New constraints and discovery potential for Higgs to Higgs cascade decays through vectorlike leptons

One of the cleanest signatures of a heavy Higgs boson in models with vectorlike leptons is $H\to e_4^\pm \ell^\mp \to h\ell^+\ell^-$ which, in two Higgs doublet model type-II, can even be the dominant decay mode of heavy Higgses. Among the decay modes of the standard model like Higgs boson, $h$, we consider $b \bar b$ and $\gamma \gamma$ as representative channels with sizable and negligible background, respectively. We obtained new model independent limits on production cross section for this process from recasting existing experimental searches and interpret them within the two Higgs doublet model. In addition, we show that these limits can be improved by about two orders of magnitude with appropriate selection cuts immediately with existing data sets. We also discuss expected sensitivities with integrated luminosity up to 3 ab$^{-1}$ and present a brief overview of other channels.


Introduction
In models with vectorlike fermions, even a very small mixing with one of the Standard Model (SM) families forces the lightest vectorlike eigenstate to decay into W/Z/h and a SM fermion. If there are more Higgs bosons, as in models with extended Higgs sector, the same mixing allows the heavy Higgses to decay into a vectorlike and a SM fermion. This leads to many new opportunities to search for new Higgs bosons and vectorlike matter simultaneously [1].
Limits from direct searches for vectorlike leptons are significantly weaker than for vectorlike quarks [1][2][3][4][5][6]. In addition, leptons in final states typically result in clean signatures. Thus searching for combined signatures of vectorlike leptons and new Higgs bosons is especially advantageous. In this work, we focus on the process: where H is the heavy CP even Higgs and the e 4 is a new charged lepton (note that, in a small region of the parameter space e ± 4 µ ∓ is also a possible decay mode for the SM Higgs [7]). We obtain new constraints on this process from recasting existing experimental searches and find future experimental sensitivities by optimizing the selection cuts. This process appears for example in a two Higgs doublet model type-II with vectorlike leptons mixing with second SM family introduced in ref. [2,8] and it was identified as Higgs decay mode Table 1. The 13 TeV LHC production rates for H → hµ + µ − for various decay channels of the SM Higgs boson in two Higgs doublet model type-II for m H = 200 GeV, tan β = 1 and BR(H → e ± 4 µ ∓ → hµ + µ − ) = 0.5. The value for h → µ + µ − assumes that the µ − µ − h Yukawa coupling is not modified; in our model however it can be suppressed or enhanced, see ref. [8].
one of the cleanest signatures of heavy Higgses in this class of models [1]. It was found that H → e ± 4 µ ∓ can be the dominant decay mode of the heavy Higgs in a large range of parameters [1]. Moreover, as we will show, the high luminosity LHC is sensitive to this process even for branching ratio ∼ 10 −5 . 1 Depending on the decay mode of the SM-like Higgs boson, h, the process (1.1) leads to several interesting final states with rates summarized in table 1 for a representative set of parameters: m H = 200 GeV, tan β = 1, BR(H → e ± 4 µ ∓ → hµ + µ − ) = 0.5. Each decay mode of the SM-like Higgs boson h → bb, W W * , ZZ * , γγ, τ + τ − , µ + µ − provides its unique signal [1]. A prominent feature of all these channels is that the dimuon pair produced with the SM Higgs does not peak at the Z boson invariant mass as is the case for most backgrounds. Moreover, in most channels, it is possible to reconstruct the H and e 4 masses.
Although specific searches for the process (1.1) do not exist, the particle content in final states is the same as for pp → Zh or pp → A → Zh and thus related Higgs searches constrain our process. We recast experimental searches for A → hZ → bb + − , where A is a heavy new particle and = e, µ, performed at ATLAS [9] and CMS [10] and for pp → h X → γγ X [11] and pp → Zγγ → + − γγ [12] performed at ATLAS. We set model independent limits on production cross section of (1.1) in bbµ + µ − and γγµ + µ − final states as functions of masses of H and e 4 . Then we suggest a simple modification of existing searches, the addition of the "off-Z" cut, which takes advantage of the two muons in the final state not originating from a Z boson, and show how the limits could be improved immediately with current data and indicate experimental sensitivities with future data sets.
After deriving model independent limits we interpret them within the two Higgs doublet model type-II. We first use the scan of the parameter space of this model for m H < 2m t presented in ref. [1], where constraints from electroweak precision observables (oblique corrections, muon lifetime, Z-pole observables, W → µν), constraints on pair production of vectorlike leptons obtained from searches for anomalous production of multilepton events [3], H → (W W, γγ) and h → γγ [1,13] have been included. In addition, we extend the scan for m H > 2m t and whole range of tan β. We show how current experimental studies constrain the allowed parameter space and what we can achieve by means of optimized search strategies. This paper is organized as follows. In section 2 we briefly summarize our analysis method such as implementing the event simulations and setting the limits on our parameter space. The new constraints recasted from the existing searches are shown in section 3 and the expected experimental sensitivities in the future with our suggested cuts are discussed in section 4. We study the impact of the new constraints and future prospects of existing and suggested searches on the two Higgs doublet model type-II with vectorlike leptons in section 5. We further analyze the parameters of heavy Higgs above the tt threshold in section 6. Finally we give conclusions in section 7.

Analysis method
In this section we discuss the tools used for the event simulation and the statistical approach we adopt to set the limits. The new physics model is implemented in FeynRules [14], events are generated with MadGraph5 [15] and showered with Pythia6 [16]. The resulting StdHEP event files are converted into CERN root format using Delphes [17]. Jets are identified using the anti-k t algorithm of FastJet [18,19] with angular separation ∆R = 0.4.
We present 95% C.L. upper limits calculated using a modified frequentist construction (CL s ) [20,21]. In recasting the searches presented in refs. [9,11,12], we follow the method described in refs. [3,22] where the Poisson likelihood is assumed. In order to calculate the number of events, N 95 s , that corresponds to the 95% C.L. upper limits, we consider a set of event numbers ({n i }) corresponding to a Poisson distribution with expectation value b equal to the number of background events. For each n i the signal-plus-background hypothesis is tested using the CL s method. The expected upper limit N 95 s is the median of the {n i } that pass the test. 2 The 95% C.L. upper limits on the total pp → H → hµ + µ − cross section normalized to the production cross section of a SM-like heavy Higgs (H SM ) are given by where A NPbb and A NPγγ are the MC level acceptances (calculated using the selection cuts of the analyses that we recast) of the bbµ + µ − and γγµ + µ − channels, ξ bb and ξ γγ are the detector level efficiencies and L is the integrated luminosity. Note that the negligible background to the γγµ + µ − mode implies N 95 s (γγ) = 3 (with Poisson statistics, a null observation over a null background is compatible with up to three signal events at 95% C.L. [3,22]). 3 For this reason the bbµ + µ − can provide a stronger constraint as long as where the ratio of experimental efficiencies (ξ bb /ξ γγ ) is about one, the ratio of Monte Carlo level acceptances (A NPbb /A NPγγ ) varies between one and three, N 95 s (γγ) is almost constant, and N 95 s (bb) increases with the integrated luminosity as can be seen in table 2.

New constraints from the 8 TeV LHC data
In this section we extract upper bounds on the heavy Higgs cascade decays we consider from existing searches with 20.3 fb −1 of integrated luminosity at 8 TeV. The process H → hµ + µ − → bbµ + µ − is constrained by searches for A → hZ → bb + − , where A is a heavy new particle and = e, µ. These searches have been performed at ATLAS [9] 4 and CMS [10] (we focus on the former because they provide the explicit number of observed and expected events, allowing us to investigate the impact of the different cuts). The process H → hµ + µ − → γγµ + µ − is constrained by the h → γγ ATLAS search [11] where the results with an inclusive lepton cut are presented (pp → h X → γγ X) and also pp → Zγγ → + − γγ [12].
The results that we obtain and describe in details in the next three subsections are presented in figures 1-3. The constraints on (σ H /σ H SM ) × BR(H → hµ + µ − ) are mostly constant as a function of the H and e 4 masses and vary in the range [0.1, 0.3]. We steeply loose sensitivity for e 4 close in mass to either the SM or the heavy Higgs (the transverse momentum of one the muons becomes too soft), or for a lighter heavy Higgs (the maximum value of the dilepton invariant mass is m H − m h , see eq. (4.1) and the related discussion, and the requirement of an on-shell Z cuts all signal events for small m H ).

Recast of the bbµ + µ − search
From the results presented in ref. [9] we extract the observed upper limit N 95 s (bb). We extract the detector level efficiency ξ bb by comparing the expected number of the Higgsstrahlung (pp → hZ) events given in ref. [9] to the fiducial number of events that we calculate. In this way our ξ bb includes the effect of the profile likelihood fit of MC background events to the data in the control region. Using the Higgsstrahlung cross section presented in refs. [24,25] and the acceptances we calculate, we find ξ bb 32%.
The fiducial region adopted in ref. [9] is defined as follows. The two muons are required to have pseudorapidity |η| < 2.5 and transverse momenta larger than 25 and 7 GeV. Their invariant mass is required to lie in the range 83 GeV < m < 99 GeV; note that this requirement cuts out a large part of our signal because we do not have an on-shell Z. A missing transverse energy cut E miss T < 60 GeV is imposed to reject the tt background. In order to reduce the Z+jets background the transverse momentum of the dilepton system  the two leptons and two b-jets. The two b tagged-jets are required to have |η| < 2.5 and p T > 45, 30 GeV to suppress Z+jets background. The invariant mass of the bb system is required to lie in the range 105 GeV < m bb < 145 GeV. Finally, in order to improve the resolution of m V H , the Higgs boson candidate jet momenta are scaled by m h /m bb where m h = 125 GeV.
Using the observed and expected background events given in table 1 of ref. [9] we obtain N 95 s (bb) 88. In figure 1 we present the upper limits on pp → H → e ± 4 µ ∓ → hµ + µ − for various choices of m H and m e 4 . The limits become very weak for m H 215 GeV because of the hard lepton selection cuts. Note that in the type-II two Higgs doublet model the ratio of Higgs production cross sections, that we show on the vertical axes, depends on tan β. For tan β < 7 this ratio is given by cot 2 β to a good approximation. At larger values of tan β the bottom Yukawa coupling increases implying a non-negligible impact on the bb and gluon fusion production cross sections. We express our result in terms of (σ H /σ H SM ) × BR(H → hµ + µ − ) because the limits on this quantity are model independent.

Recast of the γγµX search
The fiducial region adopted in ref. [11] to study the γγµX final state is defined as follows. The diphoton event is selected when the invariant mass is in the range 105 GeV ≤ m γγ < 160 GeV and p γ T > 0.35 (0.25) of m γγ for the leading (next-to-leading) photon. At least one isolated lepton with p µ T > 15 GeV is requested. The majority of our signal events pass this inclusive lepton selection cut (N ≥ 1) leading to large acceptance.
From table 3 of ref. [11] the upper limit on the fiducial cross section is about 0.80 fb at 95% C.L.. The limit on BR( 80 fb, and is presented in figure 2 for various values of m H and m e 4 . We can see that the strength of this constraint is similar to that of the bbµ + µ − search.

Recast of the γγµ + µ − search
In ref. [12] ATLAS presented a study of the γγµ + µ − final state. The fiducial cuts adopted are E γ T > 15 GeV, p µ T > 25 GeV, m µµ > 40 GeV and ∆R γγ,γµ > 0.4. Muons and photons are required to be isolated from nearby hadronic activity within a cone of size ∆R = 0.4.
In order to place a constraint on our signal we consider only three bins with m γγ ∈ [100, 160] GeV (from the right panel of figure 4 of ref. [12]). The observed number of events is 8 over a background of 5 (mainly from pp → Z(µ + µ − )γγ). The implied 95% C.L. upper limit on a new physics signal is 9.6 events.
Using a detector level efficiency of 37.7% (as given in table 6 of ref. [12]), we obtain the bounds shown in figure 3. These bounds are slightly worse than those from the γγµX analysis in part because in that analysis the observed limit was slightly better than the expected one, while in the γγµ + µ − analysis there was a small excess for 100 GeV < m γγ < 160 GeV.

Expected experimental sensitivities
In this section we suggest new selection cuts to improve the sensitivity to our signal. First let us discuss the distribution of the invariant mass of the dilepton system m . In our process the two oppositely charged muons are not produced from a Z decay. The analytic formula for m is where θ is the angle between the two muons in the heavy Higgs rest frame. As discussed in ref.
[1] a large part of our signal lies in the region |m − M Z | > 15 GeV allowing us to veto a major background process, Z + (heavy flavored) jets with Z → µ + µ − . For this reason we propose to consider separately m > M Z + 15 GeV and 20 < m < M Z − 15 GeV cuts (we added a lower limit m > 20 GeV to suppress the background events with µ + µ − from γ * ). We call these cuts "off-Z below" and "off-Z above" cuts. In each panel of figures 4 and 5 we show such regions with blue vertical lines and arrows. We see that for small m H − m h and/or m H − m e 4 the "above" cut is depleted of events.
For the bbµ + µ − channel we keep the rest of the cuts in ref. [9] other than 83 GeV < m < 99 GeV. Additionally we request that the invariant mass of all the final states m µµbb should be within 10% of each m H hypothesis. Profile likelihood fits can be used once actual data are available.
For the γγµ + µ − channel we further impose a missing transverse energy cut E miss T < 60 GeV to suppress the background from the top-quark decays. Moreover we request two leptons with p T > 15 GeV.

Sensitivity of bbµ + µ −
We begin by studying how the sensitivity of the existing 8 TeV 20 fb −1 bbµ + µ − search changes with the adoption of the new cuts we propose. This is controlled by the change in the expected number of background event that is obtained by computing the ratio of acceptances of new and original cuts:

2)
[GeV] where b 0 is the number of background events given in ref. [9], A new B and A original B are the MC level acceptances for the new and original cuts, respectively. The ratio of acceptances are obtained from the sample including Z + b-jets, tt, and Higgsstrahlung processes. 5 The 95% CL s median upper limits N 95 s obtained from the number of expected background and the ratio of acceptances are shown in table 2 for our reference parameters m H = 215, 250, 300, 340 GeV. We present separate results for the "off-Z below" and "off -Z above" cuts. Finally, the experimental sensitivities are obtained by inserting these limits in eq. (2.1).  To estimate the sensitivity at 13 TeV we start with considering the cuts used in the recent ATLAS analysis [26] performed with 3.2 fb −1 of integrated luminosity at 13 TeV. Since we are interested in m H < 340 GeV for now, we consider the low p Z T category. The basic cuts adopted in this search are the following. One of the two leptons must have p T > 25 GeV with |η| < 2.5 and the invariant mass of the dilepton should be in the 70 GeV < m < 110 GeV window. Events with two b-tagged jets are selected when one of them satisfies p T > 45 GeV on top of their basic b-jet selection criteria. The invariant mass of the two b-tagged jets must be in the range 110 GeV < m bb < 140 GeV. In order to suppress the tt background the missing transverse energy should be in the range E miss GeV where H T is the scalar sum of the p T of the leptons and b-tagged jets. To improve the resolution of the bb + − resonance signal the four momentum of the bb system is rescaled by m h /m bb where m h = 125 GeV as in the 8 TeV search [9]. Because the main goal of the search in ref. [26] is finding the resonant signal A → hZ, the four momentum of the dimuon system is rescaled by M Z /m µµ with M Z = 91.2 GeV: this requirement strongly suppresses the acceptance of our signal implying the absence of any constraint.
Our proposed cuts involve adding the "off-Z above" and "off-Z below" cuts described above, removing the rescaling of the four momentum of the dimuon system and including the invariant mass cut |m µµbb −m H | < 0.1 m H . The number of expected background events with integrated luminosities of 100 fb −1 and 3 ab −1 are calculated analogously to the 8 TeV case and the corresponding N 95 s are summarized in table 2.

Sensitivity of γγµ + µ −
The cuts that we suggest are those considered in ref. [11] (and described in section 3.2) with the inclusion of the "off-Z below"/"off-Z above" cuts, a missing transverse energy cut E miss T < 60 GeV (to suppress the htt final state) and the requirement of a second isolated muon with p T > 15 GeV. Additionally one could add a veto on high p T b-jets (for an additional suppression of the htt background) and a cut on the invariant mass of the γγµ + µ − system. The latter, in particular, could turn useful if non-irreducible sources of background turns out to be larger than expected.
The background to the γγµ + µ − channel has been studied in detail in ref. [12] (E γ > 15 GeV and p µ T > 25 GeV) and it is found to be dominated by pp → Z(µ + µ − )γγ and pp → Z + γj, jγ, jj with one or two jets misidentified as isolated photons. These backgrounds are also found to decrease steeply with the transverse energy of the photon. The E γ T cuts that we suggest are much stronger (the hardest photon has E γ T > 37 − 56 GeV depending on the diphoton invariant mass) than those considered in ref. [12] and make this background completely negligible (also taking into account the further reduction due to the off-Z cuts). Two more sources of background (that are not suppressed by a stronger E γ T cut) are pp → hZ → γγµ + µ − and pp → htt → bbµ + µ − γγν µνµ (Presently we do not require vetos on b-jets, hence any γγµ + µ − X final state is a background). At 8 TeV the combined total cross section for these two processes is about 35 ab corresponding to 0.7 events with 20 fb −1 before applying any selection cut; therefore, we set this background to zero and find N 95 s = 3. At 13 TeV the combined cross sections rises to 80 ab corresponding to 8 and 240 events with 100 fb −1 and 3 ab −1 , respectively; in this case a discussion of fiducial acceptances and detector efficiencies is crucial to estimate the expected background.
Using these selection cuts we find that the fiducial acceptances for the "off-Z below" and "off-Z above" cases are 1.4% and 1.2%, respectively. Assuming an overall detector efficiency of about 37.7% (as suggested in ref. [12]), we then find that the expected number of background events at 13 TeV with 100 fb −1 and 3 ab −1 are 0 and 1, respectively: the corresponding N 95 s are 3 and 4 events.

Constraints and future prospects in two Higgs doublet model
In this section we study the impact of the limits derived in previous sections (and indicate future prospects of existing and suggested searches) on the two Higgs doublet model type-II with vectorlike pairs of new leptons introduced in ref. [2]. We assume that the new leptons mix only with one family of SM leptons and we consider the second family as an example. In figure 6 we present the parameter space scan of this model in the plane spanned by m e 4 and (σ(pp → H)/σ(pp → H SM )) × BR(H → hµ + µ − ) for four different heavy Higgs masses (m H = 215, 250, 300, 340 GeV). 6 The charged sector Yukawa couplings are scanned in the range [-0.5, 0.5], as described in ref. [1]. Each point satisfies precision EW data constraints related to the muon and muon neutrino: muon lifetime, Z-pole observables, the W partial width and oblique observables. In addition, we impose constraints on pair production of vectorlike leptons obtained from searches for anomalous production of multilepton events [3] and constraints from searches for heavy Higgs bosons in H → W W, γγ discussed in ref. [1,13,22] and for the SM Higgs h → γγ discussed in ref. [1]. The solid red, blue and green contours in figure 6 are the new constraints obtained from recasting the existing bbµ + µ − , γγµX and γγµ + µ − searches. Note that the γγµX and γγµ + µ − constraints dominate at low m H because the bbµ + µ − search looses sensitivity due to a strong cut on the transverse momentum of the hardest muon. Dashed contours indicate expected sensitivities using our proposed off-Z cuts for three scenarios of LHC energies and integrated luminosities: (8 TeV, 20 fb −1 ), (13 TeV, 100 fb −1 ) and (13 TeV, 3 ab −1 ). The contours shown correspond to the "off-Z below" cut for m H = 215 and 250 GeV and "off-Z above" cut for m H = 340 GeV. For m H = 300 GeV both off-Z cuts result in similar bounds. A direct inspection of figure 6 shows that the analysis strategy we propose has the potential to improve the experimental sensitivity between one and two orders of magnitude depending on the heavy Higgs and vectorlike lepton masses.
From the sensitivities shown in figure 6 we see that the impact of the off-Z cuts is much more pronounced for the bbµ + µ − final state rather for the γγµ + µ − one and the expected bounds converge at very high integrated luminosity. The reason is that the background to the existing γγµ + µ − search is very small at all luminosities and, therefore, is not affected much by the additional off-Z cuts; in the bbµ + µ − channel the background is large and is sizably reduced by the cuts we propose. At very large luminosity the expected number of background events increases much more for bbµ + µ − rather than γγµ + µ − and the sensitivity of the two channels become comparable. At very high luminosities (beyond what is planned for the LHC) the di-photon channel would dominate.
Overall the potential for exclusion (discovery) of new physics in these channels in the next few years seems very strong: sensitivity to branching ratios of order O(10 −4 − 10 −3 ) is within reach and, correspondently, a very large part of this model parameter space will be tested.
We should note that, in ref. [27], ATLAS presented a search for bbµ + µ − that makes use of multivariate techniques to massively reduce the irreducible background. While we were not able to use this analysis to place constraints on our model, we expect that a dedicated experimental study of the signal we propose using a similar approach has the potential to improve significantly the bounds we presented. The sensitivity could be additionally increased by looking for the e 4 → hµ → (bb, γγ)µ resonance.
Finally let us briefly discuss the decay H → hµ + µ − with the SM Higgs decaying into the other possible channels we mention in table 1. The h → ZZ * decay yields a 4 µ + µ − final state that has negligible SM background; nevertheless the small branching ratio makes this channel less sensitive than the γγµ + µ − one. On the other hand, the sizable h → τ + τ − branching ratio (about 6.3%) makes the τ + τ − µ + µ − final state competitive with the bbµ + µ − one; a detailed study of this final state from pp → A → hZ has been performed by both ATLAS [28] and CMS [29]. The h → W W * mode yields the 2 2µ2ν final state and is expected to yield sensitivities even higher than the γγµ + µ − channel (both have negligible background and the former has a larger branching ratio). Finally the h → µ + µ − decay yields a 4µ final state with a rate that depends strongly on the model Yukawa couplings (see the discussion in refs. [7,8]).

Heavy Higgs above the top threshold
In this section we discuss the constraints and prospects for m H 2m t where the H → tt contribution to the heavy Higgs decay width reduces its branching ratio into vectorlike leptons. In this mass range, the heavy Higgs width into SM fermions is dominated by the tt channel at moderate tan β < 7 and by the bb at larger tan β.
From the analysis presented in ref. [1] (see bottom-left panel of figure 3 of that paper) it is clear that the H → e ± 4 µ ∓ branching ratio can easily be dominant for all values of tan β 20 and m H < 2m t . This implies immediately that we expect BR(H → e ± 4 µ ∓ ) to be sizable for Higgs masses above the tt threshold at large tan β (where the H → tt partial  width is suppressed with respect to the H → bb one). For tan β < 7 the H → tt partial width becomes dominant and we need a detailed numerical calculation in order to assess the size of the H → e ± 4 µ ∓ branching ratio. In order to check whether large BR(H → e ± 4 µ ∓ ) are allowed, we rescan the parameters for m H above the tt threshold up to 800 GeV and allow only parameter space points that satisfy all the constraints discussed in ref. [1]: electroweak precision data, anomalous multilepton production with missing E T , SM Higgs data for h → γγ, and heavy Higgs searches in the γγ and W W channels. As in the previous case the charged sector Yukawa couplings are scanned in the range [-0.5, 0.5].
In figure 7 we show the resulting heavy Higgs partial widths (calculated assuming H is the heavy CP even Higgs) as a function of tan β.  [30], the gg → H → tt resonant peak can be destroyed by interference with the SM background (especially for 400 GeV m H 900 GeV and tan β < 15 in the aligned two Higgs doublet model type-II). For the CP odd Higgs this effect leads to more dip-like signals in a large range of parameters but it is still hard to observe for m H < 600 GeV and tan β 5. If the heavy Higgs couples to vectorlike leptons, as in the models we consider, the H → e ± 4 µ ∓ channel offers a new and very promising avenue to discovery. In figure 9 we show the allowed parameter space in the m H and (σ H /σ H SM ) × BR(H → hµ + µ − ) plane. For simplicity we do not vary the vectorlike lepton mass and set it to m e 4 = 250 GeV; moreover we consider only the region m H < 2m e 4 to kinematically forbid the H → e 4 e 4 channel. Green, red, blue and magenta point correspond to tan β < 1, 1 < tan β < 3, 3 < tan β < 20, and 20 < tan β < 50 respectively. From figure 8 we see that our BR(H → e ± 4 µ ∓ ) can be larger than 0.25 for 3 < tan β < 20. For larger tan β > 20 the heavy Higgs production cross section is enhanced compared to σ(pp → H SM ) so the values of (σ H /σ H SM ) × BR(H → hµ + µ − ) are as large as those for 3 < tan β < 20. The solid black contour is the recasted constraint from the 13 TeV A → hZ resonance search [26]. The expected sensitivities of future bbµ + µ − and γγµ + µ − studies are displayed as dashed lines.
We conclude that recasted searches barely touch the allowed parameter space around (σ H /σ H SM ) × BR(H → hµ + µ − ) ∼ 0.05. However, future searches employing the off-Z cuts that we propose have the potential to constrain this quantity at 10 −5 level.

Conclusions
In this paper we discuss the Higgs cascade decay pp → H → e ± 4 µ ∓ → hµ + µ − that appears in models with extra vectorlike leptons and an extended Higgs sector. Among the various Figure 9. Parameter space satisfying all the constraints discussed in ref. [1] for m e4 = 250 GeV. We show estimates of the bound (black solid line) recasted from the 13 TeV A → hZ resonance search [26] and future experimental sensitivities (black dashed lines) for integrated luminosities L = 300 fb −1 and 3 ab −1 at 13 TeV. decay channels of the SM Higgs h we considered the bb and γγ ones, which yield bbµ + µ − and γγµ + µ − final states. These are two representative channels with sizable and negligible background, respectively. We were able to recast existing pp → A → hZ → bb + − , pp → h X → γγ X and pp → Zγγ → + − γγ searches into constraints on the two modes we consider. We also presented the expected sensitivities of dedicated searches in the full 8 and 13 TeV data sets.
A unique feature of cascade decay we consider is that the two leptons do not reconstruct a Z boson, while the hµ and hµµ invariant masses peak at m e 4 and m H , respectively. Therefore, we suggest to employ two off-Z cuts that focus on the region above and below the Z resonance: 20 GeV < m < M Z − 15 GeV and m > M Z + 15 GeV. In addition to these suggested cuts, the searches for two resonances corresponding to the H and e 4 masses will lead further to higher sensitivities. We find that this analysis strategy has the potential to improve the experimental sensitivity between one and two orders of magnitude depending on the heavy Higgs and vectorlike lepton masses.
We discussed an explicit realization of a new physics model in which this cascade decay is allowed to proceed with sizable branching ratio. The model has been introduced in ref. [1] and involves a new family of vectorlike leptons and an extra Higgs doublet. We found that a vast majority of this model parameter space that survives various indirect and direct constraints can be easily tested by searches for heavy Higgs cascade decays.
One major result of our analysis is that the bbµ + µ − channel dominates the γγµ + µ − in most of the parameter space up to an integrated luminosity of 3 ab −1 at 13 TeV. We also briefly discussed other possible channels and found that the τ + τ − µ + µ − and 2 2µ2ν have the potential to offer constraints comparable to those obtained from the bbµ + µ − and γγµ + µ − modes.
Furthermore we discuss the reach of our search strategy for a heavy Higgs with mass above the tt threshold. We find that the H → e ± 4 µ ∓ branching ratio can dominate over both H → tt and H → bb for 4 tan β 17 (4 tan β 32) when charged sector Yukawa couplings are allowed in [-0.5, 0.5] ([-1, 1]). However, even in the range of parameters where our process has only a small branching ratio, it can be the most promising search channel since the usual search strategies for H → tt suffer from interference effect with the SM background. Rough estimates of future experimental sensitivities are extremely promising.