Left-right symmetry and the charged Higgs bosons at the LHC

The charged Higgs boson sector of the Minimal Manifest Left-Right Symmetric model (MLRSM) is investigated in the context of LHC discovery search for new physics beyond Standard Model. We discuss and summarise the main processes within MLRSM where heavy charged Higgs bosons can be produced at the LHC. We explore the scenarios where the amplified signals due to relatively light charged scalars dominate against heavy neutral Z2 and charged gauge W2 as well as heavy neutral Higgs bosons signals which are dumped due to large vacuum expectation value vR of the right-handed scalar triplet. Consistency with FCNC effects implies masses of two neutral Higgs bosons \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ A_1^0,H_1^0 $\end{document} to be at least of 10 TeV order, which in turn implies that in MLRSM only three of four charged Higgs bosons, namely \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ H_{1,2}^{{\pm \pm }} $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ H_1^{\pm } $\end{document},and can be simultaneously light. In particular, production processes with one and two doubly charged Higgs bosons are considered. We further incorporate the decays of those scalars leading to multi lepton signals at the LHC. Branching ratios for heavy neutrino NR, W2 and Z2 decay into charged Higgs bosons are calculated. These effects are substantial enough and cannot be neglected. The tri- and four-lepton final states for different benchmark points are analysed. Kinematic cuts are chosen in order to strength the leptonic signals and decrease the Standard Model (SM) background. The results are presented using di-lepton invariant mass and lepton-lepton separation distributions for the same sign (SSDL) and opposite sign (OSDL) di-leptons as well as the charge asymmetry are also discussed. We have found that for considered MLRSM processes tri-lepton and four-lepton signals are most important for their detection when compared to the SM background. Both of the signals can be detected at 14 TeV collisions at the LHC with integrated luminosity at the level of 300 fb−1 with doubly charged Higgs bosons up to approximately 600 GeV. Finally, possible extra contribution of the charged MLRSM scalar particles to the measured Higgs to di-photon (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ H_0^0 $\end{document} → γγ) decay is computed and pointed out.


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Abstract: The charged Higgs boson sector of the Minimal Manifest Left-Right Symmetric model (MLRSM) is investigated in the context of LHC discovery search for new physics beyond Standard Model. We discuss and summarise the main processes within MLRSM where heavy charged Higgs bosons can be produced at the LHC. We explore the scenarios where the amplified signals due to relatively light charged scalars dominate against heavy neutral Z 2 and charged gauge W 2 as well as heavy neutral Higgs bosons signals which are dumped due to large vacuum expectation value v R of the right-handed scalar triplet. Consistency with FCNC effects implies masses of two neutral Higgs bosons A 0 1 , H 0 1 to be at least of 10 TeV order, which in turn implies that in MLRSM only three of four charged Higgs bosons, namely H ±± 1,2 and H ± 1 , can be simultaneously light. In particular, production processes with one and two doubly charged Higgs bosons are considered. We further incorporate the decays of those scalars leading to multi lepton signals at the LHC. Branching ratios for heavy neutrino N R , W 2 and Z 2 decay into charged Higgs bosons are calculated. These effects are substantial enough and cannot be neglected. The tri-and four-lepton final states for different benchmark points are analysed. Kinematic cuts are chosen in order to strength the leptonic signals and decrease the Standard Model (SM) background. The results are presented using di-lepton invariant mass and lepton-lepton separation distributions for the same sign (SSDL) and opposite sign (OSDL) di-leptons as well as the charge asymmetry are also discussed. We have found that for considered MLRSM processes tri-lepton and four-lepton signals are most important for their detection when compared to the SM background. Both of the signals can be detected at 14 TeV collisions at the LHC with integrated luminosity at the level of 300 fb −1 with doubly charged Higgs bosons up to approximately 600 GeV. Finally, possible extra contribution of the charged MLRSM scalar particles to the measured Higgs to di-photon (H 0 0 → γγ) decay is computed and pointed out.

Introduction
The LHC machine is working incredibly well shifting up the discovery limits for all the non-standard masses. For the same reason it is also true for the non-standard couplings and their possible values are shrinking more and more. Good examples are parameters connected with Left-Right (LR) symmetric models. These models enjoy richness of several types of beyond-the-SM particles [1,2]. No wonder that these models are interesting for theoretical and phenomenological studies, for some recent works see [3][4][5][6][7][8][9] and explored also by the LHC collaborations.
The searches at CMS and ATLAS have tightened up the limits on the masses of heavy gauge bosons. Let us mention that before the LHC era the fits to low energy charged and neutral currents were quite modest, e.g. for a charged gauge boson PDG reports M W 2 > 715 GeV [10,11]. The new LHC analysis pushed the limits already much above 2 TeV [12][13][14][15][16][17][18]. All these searches provide robust bounds on the extra gauge bosons, for JHEP05(2014)033 instance, the present limit for a charged heavy boson coming from the "golden" decay chain W R → l 1 N l → l 1 l 2 jj is [17,18] M W 2 ≥ 2.8 TeV.
(1. 1) This limit (at 95% C.L.) is for a genuine left-right symmetric model which we consider here (MLRSM) with g L = g R and three degenerate generations of heavy neutrinos and it is based on √ s = 8 TeV data. Typically, also limits for Z 2 mass are already beyond 2 TeV.
The combined LEP lower limit on the singly charged Higgs boson mass is about 90 GeV [19]. At the LHC, established limits for singly charged Higgs boson masses are M H ± = 80 ÷ 160 GeV, (1.2) if BR(t → H + b) < 5% [20] and for higher masses than 160 GeV, see the limits in [21]. For doubly charged Higgs bosons the analysis gives lower mass limits in a range M H ±± ≥ 445 GeV (409 GeV) for CMS (ATLAS), (1.3) in the 100% branching fraction scenarios [22,23]. The mass limit for heavy neutrinos is [24,25] M N R > 780 GeV, (1.4) but it must be kept in mind that bounds on M N R and M W 2 are not independent from each other [17,18]. Neutrinoless double beta decay allows for heavy neutrinos with relatively light masses, see e.g. [26][27][28][29][30][31][32]. Detailed studies which take into account potential signals with √ s = 14 TeV at the LHC conclude that heavy gauge bosons and neutrinos can be found with up to 4 and 1 TeV, respectively, for typical LR scenarios [3,4]. Such a relatively low (TeV) scale of the heavy sector is theoretically possible, even if GUT gauge unification is demanded, for a discussion, see e.g. [33,34]. In this paper we consider Left-Right symmetric model based on the SU(2) L ⊗SU(2) R ⊗ U(1) B−L gauge group [1] in its most restricted form, so-called Minimal Left-Right Symmetric Model (MLRSM). We choose to explore the most popular version of the model with Higgs representations -a bi-doublet Φ and two (left and right) triplets ∆ L,R [35,36]. We also assume that the vacuum expectation value of the left-handed triplet ∆ L vanishes, ∆ L = 0 and the CP symmetry can be violated by complex phases in the quark and lepton mixing matrices. Left and right gauge couplings are chosen to be equal, g L = g R . For reasons discussed in [37] and more extensively in [38], we discuss see-saw diagonal light-heavy neutrino mixings. It means that W 1 couples mainly to light neutrinos, while W 2 couples to the heavy ones. Z 1 and Z 2 turn out to couple to both of them [36,39]. W L − W R mixing is allowed and is very small, ξ ≤ 0.05 [10], the most stringent data comes from astrophysics through the supernova explosion analysis [40]. In our last paper we considered low energy constraints on such a model assuming κ 2 = 0, i.e., ξ = 0 [7], we do the same here. Moreover, in MLRSM tan 2ξ = − 2κ 1 κ 2 v 2 R , which is really negligible for v R ≥ 5 TeV, as dictated by eq. (1.1), where κ 1 , κ 2 (v R ) are the vacuum expectation values of Φ(∆ R ).

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We think that it is worth to show how the situation looks like if we stick to the popular and to a large extent conservative version of the model (MLRSM), giving candlelike benchmark numbers for possible signals at the LHC. We should also be aware of the fact, that there are relations between model parameters in the Higgs, gauge and neutrino sectors [7,11,36,41] and it needs further detailed studies. For estimation and discussion of observables which are able to measure final signals in the most efficient way, calculation of dominant tree level signals is sufficient at the moment. Production processes are calculated and relevant diagrams are singled out using CalcHEP [42]. For general analysis, multi lepton codes ALPGEN [43], PYTHIA [44], Madgraph [45] are used. Feynman rules are generated with our version of the package using FeynRules [46,47]. The backgrounds for multi lepton signals (3 and 4 leptons) are estimated using ALPGEN-PYTHIA.
In this paper we have grabbed the impact of the relatively light charged scalars in the phenomenology of Left-Right symmetric model. We first discuss how the decay branching ratios of W 2 , Z 2 , and N R are affected by the presence of these light charged scalars. Then we note down the possible interesting processes within MLRSM. We study the production and decay modes of the charged scalars. We have provided some benchmark points where we have performed our simulations to make a realistic estimation of the signal events over the SM backgrounds. Our study is based on the reconstruction of the invariant masses of the final state leptons and their mutual separations from where we have shown how we can track the presence of doubly charged scalars. We also note down the impact of the charged scalars in the Higgs to di-photon decay rates. Then we conclude and give an outlook.

MLRSM processes with charged Higgs boson particles at the LHC
There are already severe limits on the heavy gauge boson masses, eq. (1.1), which infer that scale in which the right SU(2) gauge sector is broken at v R > 5 TeV (for approximate relations between gauge boson masses and v R , see for example eq. (2.4) in [7]). This is already an interesting situation as for such heavy gauge bosons most of the effects connected with them decouple in physical processes at collider physics. Then there is a potential room to go deeper and estimate more sensitive Higgs boson contributions. Of course, the effects coming from the scalar sector depend crucially also on their masses. Smaller the Higgs boson masses, larger effects are expected. The question is then: how small their masses can be by keeping the right scale v R large? In the paper we assume light charged scalar masses up to 600 GeV, this choice of masses will be justified when production cross sections are considered.
The point is that all Higgs scalars are naturally of the order of v R , in addition, neutral Higgs boson scalars A 0 1 and H 0 1 contribute to FCNC effects (see the appendix) and must be large, above 10 TeV (see however [48] for alternative solutions). Let us see then if theoretically charged Higgs bosons can have masses below 1 TeV. In the model which we consider in this paper we assume that the Higgs potential is given as in [35,36], we will also use the same notation, for details on the parametrisation of the Higgs scalar mass spectrum, see the appendix. This model includes a number of parameters: µ 1 , µ 2 , µ 3 , ρ 1 , ρ 2 , ρ 3 , ρ 4 , α 1 , α 2 , α 3 , α 4 , λ 1 , λ 2 , λ 3 , λ 4 . The exact Higgs mass spectrum is calculated numerically. Minimisation conditions are used to get values of dimensionful mass parameters µ 1 , µ 2 and µ 3 which can be arbitrarily large, all other parameters are considered as free, but limited to the perturbative bound, 1 |ρ i |, |α i |, |λ i | < 10. It is assumed that the lightest neutral Higgs particle is the boson discovered by ATLAS and CMS collaborations. We have taken its mass to lie in the range 124.7 GeV < M H 0 0 < 126.2 GeV. (2.1) An example set of generated mass spectra of Higgs bosons for v R = 8 TeV is presented in figure 1 (left figure). Mass spectra have been obtained by varying uniformly the Higgs potential parameters in a range (−10, 10). We have also taken into account the bounds on neutral Higgs bosons obtained from FCNC constrains assuming m A 0 1 , m H 0 1 > 15 TeV by fixing α 3 = 7.1 (see appendix A). The spectra which did not fulfill relation (2.1) were rejected. Altogether we have 6 neutral, 2 singly charged and 2 doubly charged Higgs boson particles in the MLRSM. The figure includes possible spectra of singly and doubly charged as well as neutral Higgs bosons. Some of them can be degenerated or nearly degenerated.
This study shows that although the Higgs particles naturally tend to have masses of the order of the v R scale, it is still possible to choose the potential parameters such that some of the scalar particles can have masses much below 1 TeV (spectrum 15). To discuss spectra more quantitatively, the cumulative distribution function P of the lowest masses of singly and doubly charged and next to lightest neutral scalar particles are plotted on right figure 1, again for the same conditions as before and v R = 8 TeV. These results show that for v R = 8 TeV a fraction of the parameter space that gives lightest scalar masses below 1 TeV is at the level of 4%. It means that it is possible to generate the low mass spectra of Higgs boson masses in MLRSM keeping large v R scale. However, what can not be seen Table 1. Phenomenologically interesting MLRSM processes at the LHC with primarily produced charged scalar particles and possible final signals. Here γ denotes a photon. ν L = ν 1 , ν 2 , ν 3 are SM-like light massive neutrino states and N R = N 4,5,6 are heavy neutrino massive states dominated by right-handed weak neutrinos. From now on we will denote N R ≡ N . Here ℓ represents light charged leptons e, µ.
on those plots is that in MLRSM not all four charged Higgs bosons can simultaneously be light. It is a case for H ± 1 , H ±± 1 and H ±± 2 , for details, see the appendix. The remaining charged scalar H ± 2 is of the order of the v R scale, so its effects at LHC is negligible, to make it lighter would require to go beyond MLRSM. For a book keeping, we keep this particle in further discussion. If its mass at some points is assumed to be small (so we go beyond MLRSM), we denote it with a tilde,H ± 2 . Its coupling is kept all the time as in MLRSM (why it can be so is discussed shortly in the appendix).
In this paper we consider only the processes where charged Higgs particles can be produced directly as shown in the table 1, first column.
The decay branching ratios for heavy neutrino states N and heavy gauge bosons (W 2 , Z 2 ) in MLRSM which determine both secondary production and final signals in the last column of this table are given in [7]. However, with assumed light charged Higgs particles, new decay modes are potentially open, and discussion must be repeated. Results are given in figures 2, 3, and 4. As can be seen from figure 2, contribution of charged scalars to the total decay width of W 2 is at the percent level. Here more important are heavy neutrino decay modes. 2 Different scenarios for LH neutrino mixings [7] are discussed, i.e., see-saw mechanisms where j = 4, 5, 6 and scenarios where LH neutrino mixings are independent of neutrino masses: [49]. In a case of many heavy neutrino states (as in MLRSM), taking into account constraints coming from neutrinoless double-beta decay experiment, this limit becomes κ 2 max /2 [50][51][52]. For W 2 decays different LH neutrino mixing scenarios affect only light neutrino νl channel for which BR is small, anyway.
For the Z 2 decays, figure 3, four channels with charged Higgs bosons, namely H ++  quark decay modes dominate, and the second important are the heavy neutrino decay modes.
The most interesting situation is for the decays of heavy neutrinos. Here H + 1 decay mode is the largest in see-saw scenarios. The reason is that in case of Yukawa coupling, say H + 1 − N − e, the change in LH neutrino mixing is compensated by the proportionality of the coupling to the heavy neutrino mass, which is not the case for the gauge N − e − W and N − ν − Z couplings. That is why eW and νZ decay modes are relevant only in scenarios where LH neutrino mixings are independent of the heavy neutrino masses and are close to the present experimental limits. Large charged Higgs boson decay mode of the heavy neutrino can influence the "golden" pp → eN process [3,4,6,7,53,54].
For typical see-saw cases when charged Higgs boson masses are very large, standard model modes dominate: In scenarios with large LH neutrino mixings the standard modes dominates independently of the heavy neutrino and W 2 masses. 3 Finally, let us note that in typical Type I see-saw scenarios the TeV scale of heavy neutrino masses implies m D ∼ 10 −6 GeV to accomplish light neutrino masses at the eV level. In this situation nothing happens to the left plots in figures 2, 3, and 4 apart from the fact that lν, lN and νZ channels will disappear completely there.
In the case of heavy gauge boson decays, quarks dominate and jets will be produced while for SM-like gauge bosons hadronic decay branching is around 70%. That is why typical final signals for reactions I and II in table 1 are two or four jets plus missing energy. There are only two cases without missing energy: and However, as we can see from the table, the cleanest signals are connected with doubly charged Higgs particles, that is why we focus on them in this paper. discussions on doubly charged scalars, see e.g. [55][56][57][58][59][60][61][62][63]. The processes eqs. (2.2) and (2.3) with four charged leptons plus jets will be considered elsewhere.
For processes III-X important are charged Higgs boson decay modes. For doubly charged Higgs particles possible decay modes are where l = e, µ, τ . Apart from the above decay modes, the other possibilities for the doubly charged scalars can be (2.5) when they are not degenerate with the singly charged ones. But for nearly or exact degenerate case, the charged scalars dominantly decay through leptonic modes and here kinematics play a role too. Figure 5 shows a scenario in which pure leptonic decay modes can be realised. The crucial factor is the Yukawa coupling which depends (indirectly) on heavy right-handed neutrino mass. If heavy neutrino masses are degenerate then democratic scenario is understood where all leptonic channels are the same (i.e. BR(H ±± → e ± e ± ) ≃ 33%).

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Typically, as can be seen from figure 5, for right-handed neutrino masses to be 1 TeV, 1 TeV and 800 GeV for N 4 , N 5 , N 6 respectively, the branching ratios are the following If the first two generations neutrinos (N 4 , N 5 ) have masses above ∼ 4 TeV, τ decay mode is practically irrelevant. From the discussion it is also clear, that one of the decay modes can dominate if only one of the right-handed neutrino masses is much bigger than remaining two heavy neutrino states. Limits in eq. (1.3) assume 100% leptonic decays, in our case, taking into account figure 5, eq. (2.6) and results given in [22,23], mass limits are much weaker, at about 300 GeV, see e.g. figure 3 in [23].
For decays of singly charged H ± 1 scalars situation is analogical as for doubly charged scalars (possible decay modes to neutral H 0 1 and A 0 1 scalars are negligible for , as dictated by FCNC constraints). and

Primary production of heavy charged Higgs bosons at the LHC
Below different processes involving solely charged scalar productions are classified. In analysis which follow v R = 8000 GeV to respect with a large excess the present exclusion limits on W ± 2 , and Z 2 masses. SM-Higgs like mass is set to 125 GeV, masses of neutral scalar particles are set at very high limit (∼ 10 TeV). In this way, as already discussed, scenarios are realised with relatively light (hundreds of GeV) charged Higgs bosons while remaining non-standard particles within MLRSM are much heavier. All cross sections given in this section are without any kinematic cuts, those will be considered with final signals and distributions in section 3.
The cross section for singly charged scalar pair production as a function of their mass is given in figure 6. This process is dominated by s-channel γ, Z 1 and t-channel quark exchange diagrams. Contributions coming from s-channel H 0 0 , Z 2 and H 0 1 bosons are negligible for considered MLRSM parameters. For singly charged scalar mass equals to 400 GeV, the cross sections are (as discussed in section 2, H ± 2 Higgs boson is assumed to be light and we denote it here with a tilde, for M H ± 2 ≫ 1 TeV the considered cross section is negligible, while for singly charged scalar mass equals to 600 GeV are The dominant contribution to these processes is via neutral s-channel current, i.e., via Z 1 and γ. Contributions coming from s-channel H 0 0 , Z 2 and H 0 1 are negligible for considered MLRSM parameters.
To explore the phenomenological aspects of the doubly charged scalars in the MLRSM model we consider two scenarios. Scenario I when the doubly charged scalars are degenerated in mass, i.e., M H ±± . This scenario is motivated by analysis of the Higgs potential (a detailed study of the Higgs potential and scalar mass spectrum will be presented elsewhere). In Scenario II masses are different, i.e., M H ±± where ℓ i,j = e, µ.  The contributions to the cross sections from individual channels are given as: is projected as a contour. As can be seen from these figures, cross sections at the level of 1 fb can be obtained for doubly charged scalar masses up to approximately 600 GeV.

pp → H
The production of a doubly charged in association with a singly charged scalar goes through the charged s-channel interaction where W ± 1,2 gauge bosons are exchanged. Diagrams with schannel exchanged singly charged scalar H ± 2 is negligible (its coupling to W 1 is proportional to v L which is zero). As W ± 2 is very heavy, the dominant contribution originates from the process via W ± 1 . To give yet another benchmark, we set v R = 8 TeV and the following charged scalar masses: M H ±±  generation, see figure 5. The cross section for the process before any kinematic cuts with centre of mass energy √ s = 8 (14) TeV at the LHC is The contributions to the cross sections from individual channels are noted as:  figure 9 the total cross section for two considered processes are given. The mass of H ± 2 is allowed to be small and because, as discussed before, this is not natural in the MLRSM, its contribution is denoted with a tilde. Anyway, its contribution (keeping a form of its couplings as dictated by MLRSM) is negligible.   figure 10. We can see that the largest cross sections are for a pair production of singly with doubly charged scalars, and the cross sections for production of doubly charged scalar pair is slightly lower, while the smallest cross section is for pair production of singly charged scalars. Contributions from processes where H ± 2 is involved are negligible or at most much smaller than corresponding results where H ± 1 is involved. Keeping in mind the status of the SM background (analysed for our purposes in section 3.3) we look for multi lepton signals for three or more leptons. Thus we focus in the following sections on the processes which involve primary production of at least one doubly charged scalar. In our scenarios the production cross sections for these processes are very small and can be ignored. This is because the W 2 /Z 2 propagator diagrams are suppressed as they are as heavy as few TeV. For the other light propagators the scalar-gauge boson-gauge boson vertices are proportional to sin ξ and/or v L , which are zero here.

Simulations and results for final lepton signals
In this paper we are interested in tri-and four-lepton signal events. To enhance such signals, suitable kinematic cuts are applied in order to decrease the SM backgrounds.

Events selection criteria
The detailed simulation criteria used in our study are following: • The Parton Distribution Function (PDF): CTEQ6L1 [64].
• Smearing of electron energy and muon p T are considered. All these criteria are implemented in PYTHIA and for details see [65].
• Lepton-lepton separation: the separation between any two leptons should be ∆R ll ≥ 0.2.
• Lepton-jet separation: the separation of a lepton with all the jets should be ∆R lj ≥ 0.4, otherwise that lepton is not counted as lepton. Jets are constructed from hadrons using PYCELL within the PYTHIA.
• Hadronic activity cut: this cut is applied to take only pure kind of leptons that have very less hadronic activity around them. Each lepton should have hadronic activity, p T hadron p T l ≤ 0.2 within the cone of radius 0.2 around the lepton.
• Missing p T cut: this cut is not applied for four-lepton final states while for threelepton case due to the presence of neutrino, a missing p T cut (> 30 GeV) is applied.
• Z-veto 4 is also applied to suppress the SM background. This has larger impact while reducing the background for four-lepton without missing energy.

Signal events for doubly charged Higgs particles in MLRSM
Doubly charged scalars decay mainly to either a pair of same sign charged leptons or charged gauge bosons depending on the choice of parameters. As already discussed, we have chosen the parameter space in such a way that the doubly charged scalars decay to charged leptons with almost 100% branching ratio. This decay is lepton number violating and can also be possibly lepton flavour violating. In our scenarios we assume no lepton flavour violation as the Yukawa couplings are considered to be flavour diagonal. Thus, the four lepton final state contains two pairs of same sign and same flavoured charged leptons where each pair has opposite charges to each other. As there is no neutrino (missing energy) or jet involved it is easy to reconstruct the momentum of the final state particles. We have reconstructed invariant same sign di-leptons (SSDL) and opposite sign di-leptons (OSDL). As the doubly charged scalars are the parents of the di-lepton pairs, invariant mass of the SSDL is expected to give a clean peak around the mass of the doubly charged scalar, which is not necessarily a case for OSDL.
where ℓ i,j = e, µ. After implementing all the cuts, as described in section 3.1, the four lepton events with no missing energy can be estimated. Each pair of SSDL originates from different doubly charged scalars. We have plotted the reconstructed invariant mass distributions for both SSDL and OSDL in figure 11 with anticipated integrated luminosity L = 300 fb −1 . As both the doubly charged scalars are degenerate the invariant mass peaks occur at around 400 GeV. This clean reconstruction of the invariant mass is indeed possible even in the hadronic environment and can be a smoking gun feature indicating the presence of doubly charged scalars.
We have computed this process also with centre of mass energy 8 TeV. In this case we find that the cross section, with √ s = 8 TeV at the LHC, is 1.06 fb, about 6 times smaller than for √ s = 14 TeV. If we take present integrated luminosity to be 25 fb −1 then total number of the events even before all the cuts, is statistically insignificant to analyse this particular process at the LHC after implementing all the selection criteria. Thus to justify this four lepton signal for this scenario needs more data in future.
To select the doubly charged scalar signal properly and in an independent way, there is another interesting variable which can be used for determination of signals as sug- gested in [62] ∆R where η i and φ i denote pseudorapidity and azimuth of ℓ i , respectively. ∆R ℓℓ amounts the separation between two light charged leptons (ℓ) in azimuth-pseudorapidity plane. Its physical importance is that in the detector if ∆R ℓℓ is smaller than the specified value then one can not distinguish whether the deposited energy is really by one or two leptons. So, one chooses only events for which leptons are well separated. We expect that the leptons originated from a single doubly charged scalar will be less separated than the leptons coming from different charged scalars. In our considered processes and decays the doubly charged scalars decay mainly into pair of same flavoured same sign leptons. Thus in a case of opposite sign di-lepton pair each of them are coming from different doubly charged scalars must be well separated. We have plotted the ∆R ℓℓ distribution to address this feature. It is pretty clear from figure 12 that the distribution peaks at smaller ∆R ℓℓ for same sign lepton pair while that for the oppositely charged lepton pair peaks at larger value of ∆R ℓℓ , as expected. This implies that most of the leptons in the SSDL pairs are less separated than the leptons which belong to the OSDL pair.
Scenario II, non degenerated doubly charged mass spectrum. Here we choose another set of benchmark points where the doubly charged scalars are non-degenerate. In section 2, eq. is much larger than that for H ±± 2 . Thus the four lepton events will be generated mostly from the leptonic decays of the H ±± We also performed the ∆R ℓℓ distribution for the same benchmark point. For the same reason as explained before our expectation is reflected in figure 14.

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These processes lead to the tri-lepton events with missing p T , see table 1. For chosen MLRSM parameters, eq. (2.21), the cross section for the process pp → (H ±± 1 H ∓ 1 + H ±± 2 H ∓ 2 ) → ℓℓℓν ℓ before cuts with centre of mass energy √ s = 14 TeV is σ = 6.05 fb. The tri-lepton events can be classified into two categories: either ℓ + ℓ + ℓ − or ℓ − ℓ − ℓ + . The first and second types of signals are originated from W + 1 and W − 1 mediated processes, respectively. Thus, it is indeed possible to estimate the charge asymmetry, define as the ratio of the number of events of ℓ + ℓ + ℓ − type to the number of events of ℓ − ℓ − ℓ + type at the LHC. This is very similar to the forward-backward asymmetry at Tevatron. This charge asymmetry depends on Parton Distribution Functions (PDF) and thus is a special feature of LHC. We have estimated this ratio (R + − ) with the above choices of charged scalar masses with √ s = 14 TeV and integrated luminosity 300 fb −1 . We find 554 tri-lepton signal events after all the cuts and that leads to In SM the corresponding value calculated for the main processes given in the next section in table 2 is (R + − ) SM = 17.751 14.962 = 1.186. This value is slightly different from the calculated values in [66] where higher order corrections are taken into account and the specific kinematic cuts are different. Nevertheless, MLRSM value given in eq. (3.2) differs substantially from its SM counterpart to signify its presence.
As discussed in section 2, the H ±± 2 H ∓ 2 W ∓ 1 vertex is much more suppressed compare to H ±± 1 H ∓ 1 W ∓ 1 . Thus, in this case most of the tri-lepton events are originated from pp − → H ±± 1 H ∓ 1 process. This is clearly visible from the invariant mass distributions. Here we have plotted the same and opposite sign di-lepton invariant mass distributions, see figure 15. As similar to the earlier discussions in the opposite sign lepton pairs two leptons have different origin thus their invariant mass distribution is continuous while the same sign di-lepton invariant mass distributions always peak around the mass of the doubly charged scalars.
Here, from figure 15, it is distinctly seen that the significant amount of same sign dilepton pair peaks at M H ±± 1 = 483 GeV rather than M H ±± 2 = 527 GeV. This implies that the dominant contribution to this tri-lepton events are generated through pp → H ±± 1 H ∓ 1 process (cf. figure 9) and the further leptonic decays of the charged scalars.
In the figure 16, separations between leptons are plotted. As can be seen from this figure the SSDL separations peak at lower value of ∆R ℓℓ , while OSDL separations peak at larger value of ∆R ℓℓ . This is because same-sign leptons pair has the origin from the same mother, while opposite sign leptons pair has both the leptons from different mothers.  Figure 16. Lepton-lepton separation plot for same sign leptons (∆R ℓ ± ℓ ± ) and opposite sign leptons Here √ s = 14 TeV and integrated luminosity 300 fb −1 at the LHC.
Distributions presented so far show that it is possible to extract clear signals for doubly charged scalars at the LHC. However, for signal identification crucial is how large the SM background effects are and the significance too.

Background estimation and significance of signals
Kinematic cuts are used which have been investigated and established for the first time in [65]. The cuts are optimised in a way such that we can reduce the SM background

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Processes  In table 3 we present the total background and signal events for 25 and 300 fb −1 integrated luminosities. It is clear that four-lepton signals are well beyond the SM background. The tri-lepton signal is also very prominent over the background (what matters is the signal excess over the background fluctuations). To see it properly, in table 4 the significance of different signals is shown.
Assuming the significance at the level of 5 as a comfortable discovery limit, we can see that LHC will be in the next run sensitive to masses of MLRSM doubly charged Higgs bosons up to approximately 600 GeV.

MLRSM charged Higgs bosons contribution to H 0 0 → γγ
In LR symmetric models there are (singly-, doubly-) charged scalars and charged gauge boson (W ± 2 ) which couple to photons and hence they can contribute to H 0 0 → γγ channel where H 0 0 is the SM-like neutral Higgs taken to be 125 GeV. Since W ± 2 are heavy, their 6 In our analysis while computing the tri-lepton events (signal and background), the pT of the third hardest lepton needs to be greater than 20 GeV, and also a missing pT cut (> 30 GeV) must be satisfied, see section 3.1. Thus the tri-lepton background for process like tt where one of the lepton is coming from semi-leptonic decays of B's is reduced. Here the hadronic activity cut also reduces the hadronic activity around the selected leptons and plays a crucial role in this case. All these cuts reduces the efficiency of misidentification of b-jets as leptons. In our case this is less than 0.05%.    contributions are suppressed compared to charged scalars, so we look for charged scalar contributions. They contribute to the channel via a loop shown in the figure 17.

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Following [67][68][69] we can write the enhancement factor for this channel, which is nothing but a ratio of partial decay width in the new model to that in the SM (4.1) In the above equation Q S is electric charge of charged scalars in unit of e, M S is a mass of scalars. N c is colour factor which is 1 for colour singlet scalars and τ i = 4m 2 i /m 2 for c S are as follows Here the parameters that are involved in the above eqs. (4.2)-(4.4), are contained in the scalar potential and following the convention as suggested in [36]. A 1/2 , A 1 and A 0 are loop functions for fermions, vector bosons and scalars respectively, given as For the SM-like Higgs mass below threshold, i.e., m H 0 0 < 2m loop (m loop is a mass of a particle in the loop) f (x) = arcSin 2 ( √ x).
In figure 18 we present a contour plot to grab the contributions from the charged scalars to R γγ . We have assumed M H ++ to reduce number of free parameters. Experimental observations of the Higgs to di-photon decay normalised to the SM prediction, as pointed out by ATLAS and CMS is given as in [70,71]: As errors are still very large, it is too early to make any conclusive remarks on these results, especially that tendency seems to be that anomaly systematically approaches 1. However, MLRSM can accommodate wide range of R γγ values by the charged Higgs boson effects, for related discussions, see e.g. in [72].

Conclusions and outlook
After discovery of the SM-like neutral Higgs boson in July 2012 at the LHC, the next big issue is what is the actual shape of the Higgs potential. Thus a question is asked to reveal the further query regarding possible gauge symmetry behind the existence of elementary Higgs boson. Here we have concentrated on studies connected with LHC potential discovery of charged Higgs bosons within classical MLRSM which is already phenomenologically rich enough and worth of separate investigations. Though different low energy data and the LHC exclusion plots constrain already W 2 and Z 2 very much, still the charged scalars can be relatively light. It has been shown which of singly and doubly charged Higgs bosons can be light, in agreement with FCNC limits on neutral Higgs bosons particles, as both charged and neutral scalar sectors are connected through the Higgs potential parameters. They can be produced at the LHC with non-negligible cross sections. However, their production cross sections decrease rapidly with their masses, that is why we have undertaken here more detailed and systematic studies including the production and decays of charged scalars. We have concentrated on the single and pair production of doubly charged scalars. We have chosen the benchmark points in such a way that signals connected with doubly charged scalars can dominate over non-standard signals coming from both heavy gauge and neutral Higgs bosons. We have analysed the four-lepton and tri-lepton signals at the LHC. As a rule of thumb, for all considered processes with doubly charged scalars cross sections are about 1 fb for their masses in vicinity of 400 ÷ 500 GeV, which is about the present lowest limit on their masses. If planed integrated luminosity in the next LHC run at √ s = 14 TeV is about 10 times larger than present values, clear signals with four-leptons without missing energy and tri-lepton signals can be detected. It will be an indication

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for doubly charged scalar effects. These multi lepton final states posses very small SM background. We have shown that MLRSM model can give such signals for doubly charged masses up to approximately 600 GeV. In our analysis we have used the di-lepton invariant mass and lepton-lepton separation distributions. We also estimate the amount of charge asymmetry in signal as well as background events, and show that this might be a smoking gun feature for future discovery. The same and opposite sign charged lepton signals have been analysed using proper kinematic cuts and the clear impact of doubly charged scalars are noted carefully. Finally, as in the Left-Right symmetric models charged gauge bosons are very heavy, they do not contribute significantly to the Higgs to di-photon process, however, the relatively light charged scalars can contribute easily. We have incorporated the impact of the light charged scalars in this process and estimated the strength of this contribution over the SM one.
As an outlook, several interesting things can still be done, e.g.

1.
More detailed comparison studies including also lepton spin correlations and their angular distributions with other non-standard models where doubly charged scalars exist (e.g. Higgs Triplet Model [73]); 2. Studies of dedicated distributions for processes involving doubly charged Higgs bosons with both jets and missing energy; 3. Theoretical studies of general Higgs potentials which can realise relatively light charged Higgs bosons keeping at the same time a few TeV scale of neutral Higgs bosons (e.g. [48]); 4. To release theoretical assumptions on equality of left and right gauge boson couplings, diagonal neutrino light-heavy mixings and possible see-saw scenarios, take into account relations between model parameters in the Higgs, gauge and neutrino sectors, e.g. [11].
In summary, we are in a very exciting moment and the next LHC run should be decisive if our scenario with relatively light charged Higgs bosons can be realised. Still there is a room for Left-Right gauge symmetry signals discovery at the LHC, including MLRSM doubly charged Higgs bosons effects as long as long as their masses will be well below 1 TeV range (m H ±± 1/2 ≤ 600 GeV).

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Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.