or GeV scale. The relevant particle content of the model is given by Tab. 1

The relevant part of the Lagrangian is given by 111It is crucial in inverse seesaw to forbid the Majorana mass term for . For realization in the next-to-minimal supersymmetryic SM, see Gogoladze:2008wz ()

 L⊃−YαβD¯¯¯¯¯ℓαL~HNβR−MαβN¯¯¯¯¯¯¯SαLNβR−12μαβ¯¯¯¯¯¯¯SαLSβCL+H.c., (1)

where and are two SM-singlet heavy neutrinos with the same lepton numbers, is the SM lepton doublet, is the SM Higgs doublet, , are the lepton flavor indices, is the Dirac mass matrix and is a small Majorana mass matrix violating the lepton numbers.

The neutrino mass matrix is

 Mν=⎛⎜⎝0mD0mTD0MTN0MNμ⎞⎟⎠. (2)

Diagonalizing this mass matrix we obtain the light neutrino mass matrix

 mν≃(mDM−1N)μ(M−1TNmTD) (3)

where . Note that the smallness of the light neutrino mass originates from the small lepton number violating term . The smallness of allows the parameter to be order one even for an electroweak scale heavy neutrino. Since the scale of is much smaller than the scale of , the heavy neutrinos become the pseudo-Dirac particles.

We consider a flavor-diagonal and structure of , where there is no mixing between different flavors of heavy neutrinos. An explicit numerical fit is given in Das:2012ze (). Due to flavor dependence in electroweak precision constraints, in this paper we consider two benchmark scenarios. One is the ‘Single Flavor’ (SF) case, where only one flavor heavy pseudo-Dirac pair resides at the electroweak scale whereas the other flavors’ heavy pairs are beyond reach of the LHC. Here we consider such a SF cases for electron and muon type neutrinos, respectively. For an alternative scenario, we also consider the ‘Flavor Diagonal’ (FD) case that both the first two flavor (electron and muon) heavy pseudo-Dirac pairs are at the weak scale , while those for the thrid flavor are heavy. For simplicity we assume the (electron and muon) flavor have the same mass.

Our paper is arranged in the following way. In Sec. II we discuss the recent experimental bounds on the heavy neutrino searches. In Sec. III we discuss about the production and the subsequent decay of the Higgs boson into the heavy neutrino. We also describe the different decay modes of the heavy neutrino. In Sec. IV we study the complete collider study of the signal and the SM backgrounds. Sec. V is dedicated for the conclusion.

## Ii Bounds on the Mixings

Being SM gauge singlets, the heavy mass eigenstate of neutrinos can interact with the and bosons via its mixings into the SM neutrino, as

 ν≃νm+VℓNNm, (4)

where is the mixing between the SM neutrino and the SM gauge singlet RH heavy neutrino assuming . Here is the flavor eigenstate whereas and are corresponding light heavy mass eigenstates respectively. For convenience in notation, from now on we also use to denote the heavy mass eigenstate without further notice.

The charged current (CC) and neutral current (NC) interactions can be expressed in terms of the mass eigenstates of the light-RH neutrinos as

 LCC⊃−g√2Wμ¯eγμPLVℓNN+h.c., (5)

where denotes the three generations of the charged leptons, and is the projection operator. Similarly, in terms of the mass eigenstates the neutral current interaction is written as

 LNC⊃−g2cwZμ[¯¯¯¯¯NγμPL|VℓN|2N+{¯¯¯¯¯¯νmγμPLVℓNN+h.c.}], (6)

where with being the weak mixing angle. We notice from Eqs. 1, 5 and 6 that the production cross section of the heavy neutrinos in association with a lepton or SM light neutrino is proportional to . However, the Yukawa coupling in Eq. 1 can also be directly measured from the decay mode of the Higgs boson such as applying the bounds obtained from invisible Higgs boson decay widths. The recent and the projected bounds on the mixing angle as a function of from different experiments are shown in Fig. 1.

For , the heavy neutrino can be produced from the -decay through through the NC interaction with missing energy. The heavy neutrino can decay according CC and NC interactions. Such processes have been discussed in Dittmar:1989yg (); Das:2016hof (). In Das:2016hof (); Degrande:2016aje (); Hessler:2014ssa (), a scale dependent production cross section at the Leading Order (LO) and Next-to-Leading-Oder QCD (NLO QCD) of at the LO and NLO have been studied at the 14 TeV LHC and 100 TeV hadron collider. The L3 collaboration Adriani:1992pq () has performed a search on such heavy neutrinos directly from the LEP data and found a limit on at the CL for the mass range up to 93 GeV. The exclusion limits from L3 are given in Fig. 1 where the red dot-dashed line stands for the limits obtained from electron (L3-) and the red dashed line stands for the exclusion limits coming from (L3-). The corresponding exclusion limits on at the CL Acciarri:1999qj (); Achard:2001qv () have been drawn from the LEP2 data which have been denoted by the dark magenta line. In this analysis they searched for with a center of mass energy between 130 GeV to 208 GeV Achard:2001qv ().

The DELPHI collaboration Abreu:1996pa () had also performed the same search from the LEP-I data which set an upper limit for the branching ratio about at CL for GeV GeV. Outside this range the limit starts to become weak with the increase in . In both of the cases they have considered and decays after the production of the heavy neutrino was produced. The exclusion limits for are depicted by the blue dotted, dashed and dot-dashed lines in Fig. 1.

The search of the sterile neutrinos can be made at high energy lepton colliders with a very high luminosity such as Future Circular Collider (FCC) for the seesaw model. A design of such collider has been launched recently where nearly 100 km tunnel will be used to study high luminosity collision (FCC-) with a center-of-mass energy around 90 GeV to 350 GeV Blondel:2014bra (). According to this report, a sensitivity down to could be achieved from a range of the heavy neutrino mass, GeV GeV. The darker cyan-solid line in Fig. 1 shows the prospective search reaches by the FCC-. A sensitivity down to a mixing of can be obtained in FCC- Blondel:2014bra (), covering a large phase space for from GeV to GeV.

The heavy neutrinos can participate in many electroweak (EW) precision tests due to the active-sterile couplings. For comparison, we also show the CL indirect upper limit on the mixing angle, for respectively derived from a global fit to the electroweak precision data (EWPD), which is independent of for , as shown by the horizontal pink dash, solid and dolled lines respectively in Fig. 1 deBlas:2013gla (); delAguila:2008pw (); Akhmedov:2013hec (). For the mass range, , it is shown in Deppisch:2015qwa () that the exclusion limit on the mixing angle remains almost unaltered, however, it varies drastically at the vicinity of For the flavor universal case the bound on the mixing angle is given as from deBlas:2013gla () which has been depicted in Fig. 1 with a pink dot-dashed line.

The relevant existing upper limits at the CL are also shown to compare with the experimental bounds using the LHC Higgs boson data in BhupalDev:2012zg (); Das:2014jxa () using Chatrchyan:2012ty (); CMS:2012xwa (); Aad:2012uub (); Chatrchyan:2012ft (); Aad:2012ora (). The darker green dot-dashed line named Higgs boson shows the relevant bounds on the mixing angle. In this analysis we will compare our results taking this line as one of the references. We have noticed that the can be as low as while GeV and the bound becomes stronger at GeV as . When GeV, the bounds on become weaker.

The prospective bounds on from the linear collider at GeV with a fb luminosity has been studied in Banerjee:2015gca () where the analysis could probe down to taking . The solid orange line represents the prospective bounds at ILC.

LHC has also performed the direct searches on the Majorana heavy neutrinos. The ATLAS detector at the 7 TeV with a luminosity of 4.9 fb Chatrchyan:2012fla () studied the in the type-I seesaw model framework for GeV GeV. They have interpreted the limit in terms of the mixing angle, which is shown in the Fig. 1. The corresponding bounds for the at the 8 TeV with a luminosity of 20.3 fb Aad:2015xaa () is interpreted as the dashed darker cyan line as ATLAS8- in the same figure.222The weaker bounds at the 7 TeV ATLAS are not shown in Fig. 1, however, the bounds can be read from Chatrchyan:2012fla ().

The CMS also studied the type-I seesaw model from the and final states in Khachatryan:2016olu () at the 8 TeV LHC with a luminosity of 19.7 fb with GeV GeV. The limits from the CMS in the for is roughly comparable to the DELPHI result while GeV. The CMS limits are denoted by CMS8- and CMS8- with the magenta dashed and solid lines respectively.

Using such limits, in Das:2015toa () the prospective bounds on at the 14 TeV LHC with 300 fb (black, dott dashed line LHC14@300 fb) and 3000 fb luminosities are given for the type-I seesaw case for GeV GeV. The prospective bounds for the type-I seesaw case could be better than the ILC bounds while the LHC luminosity will be 3000 fb(black, dotted line LHC14@3000 fb) and at that point the mixing angle could be probed down to . The range of the mixing angles for the type-I seesaw case using the lepton flavor violation bounds and general parameterizations have been studied in Das:2017nvm () for the type-I seesaw case using two generations of the degenerate heavy neutrinos having masses around 100 GeV.

In Das:2015toa () the prospective upper bounds on have been obtained studying the trilepton plus missing energy final state using the inverse seesaw model at the 14 TeV LHC with a luminosity of 300 fb(dark purple, dashed line Trilep-14@300 fb) and 3000 fb(dark purple, dot-dashed line Trilep-14@3000 fb). At the 300 fb luminosity could be probed down to where as a luminosity of 3000 fb can make it better by two orders of magnitude. In Eq. 6, there is a part where the heavy neutrino can produced in a pair from the NC interaction where the production cross section will be proportional to . A detailed scale dependent LO and NLO-QCD studies of this process followed by various multilepton decays of the heavy neutrino have been studied in Das:2017pvt (). It is shown that GeV GeV could be probed well at the high energy colliders at very high luminosity while the results will be better than the results from EWPD.

In this work we will consider on GeV GeV where the heavy neutrino will be produced from the on-shell decay of the Higgs boson. Therefore we chose the Higgs boson line for the mixing angles and also picked up some ‘benchmark’ values of the mixing angles to which are favored by the current and prospective bounds. It must be clarified that on-shell decay of the Higgs boson into will show same repertoire for the Majorana type, pseudo-Dirac type and Dirac type heavy neutrinos irrespective of the models, provided that is lighter than the Higgs boson. In the mixing angles values, range are also shown for a future 100 TeV collider, where such a small mixing can be potentially probed.

## Iii Higgs boson + jet cross-sections

The Higgs boson can decay into a right handed pseudo-Dirac heavy neutrino and a SM neutrino via the mixing. If lies between GeV GeV, the Higgs boson can decay on-shell into the RH neutrino through a single production channel shown in Fig. 2.

The Higgs boson’s SM decay width is taken as 4.1 MeV, with allowance to fit in BSM physics where the Higgs boson can decay into the SM singlet RH heavy neutrino in association with missing energy. The partial decay width is given by

 Γ(h→Nν)=Y2N8πm3h(m2h−M2N)2 (7)

and it sums and cases. The branching fraction of the Higgs boson to the heavy neutrino is

 Bh→Nν=Γ(h→Nν)ΓSMh+Γ(h→Nν) (8)

We focus on the signal channel of single Higgs boson production333In the FD case, with an associated jet, and utilize the consequent decay of the Higgs boson. The inclusion of an extra jet is necessary due to the requirement of experimentally triggering on the event, and also due to the fact that most of the Higgs boson decay products are not very energetic without a transverse boost from the associated initial state jet.

The production cross-section at 13 TeV has been studied to the next-next-to-leading order (NNLO) in Boughezal:2015dra (); Boughezal:2015aha (), and we adopt the results wherein,

 σ(h+j)LO = 1.1 pb σ(h+j)NLO = 1.6 pb σ(h+j)NNLO = 1.9 pb (9)

with a jet transverse momentum, GeV. Here we increase the leading requirement to reduce the amount of background, as well as to distinguish the ISR jet from the jets from decays, as will be discussed in the following section. Including the Higgs boson decay branching ratios, the signal cross-section for a single heavy neutrino can be written as

 σ=σ(h+j)Bh→Nν (10)

depending upon , the production cross section of the heavy neutrino is shown in Fig. 3 at 13 TeV LHC, for ISR jet GeV.

To calculate the prospective cross section in this channel, we consider the maximal mixing angles constraint from leptonic Higgs channel, as discussed in BhupalDev:2012zg (); Das:2014jxa (). While the Higgs bound is most stringent in a large mass range, at mass between 100-110 GeV, the EWPD bound deBlas:2013gla () becomes stronger. We use the stronger of the two constraints to produce an upper bound of , and the heavy neutrino production cross section for the channel.

For the convenience of estimating generic signal rates, we also use showed the signal cross sections at fixed mixing angle values in In Fig. 3. Note that will be nearly magnitude below the constraint obtained in BhupalDev:2012zg (); Das:2014jxa (); deBlas:2013gla () in the SF case444 The FD case for the ‘benchmark’ mixing angles will be nearly twice as large as the corresponding SF cases..

The heavy neutrino will then decay via the SM weak bosons such as , (and for heavier ). When is heavier, it can decay to on-shell and bosons. These partial decay widths are given as,

 Γ(N→ℓW)=g2|VℓN|264π(M2N−m2W)2(M2N+2m2W)M3Nm2W (11)

and

 Γ(N→νZ)=g2|VℓN|2128πc2w(M2N−m2Z)2(M2N+2m2Z)M3Nm2Z (12)

respectively. When the heavy neutrino mass is greater than the Higgs boson mass, then it can decay into the Higgs boson through at a partial width,

 Γ(N→hν) = |VℓN|2(M2N−m2h)232πMN(1v)2. (13)

For lighter than and bosons, it decays into three-body channels through the virtual and bosons. The corresponding partial decay widths are

 Γ(N→ℓ1ℓ2νℓ2) = |VℓN|2G2FM5N192π3 Γ(N→νℓ1ℓ2ℓ2) = |VℓN|2G2FM5N96π3(14+3sin4θw−32sin2θw) Γ(N→νℓ2ℓ2ℓ2) = |VℓN|2G2FM5N96π3(14+3sin4θw+32sin2θw) Γ(N→νν1ν2ν2) = |VℓN|2G2FM5N96π3 Γ(N→ℓjj) = |VℓN|2G2FM5N64π2 Γ(N→ℓjj) = |VℓN|2G2FM5N32π3(14+3sin4θw−32sin2θw). (14)

and these are comparable to Dib:2016wge () where GeV.

Note that the channel will typically dominate both two-body and three-body decay. In our final state analysis, we require reconstruction of the boson and masses to veto SM backgrounds, thus the two-body decay followed by , as shown in Fig. 4, is the most relevant channel in the following discussions.

## Iv Collider Signals and Backgrounds

For successful triggering and background suppression, we require the leading jet in event to be at least 200 GeV. Compared to Higgs boson decay products, the ISR jet is more energetic and assumes the role of triggering jet, and at the same transversely boosts the Higgs boson system so that the Higgs boson decay products acquire larger and become more visible.

The Higgs boson then can decay into an pair. We focus on the semileptonic decay channel , in which all three daughter particles are visible. The two jets from arises from the on-shell decay of a boson, so that their invariant mass would reconstruct to . The lepton + dijet invariant mass would also reconstruct to . These two invariant mass window cuts greatly suppress SM backgrounds.

As the ISR jet is often more energetic than those from decays, the decay jets are mostly the second and third in ordering, as illustrated in Fig. 5. An peak is the most statistically pronounced between and among the three leading jets.

The after-cut cross-section is inferred from the cross-section, decay branching ratios, and the selection efficiencies, as

 σ=σ(hj)Bh→NνBN→ℓjjAeff. (15)

For the selection efficiency , we consider the following cuts on the event final state:

(2) Additional two or more jets with GeV and exactly one lepton with GeV;

(3) GeV;

(4) GeV.

The selection cuts are designed to reconstruct the characteristic heavy neutrino mass as well as the physical boson from decay. The large leading jet is important in suppressing weak boson + jets backgrounds. Vetoing a second lepton removes backgrounds with bosons. Here we focus on the hadronical decay in order to reconstruct both the boson and the masses. These cuts greatly reduces SM backgrounds while retaining signal events at a much higher acceptance rate. Note that a fully leptonic decay of can yield more leptons and suffer fewer SM background channels, but it also yields a neutrino and makes it impossible to reconstruct .

In order to obtain the cut efficiencies, we perform a Monte Carlo simulation of events with MadGraph5 Alwall:2014hca () package and its the Pythia-PGS package for event showering and detector simulation. For basic detector setup, we require a jet pseudo-rapidity , lepton pseudo-rapidity , minimal jet and lepton transverse momenta and at 30 GeV and 15 GeV, respectively. Both of ATLAS and CMS handle large number of pile-up interactions using a technique in Cacciari:2007fd (). We simply use the PGS simulation without pile-up interactions, but jets are in a fiducial volume of tracking system of to remove pile-up interactions. Note that we also choose range to agree with Boughezal:2015dra () for cross-section scaling.

The cut efficiency for signals is shown in Fig. 6 over the range of . The cut-efficiency is at the level of 1-3% for a mass between and masses. Lighter has a reduced cut efficiency due to the requirement of reconstruction from . The prospective cross section is given in Fig. 7. The maximally allowed mixing angles from BhupalDev:2012zg (); Das:2014jxa (); deBlas:2013gla () are used. For comparison, we also showed the after-cut cross-section for the ‘benchmark’ values of . 13 TeV the LHC can probe down to and a corresponding cross section can be readily tested at the future high luminosity LHC runs.

A number of SM backgrounds are relevant for the final state. The leading background channels typically arise from the presence of a boson, from either direct production or top quark decay, along with ISR jet(s). The significant background channels are listed in Tab. 2 that shows the efficiencies for the first three cuts, and Tab. 3 for the final window cut. For signal rates, we list a few masses between and masses. The mass dependence of is shown in Fig. 6.

As shown in Tabs. 2,  3, the leading background channel is jets, while those with top quarks are efficiently controlled by the mass-window cut. A large leading jet is the most effective cut against the jets channel, but it would also suppress the signal rate. In the Monte-Carlo simulation for the +jets, we use an ‘MLM’ matched bib:MLM (); Mangano:2006rw () cross-section for inclusive and processes, while for the other (sub-leading) background channels, we only showed the leading-order cross-sections.

After performing all the selection cuts, we found the leading a residue total background cross-section of 0.3 pb for the masses in Tab. 3. The maximal mixing values and corresponding cross-sections are given for the SF case, for which the EWPD is the least strigent. Adopting the NNLO product rate the heavy neutrino signals can be fb in cross-section, thus can be tested at the LHC. Considering the up-coming high luminosity runs at 3000 fb, the SF case ratio is 2.6(3.8) for 100(110) GeV.

The signal cross-section for muon flavor mixing cases can be scaled from Tab. 3 with the corresponding maximally allowed values, for relatively small . In the SF case, as the EWPD constrains for GeV, the signal rates are the same for GeV, but become smaller for heavier .

In the ‘FD’ case, the EWPD rules the common for GeV, while the combined signal cross-section is enhanced by a factor of 2. The signal optimizes at GeV with a cross-section of 1.6 fb, and for 3000 fb luminosity the , comparable to the SF case in signal significance.

A few additional cuts may be considered to help with background control. We note a central region -jet veto will be effective to reduce the top quark backgrounds, once the +jets events can be substantially reduced. A requirement of the transverse mass of the system, may further reduce the +jets background. The effectiveness of these cuts can be further investigated in high-statistics background studies.

As a note, in the mixing case the EWPD is less stringent compared to mixing cases, but the signal rate suffers from tau identification efficiency, as well as fractional energy reconstruction, which can be further studied.

## V Conclusion

We investigated the prospect of probing the single-production of a right handed heavy neutrino from the on-shell decay of the SM Higgs boson at the 13 TeV LHC. We adopt the inverted see-saw model where a sizable neutrino mixing angle is allowed. Due to the small SM width of the Higgs boson, a significant branching ratio can be achieved within the current bounds on the mixing.

We adopt the maximally allowed mixing angle, the corresponding Higgs boson decay width, to derive a maximal signal rate for the where the Higgs boson decays into the right-handed neutrino. We require a hard ISR jet to transversely boost the visibility of decay products as well as for background suppression. For identification, we require both and mass reconstruction from the jets and lepton-jet(s) systems in a final state.

A number of kinematical cuts are designed for signal selection. Signal and background analyses are carried out to evaluate the cut efficiencies, as shown in detail in Section  IV. We found an cut efficiency at 1-3% for close to Higgs boson mass and a reduced efficiency for lighter . For a few benchmark masses 100-110 GeV, a maximal signal cross-section at fb is obtained, compared to a total background at 0.3 pb from various and containing background channels. We note that transverse mass cuts may help further rejecting backgrounds. At optimal masses, the signals in SF and FD scenarios can be searched for and constrained by the up-coming LHC runs at a signal-to-background ratio around 5 by 3000 fb luminosity. The SF case has less significance because of stronger EWPD constraints. For much lighter than the Higgs boson, the signal is much less pronounced due to reduced decay branching and cut efficiencies.

Acknowledgments

The work AD is supported by the Korea Neutrino Research Center which is established by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2009-0083526). YG thank the Wayne State University for support. TK is partially supported by DOE Grant DE-SC0010813. TK is also supported in part by Qatar National Research Fund under project NPRP 9-328-1-066.

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