Probing Doubly and Singly Charged Higgs at pp Collider HE-LHC

We analyse the signal sensitivity of multi-lepton final states at collider that can arise from doubly and singly charged Higgs decay in a type-II seesaw framework. We assume triplet vev to be very small and degenerate masses for both the charged Higgs states. The leptonic branching ratio of doubly and singly charged Higgs states have a large dependency on the neutrino oscillation parameters, lightest neutrino mass scale, as well as neutrino mass hierarchy. We explore this as well as the relation between the leptonic branching ratios of the singly and doubly charged Higgs states in detail. We evaluate the effect of these uncertainties on the production cross-section. Finally, we present a detailed analysis of multi-lepton final states for a future hadron collider HE-LHC, that can operate with center of mass energy √ s = 27 TeV. ∗ rojalin.p@iopb.res.in † debottam@iopb.res.in ‡ manimala@iopb.res.in § nayak@iopb.res.in 1 ar X iv :1 90 9. 10 49 5v 1 [ he pph ] 2 3 Se p 20 19


I. INTRODUCTION
The discovery of the Higgs boson at the Large Hadron Collider (LHC) has experimentally proven that fermions and gauge bosons masses in the Standard Model (SM) are generated via Brout-Englert-Higgs (BEH) mechanism. However, one of the key questions that still remains unexplained is the origin of light neutrino masses and mixings. A number of neutrino oscillation experiments have observed that, the solar and atmospheric neutrino mass splittings are ∆m 2 12 ∼ 10 −5 eV 2 and ∆m 2 13 ∼ 10 −3 eV 2 , and the mixing angles are θ 12 ∼ 32 • , θ 23 ∼ 45 • , and θ 13 ∼ 9 • [1]. A Dirac mass term of the SM neutrinos can be generated by extending the SM to include right-handed neutrinos. However, this requires very small Yukawa couplings, that introduces O(10 −11 ) order of magnitude hierarchy between SM fermion Yukawa couplings, and hence is unappealing. A different ansatz is that neutrinos are their own anti-particles and hence, their masses can have a different origin compared to the other SM fermions. One of such profound mechanisms is seesaw, where tiny eV masses of the Majorana neutrinos are generated from lepton number violating (LNV) d = 5 operator LLHH/Λ [2,3]. Being, a higher dimensional non-renormalizable operator, there can be different UV completed theories behind this operator, commonly known as, type-I, -II, and -III seesaw mechanisms. These models include extensions of the SM fermion/scalar contents by SM singlet fermions [4][5][6][7][8][9][10], SU (2) L triplet scalar boson [11][12][13][14], and SU (2) L triplet fermion [15], respectively.
Among the above, type-II seesaw model, where a triplet scalar field with the hypercharge Y = +2 is added to the SM, has an extended scalar sector. There are seven physical Higgs states that includes singly and doubly charged Higgs, CP even and odd neutral Higgs. The details of the Higgs spectra have been discussed in [16,17]. The neutral component of the triplet acquires a vacuum expectation value (vev) v ∆ , and generates neutrino masses through the Yukawa interactions. The same Yukawa interaction between the lepton doublet and the triplet scalar field also dictates the charged Higgs phenomenology in this model. The presence of a doubly charged Higgs (H ±± ) is the most appealing feature of this model, and, hence, a discovery of this exotic particle will be a smoking gun signature of type-II seesaw.
A number of searches have already been performed to search for the signatures of the doubly charged Higgs (see [18] for Tevatron, and [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] for LHC). Depending on the triplet vev, the doubly-charged Higgs boson can have distinct decay modes. For low vev v ∆ 10 −4 GeV, this can decay into same-sign di-lepton, whearas, for v ∆ ≥ 10 −4 GeV, this can decay to same-sign gauge bosons. For non-degenerate masses of doubly and singly charged Higgs, another possible decay is the cascade decay of a doubly charged Higgs to a singly charged Higgs and SM states. This has been explored in [19][20][21]. The CMS and ATLAS collaboration have searched for the same-sign di-lepton final states with different flavors, and constrained the mass of the doubly-charged Higgs as M H ±± > 820, 870 GeV at 95% C.L. [34,35]. An alternative search where the H ±± is produced in association with two jets, i.e., vector boson fusion gives relaxed constraints [36,37]. Another scenario where doubly-charged Higgs decays to same-sign W ± boson pairs. The collider signatures and the discovery prospects of this scenario have been discussed in [38][39][40], and [41,42].
ATLAS collaboration have searched for the same final state and constrained the doublycharged Higgs mass as M H ±± > 220 GeV at 95% C.L. [43]. Previous searches for H ±± in the pair-production channel and their subsequent decays into same-sign leptons at LEP-II has put a constraint M H ±± > 97. 3 GeV at 95% C.L. [44]. For discussions on Higgs triplet model at a linear collider, see [45][46][47][48][49] and at ep collider, see [50]. Displaced vertex signatures have been discussed in Ref. [33,51]. A review on this model is presented in [52].
While a number of searches at the LHC are ongoing to experimentally verify the presence of the doubly-charged Higgs boson, in this work we explore the impact of light neutrino mass hierarchy, neutrino oscillation parameters, as well as, the lightest neutrino mass scale m 0 on H ±± searches. We relate the branching ratios of doubly and singly charged Higgs decays for both normal and inverted mass hierarchy. We find that among the different leptonic modes, the decay mode of doubly charged Higgs into two same-sign electron, and the decay mode of a singly charged Higgs into an electron and neutrino are the least uncertain for inverted neutrino mass ordering, and has the potential to differentiate neutrino mass hierarchy. We also discuss how the inclusion of uncertainties in the neutrino oscillation parameters affect the theory cross-section, which may in turn change the mass limits of doubly charged Higgs in individual channel. As it is well known that for c.m.energy √ s = 13 (or 14) TeV LHC, production of multi-TeV H ±± will be difficult due to suppressed cross-section. However, increasing c.m.energy one can probe heavier H ±± . Therefore we consider pair-production and associated production of the doubly-charged Higgs boson and its subsequent decays into leptonic states, including tau's, and analyse the discovery prospects of doubly charged Higgs at a future hadron collider (HE-LHC), that can operate with center of mass energy √ s = 27 TeV. We consider both the tri and four lepton final states, and present a detail analysis taking into account different possible SM background processes. We find that in addition to the associated production, the pair-production of doubly charged Higgs also gives a significant contribution to the tri-lepton final states. We consider a wide range of doubly charged Higgs mass, and explore the sensitivity reach with the projected luminosity (15 ab −1 ) of HE-LHC [53,54].
Our paper is organized as follows: we briefly review the basics of the type-II seesaw model in Sec. II. In Sec. III, we discuss leptonic branching ratios of doubly-charged (H ±± ) and singly charged (H ± ) Higgs, and the relation between H ±± and H ± decays. In Sec. IV, we discuss the effect of uncertainties in neutrino oscillation parameters on the production cross-section. In Sec. V, we present the simulation of multilepton signal at √ s = 27 TeV LHC. Finally, we present our conclusions in Sec. VI.

II. MODEL DESCRIPTION
In this section, we briefly discuss type-II seesaw model [11][12][13][14]. The model is based on the gauge group as of the SM gauge group, Apart from the SM particles, the particle spectrum also contains one additional SU (2) L triplet scalar ∆ with hypercharge Y ∆ = +2: The SM Higgs doublet is represented as follows, After electroweak symmetry breaking, the real part of neutral Higgs φ 0 and δ 0 acquire vevs, denoted as v φ and v ∆ , respectively. The two vevs satisfy v 2 = v 2 φ +v 2 ∆ = (246 GeV) 2 . Below, we discuss different terms of the Lagrangian.
• The kinetic Lagrangian for the scalar sector is, The covariant derivatives in Eq. 3 are defined as, Both v φ and v ∆ contribute to the masses of weak gauge bosons at tree level. Therefore, the ρ -parameter (= Electroweak precision data [55] gives a tight constraint, ρ = 1.0006 ± 0.0009, which leads to an upper bound on v ∆ , i.e., v ∆ 3 GeV. Thus the two vevs satisfy v ∆ v φ .
• The Yukawa Lagrangian of this model is given by, Here, the first term in L Y (Φ, ∆) represents the Yukawa interactions of the SM Higgs doublet (Φ) and the second term is the needed Yukawa interaction of the triplet Higgs (∆), that generates neutrino mass. Y ν is Yukawa coupling matrix, C is the charge conjugation operator, and σ 2 is the Pauli matrix. L L is the left chiral lepton doublet. Once, the triplet Higgs (∆) acquires vacuum expectation value v ∆ , the second term in L Y (Φ, ∆) generates a Majorana mass for neutrino, which is given by, In the above M ν is a complex symmetric 3 × 3 matrix, which can be diagonalized by an unitary transformation defined as , is diagonal light neutrino mass matrix, and V PMNS is the neutrino mixing matrix parametrised by the three mixing angles (θ 12 , θ 13 , θ 23 ) and three phases (φ 1 , φ 2 , δ).
• The scalar potential [16] with the two Higgs fields Φ and ∆ is All operators in the above scalar potential are self conjugate except the operator containing µ. Therefore, all parameters except µ are real. Although µ can pick up a would-be CP phase, this phase is unphysical and can always be absorbed in a redefinition of the scalar fields. Together Y ν and the µ term violate lepton number symmetry in this model. Minimization of V(Φ, ∆) gives the following two conditions [16]: Thus the two mass parameters m 2 and M 2 can be eliminated which leaves 8 free 2 , reduces this set of free parameters down to seven.
There are ten real scalar degrees of freedom present in this model, out of which three are the would be Goldstone bosons, and they give masses to the SM weak gauge bosons after electroweak symmetry breaking. The remaining seven states are the physical Higgs bosons. Doubly charged scalars, ∆ ±± (≡ H ±± ) is purely triplet, and is already in mass eigenbasis. The singly charged scalars (φ ± , ∆ ± ) and neutral scalars (χ 0 , η 0 , φ 0 , δ 0 ) are not physical fields, as they share non-trivial mixings among them. We denote the mass eigenstates of the singly charged scalars by G ± and H ± , that are linear combinations of φ ± and ∆ ± . Similarly, the two CPodd physical fields are denoted by G 0 and A (linear combinations of χ 0 and η 0 ). The SM Higgs field (h) and a heavy Higgs (H) are massbasis of the two neutral CP-even states φ 0 and δ 0 . G ± and G 0 are the three Goldstone bosons. These scalar mixings are small, as they are proportional to the triplet vev (v ∆ ). The presence doubly charged Higgs (H ±± ) is the unique feature of this model. For detail discussion on mass of these scalars and doublet triplet mixing angles, see [16].
Assuming v ∆ v φ , the masses of the physical Higgs bosons are given by [16], We identify the h field as the neutral SM Higgs, with its mass denoted as M h . The mass of the SM Higgs is primarily governed by λ. The parameter M ∆ determines the mass scale of all other Higgs bosons. Mass square differences between the scalars are given by Note that, the quartic coupling λ 4 of the potential dictates the mass splitting between H ± − H ±± and H(A) − H ± . These two mass square differences are of similar order. Taking into account the electroweak precision data [56], the mass splitting of triplet Higgs is constrained as δM <40 GeV [20,57]. Therefore, the value of λ 4 defines three different mass spectrum of the triplet Higgs, The decay properties of charged Higgs states in different v ∆ region has been discussed extensively in the literature [19,58]. Partial decay widths of charged scalars to the leptons are proportional to the respective Yukawa couplings, and that to the gauge bosons are proportional to the triplet vev v ∆ . For v ∆ < 10 −4 GeV the dominant decay channel of the doubly-charged Higgs is H ±± → l ± i l ± j and singly-charged Higgs is H ± → l ± iν . On the other hand, for triplet vev v ∆ > 10 −4 GeV, the decay to gauge bosons H ±± → W ± W ± , H ± → W ± Z, W ± h, tb dominate. Note that, in the leptonic channel, the same Yukawa coupling governs both the doubly-charged and singly-charged Higgs decays. Therefore, the leptonic decays of these two Higgs states are related. Below, we discuss the different decay channels and the relation between H ±± and H ± decays in detail.
• H ±± Decays Partial decay width of H ±± to a pair of same-sign leptons is given by where δ ij is Kronecker's delta and Yukawa coupling Y ν ij = M ν ij / √ 2v ∆ . We consider v ∆ < 10 −4 GeV, and hence, H ±± predominantly decays to leptonic final states.
The decay branching ratio has the following form, where In Fig. 1, we plot the BR(H ±± → l ± i l ± j ) as a function of lightest neutrino mass m 0 for both normal (NH) and inverted (IH) mass hierarchy. Blue and red bands represent IH and NH, respectively. We consider 3σ range of neutrino mixing angles and mass square differences [1]. We also vary all phases in between 0 − 2π. Some notable points about these plots are as follows: 1. When m 0 > 0.1 eV, which represents the degenerate neutrino mass spectrum (m 1 = m 2 = m 3 = m), the maximum value of the branching ratio that the H ±± can have in each of the leptonic modes for both NH and IH are the same. As given in Sec.VIII (Appendix), for δ = φ 1 = φ 2 = 0 we have The other decay channels are absent in this case.
2. For m 0 < 0.1 eV, and for the modes e ± e ± , e ± µ ± , e ± τ ± , the maximum value of the branching ratio in IH is larger than that in NH. For µ ± µ ± , µ ± τ ± , τ ± τ ± mode, it is the reverse. This behaviour can be understood from Eq. 16, 17, 18, which are the ratios between maximum branching in IH and NH for a given decay channel in the hierarchical regime with m 0 ≈ 0. The exact equations are presented in Sec. VIII.
In the above, we consider the values of oscillation parameters, that maximize the numerator and denominator separately, as we are interested in the relative comparison of maximum branching ratios in NH and IH. The approximate expressions in the above equations clearly show that for IH neutrino mass spectrum, e ± e ± and e ± µ ± final states will be more favourable, as these channels can have large branching ratios. Although the final state e ± τ ± has large branching, however, further leptonic decays of τ ± will give suppression in cross-section.
3. There exist a large uncertainty in branching ratios, that somewhat reduces for the choice of CP phases to be zero. Among the different leptonic modes, H ±± → e ± e ± in IH is the most favourable mode for the entire range of m 0 , as this decay mode has a less uncertainty in branching ratio, and there is a definite predicted lower value of BR(H ±± → e ± e ± ). Irrespective of the value of lightest neutrino mass, and the variation of oscillation parameters, the discovery of H ±± will therefore be more favourable in this channel. An observation of H ±± in any other leptonic decay mode except e ± e ± mode with a branching ratio limit BR(H ±± → e ± e ± ) < 0.015 will indicate normal mass hierarchy in the light neutrino sector.
4. Note that, except H ±± → e ± e ± in IH, all other decay modes heavily depend on the oscillation parameters, and m 0 . Moreover, for those decays, there may exist a cancellation region, in which the branching ratio becomes highly suppressed. This occurs when different terms in the partial decay widths cancel out each other. This is to note that, for H ±± → e ± e ± in IH, such cancellation regions do not exist. As an example, the cancellation region for H ±± → e ± e ± in NH, that exists in between 10 −3 eV m 0 10 −2 eV can be explained as follows: For the choice m 1 = 10 −3 eV, the largest neutrino mass The branching ratio in IH, is instead significantly large for the above choice of parameters. For similar values of m 0 = m 3 = 10 −3 eV, φ 1 , φ 2 and δ as mention in case of NH, one obtains, 5. For NH scenario, H ±± → µ ± µ ± /µ ± τ ± /τ ± τ ± channels have least uncertainty for m 0 < 0.01 eV, and hence the discovery of H ±± into these above mentioned final states are more favourable for NH with m 0 < 0.01 eV. Due to further decay of τ ± into leptonic states, that involves smaller branching ratio, the overall cross-section in the channel with τ will be relatively smaller than the channel with µµ. Furthermore, a doubly charged Higgs can not be fully reconstructed with the channel involving leptons from τ , due to the presence of missing energy. Therefore, H ±± → µ ± µ ± decay mode will be more effective compare to other two H ±± → µ ± τ ± /τ ± τ ± .
As we will discuss in the next section, the variation of decay branching ratios of H ±± with oscillation parameters, as well as, the dependency on neutrino mass hierarchy have large effect on the theory cross-section of the four-lepton final states.
• H ± Decay H ± decays predominantly to a lepton and neutrino for v ∆ < 10 −4 GeV. The partial decay width of H ± to a lepton and neutrino is given by, In the above, , θ + is the singly charged Higgs mixing angle.
For v ∆ < 10 −4 GeV, branching ratio for the decay, H ± → l ± j ν i is given by In Fig. 2 as a function of lightest neutrino mass m 0 , where we consider 3σ variation of neutrino oscillation parameters, and variation of CP phases between 0 − 2π. Important points to be noticed are: 1. For Degenerate spectrum of neutrino mass (m 0 > 0.1 eV), all the three decay channels of H ± have same branching ratios i.e., BR(H ± → e ± ν) = BR(H ± → µ ± ν) = BR(H ± → τ ± ν) 0.33.
2. Note that, for m 0 < 0.1 eV and for IH, H ± → e ± ν has a large branching ratio (∼ 0.5). This decay channel is however, has a smaller branching for NH. In Sec. VIII (Appendix) this branching ratio has been calculated for m 0 ≈ 0.
Maximum possible value of BR(H ± → e ± ν) in IH compare to that in NH is given by, 3. Another important point to be noticed, is that, for H ± the uncertainty in branching ratio is less compare to that for H ±± . This occurs because the Yukawa couplings in case of H ± decay are independent of two Majorana phases φ 1 and φ 2 . This is evident from the equations given in Sec. VIII.
4. Among the three decay modes of H ± , H ± → e ± ν has less uncertainty in the branching ratio, as the respective Yukawa is independent of Dirac CP phase δ (see Sec. VIII). This branching ratio depends on m 0 , θ 12 , θ 13 . The other two branching ratios for the muon and tau decay modes depend on θ 23 and δ as well.
5. The uncertainty in branching ratios for H ± → µ ± ν and H ± → τ ± ν are nearly equal. This is clear from the top right and bottom plots of Fig. 2, where both the blue bands (in case of IH) have similar spread. This feature also exists in case of NH.
Assuming 100% branching ratios in leptonic decays, CMS and ATLAS searches have constrained H ±± below 820, 870 GeV. This is evident from the above discussion, that the branching ratio in any of the leptonic channels can not reach upto 100%.
In the next section, we re-evaluate the production cross-section of four-lepton final state, originating from pair-production of doubly charged Higgs, for different leptonic channels, taking into account the uncertainties of branching ratios. As an example, we consider the decay channels H ±± → e ± e ± /e ± µ ± /e ± τ ± in IH, as they offer largest values of branching ratios compared to NH. Note that, the maximum value of branching for the other three decay modes µ ± τ ± , µ ± µ ± and τ ± τ ± are relatively smaller in IH. We provide a sample benchmark point in Table. II, that shows e ± µ ± and e ± τ ± has large branching ratios in IH as compared to the other modes. This is to clarify that simultaneously the decay modes can not have maximum branching ratios. For the estimation in NH, we assume the decay modes H ±± → µ ± τ ± /µ ± µ ± /τ ± τ ± , as they offer relatively large branching ratios.
• Relating H ±± and H ± Decays The doubly charged Higgs H ±± as well as singly charged Higgs H ± interact with the leptons through the same Yukawa couplings, that determine light neutrino masses. Therefore, the branching ratios of H ±± into l ± l ± , and the branching ratio of H ± into l ± ν are related. in BR(H ±± → l ± i l ± j ) and BR(H ± → l ± i ν), respectively. In the upper left panel of Fig. 3, we show the variation of BR(H ±± → e ± e ± ) with the variation of BR(H ± → e ± ν), where we assume IH for neutrino mass ordering. It is clear that for m 0 = 1 eV, BR(H ± → e ± ν) is very well determined with negligible uncertainty. For other values of m 0 , there is a small variation in BR(H ± → e ± ν) for a given value of BR(H ±± → e ± e ± ) that occurs due to the variation of oscillation parameters. Upper right panel of Fig. 3 represents the variation of BR(H ± → e ± ν) with BR(H ±± → e ± µ ± ), again assuming IH as neutrino mass ordering. This also shows similar features as the previous plot. The plot in the lower panel in Fig. 3 shows large However, for smaller m 0 , the BR(H ±± → µ ± ν) has a large dependency. It is clear from Fig. 3 that, for m 0 ≥ 0.2 eV, irrespective of NH and IH, the branching ratio of BR(H ±± → l ± i ν) is very well predicted, for a given value of BR(H ±± → l ± i l ± j ), with l i = e, µ.
As we quantify in the next section, the uncertainty in branching ratios can have large impact on the theory cross-section. At pp collider both are the same. We consider a K-factor as 1.25 [59] for the left panel of Fig. 4. In our analysis we assume degenerate mass spectrum for the singly and doubly charged Higgs.  [34,35]. A degenerate mass spectrum for charged Higgses and BR(H ±± → l ± i l ± j )= 100% have been assumed in the analysis. The CMS analysis focussed on the tri-lepton and four-lepton final states originating from the leptonic decays of H ±± and H ± . ATLAS searches considered pair production of H ±± and their subsequent decay into e ± e ± , e ± µ ± , µ ± µ ± states. As a result of these searches, limits on M H ±± vary between 770 GeV and 870 GeV at 95% C.L. CMS collaboration studied both pair and associated production channels of H ±± and subsequent decay of H ±± and H ± to different leptonic states. Limits on M H ±± obtained from the combined study of both the channels vary between 535 to 820 GeV at 95% C.L, for 100% branching to each leptonic state. This limit vary between 396 to 712 GeV, if only the pair production channel is considered. The most stringent constraint M H ±± > 820 GeV has been given by assuming H ±± → e ± µ ± decay, and this takes into account both pair and associated productions.
The CMS analysis [35] has further considered few benchmark points, and has given limits on M H ±± . However, the PMNS mixing angle θ 13 has been assumed as zero, that is inconsistent with the present neutrino oscillation data. The above mentioned searches include pair and associated production of H ±± and only its leptonic decay modes, so the observed limit on M H ±± is valid only for low triplet vev v ∆ ≤ 10 −4 GeV, where the di-leptonic branching is maximum. As this is evident from the discussion presented in the previous section, the maximum possible branching in each channel can never be 100%, rather can be at most 73% (for H ±± → µ ± τ ± in NH). Instead of considering BR(H ±± → l ± i l ± j ) = 100%, we re-scale the theory cross-section with appropriate branching ratios. This somewhat weakens the individual bounds from different channels. For illustration, we focus on the final states with e ± e ± e ∓ e ∓ , e ± τ ± e ∓ τ ∓ and e ± µ ± e ∓ µ ∓ . Due to the absence of any cancellation region, the first channel is the least uncertain. We note that, apart from the dependency on neutrino oscillation parameter, the limit from individual channel also depends on the value of lightest neutrino mass m 0 .
FIG. 5: The blue (red) bands for IH (NH) correspond to the theory cross-section for the channel pp → H ++ H −− → l + i l + j l − k l − l obtained by including 3σ variation of neutrino oscillation parameters. Black line represents the observed limit from CMS analysis. The horizontal panels in row 1-3 represent m 0 = (0.0008, 0.02, 0.2 eV). In 1st, 2nd and 3rd columns we consider the decay of H ±± to e ± e ± , e ± µ ± and e ± τ ± , respectively.
In Fig. 5, we show the production cross-section of pp → H ++ H −− → e + e + e − e − , e + µ + e − µ − , and e + τ + e − τ − at LHC for √ s = 13 TeV. The coloured band represents the variation of cross-section due to 3σ uncertainty in neutrino oscillation parameters. As illustrative points, we choose three values of lightest neutrino masses m 0 = 0.0008, 0.02, 0.2 eV, that falls in hierarchical and quasi-degenerate mass regime. The blue (red) band corresponds to IH (NH) neutrino mass spectrum. The black line represents the observed limit from 13 TeV CMS analysis [35]. For a given value of the lightest neutrino mass m 0 , the upper boundary in these bands is determined from σ(pp → H ++ H −− ) folded with the square of maximum possible BR(H ±± → l ± i l ± j ). Similarly, the lower line represents the minimum value of BR(H ±± → l ± i l ± j ). Couple of points are in order: • The total cross-section has a large variation, specially for e + µ + e − µ − and e + τ + e − τ − channel. The e + e + e − e − channel in IH is the least uncertain, as this has a definite lower value of the cross-section.
• Due to relatively smaller branching ratio, the cross-section in NH for these modes are lower than the maximal possible cross section in IH.
• For large m 0 in the quasi-degenerate range, both the NH and IH cross-section overlaps.
• The drop in cross-section for e + µ + e − µ − and e + τ + e − τ − occurs, due to the cancellation between different terms in M ν 12 and M ν 13 .
Taking into account the branching ratios, the limit from each of the leptonic channels somewhat weakens, as compare to the analysis presented in [35]. However, the combined limit might be comparable to that analysis. For the above modes, IH can give the best constraint. The cross-section for NH is order of magnitude smaller in the hierarchical limit, and therefore, competitive limits can not be placed on M H ±± in the above channels, if light neutrinos follow NH. For quasi-degenerate spectrum m 0 0.1 eV, both NH and IH can place similar constraints. We tabulate the predicted value of maximum possible branching ratios in Table. I, where each entry represents the maximum possible value of BR(H ± → l ± i l ± j ) for a given value of m 0 . The value within the bracket denotes the best lower limit on M H ±± , from each channel. In CMS search combined limits have been presented which result from the combined analysis of both the pair and associated production channels. Also, for the benchmark studies, their analysis combined different leptonic modes. Such a study for the combined limit is beyond the scope of this paper.
It is evident from Fig. 4 that the production cross-section of H ±± at 13 TeV LHC becomes smaller for higher mass. Beyond 1.3 TeV mass, it is less than 10 −5 pb. As We also show the corresponding lower limit on M H ±± in bracket obtained from the channel Here l + i = e + /µ + /τ + ). We use [35] to derive the limits.
integrated luminosity have been assumed. Increase in sensitivity for higher mass range will be possible if c.m.energy is increased. Therefore, to study the discovery prospects of heavier H ±± and H ± , we consider higher center of mass energy, i.e., the HE-LHC setup with √ s = 27 TeV 1 .
In the next section we present the collider analysis for multilepton signatures of H ±± , where we assume BR(H ±± → e ± µ ± ) = 0.547, corresponding to m 0 =0.007 eV, and IH as neutrino mass ordering. The other branching ratios are given in Table. II. For completeness, in our analysis, we however consider all leptonic modes, with their corresponding branching ratios. Note that, other than the pair-production by DY, the photon fusion can also contribute to the pair-production of doubly charged Higgs. It has been pointed out in [52], that for 13 TeV, the channel contributes at most 10% to the pair-production of doubly charged Higgs states. However, there are different issues, regarding large uncertainties in PDFs. Therefore one needs to evaluate this channel carefully. We do not consider this channel in our present analysis.   [66]. Finally data analysis and ploting is done in ROOT(v6.14/04) [67]. We choose the degenerate mass spectrum for charged Higgses for which the most promising signals are 4 lepton and 3 lepton final states, arising from pair and associated production of doubly charged Higgs.

A. 4l Final State
This originates from the pair-production of H ++ and its subsequent decays H ±± → l ± l ± . Therefore, the signal is represented by the following chain, The τ in the final state, further decays into fully hadronic, or leptonic final states. For our analysis, we consider leptonic decays of τ , and therefore, collect all the event samples with e, µ in the final state. There are a number of SM processes that can mimic the signal, hence are considered as SM background. Here we list the following processes as dominant SM background: Among all these backgrounds, ZZ, ttZ, W ± W ∓ Z processes lead to irreducible backgrounds. However, a few other SM processes, such as, tt, ttj, ttjj, ttW, W ± Z, W ± Zj W Z + jets, ttW etc with their subsequent decays can also give rise to four-lepton final states, due to the misidentification of jets as leptons. Multi-lepton events (N l > 4) from pp → ZZZ → 6l (l = e, µ) can also mimic the signal due to detector inefficiency in lepton reconstruction, or if the lepton is too soft, and does not pass the selection cuts.
Additionally, one of the Z bosons in the above mentioned background can decay to two hadronic taus, that can also mimic the signal. As we will show below, most of the backgrounds are reduced significantly after imposing Z-veto, as well as, selecting a window on the l ± l ± invariant mass.
As the cross-section is gradually decreasing with increasing mass, it will be difficult to probe very heavy H ±± . Here we present a benchmark point with M H ±± = 1 TeV to show a detail cut-efficiency. We consider a triplet vev v ∆ as 10 −8 GeV. We re-iterate that, for the analysis, we consider IH neutrino mass ordering and the following set of oscillation parameters, for which H ±± → e ± µ ± is the most dominant decay channel with a branching ratio 0.547: This set of parameters is assumed because it puts the strongest limit on M H ±± , as evident from We apply the following set of basic cuts on transverse momentum, pseudo-rapidity, and separation between two leptons, p T (l) > 10 GeV (l = e or µ), |η(l)| < 2.5, ∆R ll > 0.4, e ± e ± e ± µ ± e ± τ ± µ ± τ ± µ ± µ ± τ ± τ ± BR 0.026 0.547 0.365 0.001 0.001 0.053  shows the distribution of same-sign di-lepton invariant mass M (l ± l ± ). Here the signal distribution peaks at M H ±± , which is very clear and well separated from backgrounds.
Such a distinguished peak of M H ±± at a high value of M (l ± l ± ) distribution helps to discover H ±± . In the lower panel of Fig. 6, we show the distribution of opposite sign dilepton invariant mass, which shows that most of the dominant backgrounds peak around Z boson mass. Therefore, a veto on opposite sign di-lepton invariant mass around M Z will reduce most of the backgrounds involving Z.
The above distributions motivate to consider the following set of selection cuts that suppress backgrounds: we demand 4 isolated leptons in the final state. The leptons are e, µ.
• A 2 : We demand sum of charges of four leptons to be zero.
• In Table. III, we show the changes in signal and background cross-sections after each selection cut.
• c 4 : c 3 and |M (l ± l ± ) − M H ±± | 50. From and background cross-sections for √ s = 27 TeV after the different selection cuts for the channel. Here l + i = e + /µ + . significant extent. Invariant mass window on same-sign di-lepton finally help to suppress almost all background events.
Note that, although we present the pp → ZZ → 4l background in Table. III, we also estimate pp → 4l, that includes virtual photon contribution. The channel pp → l + i l + j l − k l − l has cross-section 117.1 fb. We find a cross-section 2.8 fb after applying cut c 3 . However after cut c 4 , the cross-section becomes negligibly small. This is expected, as we choose a very large value of same-sign di-lepton invariant mass, for which this background already falls off. In addition, we also checked ttW, ttj, ttjj backgrounds, which after cut c 4 gives insignificant contributions. Although the SM background cross-section is much higher than that of signal before applying cut c 1 , the backgrounds become insignificant after applying selection cuts. We find that, with 1000 fb −1 luminosity, 19 events can be obtained for M H ±± = 1 TeV. We give the variation of number of events versus mass of doubly charged Higgs in Fig. 8.

B. 3l FINAL STATE
Here we consider the signal containing tri-lepton (two same-sign lepton and other of opposite sign) and missing transverse energy / E T in the final state. Associated production of H ±± with H ± and their subsequent leptonic decay dominantly contribute to the desired signal events. However pair production of H ±± also contribute to the same when atleast one hadronically decaying tau lepton is present in the decay products of H ±± . Therefore, the signal events we are analysing originate from the following decay chains: We consider the following dominant SM backgrounds: To suppress the backgrounds, we consider the following selection criteria: • A 1 : Number of leptons N l = 3. We demand exactly 3 isolated leptons in the final state. • A 4 : The transverse momentum of leading lepton, p T (l 1 ) ≥ 150 GeV. We implement a 150 GeV cut on p T of leading lepton, as SM background events contain soft lepton compare to that of signal events.
• A 5 : The missing transverse energy, / E T > 100 GeV. We collect events with / E T > 120 GeV.
In Table IV, we show signal and background cross-sections after applying each of the selection cuts.
• c 5 : c 4 and / E T ≥ 120 GeV. Finally, we calculate the statistical significance for the tri-lepton channel: In the above, s and b are the number of signal and background events after all of the above mentioned selection cuts. The required luminosity (L) to achieve a desired significance (S) therefore scales as pp → ℓ + ℓℓ + ν + h.c. pp → ℓ + ℓℓ + ν + h.c.  pp → ℓ + ℓℓ + ν + h.c. where σ s and σ b are the signal and background cross-sections after all the cuts. We obtain, a doubly charged Higgs with M H ±± = 1 TeV can be probed with more than 5σ significance for 1000 fb −1 luminosity. For the four-lepton final states, and for tri-lepton channel in higher mass range, there is no SM background. This happens due to the very high invariant mass cut of the same-sign di-lepton. Therefore, for these cases, we simply scale the required luminosity as where N is the number of signal events, and σ s is the cross-section after all cuts. The two plots in the middle panel show the required luminosity to observe tri-lepton states for the M H ±± in between 820-2500 GeV. In the left plot, we impose a flat 100 GeV window of invariant mass l ± l ± around M H ±± . The orange and red lines have been obtained by using

VI. CONCLUSION
We analyse discovery prospect of a doubly charged Higgs -a particle content of type-II seesaw model in pp collider (HE-LHC). We focus on the region of small triplet vev, where the doubly and singly charged Higgs naturally decays to same-sign di-leptons and a charged lepton and neutrino final states, respectively. We analyse in detail multi-lepton signature, containing tri and tetra-leptons in the final states. The model signature in this low vev regime strongly depends on the neutrino oscillation parameters, neutrino mass hierarchy, and the lightest neutrino mass scale. We perform a robust estimation of the maximal possible branching ratios, that each of the leptonic modes can accommodate.
The constraint on doubly charged Higgs mass from individual leptonic channel somewhat weakens, after taking into account correct branching ratios. The doubly charged Higgs and singly charged Higgs couple to the leptons through the same Yukawa coupling. We explore the relation between the branching ratios of singly and doubly charged Higgs decays. Our major findings are, • The branching of doubly charged Higgs into same-sign leptons is augmented with large variation due to the uncertainty of neutrino oscillation parameters. We find that in IH neutrino mass spectrum, and among all the leptonic decay modes of H ±± , e ± e ± mode is least uncertain for the entire range of lightest neutrino mass m 0 . This decay mode predicts a lower value of branching ratio, which is BR(H ±± → e ± e ± ) > 0.015. Therefore, observation of doubly charged Higgs in any other leptonic decay mode except e ± e ± with an upper limit on branching ratio BR(H ±± → e ± e ± ) < 0.015 will rule out IH. The singly charged Higgs decay to H ± → e ± ν is the least uncertain among all charged Higgs decays, with a predicted branching ratio, that vary between ∼ 33% − 50% for the variation of the lightest neutrino mass m 0 ∼ 10 −4 eV − 1 eV.
• In IH, for a fixed m 0 , and for a fixed BR(H ±± → e ± e ± ), the branching ratio of singly charged Higgs BR(H ± → e ± ν) is very well predicted. The uncertainty becomes negligible for higher value of the lightest neutrino mass scale m 0 ∼ 0.2 eV, or higher. Similar result also exists between BR(H ±± → e ± µ ± ) in IH.
• We perform a detailed analysis to find out discovery prospect of tri and tetra-lepton final states at a future pp collider, that can operate with c.m.energy √ s = 27 TeV.
We consider both the pair and associated productions, and a benchmark point of H ±± with a mass 1 TeV. In tetra-lepton final state, we find using 1000 fb −1 integrated luminosity, 19 events can be observed. In tri-lepton final state, we find that the same mass can be discovered at 27 TeV LHC with a significance of more than 5σ for 1000 fb −1 luminosity. Higher mass region of H ±± can be probed with more luminosity. We find that sensitivity reach for H ±± in tri-lepton channel is more compared to that in four-lepton channel, as both the pair and associated production of H ±± contribute to the former. H ±± upto mass ∼ 2.2 TeV can be probed in tri-lepton channel with 15ab −1 integrated luminosity. In four-lepton channel, five events can be observed for M H ±± 1.7 TeV with the same luminosity.

VIII. APPENDIX
Here we expand neutrino mass matrix in terms of the PMNS mixing angles, CP phases, and the mass square differences [19]. We first consider the H ±± decay and then H ± decay.
• H ±± Decays The branching ratio has the following form The Yukawa and neutrino mass matrix are related as Neutrino mass matrix elements can be written as a function of light neutrino masses and mixing parameters in the following forms (Here c ij ≡ cosθ ij and s ij ≡ sinθ ij ): branching ratio in ee, µµ and τ τ occurs for the CP phases to be zero δ = φ 1 = φ 2 = 0 gives M ν ij = mδ ij . The branching ratio is BR (H ±± → e ± e ± ) = BR (H ±± → µ ± µ ± ) = BR (H ±± → τ ± τ ± ) ≈ m 2 0 3m 2 0 ≈ 0.33. Note that, the branching ratios for all other decay modes are zero. For δ, φ 1 , φ 2 different from zero, the off-diagonal elements can be non-zero.
• H ± Decays The coupling through which H ± interact with charged lepton and neutrino is Y + = cos θ + m ν d V † -X 1 = c 2 13 m 2 gives BR (H ± → e ± ν) = c 2 13 2 ≈ 0.49. Since there is only θ 13 dependency in X 1 , and θ 13 is very well measured, therefore H ± → e ± ν decay modes has very less uncertainty.