Type-II Seesaw and Multilepton Signatures at Hadron Colliders
We investigate multilepton signatures, arising from the decays of doubly charged and singly charged Higgs bosons in the Type-II Seesaw model. Depending on the vacuum expectation value of the triplet , the doubly and singly charged Higgs bosons can decay into a large variety of multi-lepton final states. We explore all possible decay modes corresponding to different regimes of , that generate distinguishing four and five leptonic signatures. We focus on the 13 TeV Large Hadron Collider (LHC) and further extend the study to a very high energy proton-proton collider (VLHC) with a center-of-mass energy of 100 TeV. We find that a doubly charged Higgs boson of masses around 375 GeV can be discovered at immediate LHC runs. A heavier mass of 630 GeV can instead be discovered at the high-luminosity run of the LHC or at the VLHC with 30 .
The observation of nonzero neutrino masses and their mixings provide unambiguous experimental evidence of physics beyond the SM (BSM). So far, oscillation experiments have measured the solar and atmospheric mass square differences , and the mixing angles , and Gonzalez-Garcia:2015qrr (). Additionally, the cosmological constraints on the sum of light neutrino masses Ade:2015xua () bound the SM neutrinos to be less than eV. A natural explanation for small neutrino masses is provided by the seesaw mechanism, where eV-scale neutrino masses are generated from lepton number violating (LNV) operators of dimension 5 Weinberg:1979sa (); Wilczek:1979hc (). UV complete models generating the higher dimensional operator can have a right handed neutrino (Type-I seesaw) Minkowski:1977sc (); Mohapatra:1979ia (); Yanagida:1979as (); GellMann:1980vs (); Schechter:1980gr (); Shrock:1980ct (), triplet Higgs (Type-II seesaw) Magg:1980ut (); Cheng:1980qt (); Lazarides:1980nt (); Mohapatra:1980yp (), or, a triplet fermionic field (Type-III seesaw) Foot:1988aq (). The Type-I and Type-II seesaw models can further be embedded into Left-Right symmetric models LR (). Another very popular model is the inverse seesaw model invo (); inverseso10 () where the light neutrino masses are proportional to a small LNV parameter, and thus tend to zero for a vanishingly small value of the parameter. In this model, the smallness of the neutrino mass is protected by the lepton number symmetry of the Lagrangian111For reviews of TeV-scale seesaw models and their phenomenology see Refs. Chen:2011de ().. If we have a right handed neutrino or, a Higgs triplet states with low masses (few hundreds GeV upto a few TeV), these BSM states can be directly produced at the LHC and can be detected via their decay products in direct searches KS (); Chen:2013fna (); Mitra:2016kov (); Perez:2008ha (); Melfo:2011nx (); delAguila:2008cj (); Chakrabarti:1998qy (); Aoki:2011pz (); Chun:2013vma (); Akeroyd:2005gt (); Banerjee:2013hxa (); Dev:2013ff (). Apart from direct production, these states may appear in loop for various processes/decays. Strong constraints can be put on doubly and singly charged scalar masses from Lepton Number Violating processes at the LHC delAguila:2013mia (); delAguila:2013aga ()222For further discussion on the recent developments on muon anomalous magnetic moment and Lepton flavor violation in the context of several extensions of the SM, see review Lindner:2016bgg ().. Another way to infer the existence of such resonances are indirect detection experiments which also cover a wide range of masses and mixings MSV ().
Here we focus on the Type-II seesaw mechanism. The model is augmented with a doubly charged Higgs boson that can give rise to the smoking gun signal of same-sign dilepton pairs Muhlleitner:2003me (); Perez:2008ha (); Melfo:2011nx (); delAguila:2008cj (). The neutral component of the triplet Higgs develops a vacuum expectation value (vev) , and generates neutrino masses through the Yukawa Lagrangian. In addition to the doubly charged Higgs, the model also contains a singly charged Higgs state. The details of the Higgs spectrum have been discussed in Arhrib:2011uy (); Dev:2013ff (). The particles’ branching ratios and some collider signatures have been outlined in Perez:2008ha (); Melfo:2011nx (); delAguila:2008cj (). CMS and ATLAS have searched for pair production of doubly charged Higgs bosons, followed by their decay into same-sign dileptons and, hence, set a limit on the mass of atlashpp (). An alternative search where the is produced in association with two jets was found to be less constraining Khachatryan:2014sta (). Other than the dileptonic decay mode, in parts of the parameter space with relatively large triplet vev , the charged Higgs dominantly decays into gauge bosons or via cascade decays with on/off-shell bosons Chakrabarti:1998qy (); Melfo:2011nx (); Aoki:2011pz (). The later can give rise to the distinctive same-sign dilepton signatures, with additional b-jets Aoki:2011pz (). In particular, same-sign diboson scenario has been studied in the context of LHC in Kanemura:2013vxa (); Kanemura:2014goa (); Kanemura:2014ipa ().
Other than the conventional channel of pair production of that leads to four leptonic final states, one can have even up to five or six leptons via cascade decays into gauge bosons333Multilepton signature with triplet Higgs in supersymmetric scenario has also been studied in Bandyopadhyay:2014vma () where singly charged Higgs decays into two gauge bosons.. The multileptonic final states provide very clean signatures at hadron colliders. Hence, a handful of events can confirm or rule out the model. In this work, we carry out a thorough investigation on the collider search of such multilepton (four or five leptons) final states, that will be useful to probe the complete range of GeV GeV. We divide this range into three regimes: small, intermediate and large . We focus on both, the immediate run-II of the LHC with 13 TeV center-of-mass energy and also its future high-luminosity upgrade (HL-LHC). We further analyse the detection prospects of such multilepton signatures at a possible future TeV proton-proton collider (Very Large Hadron Collider (VLHC)) Arkani-Hamed:2015vfh (); Golling:2016gvc ().
Our paper is organized as follows: we briefly review the basics of the Type-II seesaw model in Section II. In Sec. III, we discuss the relevant decay modes and branching ratios. In the subsequent sections, Sec. IV and Sec. V, we analyse in detail the production cross sections and the discovery potential of the multilepton final states. Finally, we present our conclusion in Sec. VI.
In this section, we briefly review the basics of the Type-II seesaw scenario Magg:1980ut (); Cheng:1980qt (); Lazarides:1980nt (); Mohapatra:1980yp (). The model consists of the SM fields, with a Higgs doublet and an additional triplet Higgs that has hypercharge :
The neutral components of the doublet and triplet Higgs fields are and respectively. The components and develop a vev denoted as and with the light neutrino masses being proportional to the triplet vev . The two vevs satisfy . The kinetic term of the new scalar field that generates the interactions with the SM gauge bosons, has the form
The covariant derivative of Eq. (2) is defined as
In addition, also interacts with the leptons through the Yukawa interaction
Here, represents the charge conjugation transformation, and is a matrix. The triplet field carries lepton number +2 and hence the Yukawa term conserves lepton number. The scalar potential of the Higgs fields and is
where and are real parameters with mass dimension 2, is the lepton-number violating parameter with positive mass dimension and , are dimensionless quartic Higgs couplings. Minimization conditions for each of the scalar fields can be used to replace any two of the parameters444For the discussion on the minimization of the scalar potential, see Arhrib:2011uy ().. Usually the two mass parameters and are eliminated which leaves six independent parameters.
After transforming into the mass eigenbasis the two charged scalar fields and mix to the charged Higgs bosons and Aoki:2011pz (). Similarly, the mixing between the two CP-odd fields ( and ) gives rise to and . Finally, we obtain the SM Higgs field () and a heavy Higgs () by mixing the two neutral CP-even states and . and act as the three Goldstone bosons which give masses to the SM weak gauge bosons. The remaining seven states are the physical Higgs bosons.
The masses of the doubly and singly charged Higgs states and are expressed in terms of the parameters in the Lagrangian as
The CP-even and CP-odd neutral Higgs , and have the following masses:
where , and are given by Aoki:2011pz (),
Note that, the difference between and is proportional to the coupling , i.e.
The Higgs triplet contributes to the gauge boson masses through its vacuum expectation value . The measurement of the -parameter severely constrains the vev to GeV Kanemura:2012rs (). Since, in our case, , the difference between the charged Higgs masses and is governed by the electroweak vev . In Fig. (a)a, we show the mass spectrum of all the Higgs states, assuming the other parameters , and . Note that, for our choice of parameters, the CP-odd state and the CP-even states are heavier than the charged Higgs states . Between the charged Higgs states, is heavier than , as . Finally, is the SM-like Higgs boson, assumed to have a mass of 125 GeV. The other regime gives the opposite hierarchy between the charged Higgs masses, and has been explored in Aoki:2011pz (). We show the variation of mass spectrum of the different Higgs states with the ratio in Fig. (b)b.
It is evident from Fig. (a)a that for all the Higgs bosons are almost degenerate in masses. For larger , the charged Higgs bosons , become lighter than the neutral Higgs states . Higher (well within the perturbative regime) results in a splitting between singly charged and doubly charged Higgs masses. In the subsequent analyses, we focus on the charged Higgses with masses avoiding LEP/LHC bounds and analyse their decay widths, branching fractions and collider signatures. Note that, both the charged Higgses and contribute to process at one loop Arhrib:2011vc (); Arhrib:2014nya (); Das:2016bir (). Very low masses can cause deviation in the measured signal strength at the LHC atlas-cms-mu-gammagamma (). Since no direct bound exists from LHC on these masses for GeV, it might be, therefore, possible to set lower bound on the masses of charged scalars from the observed value of the diphoton signal strength. As mentioned in Das:2016bir (), the lower bounds on the charged scalar masses can be considered as GeV and GeV allowing deviation from the central values of the T-parameter and observed diphoton signal strength.
Iii Decay Widths and Branching Ratios
As outlined in the previous section, we consider a mass spectrum, where the singly charged Higgs is heavier than the doubly charged Higgs, . The doubly charged Higgs has only a limited number of decay modes, i.e. decays into same-sign dileptons and same-sign dibosons. The partial decay widths of the dileptonic channel depends on the strength of the corresponding Yukawa coupling . For small GeV, this gives rise to large coupling strength and hence, a large partial width. The bosonic decay mode is, on the other hand, proportional to the . Therefore, the partial width (and, also the branching ratio) for this channel becomes large for a large Perez:2008ha (); Melfo:2011nx ().
With the choice for our mass spectrum, remains absent. We show the decay widths and branching ratios in Fig. 2, for the illustrative mass point GeV. This value is in agreement with current limits from ATLAS atlashpp (). The variation of the decay width and branching fractions with the doubly charged Higgs mass is nominal. Hence, we do not show them explicitly. A couple of comments are in order:
The decay widths and the branching ratio of depends on the neutrino oscillation parameters , the light neutrino masses , and the CP violating phases. In our analysis we consider the best fit value of the oscillation parameters Gonzalez-Garcia:2015qrr (), and the light neutrino masses eV, eV and eV. We choose the CP-phases to be zero. In Fig. 2, the leptonic mode involves all three leptons and we separately show the channel.
The branching ratio of is 31.5 for small GeV. The branching ratio to and are also comparable, while the , and other off-diagonal branching ratios are relatively smaller.
The singly charged Higgs, on the other hand, can decay to a number of final states, including , , , and . For , will also decay via the off-shell mode . We show the branching ratios of the different decay modes in Fig. 3 for the scenario . It is evident from the left panel that for GeV, the leptonic mode () is the dominant decay channel. In the intermediate range of GeV, is maximised. A similar feature of the branching ratios is present for the on-shell mode . Interestingly, for this case, the above mode remains dominant even for much lower values of GeV. Note that, although we have only shown the branching ratios for few illustrative mass points of and , the features remain unaltered for other masses as well. This intermediate region is of particular interest, as the decay mode can give distinctive multilepton signatures (with five/six leptons in the final state) at the LHC (and VLHC). We will explore this in detail in Sec. V.2.
Iv Production cross section at LHC and VLHC
In this section we discuss the production of the charged Higgs boson states at the LHC at 13 TeV and the VLHC with center-of-mass energy of 100 TeV. The dominant processes are pair production of through s-channel exchange and associated production of singly and doubly charged Higgs bosons, i.e. , mediated by the boson.
We use FeynRules Alloul:2013bka () to generate suitable model file via Universal Feynrules Output (UFO) Degrande:2011ua (); deAquino:2011ub () interface and compute the hard process with MadGraph5_aMC@NLO Alwall:2014hca (). Eventually, the generated events are showered and hadronised using Pythia Sjostrand:2001yu (); Sjostrand:2007gs (). To mimic the detector response, a fast detector simulation is performed using Delphes-3.3 deFavereau:2013fsa (). All cross sections have been evaulated with NN23LO1 Ball:2013hta () as parton distribution function. We show the production cross section for the processes , and in Fig. (a)a and Fig. (b)b for the center-of-mass (c.o.m.) energies and TeV, respectively. For the 13 TeV c.o.m. energy we multiply the LO cross section by the K-factor K=1.25 Akeroyd:2005gt (). As mentioned earlier, the production of and provide the largest cross sections among all channels. Due to their electromagnetic charge, the cross section of pair produced doubly charged Higgs bosons is large compared to singly charged Higgs pair production.
V Multilepton Signature at LHC and VLHC
A large number of final states can arise from the pair production of doubly or singly charged Higgs bosons. ATLAS has performed searches for doubly charged Higgs bosons in the same-sign dielectron channel for TeV with of data atlashpp (). Assuming a 100 branching ratio of , a lower bound on the doubly charged Higgs mass is obtained GeV. However, depending on the parameter space, this limit can be relaxed due to the presence of other decay modes. For illustration, we consider a scenario where GeV resulting in BR(). The bound on the mass of doubly charged Higgs bosons becomes significantly weaker, as shown in Fig. 5. The red line corresponds to the theory prediction from atlashpp (). The limit on remains mostly unchanged as the branching ratio of the decaying into leptons are largely constant for GeV (see Fig. (b)b). Instead, for larger GeV, the branching ratio into leptonic final states is even more suppressed, as the other modes, i.e. decays into gauge bosons, start to dominate and, hence, the limit becomes irrelevant. Another bound presented by CMS for the channel can only constrain the triplet vev GeV Khachatryan:2014sta () which is out of our region of interest.
Below, we consider three separate regions for the triplet vev, namely; low, intermediate and large, and discuss various multilepton signatures relevant for each.
v.1 Small ( GeV)
The most promising channel for small is the search for pair produced decaying into dilepton. Hence, the final state consists of 4 leptons. We show the variation of cross section of with for different c.o.m energies and TeV in Fig. 6. For the 13 TeV c.o.m energy the cross section is greater than 1 fb upto mass GeV. We perform a detailed signal and background analysis for the 4l case at 13 TeV c.o.m. energy at the LHC. We also show the results for 100 TeV c.o.m. energy relevant for the VLHC.
Analysis: We consider two benchmark scenarios, a low and a high mass doubly charged Higgs boson, both in agreement with the present bound from the LHC (see Fig. 5):
GeV, obtained from GeV and GeV.
GeV with GeV and GeV.
We generate the 4l background which arises predominantly through SM diboson production. In Fig. 7 we show the distribution of various variables before cuts. Fig. 7 (left) describes the of the hardest final state lepton. The invariant mass of the two positively-charged leptons is shown in the right panel of Fig. 7. We use the following isolation and selection criteria for the final state leptons ( and ):
To avoid any contamination from jet fakes, we require the hadronic activity within a cone around an isolated lepton to be .
We apply a series of analysis cuts in order to improve the separation of signal and background:
a strict requirement for the hardest lepton: GeV.
invariant mass of the same-sign lepton pair: GeV.
veto events with invariant mass around the peak: GeV.
The cross sections after analysis cuts are given in Table. 1 for the two illustrative mass points. For the lower charged Higgs mass of 375 GeV, the cross section before and after cuts are 1.659 fb and 0.827 fb, respectively. For the higher mass 630 GeV the cross sections are 0.149 fb and 0.074 fb. In addition, we also investigate the above channel for the TeV collider, where the cross-section increases by a factor .
|Masses||Cross section||Cross section||Number||Cross section||Cross section||Number|
|(GeV)||before cuts (fb)||after cuts (fb)||of events||before cuts (fb)||after cuts (fb)||of events|
|Masses||Cross section||Cross section||Number||Cross section||Cross section||Number|
|(GeV)||before cuts (fb)||after cuts (fb)||of events||before cuts (fb)||after cuts (fb)||of events|
The inclusive partonic cross section for the SM background at 13 TeV is fb, and thus much larger than the signal cross section. However, the dilepton invariant mass cut along with the veto are extremely helpful to reject the background. We compute the statistical significance of this channel as
where and represent the number of signal and background events. We find that
The doubly charged Higgs boson of mass GeV can be discovered at the LHC with 300 luminosity with more than 5 significance, while for the higher mass of GeV, the significance is around 4.66 with the same amount of data.
A heavier doubly charged Higgs of mass 630 GeV can be discovered at HL-LHC (13 TeV) or VLHC (30 fb) with more than 5 significance.
v.2 Intermediate ( GeV)
In this region, preferably decays into, either on-shell or off-shell, , depending on the mass splitting between the two Higgs states. subsequently decays either into two leptons or into two bosons. The branching fraction into gauge bosons, i.e. , becomes dominant for GeV. This intermediate range of allows for signatures with five (or even six) leptons. Below, we discuss two channels with four and five leptons in the final states
, subsequently .
, subsequently .
The large lepton multiplicity reduces the cross section, but results in a cleaner (i.e. background free) signal. The parton level cross section for is shown in Fig. 8. We adopt the following criteria for the leptons and jets reconstruction:
and GeV and hadronic activity around an isolated lepton within a cone of has to be .
|Channel||(GeV)||No. of events|
|()||(169, 298)||0.024||0.0054||2, 16|
|(223, 332)||0.0124||0.0034||1, 10|
|()||(169, 298)||0.076||0.036||10, 107|
|(223, 332 )||0.0393||0.016||5, 47|
In Table. 2, we show the cross sections for the above channels assuming on-shell decays only. Again, we consider two benchmark points with masses () GeV, and () GeV. In order to obtain large enough mass splittings for decays into on-shell , needs to be tuned to values .
We find that the final state with five leptons occurs only in a handful of events for an integrated luminosity of 300 at the LHC. As these processes are limited only by their rate, the HL-LHC provides a promising environment. The main contribution for the five-leptonic states comes from triple gauge boson production with a cross section of fb. Hence, we do not analyse the background for the 5l channel.
The dominant background for is with fb. After applying a veto cut, the remaining cross section is reduced to a manageable rate of fb. After all cuts we find a signal cross section of fb for the masses GeV and GeV. The signal for the above masses can be probed with a significance of with and for , respectively.
v.3 Large ( GeV)
In the large region ( GeV), the branching ratio of is enhanced (see Fig. 2). We consider pair production of where subsequent decays of the gauge bosons into leptons gives rise to the signature. This has recently been analyzed in non-minimal composite Higgs scenario Englert:2016ktc (). Note that, this decay mode is very poorly constrained by LHC searches Khachatryan:2014sta () and a lighter doubly charged Higgs is yet not ruled out. We consider GeV and as low as 235 GeV for this analysis. We show the production cross section for the process in Fig. 9.
The cross section of the fully leptonic channel at 13 TeV is too small. Hence, we focus on higher c.o.m energy TeV. This channel can also produce a combination of leptonic and hadronic final states which will not be considered here. We estimate the following SM processes as backgrounds:
with subsequent decays of (with a lepton escaping detection).
with subsequent decays of .
In addition to the above processes, we also consider the process followed by the further decays of and , that can generate associated with -jets. Note that, the -jet from the above mentioned background has large . Hence, in spite of large cross section, most of this background events can be rejected applying jet and veto.
In the signal, the decay into a pair of bosons which subsequently decay into leptons, hence, final states are collimated in the lab-frame and populate the same hemisphere in the detector (see Fig. 10). Such configurations are much less likely in SM processes. We exploit this by applying a cut on the separation of the same-sign dilepton system. We demand four leptons in the final state and employ the following sets of analysis cuts:
veto events with jet leading jet GeV,
between two same-sign leptons,
veto events with GeV.
|Channel||(GeV)||No. of events|
The cross sections are shown in Table. 3 for two illustrative mass points and GeV. We find that the above mass points can be discovered at a VLHC with the following significance:
We investigated various multilepton signatures that arise in a Type-II seesaw model with a Higgs triplet . The model contains singly charged Higgs bosons as well as doubly charged Higgs states. Depending on the triplet scalar vev , and can have a number of decay modes. We focus on three different regimes of and investigate the multilepton final states for each different regime. For small ( GeV), prefers to decay to two same-sign leptons. Therefore, pair production of leads to a distinctive four leptonic signature. Assuming a 100 branching ratios of , the recent LHC search have constrained GeV. However, the limit is considerably weakened for a parameter space with lower branching ratio to leptons. We discuss in detail the prospects to observe this mode at the current run of the LHC and also at a future hadron collider to be run at a c.o.m energy of TeV. We summarize our observations as follows :
The channel with four leptons, arising from decays offers the most promising signature for small . We conclude that a doubly charged Higgs boson of mass 375 GeV can be discovered at 13 TeV LHC with luminosity. Higher mass range 630 GeV can further be discovered at a high-luminosity LHC or at a VLHC with 30 fb luminosity.
For the intermediate range, the most distinctive channel arises from cascade decays of the singly charged Higgs (both on-shell and off-shell). Further, can decay either in dilepton or modes. This leads to a final state consisting of . If all W decay leptonically rates are very small, resulting in tens of events for luminosity at 13 TeV. But the signal is very clean. We also analyze another topology with . SM backgrounds for these channels are extremely small which makes it an interesting search strategy. A lighter doubly charged Higgs mass around 169 GeV can be conclusively discovered with more than at high luminosity run of LHC.
Finally, the large region, which is poorly constrained at the LHC seems to be the most promising channel to probe lighter doubly charged Higgs bosons at the VLHC. In this case, the four leptons in the final state appears from the pair production of followed by the decay of . We find that a doubly charged Higgs of mass 235 GeV can be discovered at significance at the VLHC.
The properties of the SM-like Higgs boson has been quite well established by the LHC. No new physics has been observed so far, barring some initial statistical fluctuations, fuelling hope for potential signals. Many of the new physics models, although proposed long ago, lack detailed studies covering all their parameter regions. We explored parts of the parameter space of a SM extension with a Higgs triplet which is, otherwise, difficult to probe at existing (and future) colliders. Finding a (doubly) charged Higgs boson will be an immediate proof for the existence of at least another scalar multiplet.
The work of MM has been supported by the Royal Society International Exchange Program and DST-INSPIRE-15-0074 grant. MM thanks IPPP, Durham University, UK for hospitality where part of the work was being carried out. SN acknowledges Dr. D. S. Kothari Post Doctoral Fellowship awarded by University Grant Commission (UGC) for financial support. MM and SN thank Dr. Shankha Banerjee and Prof. C. Lester for their invaluable inputs and Dr. Santosh Kumar Rai for providing the FeynRules model file.
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