Search for a doubly-charged boson in four lepton final states in type II seesaw

CMS and ATLAS have searched for a doubly-charged boson $H^{\pm\pm}$ which may arise from type II seesaw in the 7 TeV run at the LHC by considering pair or associated production of doubly-charged bosons under the assumption of degenerate triplet scalars. In this work, we consider non-degenerate triplet components with the mass gap $\Delta M \sim 1 - 40$ GeV which leads to enhanced pair-production cross-sections of $H^{\pm\pm}$ added by the gauge decays of the heavier neutral and singly-charged bosons. We reevaluate the constraints in the $\Delta M-M_{H^{++}}$ plane depending on the triplet vacuum expectation value $v_\Delta$ in the type II seesaw model which are much more stringent than the current search limits. We further study the possibility of observing same-sign tetra-lepton signals in the allowed parameter space which can be probed in the future runs of the LHC.


I. INTRODUCTION
One of the key questions in physics beyond Standard Model is the origin of the neutrino masses and mixing. It can be attributed to an SU (2) triplet boson which couples to both the lepton doublet fermions and the Higgs doublet boson realizing the so-called type II seesaw mechanism [1]. An essential feature of this scenario is the presence of a doublycharged boson H ±± whose decay to same-sign di-leptons with different flavor states may allow us to probe the neutrino mass structure at the LHC [2]. CMS [3] and ATLAS [4] have searched for doubly-charged bosons at √ s = 7 TeV with about 5 fb −1 of integrated luminosity of data. CMS have considered three-and four-lepton final states coming from the associated production process pp → H ++ H − → + i + j − k ν l [5] and the pair production process [6] to put constraints on the doubly-charged boson mass M H ++ in four different benchmark points that would probe different neutrino mass structure. On the other hand, ATLAS looked at same-sign di-lepton (SS2L) signals to probe H ±± in pair production of doubly-charged boson at the LHC. In their analysis, they put strong bound on leptonic branching fractions of the doubly-charged boson depending on its mass.
In both analyses, degenerate masses for the triplet bosons, H ±± , H ± , H 0 and A 0 are assumed, which is possible only when a particular scalar coupling called λ 5 in the scalar potential vanishes. But there is no reason to assume this particular coupling to be zero.
Indeed, interesting phenomena arise for non-vanishing λ 5 [2,[7][8][9]. When λ 5 is positive leading to ∆M ≡ M H + − M H ++ ≈ M H,A − M H + > 0, H ±± is the lightest among triplet scalars and other triplet scalars decay dominantly to H ±± through cascade decay associated with several W ∓ * in a large parameter space of λ 5 . 1 In this parameter space, pair-production cross section is enhanced significantly since other (pair and associated) triplet production channels contribute to pair-production of doubly-charged bosons. This leads to a more stringent bound on doubly-charged boson mass M H ++ as compared to the current CMS and ATLAS bounds.
In this paper, we evaluate the exclusion regions in the M H ++ -∆M plane in the type II seesaw model utilizing the search strategy employed by CMS and ATLAS collaborations.
We consider λ 5 (and thus ∆M ) to be non-vanishing and thus expect much stronger bound on 1 The mass gap ∆M is restricted by |∆M | 40 GeV independently of M H ++ due to electroweak precision constraints [10] and thus the associated W ± are always off-shell.
M H ++ than obtained by CMS and ATLAS. This bound depends also on the triplet vacuum expectation value v ∆ which controls the ratio of the branching fractions for H ++ → l + i l + j and W + W + through the neutrino mass relation [2]. For the illustration of our analysis, we choose three different values of v ∆ to examine the parameter regions of (M H ++ , ∆M ) allowed by the current data and then look for the possibility of observing same-sign tetra-lepton (SS4L) signal [11] at 8 TeV LHC (LHC8), and 13 TeV LHC (LHC13) with 20 fb −1 and 100 fb −1 integrated luminosities, respectively. When v ∆ 10 −4 GeV, the branching fraction of H ++ → W + W + is almost 100 % resulting in highly suppressed same-sign di-lepton [12] or four lepton signals [13] from W decays and thus very loose bounds on M H ++ . We take v ∆ as large as 2 × 10 −4 GeV for which the branching fraction of H ++ → l + l + is around 20 % and thus still a sizable number of four lepton final stastes can arise. Note that SS4L signals arise due to a novel phenomenon of the triplet-antitriplet oscillation guaranteed by a tiny mass splitting between H 0 and A 0 related to the neutrino mass, which leads to pair-production of same-sign doubly-charged bosons after the chain decays of H 0 , A 0 → H ± → H ±± allowed by sizable ∆M [11].

II. TYPE II SEESAW MODEL
When the Higgs sector of the Standard Model is extended to have a Y = 1 complex SU (2) L scalar triplet ∆ in addition to the standard doublet Φ, the gauge-invariant Lagrangian is written as where the leptonic part of the Lagrangian required to generate neutrino masses is and the scalar potential is Here used is the 2 × 2 matrix representation of ∆: Upon the electroweak symmetry breaking with Φ 0 = v 0 / √ 2, the µ term in Eq. (2) gives rise to the vacuum expectation value of the triplet For non-vanishing v ∆ , the neutrino mass matrix is generated as a product of the leptonic Yukawa coupling (1) and v ∆ : This allows us to reconstruct the Yukawa matrix f ij from the current neutrino oscillation data up to unmeasured CP phases and mass hierarchy. For our analysis, we use two neutrino mass matrices for normal and inverted hierarchies derived in Ref. [11] assuming vanishing CP phases.
After the electroweak symmetry breaking, there are seven physical massive scalar eigen- the first five states are mainly from the triplet scalar and the last from the doublet scalar.
For the neutral pseudoscalar and charged scalar parts, where G 0 and G + are the Goldstone modes, and for the neutral scalar part, . Neglecting the triplet-doublet mixing, the masses of the triplet bosons are The mass of the Standard Model boson h 0 is given by Eq. (7) tells us that the mass splitting among triplet scalars to the linear order for small splitting (that is, for |λ 5 |M W gM ) can be written as Furthermore, depending upon the sign of the coupling λ 5 , there are two mass hierarchies among the triplet components: In this work, we focus on the latter scenario, where the doubly-charged scalar H ±± is the lightest so that it decays only to l ± i l ± j or W ± W ± whose coupling constants are proportional to f i j or ξ, respectively: Thus the branching fraction for H ++ → l + i l + j is completely determined for given v ∆ and the neutrino matrix (4). On the other hand, unless the mass splitting ∆M is negligibly small.
The di-lepton decay rates of H ++ are given by where S = 2 (1) for i = j (i = j). From the neutrino mass relation, M ν ij = f ij v ∆ , one gets the total di-lepton rate which is inversely proportional to v 2 ∆ : wherem 2 ν = i m 2 ν i is the sum of three neutrino mass-squared eigenvalues. On the other hand, the di-W decay rate Γ W W = Γ(H ++ → W + W + ) is proportional to v 2 ∆ , and thus the leptonic branching fraction BF( Given the neutrino mass matrices for the normal (NH) and inverted (IH) hierarchies [11], the individual di-lepton decay rates Γ l i l j normalized by the total leptonic decay rate Γ ll are given by For given v ∆ one can read off the flavor-dependent branching fraction BF(H ++ → l + i l + j ) = Γ l i l j /Γ H ++ combining Eq. (12) and Fig. 1.
An important quantity for a SS4L signal is the mass splitting δM HA between H 0 and A 0 which is much smaller than the mass difference ∆M between different triplet components.
The µ term in Eq. (2), which is lepton number violating, generates not only the triplet VEV: but also the mass splitting between the heavy neutral scalars, As will be shown later, δM HA can be comparable to the total decay rate of the neutral scalars, Γ H 0 /A 0 , for a preferable choice of v ∆ , which enhances the same-sign tetra lepton signal [11]. which can contribute to pair-production of doubly-charged bosons which are listed below: In Fig. 2 One of our aims in this paper is to revise the constraints on M H ++ obtained by CMS and ATLAS after including all the processes which contribute to pair-production of doublycharged bosons. We use CTEQ6L [14] parton distribution function (PDF) and the renormalization/factorization scale is set at 2M H + . CALCHEP [15] is used to generate the parton level events for the relevant processes. Then, using LHEF [16] interface, we pass these parton level events to PYTHIA [17] for fragmentation and initial/final state radiations. We use PYCELL, a toy calorimeter in PYTHIA, for hadronic level simulation for finding jets using a cone algorithm. For a more realistic simulation, we utilize the same analysis strategy as employed by CMS and ATLAS collaborations [3,4] in the study of doubly-charged boson. We use selection criteria for four lepton events from table 3 of the CMS paper [3]. As for the samesign dilepton analysis which was performed by ATLAS, we put following selection criteria.
Leptons must have a transverse momentum above 20 GeV and be well isolated. In pairs where the higher-p T lepton is an electron, it is required to have p T > 25 GeV. All pairs of electrons or muons with the same electric charge are considered. The invariant mass of the lepton pair must be larger than 15 GeV, and for e ± e ± the region close to the Z-boson mass (70 GeV < m(e ± e ± ) < 110 GeV) is excluded due to a large background from Z → e + e − events with an electron charge misidentification.
In GeV. Notice that the constraints are weaker for NH as BF(H ++ → e + e + + µ + µ + + e + µ + ) is considerably smaller than that for the case of IH as can be seen from the table (12).
Thus, the constraints on the doubly-charged boson mass gets stronger for smaller v ∆ . Note behavior has to do with the branching fraction of, e.g., H + → H ++ W + shown in Fig. 2. One can see that BF(H ± → H ±± W ∓ * ) is always below 90% for v ∆ = 10 −6 GeV unless ∆M > 10 GeV, and thus none of the processes for triplet production mentioned above will contribute to pair-production of H ++ unless ∆M > 10 GeV. On the other hand, for v ∆ = 5 × 10 −5 GeV, the BF is more than 90% even for ∆M as low as 2 GeV and thus have large number of events for H ++ -H −− production which lead to stringent constraints on M H ++ even for small ∆M .
The gray region in M H ++ -∆M plane for ∆M > 38 GeV is excluded by considering electroweak precision constraints on λ 5 , hence on ∆M [10]. This bound on ∆M is found to be independent of doubly-charged boson mass M H ++ . One can also see that bounds obtained by utilizing ATLAS analysis are stronger than those obtained by following CMS. This is because ATLAS collaboration have considered same-sign di-lepton signals coming from the decay of only one doubly-charged boson in pair production while CMS have looked at four lepton final states. It is clear that ATLAS would have large number of signal events as compared to CMS.

IV. SS4L SIGNALS AT LHC8/13
Apart from the well-studied same-sign di-lepton signals, there can appear also a novel phenomenon of same-sign tetra-leptons indicating the neutral triplet-antitriplet oscillation [11]. Such a signal would be an indisputable evidence for the discovery of a doubly-charged boson in type II seesaw. For this to occur, one needs a condition for the oscillation parameter: where δM HA is the mass splitting (14) between two real degrees of freedom of the neutral triplet boson, and Γ ∆ 0 Γ(∆ 0 → H + W − * ). Arising from the lepton number violating effect, δM HA is proportional to ξ 2 and thus can be comparable to the decay rate of Γ ∆ 0 ≈ G 2 F ∆M 5 /π 3 which is also quite suppressed for a small mass gap ∆M ≈ M H 0 − M H + . Once the oscillation parameter is determined, one can calculate the production cross-sections for the same-sign tetra-lepton final states from the following formula [11]: To analyse the effect of oscillation, let us define,   for which the doubly-charged boson is the lightest, we studied the LHC bounds on its mass depending on ∆M and v ∆ utilizing the current CMS and ATLAS search for the doublycharged boson from same-sign di-lepton (SS2L) resonances. In the range of ∆M 1 GeV, the gauge decays of the heavier triplet components end up with producing doubly-charged bosons and associated W * 's and thus augment the search limit of M H ±± . On the other hand, the bound is weakened for larger v ∆ for which the leptonic decay modes of the triplet bosons are more suppressed. The results are summarized in Fig. 3 taking three representative values of v ∆ for the cases of two neutrino mass hierarchies (NH and IH).
When the tiny mass splitting between two neutral components H 0 and A 0 is comparable to the decay rate Γ H 0 /A 0 , there can appear an oscillation phenomenon which leads to pairproduction of same-sign doubly-charged bosons and thus same-sign tetra-lepton (SS4L) final states at the LHC. For allowed parameter region from the current SS2L search, we analyzed the prospects for observing SS4L signals at LHC8 and LHC13 which are summarized in Figs. 5 and 6. Note that more leptonic final states (with e and µ) are produced in the case of IH compared to NH and thus better search sensitivity is obtained for IH. Observable