Search for doubly charged Higgs bosons
through vector boson fusion at the LHC and beyond
Abstract
Production and decays of doubly charged Higgs bosons at the LHC and future hadron colliders triggered by vector boson fusion mechanism are discussed in the context of the Minimal LeftRight Symmetric Model. Our analysis is based on the Higgs boson mass spectrum compatible with available constraints which include FCNC effects and vacuum stability of the scalar potential. Though the parity breaking scale is large ( few TeV) and scalar masses which contribute to FCNC effects are even larger, consistent Higgs boson mass spectrum still allows us to keep doubly charged scalar masses below 1 TeV which is an interesting situation for LHC and future FCC colliders. We have shown that the allowed Higgs bosons mass spectrum constrains the splittings (), closing the possibility of decays. Assuming that doubly charged Higgs bosons decay predominantly into a pair of same sign charged leptons through the process , we find that for LHC operating at TeV with an integrated luminosity at the level of (HLLHC), there is practically no chance to detect such particles at the reasonable significance level through this channel. However, at 33 TeV HELHC and (or) 100 TeV FCChh a wide region opens up for exploring the doubly charged Higgs boson mass spectrum. In FCChh, doubly charged Higgs bosons mass up to 1 TeV can be easily probed.
pacs:
12.60.i, 12.60.Fr, 14.80.Fd, 14.80.EcI Introduction
Weak vector boson fusion (VBF) processes were suggested quite some time ago in the context of Higgs searches Cahn:1983ip (); Rainwater:1997dg (); Rainwater:1998kj (). They are characterized by the presence of two jets with large transverse momentum in the forward region in opposite hemispheres along with other observables, like charged leptons. In fact, many interesting Standard Model (SM) processes, e.g. diffractive interactions, lowx QCD physics, VBF Higgs production, photoproduction are also accompanied by production of forward particles. Interestingly LHC has a very rich “forward physics” program and for the necessary investigation there are dedicated detectors like LHCf Kawade:2013bva () and(or) FP420 Albrow:2008pn (). Due to uncertainties in jet tagging the efficiency is relatively low and, thus, the significance of these channels is rather suppressed. Nevertheless, from the discovery perspective, many Beyond Standard Models (BSM) can also be tested using forward jets. Such related studies are also important for dark matter searches through monojet plus missing energy Fox:2011pm (); ATLAS:2012zim (); Khachatryan:2014rra ().
In this paper we continue Chakrabortty:2012pp (); Bambhaniya:2013wza (); Bambhaniya:2014cia () a dedicated analysis of the Minimal LeftRight Symmetric Model (MLRSM) Mohapatra:1974gc (); Senjanovic:1975rk (); Mohapatra:1986uf () aiming at exhaustive exploration of interesting BSM signals at present and future hadron colliders^{1}^{1}1The main features of this model are equal left and right gauge couplings, , and a scalar potential which contains a bidoublet and two triplet scalar multiplets, considered for the first time in Mohapatra:1980yp (), see also Gunion:1989in (); Duka:1999uc ().. For many reasons the parity breaking scale of the right group in MLRSM must be already around TeV Chakrabortty:2012pp (); Bambhaniya:2013wza (); Bambhaniya:2014cia (); Zhang:2007da (); Melfo:2011nx (). However, as discussed recently in Bambhaniya:2013wza (); Bambhaniya:2014cia (), in such models charged Higgs bosons can have masses at the much lower level of a few hundred GeV, and that scenario is still consistent with experimental data. In this case, it is imperative to cover all possible scenarios, and their potential effects at the LHC should be analyzed carefully. Interestingly enough, a recent CMS study Khachatryan:2014dka () can be interpreted as favoring right handed currents.
In our previous analyses we have worked with the scalar mass spectra which are compatible with the unitarity of the potential parameters, the large parity breaking scale and the severe bounds on neutral scalar masses () derived from Flavor Changing Neutral Currents (FCNC). In this work we have further implemented another necessary condition: vacuum stability of the scalar potential. It appears that even after taking into account all these constraints, the consistent scalar mass spectra can accommodate doubly charged Higgs boson masses in a region which can be explored by the LHC.
In the past, we have focused on searches for multilepton signals associated with any number of jets; i.e., there was no jet veto. Here, the analysis of possible VBFtype signals with four leptons and two jets using suitable VBF cuts is presented.
We have used our version of the LeftRight symmetric model implemented in FeynRules (v2.0.31) Christensen:2008py (); Degrande:2011ua (). The general signal and background analyses for multilepton and tagged forward jets are performed using ALPGEN (v2.14) Mangano:2002ea (), Madgraph (v2.2.2) Alwall:2011uj () and PYTHIA (v6.421) Sjostrand:2006za ().
Ii Possible processes which identify doubly charged Higgs through VBF in MLRSM
There are many interesting channels in which doubly charged Higgs particles can be produced in MLRSM. In the hadron collider, productions of doubly charged Higgs particles crucially depend on their couplings with vector bosons. These charged scalars () are produced either through neutral and charged currents or fusion processes. Representative classes of diagrams which contribute to productions associated with two jets are given in Fig. 1.
If in Fig. 1, then doubly charged Higgs particles are produced in pairs. Assuming further that decays predominantly into leptons, a signal of four leptons associated with two forward jets in the final state is foreseen, . In the DrellYan case also [see the diagram (d) in Fig. 1], if , a four leptons plus two jets signal is possible, though its contribution is suppressed once the VBF cuts are activated.
We should also mention that vector boson fusion diagrams interfere substantially with Bremsstrahlunglike (or DrellYan) processes Massironi:2014fma ().
Here we focus on the pair production of doubly charged scalars associated with two forward jets. As mentioned already, this signature can be promising since LHC has dedicated search channels for tagged forward jets. VBF processes with doubly charged Higgs bosons have been considered lately in Dutta:2014dba () with the main focus on three lepton signals with missing energy and in Englert:2013wga () where doubly charged Higgs bosons decay into samesign bosons. In Dutta:2014dba () there is also an interesting discussion on scalar corrections to the selfenergy of and the parameter. It has been argued that there exist severe constraints on the charged scalar mass splitting. However, in our opinion conclusions based on partial results and a single class of (scalar) diagrams can be deceptive; thus, we need to consider complete calculations including renormalization. We recall a series of papers on the 1loop corrections to the muon decay in MLRSM, starting with qualitative results Czakon:1999ue (); Czakon:1999ha () and finishing with quantitative analysis Czakon:2002wm (). The upshot of all these analyses, important for our present discussion, is that there is a strong finetuning between contributions to from different classes of nonstandard particles: Higgs and additional gauge bosons and heavy neutrinos (fermions). By their nature, cancellations among bosonic and fermionic types of diagrams are present, and a change of mass spectrum of the Higgs bosons can be compensated for by different choices of scale (gauge bosons) and masses of heavy neutrinos. These analyses in the context of the LHC have been considered in detail in Chakrabortty:2012pp ().
Iii Constraints on and : adding vacuum stability condition
Analysis of the LHC data provides lower limits on the doubly charged Higgs mass ATLAS:2014kca () depending on their leptonic decay branching fractions. In the scenario where , that limit is ; see Fig. 2 for details.
Limits on the MLRSM potential parameters have been discussed lately in Bambhaniya:2014cia (). Similar to the earlier case, we focus on the and parameters, which are important for the scalar mass spectrum (all notations are as in Bambhaniya:2013wza (); Bambhaniya:2014cia ()). First, to suppress FCNC effects generated by and , we assume^{2}^{2}2To our knowledge, their effects have been discussed for the first time in the context of LeftRight models in Ecker:1983uh (), see also Mohapatra:1983ae (); Pospelov:1996fq (); Zhang:2007da (); Maiezza:2010ic (); Chakrabortty:2012pp () and recently Bertolini:2014sua (). In general, their masses need to be at least of the order of 10 TeV, though some alternatives also have been considered in Guadagnoli:2010sd (). that their mass is bigger than . Because , this results in the following lower limit on :
(1) 
Taking into account that , one gets
(2) 
where is the electroweak symmetry breaking scale. The third constraint originates from the necessary condition of the boundedness of the potential Chakrabortty:2013mha ():
(3) 
The value of is fixed by the lightest neutral Higgs boson mass as .
Now it is interesting and important to ask what is the maximum allowed mass splitting that will be consistent with the bounds on derived above. Such queries cannot be unnoticed from a phenomenological perspective because only for can the doubly charged Higgs have the following decay: . This has a massive impact on the decay branching ratios of . It is straightforward to check that the biggest is reached for , saturating both inequalities in Eqs. (2) and (3) which imply
(4) 
The physical solution to this equation and the corresponding maximal value of is
(5) 
where ‘’ stands for corrections of the order of . One can check that depends on very weakly and is nearly equal to the asymptotic value , for . As , this implies that onshell decay is kinematically forbidden regardless of the scale . Interestingly, we came to the same conclusion as in Dutta:2014dba (), but based on different kinds of arguments. There is another consequence of the requirement that the scalar potential is bounded from below. Namely, one can show that, using Eqs. (1) and (3), in the allowed parameter space there is an upper limit on the mass:
(6) 
where ‘’ stands for the corrections of order of . The maximal value of is reached for satisfying and , which correspond to the intersection point of lines restricting regions defined by Eqs. (1) and (3). The situation is summarized in Fig. 3.
Naturally, the minimal value of the mass in the discussed setup is . For the sake of completeness, let us note that if there are no experimental limits on and , then the lowest possible mass of consistent with the vacuum stability bound, Eq. (3), would be , which corresponds to and . On the other hand, the MLRSM does not provide any relevant constraints on the mass^{3}^{3}3The only constraint which could arise is for . It comes from the assumption that scalar potential parameter is in the perturbative regime .. We would like to mention that when satisfies
(7) 
then a similar type of decay of is kinematically forbidden as is too light to decay into and , respectively; see the benchmarks in the next section.
Iv Predictions for in MLRSM
Before we discuss our simulated results, selection criteria should be defined, which are crucial for extracting proper signals and reducing the SM background. For selecting leptons, we use the same criteria as defined in previous papers gbjdsgpk (); Bambhaniya:2013wza (), which are read as follows:

Lepton identification criteria: pseudorapidity and ;

Detector efficiency for charged leptons:

electron (either ): ;

muon (either ): ;


Smearing of muon and electron energy are implemented in PYTHIA;

Leptonlepton separation: ;

Leptonphoton separation: where all the photons have ;

We have implemented a veto to suppress the SM background, and this has a larger impact while reducing the background for the fourlepton without missing energy. This veto reads as follows: The same flavored but opposite sign lepton pair invariant mass must be sufficiently away from the SM boson mass, say, GeV;

Leptonjet separation: The separation of a lepton with all nearby jets must satisfy . If this is not satisfied, then that lepton is not counted as a lepton. For completeness, we must mention that jets are constructed from hadrons using PYCELL within PYTHIA;

Hadronic activity cut: this cut is applied to consider only those leptons that have much less hadronic activity around them. Each lepton should have hadronic activity which is accounted as within the cone of radius around the lepton;

Hard cuts for four lepton events: , , , .
Cuts  

VBF  500 
The Parton Distribution Function (PDF) for protons is defined by CTEQ6L1 Pumplin:2002vw (). After satisfying the above selection criteria, additional cuts are applied to identify the forward jets. The detail of these VBF cuts are depicted in Tab. 1.
Considering the constraints on potential parameters discussed in section III, in Fig. 4 the results are presented for the doubly charged Higgs production process with two jets as a function of their mass. While computing the MLRSM mass spectrum, we have set (which leads to ). The analyses are performed for the LHC with collision energy considering the high luminosity HLLHC option Barletta:2013ooa () as well as for future scenarios such as HELHC with center of mass energy Assmann:1284326 (); Barletta:2013ooa () or the 100 TeV FCChh facility fcc (); fccprep (); fccbrief (); fccweek2015 (). The cross section for this process has been computed with a large and VBF cuts as defined in Tab.1
As an example of a representative Higgs mass spectrum (benchmark) used in calculations, we assume degenerate doubly charged Higgs masses where masses of remaining scalar particles compatible with results of section III can be chosen as (in ):
(8)  
(9)  
(10)  
(11) 
This spectrum is obtained with the following set of potential parameters ():
(12)  
(13)  
(14)  
(15)  
(16) 
The cross sections for the following process at the parton level with minimal imposed cuts are given as follows:
(17)  
where . These minimal cuts are e.g. minimum cuts for leptons and jets such that they are identified as observable in the detector and do not contribute to missing energy.
The result in Eq. (17) is further processed using the VBF cuts
(18)  
For the sake of completeness let us display contributions from two intermediate channels^{4}^{4}4In Bambhaniya:2013wza () we wrongly assigned with right triplet and with left triplet in Eq. (A.13). We would like to thank Juan Carlos Vasquez for directing our attention to this fact as he considered this process in Vasquez:2014mxa (). with the default cuts in Madgraph (MG):
(19)  
and
(20)  
As one can see, the cross sections in Eqs. (19) and (20) are larger than these given in Eq. (17). The reason for this is while computing the cross section for the leptonic final state, i.e., Eq. (18), all the selection cuts are incorporated and that reduces the cross section by a large amount.
Some technical details related to the computing method are in order here. At the MG level, one can control the gluon contributions using option QCD=0. The cross section for with switched off gluons turns out to be about times smaller than for that with gluons. Hence, QCD contributions to that signal are really important. However, in both cases, distributions of the rapidity () of jets are quite different. Allowing for gluons, they are peaked around , which implies that jets are emitted mostly perpendicular to the beam. Otherwise, rapidities are peaked around and ; i.e., there are two backtoback jets emitted along the beam. Hence, setting QCD=0 allows us to preselect processes which are consistent with VBF cuts. Effectively, it shortens computing time^{5}^{5}5Typical run times for generating events of and with QCD=0 are, respectively, about h and h on core CPU..
Let us comment on the decay scenario used in the calculations. It is assumed that the decay of is dominantly into a pair of the same sign and sameflavor charged leptons (for all possibilities within MLRSM, see Bambhaniya:2013wza ()). In other words, it is assumed that the Yukawa coupling matrix of doubly charged scalar with charged leptons is diagonal. Assuming no mixed leptonic decay modes (), i.e., no lepton flavor violation, the coupling of doubly charged scalar with charged leptons in MLRSM is proportional to the heavy neutrino mass of the corresponding lepton generation. Thus the decay modes will be larger compared to the case if the first and second generations of righthanded neutrinos are more massive than the thirdgeneration one. This point has been clarified and shown numerically in Fig. 2.5 in Ref. Bambhaniya:2013wza (). In the present analysis, the masses of the first two generations of righthanded neutrinos are taken to be and the mass of the third one is at the level of . As TeV, the Yukawa couplings are within the perturbative limit. If the decay mode would be larger, predictions given here should be rescaled properly using corresponding branching ratios (for instance, in the democratic threegeneration case, the branching ratio for the and channels would be decreased by about each).
Process:  Cross section [fb]  Cross section [fb] 

with  at parton level  after showering, 
in TeV  in Madgraph  and hadronization 
in PYTHIA  
14  0.115  0.003 
33  1.109  0.008 
100  4.794  0.038 
The SM background at the LHC for the signal jets is accounted from the process . We have noted that after implementation of the selection cuts, the dominant background is contributed from the process.
For , , collisions, the SM background is given in Tab. 2 both at the parton level and after hadronization and passing through implemented cuts.
We can see that the background is suppressed very effectively. The results in Tab. 2 are obtained in the leading order; electroweak corrections can change the results not more than Catani:2009sm () which can change the significance of signals at the level of about one percent at most.
Finally, to judge the strength of the MLRSM signals we decided to show the dependence of the significance of the result as a function of the integrated luminosity. As can be seen in Fig. 5 (lefttop), a comfortable value of the significance at the level of can be reached for in collisions with

TeV and with 100 integrated luminosity;

TeV and with 700 integrated luminosity.
No signal at this significance level () can be reached with collisions, even if the integrated luminosity is around 3000 .
In Fig. 5 (righttop) we can see that doubly charged Higgs bosons with masses up to with significance at the level of 5 can be probed for both center of mass energy 33 and 100 TeV with integrated luminosities around 3000 and 300 , respectively. In Fig. 5 (leftbottom) it is evident that the 1 TeV doubly charged scalar can be probed with a significance of 5 only with 100 the TeV collider with luminosity at least 1000 . The Fig. 5 (rightbottom) summarizes the situation for the FCChh collider option for three different sets of masses of doubly charged scalars: 500, 600, 700, 800, 900 and 1000 GeV. This figure also shows that significance at the level of 7 can be reached for and TeV with integrated luminosities around 3000 . We can see that this collider opens up a very wide range of Higgs boson masses which can be explored.
V Conclusions and Outlook
In this paper we have considered production and decays of a pair of doubly charged Higgs bosons through vector boson fusion within the MLRSM framework. To do so we have evaluated suitable benchmark points for masses of Higgs bosons, which are in agreement with several constraints coming from FCNC, vacuum stability, LEPII and recent ATLAS searches on doubly charged scalars. There are strong relations among masses of doubly and singly charged and neutral scalars which prevent us from choosing their individual values freely, leaving us with the suitable benchmarks we are using in this paper. We have further noted and shown that the splitting between the doubly ( ) and singly () charged scalars is less than , irrespective of the breaking scale. Thus, the onshell decay is protected and the decay branching ratio of the doubly charged scalar is affected.
After settling these issues regarding the spectrum, we have computed the signal cross section for the process using realistic cuts. The necessary SM background for this final state is also evaluated. It has been shown that LHC2 even with high integrated luminosity will be not be sensitive to the VBFlike signals , even with relatively light doubly charged Higgs bosons (say, ). We have shown that much better perspective exists for the future FCC colliders with center of mass energies 33 and (or) .
In passing we would like to mention that we have used the VBF cuts as adopted in Dutta:2014dba (). We have compared the ATLAS and CMS (tight and loose) suggested cuts which are not very widely different from significance point of view.
Let us conclude with a comparative comment: MLRSM VBFlike signals connected with scalar production (which is part of the righthanded triplet) is comparable with the scalar production, see Eqs. (19) and (20). Thus the cross section for signal events are larger compare to that for TypeII seesaw scenario with same masses for triplet scalars. It may give a chance to disentangle between MLRSM and SM with an additional triplet, e.g. the Higgs Triplet Model Melfo:2011nx (); Han:2007bk (); Perez:2008ha (); Englert:2013zpa (); kang:2014jia (); Kanemura:2014goa (), though detailed analyses are needed for comparison.
Acknowledgements
The authors would like to thank Benjamin Fuks for sharing with them a modified version of FeynRules. This work is supported by the Department of Science and Technology, Government of India under the Grant Agreement No. IFA12PH34 (INSPIRE Faculty Award) and the Polish National Science Centre (NCN) under Grant Agreement No. DEC2013/11/B/ST2/04023 and under Postdoctoral Grant No. DEC2012/04/S/ST2/00003. The work of R.S. is supported by Science and Engineering Research Canada (NSERC).
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