Heavy Neutrino Search via the Higgs boson at the LHC

In inverse see-saw the effective neutrino Yukawa couplings can be sizable due to a large mixing angle. When the right-handed neutrino $(N)$ is lighter than the Higgs boson $(h)$, 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 $N$ below the Higgs mass, and found the QCD dominated $pp\rightarrow h j$ channel can lead to a signal by singly producing $N$ at the LHC. In such a process, the SM Higgs boson can decay via $h\rightarrow N\nu$ at a significant branching fraction, and the $N$ mass can be reconstructed in its dominant semilpetonic decays. We perform an analysis on this channel and its relevant backgrounds, among which the $W+$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.


I. INTRODUCTION
The existence of the tiny neutrino mass and the flavor mixing have been observed by the recent neutrino oscillation experiments [1][2][3][4][5][6] which requires us to extend the Standard Model (SM). Among the different extensions of the SM, the seesaw or type-I seesaw mechanism [7][8][9][10][11][12][13] is the probably the simplest idea to naturally explain the tiny neutrino mass. There is another type of seesaw mechanism, commonly known as the inverse seesaw mechanism [14][15][16] 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 Y D ∼ O(1) 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. I The relevant part of the Lagrangian is given by 1 where N R and S L are two SM-singlet heavy neutrinos with the same lepton numbers, L is the SM lepton doublet, H is the SM Higgs doublet, α, β are the lepton flavor indices, m N is the Dirac mass matrix and µ is a small Majorana mass matrix violating the lepton numbers.
The neutrino mass matrix is Diagonalizing this mass matrix we obtain the light neutrino mass matrix Note that the smallness of the light neutrino mass originates from the small lepton number violating term µ. The smallness of µ allows the m D M −1 N parameter to be order one even for an electroweak scale heavy neutrino. Since the scale of µ is much smaller than the scale of M N , the heavy neutrinos become the pseudo-Dirac particles.
We consider a flavor-diagonal m D and M N structure of µ, where there is no mixing between different flavors of heavy neutrinos. An explicit numerical fit is given in [19]. 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 N 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 h + j 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 W and Z bosons via its mixings into the SM neutrino, as where V N is the mixing between the SM neutrino and the SM gauge singlet RH heavy neutrino assuming |V N | 1. Here ν is the flavor eigenstate whereas ν m and N m are corresponding light heavy mass eigenstates respectively. For convenience in notation, from now on we also use N 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 where e denotes the three generations of the charged leptons, and P L = 1 2 (1 − γ 5 ) is the projection operator. Similarly, in terms of the mass eigenstates the neutral current interaction is written as where c w = cos θ w with θ w 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 |V N | 2 . However, the Yukawa coupling in Eq. 1 can also be directly measured from the decay mode of the Higgs boson such as h → N ν applying the For M N < M Z , the heavy neutrino can be produced from the Z-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 [18,20]. In [20][21][22], a scale dependent production cross section at the Leading Order (LO) and Next-to-Leading-Oder QCD (NLO QCD) of N ν at the LO and NLO have been studied at the 14 TeV LHC and 100 TeV hadron collider. The L3 collaboration [23] has performed a search on such heavy neutrinos directly from the LEP data and found a limit on B(Z → νN ) < 3 × 10 −5 at the 95% 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-e) and the red dashed line stands for the exclusion limits coming from µ (L3-µ). The corresponding exclusion limits on |V ( =e)N |at the 95% CL [24,25] have been drawn from the LEP2 data which have been denoted by the dark magenta line. In this analysis they searched for 80 GeV ≤ M N ≤ 205 GeV with a center of mass energy between 130 GeV to 208 GeV [25].
The DELPHI collaboration [26] had also performed the same search from the LEP-I data  [28] which has been depicted in Fig. 1 with a pink dot-dashed line.
The relevant existing upper limits at the 95% CL are also shown to compare with the experimental bounds using the LHC Higgs boson data in [32,33] using [34][35][36][37][38]. 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 |V N | 2 can be as low as 4.86 × 10 −4 while M N = 60 GeV and the bound becomes stronger at M N = 100 GeV as 3.73 × 10 −4 . When M N > 100 GeV, the bounds on  The CMS also studied the type-I seesaw model from the e ± e ± + jets and µ ± µ ± + jets final states in [42] at the 8 TeV LHC with a luminosity of 19.7 fb −1 with 30 GeV≤ M N ≤ 500 GeV. The limits from the CMS in the for µ is roughly comparable to the DELPHI result while M N < 70 GeV. The CMS limits are denoted by CMS8-e and CMS8-µ with the magenta dashed and solid lines respectively.
Using such limits, in [43] the prospective bounds on |V N | 2 at the 14 TeV LHC with 300 fb −1 (black, dott dashed line LHC14@300 fb −1 ) and 3000 fb −1 luminosities are given for the type-I seesaw case for 91.2 GeV ≤ M N ≤ 500 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 −1 (black, dotted line LHC14@3000 fb −1 ) and at that point the mixing angle could be probed down to 10 −5 . 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 [44] for the type-I seesaw case using two generations of the degenerate heavy neutrinos having masses around 100 GeV.
In [43] the prospective upper bounds on |V ( =e,µ)N | 2 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 −1 (dark purple, dashed line Trilep-14@300 fb −1 ) and 3000 where as a luminosity of 3000 fb −1 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 |V N | 4 . 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 [45]. It is shown that 95 GeV≤ M N ≤ 160 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 20 GeV ≤ M N ≤ 120 GeV where the heavy neutrino will be produced from the on-shell decay of the Higgs boson. Therefore we chose the Higgs The Higgs boson's SM decay width is taken as Γ SM h = 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 and it sums h → N ν and h → N ν cases. The branching fraction of the Higgs boson to the heavy neutrino is We focus on the signal channel of single Higgs boson production 3 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 pp → hj production cross-section at 13 TeV has been studied to the next-next-toleading order (NNLO) in [47,48], and we adopt the results wherein, with a jet transverse momentum, p j T > 100 GeV. Here we increase the leading p j T requirement to reduce the amount of background, as well as to distinguish the ISR jet from the jets from N 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 depending upon M N , the production cross section of the heavy neutrino is shown in Fig. 3 at 13 TeV LHC, for ISR jet p j T > 100 GeV. To calculate the prospective cross section in this channel, we consider the maximal mixing angles constraint from leptonic Higgs channel, as discussed in [32,33]. While the Higgs bound is most stringent in a large N mass range, at N mass between 100-110 GeV, the EWPD bound [28] becomes stronger. We use the stronger of the two constraints to produce an upper bound of |V lN | 2 , and the heavy neutrino production cross section for the h + j 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 |V N | 2 = 10 −5 will be nearly O(1) magnitude below the constraint obtained in [28,32,33] in the SF case 4 .
The heavy neutrino will then decay via the SM weak bosons such as W , Z (and h for heavier N ). When N is heavier, it can decay to on-shell W and Z bosons. These partial decay widths are given as, and 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, For N lighter than W and Z bosons, it decays into three-body channels through the virtual W and Z bosons. The corresponding partial decay widths are and these are comparable to [49] where G F = 1.166 × 10 −5 GeV −2 .
Note that the W channel will typically dominate both two-body and three-body N decay.
In our final state analysis, we require reconstruction of the W boson and N masses to veto SM backgrounds, thus the two-body decay N → W followed by W → jj, 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 p j T in pp → hj 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 p j T and become more visible.
The Higgs boson then can decay into an N − ν pair. We focus on the semileptonic N decay channel N → jj, in which all three daughter particles are visible. The two jets from N arises from the on-shell decay of a W boson, so that their invariant mass would reconstruct to M W . The lepton + dijet invariant mass would also reconstruct to M N . These two invariant mass window cuts greatly suppress SM backgrounds. N (M N = 100 GeV) decay jets are mostly represented by j 2 and j 3 . In these histograms, the signal events only assume selection cuts N j ≥ 3 and N ≥ 1.
As the ISR jet is often more energetic than those from N decays, the N decay jets are mostly the second and third in p j T ordering, as illustrated in Fig. 5. An M W peak is the most statistically pronounced between j 2 and j 3 among the three leading jets.
The after-cut cross-section is inferred from the pp → hj cross-section, decay branching ratios, and the selection efficiencies, as For the selection efficiency A eff , we consider the following cuts on the event final state: (1) leading jet p T >200 GeV; (2) Additional two or more jets with p T > 30 GeV and exactly one lepton with p T > 15 GeV; The selection cuts are designed to reconstruct the characteristic heavy neutrino mass as well as the physical W boson from N decay. The large leading jet p j T is important in suppressing weak boson + jets backgrounds. Vetoing a second lepton removes backgrounds with Z bosons. Here we focus on the hadronical W decay in order to reconstruct both the W boson and the N masses. These cuts greatly reduces SM backgrounds while retaining signal events at a much higher acceptance rate. Note that a fully leptonic decay of N can yield more leptons and suffer fewer SM background channels, but it also yields a neutrino and makes it impossible to reconstruct M N . In order to obtain the cut efficiencies, we perform a Monte Carlo simulation of pp → hj events with MadGraph5 [50] package and its the Pythia-PGS package for event showering and detector simulation. For basic detector setup, we require a jet pseudo-rapidity |η j | < 2.5, lepton pseudo-rapidity |η | < 2.4, minimal jet and lepton transverse momenta p j T and p T at 30 GeV and 15 GeV, respectively. Both of ATLAS and CMS handle large number of pile-up interactions using a technique in [46]. We simply use the PGS simulation without pile-up interactions, but jets are in a fiducial volume of tracking system of |η j | < 2.5 to remove pile-up interactions. Note that we also choose |η j | < 2.5 range to agree with [47] for cross-section scaling.
The cut efficiency for signals is shown in Fig. 6 over the range of M N . The cut-efficiency is at the level of 1-3% for a N mass between W and h masses. Lighter N has a reduced cut efficiency due to the requirement of M W reconstruction from j 2 j 3 . The prospective cross section is given in Fig. 7. The maximally allowed mixing angles from [28,32,33] are used.
For comparison, we also showed the after-cut cross-section for the 'benchmark' values of |V N | 2 . 13 TeV the LHC can probe |V N | 2 down to 10 −5 and a corresponding cross section can be readily tested at the future high luminosity LHC runs.    ground channels typically arise from the presence of a W boson, from either direct production or top quark decay, along with ISR jet(s). The significant background channels are listed in Tab. II that shows the efficiencies for the first three cuts, and Tab. III for the final M N window cut. For signal rates, we list a few N masses between Z and h masses. The mass dependence of A eff is shown in Fig. 6.
As shown in Tabs. II, III, the leading background channel is W +jets, while those with top quarks are efficiently controlled by the N mass-window cut. A large leading jet p T is the most effective cut against the W +jets channel, but it would also suppress the signal rate.
In the Monte-Carlo simulation for the W/Z+jets, we use an 'MLM' matched [51,52] crosssection for inclusive V + j, V + jj and V + jjj 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 N masses in Tab In the 'FD' case, the EWPD rules the common |V lN | 2 < 6.3 × 10 −4 for M N > 105 GeV, while the combined signal cross-section is enhanced by a factor of 2. The signal optimizes at M N = 105 GeV with a cross-section of 1.6 fb, and for 3000 fb −1 luminosity the S/ √ B + S = 5.0, comparable to the ν e SF case in signal significance.
A few additional cuts may be considered to help with background control. We note a central region b-jet veto will be effective to reduce the top quark backgrounds, once the W +jets events can be substantially reduced. A requirement of the transverse mass of the j 2 j 3 / E T system, M T ( j 2 j 3 / E T ) < M h may further reduce the W +jets background. The effectiveness of these cuts can be further investigated in high-statistics background studies.
As a note, in the ν τ mixing case the EWPD is less stringent compared to ν e,µ mixing cases, but the signal rate suffers from tau identification efficiency, as well as fractional τ 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 h → N ν branching ratio can be achieved within the current bounds on the N ν mixing.
We adopt the maximally allowed N ν mixing angle, the corresponding Higgs boson decay width, to derive a maximal signal rate for the pp → hj where the Higgs boson decays into the right-handed neutrino. We require a hard ISR jet to transversely boost the visibility of h, N decay products as well as for background suppression. For N identification, we require both W and N mass reconstruction from the jets and lepton-jet(s) systems in a 3j + 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 M N close to Higgs boson mass and a reduced efficiency for lighter N . For a few benchmark N masses 100-110 GeV, a maximal signal cross-section at ∼fb is obtained, compared to a total background at 0.3 pb from various W and t containing background channels. We note that transverse mass cuts may help further rejecting backgrounds. At optimal N masses, the signals in ν e 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 −1 luminosity. The ν µ SF case has less significance because of stronger EWPD constraints. For N much lighter than the Higgs boson, the signal is much less pronounced due to reduced decay branching and cut efficiencies.