Probing the Type-II Seesaw Mechanism Through the Production of Higgs Bosons at a Lepton Collider

PHYSICAL REVIEW D 98, 015024 (2018)

Probing the type-II seesaw mechanism through the production of Higgs bosons at a lepton collider

† ‡ ∥ Pankaj Agrawal,1,2,* Manimala Mitra,1,2, Saurabh Niyogi,3, Sujay Shil,1,2,§ and Michael Spannowsky4, 1Institute of Physics, Sachivalaya Marg, Bhubaneswar, Odisha 751005, India 2Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India 3Gokhale Memorial Girls’ College, Harish Mukherjee Road, Kolkata 700020, India 4Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, United Kingdom

(Received 23 March 2018; published 16 July 2018)

We investigate the production and decays of doubly-chargedp Higgsffiffiffi bosons for the Type-II seesaw mechanism at an eþe− collider with two center of mass energies, s ¼ 380 GeV and 3 TeV, and analyze the fully hadronic final states in detail. Lower mass ranges can be probed during the 380 GeV run of the collider, while highpffiffiffi mass ranges, which are beyond the 13 TeV Large Hadron Collider discovery reach, can be probed with s ¼ 3 TeV. For such a heavy Higgs boson, the final decay products are collimated, resulting in fat-jets. We perform a substructure analysis to reduce the background and find that a doubly- charged Higgs boson in the mass range 800–1120 GeV can be discovered during the 3 TeV run, with integrated luminosity L ∼ 95 fb−1 of data. For 380 GeV center of mass energy, we find that for the doubly- charged Higgs boson in the range 160–172 GeV, a 5σ significance can be achieved with only integrated luminosity L ∼ 24 fb−1. Therefore, a light Higgs boson can be discovered immediately during the run of a future eþe− collider.

DOI: 10.1103/PhysRevD.98.015024

I. INTRODUCTION number violating (LNV) d ¼ 5 operator LLHH=Λ [1,2]. Such operator is not forbidden as the lepton number is only With the discovery of the Higgs boson at the Large a classical symmetry of the SM, violated by quantum Hadron Collider (LHC), we start to develop an under- effects. standing of how the standard model (SM) fermion and There are three proposed categories, commonly known gauge boson masses are generated in terms of the Brout- as, Type-I, -II, and -III seesaw mechanisms in which the Englert-Higgs (BEH) mechanism. However, one of the SM is extended by a SUð2Þ singlet fermion [3–9], main puzzles that still remains unclear is the origin of light L SUð2Þ triplet scalar boson [10–13],andSUð2Þ triplet neutrino masses and mixings. The same BEH mechanism L L fermion [14], respectively. In particular, the second can, in principle be employed to generate Dirac mass of SM possibility, i.e., where a triplet scalar field with the neutrinos by extending the SM to include right-handed hypercharge Y ¼þ2 is added to the SM, is the simplest neutrinos. However, the required large hierarchy of the model with an extended Higgs sector. The neutral com- Yukawa couplings raises uncomfortable questions. A ponent of the triplet acquires a vacuum expectation value completely different ansatz is that neutrinos are their (vev) vΔ, and generates neutrino masses through the own antiparticles and hence, their masses have a different Yukawa interactions. Perhaps, the most appealing feature origin than the other SM fermions. A tiny eV Majorana neutrino mass can be generated by the seesaw mechanism, of this model is its minimality. The same Yukawa where light neutrinos acquire their masses from a lepton interaction between the lepton doublet and the triplet scalar field generates Majorana masses for the neutrinos, and also dictates the phenomenology of the charged Higgs *[email protected] † bosons. [email protected] ‡ [email protected] A number of detailed studies have already been §[email protected] performed for the Hadron colliders like, Tevatron [15] ∥ [email protected] and LHC [15–29] to search for the triplet Higgs scenario. One attractive feature of this model is the presence of the Published by the American Physical Society under the terms of doubly-charged Higgs boson, and its distinguishing decay the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to modes. Depending on the triplet vev, the doubly-charged the author(s) and the published article’s title, journal citation, Higgs boson can decay into same-sign dilepton, same- and DOI. Funded by SCOAP3. sign gauge bosons, or even via a cascade decay [16–18].

2470-0010=2018=98(1)=015024(13) 015024-1 Published by the American Physical Society AGRAWAL, MITRA, NIYOGI, SHIL, and SPANNOWSKY PHYS. REV. D 98, 015024 (2018)

The details of the Higgs spectrum have been discussed in CLIC with 95 fb−1 of data. For lower masses, the range [30–32]. For the branching ratios and collider signatures, 160–172 GeV can be covered with only L ∼ 24 fb−1 of see [16–20]. The CMS and ATLAS collaborations have luminosity. For the earlier discussions on Higgs triplet searched for the same-sign dilepton final states for all model at a linear collider, see [49–52]. For the other SM flavors, and constrained the mass of the doubly-charged and BSM searches at CLIC and other linear colliders, see 820 Higgs as MH > , 870 GeV at 95% C.L. [33,34]. [47,53–67] for Higgs physics and effective field theory, However, this is only relevant for a very tiny vev [68–72] for different BSM scenarios, and [73–80] for −4 vΔ < 10 GeV, where the doubly-charged Higgs boson seesaw and radiative neutrino mass model searches. For decays into the same-sign dilepton with 100% branching the discussion on probing dark-sector at eþe− collider, ratio. For larger triplet vev such as vΔ ≳ 0.01 GeV, this see [81,82]. branching ratio is negligibly small. Therefore, a direct Our paper is organized as follows: we briefly review the bound on the mass of the H from the same-sign basics of the Type-II seesaw model in Sec. II. In Sec. III,we dileptonic final state cannot be obtained. An alternative discuss existing experimental constraints. In the subsequent search where the H is produced in association with two subsections, Secs. IVA and IV B, we analyze in detail the jets (vector boson fusion channel) gives relaxed con- production cross-sections and the discovery potential of the −4 þ − straints [35,36].ForvΔ ≥ 10 GeV, the doubly-charged multi-jet final states at the e e collider. Finally, we present Higgs boson predominantly decays into same-sign dibo- our conclusions in Sec. V. son. The collider signatures and the discovery prospect of this scenario have been discussed in [37–39],and[40,41] II. MODEL DESCRIPTION (see [42] for the discussion on the composite Higgs model In addition to the SM Higgs field Φ, the type-II seesaw and [43] for discussion on flavor violating τ decays). model [10–13] contains an additional SUð2Þ triplet Higgs Previous searches for H in the pair-production channel L field and their subsequent decays into same-sign leptons 97 3 þ ! at LEP-II has put a constraint MH > . GeV at Δpffiffi Δþþ 95% C.L. [44]. Δ ¼ 2 ∼ ð1 3 2Þ ð Þ þ ; ; : 2:1 While a number of searches at the LHC are ongoing to Δ0 − Δpffiffi 2 experimentally verify the presence of the doubly-charged Higgs boson, in this work we perform a detailed collider We denote the neutral components of the SM doublet analysis to explore the discovery prospects at a future and triplet Higgs fields as Φ0 ¼ p1ffiffi ðϕ0 þ iχ0Þ and Δ0 ¼ lepton collider. For a large mass of the doubly-charged 2 p1ffiffi ðδ0 þ η0Þ ϕ0 δ0 Higgs boson, the pair-production cross-section at the LHC 2 i , respectively. The real scalars and 2 2 2 becomes small. Furthermore, the presence of numerous acquire vevs denoted as vΦ and vΔ with v ¼ vΦ þ vΔ ¼ backgrounds weakens its discovery prospects. Therefore, a ð246 GeVÞ2. The light neutrino mass is proportional to the lepton collider with a much cleaner environment will be triplet vev vΔ. The new scalar field Δ, being a triplet under more suitable to search the high mass regime of the doubly- SUð2Þ, interacts with the SM gauge bosons. The relevant charged Higgs boson. In addition, we also exhaust the low kinetic term has the form mass regime, yet unconstrained by the LHC, and by LEP-II L ðΔÞ¼ ½ð ΔÞ†ð μΔÞ ð Þ measurements. kin Tr Dμ D ; 2:2 We consider the pair-production of the doubly-charged g a a Higgs boson at a lepton collider and its subsequent decays with the covariant derivative DμΔ ¼ ∂μΔ þ i 2 ½τ Wμ; Δþ 0 into same-sign gauge bosons. We focus on the hadronic ig BμΔ. The Yukawa interactions of Δ with the lepton decays of the produced gauge bosons and analyze the fields are multijet final states in detail. As a prototype example, we consider the future eþe− collider Compact Linear Collider L ðΦ ΔÞ¼ c τ Δ þ ð Þ Y ; YΔLLi 2 LL H:c: 2:3 (CLIC) [45pffiffiffi–48], that will operate with the center of mass energies s ¼ 380 GeV, 1.4 and 3 TeV. We first analyze In the above, YΔ is a 3 × 3 matrix and c denotes charge the discovery reach of the doubly-charged Higgs boson at conjugation. The triplet field Δ carries lepton number þ2 380 GeV center of mass energy. Subsequently, we carry out and hence the Yukawa term conserves lepton number. The a detailed simulation for the very heavy doubly-charged scalar potential of the Higgs fields Φ and Δ is Higgs boson with a mass around and beyond one TeV. For 2 † ˜ 2 † T † such a heavy Higgs, its final decay products are collimated, VðΦ;ΔÞ¼mΦΦ Φ þ MΔTrðΔ ΔÞþðμΦ iτ2Δ Φ þ H:c:Þ leading to fat-jets. We perform a jet-substructure analysis λ þ ðΦ†ΦÞ2 þ λ ðΦ†ΦÞ ðΔ†ΔÞþλ ½ ðΔ†ΔÞ2 and tag the gauge bosons. We find that a heavy Higgs boson 4 1 Tr 2 Tr with a mass up to 1120 GeV can be most optimally þ λ ½ðΔ†ΔÞ2þλ Φ†ΔΔ†Φ ð Þ discovered with 5σ significance at the 3 TeV run of 3Tr 4 ; 2:4

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˜ where mΦ and MΔ are real parameters with mass dimension The other Lagrangian parameters are chosen as—λ1 ¼ þþ 1, μ is the lepton-number violating parameter with positive λ2 ¼ λ3 ¼ λ4 ¼ 1.0, λ ¼ 0.52. To change the H mass we mass dimension and λ, λ1−4 are dimensionless quartic vary μ. Here we vary μ from 0.105 to 0.15 for 380 GeV Higgs couplings. center of mass energy and from 1.56 to 4.65 for 3 TeV There are seven physical Higgs states in mass basis, that center of mass energy. arise after diagonalization of the scalar mass matrix written Due to the nontrivial representations of Δ, the Higgs in the gauge basis. They are: the charged Higgs bosons triplet has interactions with a number of SM fermions and H, H, the neutral Higgs bosons h0, H0 and A0. The two gauge bosons. This opens up a number of possible decay charged scalar fields Φ of Φ and Δ of Δ mix to give modes that can be explored at the LHC, and at future linear singly-charged states H and the charged Goldstone χ colliders. In the next section, we summarize the different bosons. Similarly, the mixing between the two CP-odd direct experimental constraints on the doubly-charged fields (χ0 and η0) gives rise to A0, and the neutral Goldstone Higgs boson mass and triplet vev. boson ρ0. Finally, we obtain the SM Higgs boson (h) and a heavy Higgs boson (H) via the mixing of the two neutral III. DECAY MODES AND EXPERIMENTAL CP-even states Φ0 and δ0. CONSTRAINTS The physical masses of the doubly and singly charged Higgs bosons H and H can be written as The most characteristic feature of the type II seesaw model is the presence of the doubly-charged Higgs boson 2 2 2 λ4 2 H , that can decay into the leptonic or bosonic states m þþ ¼ M − v λ3 − v ; H Δ Δ 2 Φ and gives unique signatures at high energy colliders. The λ 2 2 different decay modes and the branching ratios of the H 2 ¼ 2 − 4 2 1 þ vΔ ð Þ mHþ MΔ vΦ 2 : 2:5 depend on the triplet vev vΔ. For smaller triplet vev, the 4 vΦ H predominantly decays into the same-sign leptonic → The CP-even and CP-odd neutral Higgs bosons h, and H states H l l , whereas for larger vΔ, the gauge boson → have the physical masses mode H W W becomes dominant [16,17]. The relevant decay widths are calculated to 2 2 2 2 2 2 m ¼ T cos α þ T sin α − T sin 2α; 2 h 11 22 12 Mν MH ij 2 2 2 2 2 2 ΓðH → l l Þ¼Γ ¼ ; ¼ T α þ T α þ T 2α ð Þ i j lilj mH 11sin 22cos 12 sin : 2:6 ð1 þ δijÞ8π vΔ

Mν ¼ YΔvΔ; ð3:1Þ In the above T 11, T 22 and T 12 have the following expressions: ΓðH → WWÞ 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 vΦλ 2 2 T ¼ g vΔ 4 2 11 ; ¼ Γ ¼ 1 − ½ð2 þð 2 − 1Þ Þ 2 W W 2 rW= : 8πM r 2 2 2 H W T 22 ¼ MΔ þ 2vΔðλ2 þ λ3Þ; ð3:2Þ 2 2vΔ 2 T 12 ¼ − MΔ þ vΦvΔðλ1 þ λ4Þ: ð2:7Þ vΦ In the above Mν denotes the neutrino mass matrix, i, j are 0 the generation indices, Γ and Γ are the partial decay The CP-odd Higgs field A has the mass term lilj W W widths for the H → ll, and H → WW channels, i j 2 2 2 2 4vΔ 2 vΦμ respectively. The parameter rW denotes the ratio of H m ¼ M 1 þ ; with M ¼ pffiffiffi : ð2:8Þ M A Δ v2 Δ 2 and the W gauge boson masses, r ¼ H . The branching Φ vΔ W MW fraction of the leptonic and bosonic mode becomes equal −4 The difference between H and H masses is dictated around the triplet vev vΔ ∼ 10 GeV [16,17]. by the coupling λ4 of the scalar potential. For a positive λ4, A number of searches have been proposed at the LHC to the H is lighter than H. The mass difference ΔM2 is discover H using multilepton signatures. The searched modes in [16–18,40] are pair and associated production 2 2 2 λ4 2 2 ΔM ¼ M − M ∼ v þ Oðv Þ: ð2:9Þ with the H decaying into leptonic or gauge boson states. H H 2 Φ Δ Below we discuss the existing constraints on H from Throughout our analysis, we consider the mass hierarchy LEP and LHC searches. ¼ 0 1 MH

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leptons have been performed at LEP-II. This con- that is still experimentally allowed, and (b) a very heavy 97 3 strains the mass parameter MH > . GeV [44] highly boosted H . at 95% C.L. (ii) Constraints from pair and associated production: IV. LARGE TRIPLET VEV AND COLLIDER Stringent constraint on the MH by analyzing SIGNATURES H → ll have been placed at the 13 TeV In this section, we analyze the collider signatures of a LHC. The CMS collaboration looked for different þ − leptonic flavors including ee, eμ, eτ, μμ, μτ and ττ. doubly-charged Higgs boson at an e e collider and In addition, the CMS searches also include the explore the sensitivity reach to probe low and high mass ∓ regimes. Throughout our analysis, we consider a large associated production pp → H H and the sub- −4 triplet vev vΔ ≥ 10 GeV, where the present experimen- sequent decays, H → l ν. This combined channel tal constraints are weak. As the prototype example, we of pair-production and associated production gives consider CLIC [45–48] that will operate with three the stringent constraint M > 820 GeV [34] at pffiffiffi H different center of mass energies s ¼ 380, 1400 GeV 95% C.L for e, μ flavor. The constraint from and 3 TeV. We present our simulation for 380 GeV and ATLAS searches comes from pair-production. 3 TeV center of mass energies. The doubly-charged Higgs The bound is M > 870 GeV at 95% C.L H boson, H, can be produced at eþe− collider via photon [33]. Note that these limits are valid only for a −4 and Z-boson mediated diagrams, as shown in Fig. 1.We small triplet vev vΔ < 10 GeV. show in Fig. 2 the respective production cross sections. As (iii) Constraint from VBF: For larger values of the triplet −4 both of the diagrams are s-channel processes, the cross vev vΔ ≥ 10 GeV, the leptonic branching ratio → section reduces with increasing center-of-mass energy.pffiffiffi becomes smaller. Instead the decay mode H ¼ For a relatively small center-of-mass energy s W W is dominant. Therefore the searches in vector 380 GeV, the maximum cross section reaches up to σ ∼ boson fusion (VBF) become more important. A 506 fb for M ¼ 102 GeV. A rapid decline in the cross → → H search for pp jjH jjW W at the 8 TeV ∼ 190 section occurs near MH GeV, close to kinemati- LHC in the VBF channel sets a constraint on the cal threshold. For the choice of large vΔ, the produced ∼ 25 ∼ 300 triplet vev vΔ GeV for MH GeV [35]. particles H will decay into W W gauge bosons with This constraint has been updated [36] using 13 TeV almost 100% branching ratio. In the following, we will data at the LHC. firstp discussffiffiffi the low-mass regime, that can be probed in Note that, for extremely small vΔ, the mass of the the s ¼ 380 GeV run. Following that we discuss the doubly-charged Higgs boson is very tightly constrained high-mass regime, that can be explored at 3 TeV center from pair-production searches. For a larger triplet vev, of mass energy and gives rise to specific signatures of this constraint significantly relaxes. The VBF cross- boosted Higgs boson. In both cases we focus on multijet section scales quadratically with the triplet vev and final states. hence, increases for a very large vev. However, the −4 −1 range of vΔ ∼ 10 –10 GeV cannot be probed at the 13 TeV LHC in VBF channel, as the cross-section becomes extremely small in this range. Recently, in [41], the authors have looked for pair-production of H in large vΔ region and analyzed the signature where the final state contains dilepton, multijet, and ≲ 190 missing energy. The lighter mass MH GeV can be probed at the 14 TeV LHC with 3000 fb−1 of data. In [39], the authors have used LHC 8 TeV run-I result of ≥ 84 same-sign dilepton to derive a bound MH GeV, relevant for large vΔ. For large mass of the doubly- charged Higgs, the LHC cross section however becomes significantly smaller, as shown in Fig. 2. On the other hand, the fall in the cross-section at a eþe− collider is relatively smaller. This motivates us to explore the signatures of doubly-charged Higgs at a lepton collider, where the cross-section still remains larger for heavy charged Higgs masses. In the following sections, we explore the scope of a future linear collider to probe FIG. 1. The Feynman diagram for HþþH−− pair-production large vΔ region with (a) a very low mass range of H , and its subsequent decays into gauge bosons.

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we demand a high jet multiplicity, i.e., the number of jets ≥ 7 Njet . For the signal, the production processes are þ − ∓∓ → → 4 ≥ 7 ≳ 2 (i) e e H H W j for MH MW þ − ∓∓ ∓ → → ≥ 7 (ii) e e H H W jjW jj j for MH < 2MW In the former scenario the H decays predominantly into on-shell WW, while in the latter case H decays into one on-shell and one off-shell gauge bosons with subsequent decays into jets. To simulate the events, we use first FEYNRULES [83] and generate the model file via Universal Feynrules Output (UFO) [84,85]. We compute the hard processes with the package MADGRAPH5_AMC@NLO [86], and pass the output (in LHE format) through PYTHIA 6 [87] for shower- ing and hadronization. The detector simulation has been taken into account by DELPHES-3.3.0 [88], where we use the þ − ILD card. Here we use anti-k jet clustering algorithm [89] FIG. 2. The production cross-sectionpffiffiffi at e e collider. The t center of mass energies are s ¼ 380 GeV and 3 TeV. For to form jets. Similar final states will be generated from a comparison, we also show the cross section at 13 TeV LHC. The number of SM processes. We consider the following sets of pair-production cross section increases by a factor of two, if CLIC backgrounds and perform a detailed simulation: uses 80%, and 30% beam polarization for electron and positron (i) eþe− → tt¯ → 6j beam. (ii) eþe− → WþW− þ 3j, W → 2j, and eþe− → ZZþ 3j, Z → 2j pffiffi (iii) eþe− → 7j H s GeV þ − þ − A. Low mass at = 380 (iv) e e → W þ 5j, W → jj, and e e → Zþ We consider the pair-production of H, and its 5j, Z → jj pffiffiffi þ − subsequent decay into WW at s ¼ 380 GeV. The Among the backgrounds, e e → 7j includes diagrams α2 α5 produced W decay dominantly into hadronic final states. of coupling order EW S with quarks and gluons as Thus, to retain as much signal rate as possible, we focus intermediate particles. As listed above, we treat the tt¯ on fully hadronic channel. Therefore, our model signature and gauge boson mediated backgrounds separately. For comprises of multijet events. In the subsequent analysis, the partonic event generation, we implement the following

TABLE I. The cross sections for the signal and background for the fully hadronic final states, arising from þ − → ∓∓ σ σ e e H H . p refers to the partonic cross section. d is the cross section after taking intopffiffiffi account detector effects. The last column represents the cross section with b-veto. The center-of-mass energy is s ¼ 380 GeV and kinematic cuts are specified in the text.

þ − þþ −− e e → H H → Nj ≥ 7j

Mass (GeV) σp (fb) σdðNj ≥ 7jÞ (fb) σdðNj ≥ 7j þ b vetoÞ (fb) 121 0.80 0.30 0.20 137 2.08 0.94 0.66 159 5.45 2.58 1.82 172 5.04 2.48 1.74 184 1.11 0.53 0.38

Backgrounds −2 −2 −2 Processes σp (fb) ×10 σdðNj ≥ 7jÞ (fb) ×10 σdðNj ≥ 7j þ bvetoÞ (fb) ×10 eþe− → tt¯ → 6j 10341.0 338.0 36.0 WþW−3j, W → 2j 8.89 1.18 0.88 ZZ þ 3j, Z → 2j 0.98 0.13 0.10 7j 30.32 1.13 0.88 W þ 5j, W → jj 30.18 4.64 3.54 Z þ 5j, Z → jj 18.32 2.15 1.61

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−1 sets of cuts at MADGRAPH level both for the signal TABLE II. The statistical significance ns for L ¼ 100 fb . The and backgrounds: the transverse momentum of light jets third column displays the required luminositypffiffiffi to achieve 5σ ¼ 380 pTðjiÞ > 20 GeV for all the final state partons, the significance. The center-of-mass energy is s GeV. pseudorapidity jηj < 5.0, and the separation between the þ − þþ −− e e → H H → Nj ≥ 7j light jets ΔRðji;jjÞ > 0.4. Lð −1Þ We consider few illustrative mass points between Mass (GeV) ns fb ∼ 121 ∼ MH GeV and the kinematic threshold MH 121 1.54 1054.14 184 GeV, and display the signal cross sections in Table I. 137 4.47 125.11 The cross sections σp refers to the partonic cross section, 159 10.48 22.76 172 10.16 24.21 while σd is after taking into account reconstruction and detector effects. In addition to the cuts at the partonic 184 2.65 355.99 level, we further implement few more selection cuts: the ð Þ 20 transverse momentum of jets pT ji > GeV for all the ð Þ L ¼ 100 −1 jηj 4 5 TABLE III. The statistical significance ns b for fb jets, pseudo-rapidity < . for jets, and the number of and the required luminosity to achieve 5σ significance, after jets N ≥ 7j. The largest background arises from tt¯ → 6j, j pimplementingffiffiffi the b-veto. The center of mass energy is where the cross section is about 103 fb at the partonic s ¼ 380 GeV. level. This is much larger than the largest signal cross þ − → þþ −− → ≥ 7 þ ¼ 159 e e H H Nj j bveto section 5.45 fb, corresponding to MH GeV. For −1 other mass points, the ratio is even bigger. However, Mass (GeV) nsðbÞ Lðfb Þ demanding high jet multiplicity N ≥ 7j reduces this j 121 2.52 393.67 σ ∼ 3 background to d fb. For the masses of the doubly- 137 6.32 62.59 ¼ 159 charged Higgs boson MH and 172 GeV, the 159 12.13 16.99 signal and background cross sections become almost 172 11.81 17.92 equal after demanding higher jet multiplicity. A few 184 4.22 140.38 comments are in order: (i) Between the higher and lower mass ranges, i.e., and 184 GeV, all other mass points have a large discovery 2 2 MH > MW and MH < MW, the former sce- 125 −1 nario corresponds to larger pair-production cross prospect with fb of data. In particular, we show that sections. The fall in cross section in the higher mass the doubly-charged Higgs boson with intermediate masses of 159 GeV (172 GeV) can be discovered with 5σ range occurs when M ∼ 184 H GeV, where it L ∼ 22ð24Þ −1 approaches the kinematic threshold. For lower mass significance with only fb , respectively. From Table III, we can see that it further improves to L ∼ ranges, M ∼ 121 GeV, the reduction of cross- H 16ð17Þ −1 – section after the detector effect occurs due to fb after applying a b-veto (50 60% efficiency and stronger kinematic cuts. The produced jets from a 1% miss-tag efficiency), that helps in reducing the dom- ∼ 121 inant top-quark pair background. H with mass MH GeV are often quite soft. With the constraint on jet transverse momentum pffiffi B. Boosted heavy H at s =3 TeV pT > 20 GeV the reconstruction efficiency becomes ∼ smaller. We now consider heavy H with a mass MH (ii) The signal comprises of hadronic final states with 1 TeV and its decay into like-sign WW gauge bosons. higher jet multiplicity. For the signal, H decays The produced W decays into hadronic as well as leptonic into two W with subsequent decay into quarks, states. As before, we focus on the purely hadronic final þ − resulting in a final state with Nj ¼ 8.Atae e states, which has the largest branching ratio. For such collider, there are only a few SM processes that can heavy H, each of the produced W boson will have generate a similar final state. A full reconstruction of large transverse momentum. For a 1.1 TeV H, their the signal results in a fairly low reconstruction transverse momentum peaks around pT ∼ 1 TeV, and most efficiency. Thus, we allow for one jet to be too soft of the W are produced in the central region. We show the or out of the kinematic cuts range. transverse momentum, and the pseudo-rapidity distribution ¼ In Tablepffiffiffiffi pIIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, we derive the statistical significance ns of H in Fig. 3, for the illustrative benchmark points σ ð Þ L σ ð Þþσ ð Þ ¼ 800 d S = d S d B for our benchmark points MH GeV, 1120 GeV and 1.4 TeV. corresponding to Table I. Here σdðSÞ and σdðBÞ represent The final decay products of such heavy Higgs bosons are the final cross-sections for the signal and background after highly collimated, and can be reconstructed as fat-jets, see all the selection cuts. Additionally, we also show the Fig. 4. Therefore, our model signature for such high mass required luminosity to achieve a 5σ significance. Other H is þ − ∓∓ ∓ ∓ ¼ 121 → → → 4 − than the extreme low and high mass ranges MH (i) e e H H W W W W fat jet.

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FIG. 3. The normalized distribution of the transverse momentum and the pseudorapidity for the produced H.

WþW−Zjj and tt¯, with subsequent decays of W boson and the top quark into jets. The partonic cross sections of the signal and backgrounds are shown in Table IV. The cross-sections for WþW−Zjj and tt¯ are small compared to other backgrounds. Therefore, we do not include these backgrounds in our final analysis. Below we discuss in detail the preselection and selection cuts for the signal and backgrounds: (i) Most of the signal events are in the central region η ∼ 0 with pseudorapidity distributed around H ,as can be seen in Fig. 3. Additionally, the signal jets have a very high HT(scalar sum of transverse momentum of all final state particles), as shown

þþ −− in Fig. 6. We consider no cuts on the signal at the FIG. 4. The Feynman diagram for H H pair-production parton level. While generating the backgrounds, we and its subsequent decays to 4 fat-jet. consider the following partonic cuts for 4j—the transverse momentum of the jets pT > 60 GeV, To generate signal and backgrounds we use the same and the jet-jet separation ΔRðj; jÞ > 0.6; for þ − þ tool-chain as in Sec. IVA except the use of DELPHES. Here W W 2jðW > 2jÞ and W 3jðW > 2jÞ- pT > we analyze the output of PYTHIA8 [90] (in HEPMC [91] 60 GeV for the leading 4-jets, the transverse mo- format)and recluster fat-jets using Cambridge-Achen algo- mentum pT > 20 GeV for the remaining jets, and rithm [92] in FASTJET-3.0.0 [93] with radius parameter the jet-jet separation ΔRðj; jÞ > 0.4. The HT and R ¼ 1.0. In Fig. 5, we show the transverse momentum pseudo-rapidity cut is the same for all the back- 1000 jηj 2 5 ¯ of the leading fat-jet j1 and the 4th leading fat-jet j4. grounds, HT > GeV and < . .Fortt A number of backgrounds can lead to the final states samples we have put ΔRðb; jÞ > 0.4 separation with multiple fat-jets. These are: 4j (includes both the QED cut and transverse momentum cut on leading two þ − þ − 60 0 and QCD contributions), W W 2j, and W =W 3j, light jet as pT > . GeV. Additionally, we also

¼ 1120 FIG. 5. The pT distribution of the leading and 4th leading fat-jets. For signal, we consider MH GeV.

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TABLE IV. The cut-flow for the signal and backgrounds. The cross sections are in fb. σp refers to the partonic cross section. In the backgrounds the decays of the W boson and top quark to jets are included. Here MD refers to mass-drop. See text for details. þ − → þþ −− → þ þ − − → e e H H W W W W Njfat σ 4 120 Masses (GeV) p (ab) jfat (> GeV) 4 MD 1 tagged 2 tagged 3-tagged 4-tagged 800 1250 812.9 758.0 757.9 748.9 671.8 389.0 1000 850.6 527.0 492.5 492.3 486.1 436.6 258.9 1120 670.0 380.0 358.4 358.3 354.2 321.9 193.1 1350 167.1 80.4 75.54 75.52 74.88 68.2 42.0 1400 94.36 45.54 42.85 42.84 42.42 38.6 24.0

Backgrounds

Processes σp (ab) 4j (>120 GeV) 4 MD 1 tagged 2 tag ged 3-tagged 4-tagged 4j 6900.0 1310.0 895.0 360.0 68.0 5.5 0.0 Wþ3j & W−3j 1900.0 320.0 220.0 166.0 44.0 4.8 1.52 × 10−1 WþW−2j 190.0 25.6 17.7 15.6 8.3 1.23 5.7 × 10−2 WþW−Zjj 4.23 ……………… tt¯ 42 ………………

−− demand pT of the bottom quarks more than 60 GeV other coming from another H . This leads to and the pT of the remaining light quarks more smaller number of 4 fatjet events. From 2nd column than 20 GeV. and 3rd column in Table IV, this is evident that after þ þ þ − (ii) The ΔR separation of the produced W W , W W demanding four fatjet with pT > 120 GeV the drop are shown in Fig. 7. It is evident that for relatively in the cross section is larger for higher masses as lower masses of H, such as 800 GeV, the Wþ and compare to that of the lower masses. Wþ are closer, as compared to 1400 GeV. This (iii) The model signature contains four fat-jet with high occurs as the H with 800 GeV mass is more momentum. We show in Fig. 5,thetransverse boosted than the higher mass H. Hence, the momentum of leading and 4th leading fat-jet for ¼ 1120 produced W W are more collimated. For the MH GeV. Additionally, we also show the separation between Wþ and W− this is opposite, distributions of the backgrounds. It is evident that i.e., for higher Hþþ mass, the Wþ and W− separa- most of the jets have larger transverse momentum ≫ 100 tion is smaller as compared to the lower mass. When for signal, with pT GeV. Therefore, we the mass of Hþþ is large, the momentum of Hþþ is design our selection cuts as (a) the number of þþ fat-jets Nj ¼ 4,(b)pT > 120 GeV for all the relatively low. Therefore, the decay products of H fat jfat are less collimated. Therefore in this scenario, there fat-jets. is a chance for overlap between jets from two (iv) We further carry out substructure analysis for the W-bosons—one of them coming from Hþþ and fat-jets. To reconstruct the W bosons we use the

¼ 800 FIG. 6. The HT distribution of the jets at the partonic level. We consider three illustrative benchmark points MH , 1120, and 1400 GeV.

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FIG. 7. The ΔRWW distribution of the different W , produced from the doubly charge Higgs H . The W’s in this figure are pT ordered.

FIG. 8. The invariant mass of the fat-jet(leading and 4th leading) constructed using subjets four momentum. For signal, we consider ¼ 1120 MH GeV.

mass-drop tagger [94] of which compares the a fat-jet. A detailed cut-flow chart is given in energy-sharings of subjets to indicate if the fat-jet Table IV. If at least one fat-jet passes the invariant was initiated by a W boson or a parton. For the signal mass selection cut, we have 1-tagged event; if at and background, we show the invariant mass of the least two fat-jet pass the cut, we have 2-tagged event two subjets inside the fat-jet in Fig. 8. For the signal, and so on. the subjets inside a fatjet are generated from the W. From Table IV, the effect of the substructure analysis is Therefore, the distribution peaks around the W mass. clearly evident. The largest background arises from the For the different backgrounds, 4j gives flat distri- eþe− → 4j events. At the partonic level we find a cross þ − þ bution, while W W 2j and W 3j shows smaller section of σpð4jÞ ∼ 6.9 fb ≫ σpðsignalÞ. The higher trans- peak around MW. As shown in Table IV, the back- verse momentum cut on jet pT reduces the signal nomi- grounds are significantly reduced after applying the nally, and the background by more than Oð5Þ for 4j, WW2j j − j ≤ 20 selection cut MJ1J2 MW GeV. Here, MJ1J2 and W þ 3j. Demanding that 4 fat-jets have a nontrivial is the invariant mass of the subjets J1 and J2 inside substructure (referred to as mass-drop MD in Table IV)

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−1 TABLE V. The statistical significance ns for L ¼ 500 fb and We consider two mass regimes, (a) light H with mass 5σ the requiredpffiffiffi luminosity to achieve significance. The c.m.e- M ≲ 180 GeV, and (b) a very heavy H with mass ¼ 3 H nergy is s TeV. In the 2nd column, to derive significance, M ∼ 800–1400 GeV. We consider fully hadronic – H we consider 2 tagged events for 800 1120 GeV mass range and 3 decays of the produced W’s and perform a detailed analysis tagged events for the higher mass range. Here 2-tag implies two for the multi-jet final states. or more than two fat-jet masses are within the window of – W For the 380 GeV center of mass energy, we look into 60 100 GeV, and the fat-jets are tagged as jets. Similar ≥ 7 criteria applies for 3-tagged jets. multijet final states with Nj j. We find that a doubly- ∼ 160–172 charged Higgs boson with mass MH GeV can þ − → þþ −− → þ þ − − → þ − e e H H W W W W Njfat be discovered in the immediate run of the e e collider, −1 L ∼ 24 −1 Masses ns (2,3-tagged Lðfb Þ (with with only integrated luminosity fb . This improves (GeV) L ¼ 500 fb−1) 2,3-tagged) considerably once we apply a b-veto, reducing the tt¯ σ ∼ Oð0 1Þ 800 17.96(2-tag) 38.75 background to . fb. ≥ 1 Thepffiffiffi higher mass range MH TeV can be probed in 1000 13.95(2-tag) 64.23 þ − 1120 11.49(2-tag) 94.68 the s ¼ 3 TeV run of the e e collider. Note that, for 1350 5.40(3-tag) 428.66 such high masses of H the pair-production cross section 1400 3.85(3-tag) 843.31 at 13 TeV LHC is significantly smaller. Therefore, an eþe− collider with large center of mass energy is more suitable to probe the high mass range. For such heavy mass, the reduces the background even more. Finally, with the produced W s are boosted and their subsequent decay invariant mass cut for the subjets, all backgrounds become products will be collimated, resulting in fat-jets. A number almost negligible. For the H masses between 800 GeV of SM processes, including 4j, W 3j, W W 2j can mimic to 1.1 TeV one can achieve a S=B ∼ Oð10Þ. We show the the signal. To reduce backgrounds, we carry out a jet- required luminosity to achieve a discovery in Table V. The – substructure analysis with W-tagging. We find that for the 800 1120 GeV doubly-charged Higgs boson can be dis- – 39–95 −1 800 1120 GeV mass range, a minimum of two tagged covered with fb of data with at least 2 fat-jet jets can effectively reduce the total backgrounds to a level tagged as W-bosons. However, for higher masses, such as of σ ∼ Oð0.1Þ fb, whereas the signal cross section is 1.4 TeV a minimum 3 tagged jets will be required. σ ∼ Oð0.3–0.7Þ fb. For higher masses, three tagged jets are needed. A doubly-charged Higgs boson with mass V. DISCUSSION AND CONCLUSIONS between 800–1120 GeV can be discovered with L ≲ −1 95 ∼ The Type-II seesaw model consists of an extension of the fb of data. For even higher masses, such as MH scalar sector by a Higgs triplet field Δ with hypercharge 1400 GeV, a discovery will require much higher integrated Y ¼þ2. The neutral component of the triplet acquires a luminosities. vev and generates the light neutrino mass. One of the most Thus, a future high-energy eþe− collider can provide an attractive features of this model is the presence of the outstanding opportunity to probe weakly-coupled heavy doubly-charged Higgs boson H . Depending on the particles, which are beyond the reach of the LHC. triplet vev, H can decay into a number of final states, including same-sign leptons, same sign gauge bosons, and ACKNOWLEDGMENTS via cascade decay to three body final states. For the lower triplet vev where H → ll decays are predominant, M. M. acknowledges the support of the DST-INSPIRE the doubly-charged Higgs boson mass is tightly constrained research Grant No. IFA14-PH-99. M. M. also thanks to the ‘ ’ by LHC pair and associated production searches, MH > workshop Physics at CLIC , held at CERN, Geneva, 820, 870 GeV. However, the higher triplet vev region is where part of the work has been carried out. S. S. acknowl- poorly constrained by the VBF searches. Moreover, the edges the funding assistance provided by Royal Society LHC search is limited in the very high mass region International Exchange program and the hospitality of the ∼ 1 MH TeV, where the cross section is tiny. Institute for Particle Physics Phenomenology (IPPP) at þ − In this work, we consider an e epffiffifficollider operating Durham University where part of the work has been carried with two center-of-mass energies s ¼ 380 GeV and out. We also acknowledge the use of SAMKHYA, the −2 3 TeV, and probe the large vΔ region vΔ ≥ 10 GeV. Institute of physics high performance computing facility.

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