Searching for Additional Higgs Bosons via Higgs Cascades

The discovery of a 125 GeV Higgs boson at the Large Hadron Collider strongly motivates direct searches for additional Higgs bosons. In a type I two Higgs doublet model there is a large region of parameter space at $\tan\beta>5$ that is currently unconstrained experimentally. We show that the process $gg \to H \to A Z \to ZZh$ can probe this region, and can be the discovery mode for an extended Higgs sector at the LHC. We analyze 9 promising decay modes for the $ZZh$ state, and we find that the most sensitive final states are $\ell\ell\ell\ell bb$, $\ell\ell jjbb$, $\ell\ell\nu\nu\gamma\gamma$ and $\ell\ell\ell\ell +{}$missing energy.


Introduction
The discovery of a Higgs-like 125 GeV particle at the Large Hadron Collider (LHC) began a new era in elementary particle physics [1,2]. The experiments have moved rapidly from discovery to precision measurements of the properties of the new particle. We now have strong evidence that the 125 GeV particle is a scalar, and we know that its couplings agree with the couplings of the Standard Model (SM) Higgs at the 15% level [3,4]. This implies that electroweak symmetry breaking is (at least mostly) a weakly-coupled phenomenon.
As a direct result of this, for the first time in the history of particle physics we have an experimentally complete theory that can be consistently extrapolated to energies far above the TeV scale. This is a tremendous achievement, but it also raises the question of whether there is any additional new physics to be found at the LHC. The existence of an elementary scalar particle brings to the fore the problem of naturalness of the standard model, and strongly motivates new physics at the weak scale accessible to the LHC. In particular, extensions of the standard model that address the naturalness problem generally require an extension of the Higgs sector (for example SUSY or PNGB Higgs models). Conversely, if the weak scale is unnatural and instead has an anthropic explanation, we do not expect any additional light scalars. Searching for additional Higgs bosons is therefore an important part of the program of probing naturalness at the LHC.
There are many candidate models for physics beyond the standard model, but the absence of any signal has ruled out the simplest and most natural models. This motivates searching as widely as possible for new physics, and suggests a phenomenological approach of looking for signals based on plausible event topologies. It is important not to miss any possible signal, and at a hadron collider like the LHC one has to know exactly what to look for to find new physics. Simplified models that contain the minimum degrees of freedom relevant for a particular type of signal are useful tools for generating signal events and interpreting the results of searches [5]. This is the philosophy adopted in the present paper.
Our simplified model for additional Higgs bosons is the two Higgs doublet model (2HDM). This is the simplest model that has an additional source of electroweak symmetry breaking beyond the Standard Model. In this paper, we study the Higgs cascade process gg → H → ZA → ZZh. We demonstrate that this can be important in a type I 2HDM for tan β > ∼ 5. Of course, the masses must be such that the decay is allowed, and we must have m A < 2m t , otherwise the decay A → tt dominates and reduces our signal. Our search is therefore sensitive in the mass region 215 GeV < m A < 355 GeV, m H > m A + 90 GeV. (1.1) This is a region of parameter space where other direct searches are insensitive. We demonstrate that the searches we consider can be more sensitive than indirect constraints from Higgs coupling measurements, and in fact can be the discovery mode for new Higgs bosons. We analyzed 9 different final states for the ZZh decays that we believe are the most promising. These are listed in Table 1. We use the notation We find that the most sensitive final state is the "golden mode" + − + − bb, which is essentially background-free, and can lead to a 5σ discovery of our our benchmark model at 66 fb −1 at the 14 TeV LHC. Perhaps more surprisingly, we also find that the final state + − jjbb is also sensitive. This mode has large background, and a careful treatment of background uncertainty is needed to draw any conclusion. We obtain a 3σ sensitivity with 300 fb −1 with a cut-and-count analysis, and find that a boosted decision tree technique may be able to boost the significance above 5σ. We also find that the final states ( + − )(νν)(γγ) and + − + − + / E T are sensitive at the 3σ and 2σ level, respectively. Searches for ZZh are therefore very strongly motivated in the current run of the 14 TeV LHC.
Because several of the searches are rate-limited, the high-luminosity LHC (3000 fb −1 at 14 TeV) is very effective in exploring the ZZh signal. We find that all five of the modes listed above can give a 5σ signal for our benchmark model, illustrating the possibility of studying the signal in multiple channels. This paper is organized as follows. In Section 2, we briefly review the 2HDM and explain why the ZZh final state is a sensitive probe when in a type I 2HDM at large tan β. In Section 3, we report our analysis of experimental searches in a number of final states and compute the significance for the 14 TeV LHC. Section 4 contains our outlook and conclusions.

Additional Higgs Bosons in the Two Higgs Doublet Model
In this section we briefly review the experimental constraints on the two Higgs doublet model (2HDM) and motivate our search. The 2HDM extends the SM by adding an additional Higgs doublet. It is by now a textbook topic [6].
There are many parameters in a general 2HDM, but only a small number of them are the most important for phenomenology. One important parameter of the model is the ratio of the VEVs of the two Higgs doublets H 1,2 , conventionally parametrized by tan β = v 2 /v 1 , with v = v 2 1 + v 2 2 = 246 GeV. Another important parameter is the mixing angle α that defines the mass eigenstates of the neutral CP even scalar states: (2.1) For the interactions of the Higgs bosons with gauge bosons and other Higgs bosons, there is no natural choice for H 1,2 , so α and β are not separately meaningful. What is meaningful is the mixing angle between the mass basis (h 0 , H 0 ) and the basis where one of the fields has vanishing VEV. This "Higgs angle" is given by θ H = β − α + π/2. (The π/2 is due to unfortunate standard conventions.) The coupling of all of the Higgs bosons to vector bosons is therefore determined by β − α. Some examples relevant for our work are The fact that the hZZ coupling is modified for cos(β − α) = 0 is an important constraint on this model. In the "alignment limit" cos(β − α) → 0 the light mass eigenstate h 0 is solely responsible for electroweak symmetry breaking, and so its couplings to all states are standard-model like.
The parameters α and β become separately meaningful when we consider Yukawa couplings between the Higgs fields and fermions, which pick out particular linear combinations of H 1,2 . The most well-studied possibilities are so-called type I models where H 2 couples to all fermions, and type II models where H 1 couples to leptons and down-type quarks, and H 2 couples to up-type quarks. Type II models have received the most attention because the minimal supersymmetric standard model (MSSM) Higgs sector is type II, but extensions of the MSSM can have have an effective type I Higgs sector at low energies [7][8][9]. There are other possibilities beyond type I and II, but these are sufficient to illustrate the physics being studied here.
In type I models, the coupling of neutral Higgs fields to fermions are The values of α and β determine much of the phenomenology, and we will plot constraints in the plane of cos(β − α) and tan β. The vertical line cos(β − α) = 0 is the alignment limit, which is very difficult to probe experimentally. In Figs.1 and 2 we show the experimental constraints from the 8 TeV run of the LHC on type I and II 2HDM models, for the benchmark masses m H = 450 GeV and m A = m H ± = 250 GeV. The indirect constraints from h → γγ and h → ZZ are independent of the masses of the heavy Higgs bosons, while the direct search constraints from H → ZZ and A → Zh weaken rapidly when this mass is increased. Both direct and indirect probes are therefore essential for probing the Higgs sector.
In type I models, we see from Fig.1 that there is a large region of parameter space of the model at large tan β that is currently unconstrained experimentally. The indirect constraints from h → γγ and h → ZZ are approximately independent of tan β in this region. The constraint from A → Zh becomes ineffective at large tan β because the Att coupling becomes small, suppressing the dominant production gluon fusion production of A. The production of H is unsuppressed, and the process H → ZZ is the main direct constraints, but its effectiveness is limited by the large background from SM ZZ production. Fig .2 shows the same constraints for a type II model. The indirect constraints are much more constraining in this case, and there is much less parameter space open for direct searches. This is mainly due to the fact that for large tan β the hbb coupling becomes large there, which affects the h branching ratios.
In this paper we investigate the cascade decay H → ZA → ZZh as a way of probing the unconstrained region of the type I 2HDM. The motivation for this is that the H production is unsuppressed at large tan β. The decay A → Zh is suppressed for cos(β − α) → 0, but is still significant for much of the unexplored region. This can be seen in Fig.1b, which shows the σ × BR for gg → H → ZA → ZZh superimposed on the other experimental constraints. We will demonstrate that this is more effective than gg → H → ZZ in this parameter range, because the latter suffers from larger standard model backgrounds.
To compare the various channels, we use the benchmark mass values m A = m H ± = 250 GeV, m H = 450 GeV. We choose the other parameters in the 2HDM potential so that the decay H → hh is negligible, which is easily accomplished without any large couplings or tunings. This benchmark model has a σ × BR for ZZh production of 0.45 pb. Additional properties of the benchmark are given in Appendix A. We also give results from a scan over m H at the end of the paper.

Searching for ZZh Final States
To examine the experimental prospects for ZZh production, we calculate the expected signal significance for the benchmark model with m A = 250 GeV and m H = 450 GeV, which has σ × BR(ZZh) = 0.45 pb for the 14 TeV LHC, with total luminosity of 300 fb −1 , as reported in Table 1. Simulated events for both signal and SM backgrounds were generated by MadGraph5 [10], with showering and hadronization simulated by Pythia8 [11], and the detector response simulated by Delphes3 [12]. For the multijet backgrounds, jet matching was used. The tagging rate, particle reconstruction efficiency and particle isolation requirement are reported by CMS in Run I [13][14][15][16][17].
The LO cross-sections of the SM backgrounds for each channel are calculated by MadGraph5.
To distinguish the Higgs Cascade signal over much larger SM background, we apply event selection requirements, separately optimized for each final state, as described below.

Requirements on Reconstructed Particles
Detector limitations, such as trigger requirements and detector acceptance, are common across all channels, and so common selection requirements are applied to reconstructed jets, muons, electrons, and taus, before further selection requirements, optimized for each final state, are applied.
Leptons are required to have p T > 10 GeV and pseudorapidity |η| < 2.5. We further require isolated leptons, as determined from the isolation ratio R iso = p T,j /p T, where p T,j is the clustered transverse energy, contained in a cone of radius ∆R around the lepton, and p T, is the lepton transverse energy. The lepton isolation requirement used in this analysis is ∆R < 0.3 with R iso < 0.1, except for signals where both Z's decay to leptons. In this case, the leptons are boosted in the Z direction and therefore tend to be close together. We therefore use a different isolation requirement with ∆R < 0.2, with R iso < 0.05 for electrons and R iso < 0.1 for muons. Similar isolation criteria have been used by ALTAS for their multilepton searches in LHC Run I [18,19].
Jets are required to satisfy p T > 20 GeV and |η| < 5. Photons are required to satisfy p T > 10 GeV and |η| < 2.5. The b-tagging rate is adjusted to be the same as one of the commonly used b-taggings in CMS detector, which is 75% tagging efficiency and 1.5% misidentification rate [13]. According to the Z → τ τ cross section measurement in CMS run II, the hadronic decayed tau identification efficiency is set to be 60% and the mis-identification rate from jets is set to be 3%.
The remaining event selection is optimized for each individual channel, as described below.

ZZh
This is the "golden channel" for the ZZh final state, with a clean signal and essentially no background. For this channel, we require two b-tagged jets and two opposite-sign same-flavor (OSSF) isolated lepton pairs. The main backgrounds for this channel come from ttZ and ZZ + bb. As the probability of detecting a b quark from misidentification of a jet is about 1.5%, the ZZ + jets with two misidentified b jets is much smaller than ZZ + bb. To ensure that the trigger efficiency is nearly 100% for the selected events, we require that the leading lepton has p T > 20 GeV, while the second has p T > 15 GeV.
The remaining requirements were chosen to maximize the significance, approxi-mated by where S is the number of signal events and B is the number of background events, at 300 fb −1 . To suppress the ttZ background, the total missing transverse energy is required to satisfy / E T < 80 GeV.
All normalized to 1.   Table 2 displays the number of events after each cut for both signal and backgrounds. The expected significance for our benchmark model in this channel is 11σ. The integrated luminosity required to reach 5σ is 66 fb −1 , and 3σ is 24 fb −1 . Initial  Table 2: Cut flows after each selection for the + − + − bb channel. The number of signal and backgrounds are estimated for a luminosity of 300 fb −1 . The third column gives the number of events after requiring 2 OSSF lepton pairs and 2 b-tagged jets.

ZZh
This channel benefits from the large branching ratios of H → bb and Z → jj, but has significant ttjj and Zbbjj background. Additional backgrounds such as W + W − +jets and Z +jets, where two jets are misidentified as originating from a b-quark, were found to be negligible compared to the two primary backgrounds.
We require two b-tagged jets, two non-b-tagged jets, and an OSSF lepton pair. To ensure that the trigger is nearly 100% efficient, the leading lepton must have p T > 30 GeV.
To devise selection requirements which optimally separate the Cascade Higgs signal from SM background, several kinematic variables were considered, including the p T of the bb system and its invariant mass; the p T of the jet pair and its invariant mass; the p T of the + − system and its invariant mass; the missing transverse energy; and the reconstructed masses of A and H. Among all the variables, m bb , m + − , / E T , m A and m H show the most promise for rejecting SM background. We plot the m bb and m + − jjbb distributions in Fig. 4a and Fig. 4b.   The event yields for each background and the signal are given in Table 3. The significance for this decay mode is 3.6σ after the invariant mass selections on the candidate A and candidate H.
In this channel, the background yield is much larger than the signal. So unlike the other channels, the uncertainty of the background may largely affect the outcome. In the calculation, the background uncertainty is set to be 5% for cross section and 3% for luminosity. By using likelihood ratio (LR) method, instead of simple S/ √ B, we calculate the significance to be 2.2σ. Moreover, by using boosted decision tree (BDT) method, we find that the signal significance could reach 5.2σ. In this method, the same five variables previously used in the cut-and-count analysis and m + − jjbb constitute the input of the BDT. The output, the BDT response, is used to calculate the significance with LR method, see Fig. 5.  Table 3: Cut flows after each selection for the + − jjbb channel. The number of signal and backgrounds are estimated for a luminosity of 300 fb −1 . The third column gives the number of events after requiring an OSSF lepton pair, 2 b-tagged jets and 2 jets.

ZZh
In this channel, the relatively small decay branching ratios involved are partially compensated by the large number of combinations of decays which result in this final state. The main contribution is from cases where at least one Z boson decays as Z → + − while the Higgs decays either as h → ν ν or h → τ τ or the other Z → τ τ where τ denotes a τ which subsequently decays leptonically.
The primary SM backgrounds are as follows:: • ZZ production, with each Z decaying either as Z → + − or Z → τ τ .
The leading lepton must have p T > 20 GeV and the sub-leading lepton p T > 15 GeV. In addition, at least one OSSF lepton pair is required to have a reconstructed invariant mass in the range 81 GeV < m( + − ) < 101 GeV. The signal processes have larger / E T than most of the SM background, as shown in Fig. 6, and the selection requirement which maximizes the signal significance was found to be / E T > 150 GeV. Fig. 6: / E T distribution for signal and backgrounds after 4 lepton selection with one OSSF at Z boson mass resonance. A high / E T cut is favored as can be seen. An integrated luminosity of 300 fb −1 is assumed. Table 4 lists the number of signal and background events obtained after the final cuts. This significance of the benchmark model after all cuts is 2.1σ.

ZZh
The main SM backgrounds for this channel are ttγj (where j is misidentified as a photon), ttγγ, W Zγγ, + − ννγγ and Zγγ. We also considered τ + τ − γγ with the τ s decaying leptonically, but it was completely negligible after applying invariant mass cuts. For the ttγ + jets background, we use 10 −3 for the probability of a jet faking a photon, which is consistent with the CMS detector performance [20]. For the Zγγ and the + − ννγγ backgrounds, we also take into account the contribution from h → γγ.
Despite of a very clean signature, this channel suffers from very small cross sections for both the signal and backgrounds. We have applied p T cuts for the photons and Initial Final Yields Signal 1600 9.7 2.3 0.09 Total background 2.3 × 10 4 18 Table 4: The event yields for the signal and backgrounds after the selection for the An integrated luminosity of 300 fb −1 is assumed.
leptons, invariant mass cuts for the two leading charged leptons and photons, and a MET cut to take advantage of the neutrinos in the final state. After optimizing the cuts for the significance, the final selections are as follows: • Two photons with p T > 17 GeV  Table 5 lists the number of events obtained after the final selection for the signal and the backgrounds. Despite of a sharp drop in the signal cross section due to the tiny h → γγ branching ratio (∼ 10 −3 ), the good resolution in the reconstructed M γγ is especially effective in suppressing the backgrounds. The significance of this channel was found to be 2.8σ, provided that the signal yields is 2.1 and that the background yields is 0.14.  Table 5: Cut flows for the γγνν + − channel. An integrated luminosity of 300 fb −1 is assumed. The third column gives the number of events obtained after requiring an OSSF lepton pair and two photons.

ZZh → ( + − )(jj)(γγ)
This channel faces the similar challenges as the + − ννγγ channel, where both the signal and the background cross sections are fairly small. However, the sharp resolution in M inv (γγ) for the signal helps significantly suppress the backgrounds. The main SM backgrounds for this channel contain the irreducible background + − jjγγ, + − γ + jets with one jet-faked photon and + − + jets with two fake photons. Other SM processes, such as tt+ fake γs, ttγγ and ZZγ+ fake γ can also contribute but their final yields are much smaller compared to the main backgrounds due to their smaller cross sections and the tiny jet-faking-photon rate. Similarly to the Z → jj decay in the + − jjbb final state search, the reconstructed m jj has so broad a peak that it cannot be exploited. The final selections are as follows: • Two photons with p T > 24 GeV • Two jets with p T > 24 GeV • Two leptons with p T > 13 GeV • Invariant mass m γγ ∈ [120, 130] GeV • Invariant mass m + − ∈ [81, 101] GeV • Missing E T < 120 GeV Table 6 shows the cut flows and signal and background yields for this channel. With 5.7 signal events and 9.6 background events, we get a 1.7 σ significance.  Table 6: Cut flows for the γγjj + − channel. An integrated luminosity of 300fb −1 is assumed.

Other Channels
There exist other channels that do not perform as well as the previously described 5 channels, nevertheless show interesting features that are worth considering given the prospect of a higher integrated luminosity.
One of them is Z → νν, Z → jj, h → γγ. As in the case of + − jjbb (Fig. 4b), the reconstructed Z from dijet is almost useless in differentiating between the signal and the backgrounds. Therefore, this channel suffers not only from a small cross section, but also from "wasting" two Zs. However, just as those channels with h → γγ, the outstanding resolution in the reconstructed m h can be very powerful in suppressing the background. The event selection requires two photons that satisfy 122 < m γγ < 128 GeV, two jets that satisfy m jj > 60 GeVand a / E T requirement of / E T > 140 GeV. Due to the massive cross section, QCD production of two photons still dominates after the selection of m h and high / E T requirement. The final signal yield is 7.4 while background yield is 240, giving a significance of 0.5σ assuming an integrated luminosity of 300 fb −1 . Table 7 displays the cut flows for the signal and the total background for this channel.  Table 7: Cut flows for the γγννjj channel. An integrated luminosity of 300fb −1 is assumed.
Another interesting decay mode is Z → + − , Z → jj, h → τ h τ h . This channel utilizes the hadronic tau tagging in LHC detectors. Compared to Z → + − , Z → jj, h → bb, it successfully avoids the large background from tt+jets. But it is seriously inflicted by the high tau mis-tagging rate. Hence, Z + jets with two misidentified τ h s dominates. The event selection requires an OSSF lepton pair that satisfies 76 < m + − < 106 GeV, an OSSF tau pair that satisfies 80 < m τ h τ h < 150 GeV, two non tau-tagged jets, / E T < 130 GeV, m A < 330 GeVand m H < 670 GeV. m + − and / E T selection is applied to ensure that the other SM backgrounds are negligible compared to DY lepton pair production. The final significance is about 0.7σ. Table 8 gives the the cut flows for the signal and the backgrounds. Initial Signal  630  26  18  17  17  15 11 Total background 2.3 × 10 6 4.9 × 10 3 1.3 × 10 3 1.3 × 10 3 1.2 × 10 3 620 290 Table 8: Cut flows for the + − jjτ h τ h channel. An integrated luminosity of 300fb −1 is assumed.

Results of the Benchmark Study
In Table 9, we list the number of signal and background yields for each channel studied and the significance reached at both 300 fb −1 and 3000 fb −1 .  Among all the channels studied, + − + − bb performs the best; the four-lepton requirement provides a clean signal, and h → bb has a relatively large branching ratio. The next best performing channel is + − jjbb. Although + − jjbb gives the most signal events, it is hard to suppress the Z + jets backgrounds, for the jet shower is severe, the resolution of jet energy is not as good as that of leptons, and the reconstructed dijet mass peak is not significant enough to suppress the backgrounds. + − ννγγ and + − jjγγ enjoy an outstanding resolution in the reconstructed m h , meanwhile suffering from a much smaller cross section compared to the three other channels.
For the most sensitive channel + − + − bb, we compare the significance reach of this channel with those of the direct A and H searches at 14 TeV for our benchmark. For simplicity, we only consider A → Zh → + − bb and H → ZZ → + − + − for the direct searches, both of which were studied by CMS and ATLAS in LHC Run I. Details of the direct searches considered here can be found in Appendix B and C. In Fig. 7a, we give projections of the A and H direct searches, assuming an integrated luminosity of 300 fb −1 . We also display the ATLAS' projections of 95% CL likelihood contours for κ V and κ F 1 at 14 TeV with 300 fb −1 [21] in the same plot. In Fig. 7b, the limits that can be reached by the H cascade search are shown side by side with the direct searches. It can be clearly seen that the + − + − bb channel from the H cascade search is more sensitive for tan β 8. To demonstrate that our search is less sensitive in typeII model, we compare the significance reach of the + − + − bb channel from the H cascade search with the direct search A → Zh → + − bb for our benchmark in Fig. 8. We also display the ATLAS' projection on h → γγ cross section at 14 TeV in the same plot. As one can see, the direct A search is slightly more sensitive compared to the H cascade search. Type I 2HDM tanβ=10 m H ± =m A =250 GeV The benchmark study shows that the H cascade search is most sensitive at large tan β. We consider as a benchmark tan β = 10, and investigate the range in m H for which this search provides new sensitivity. For tan β = 10, the direct A search is completely ineffective (see Fig. 7b) because the production of A via quark loops is suppressed by tan 2 β in Type I 2HDM. That leaves the direct H search as the only relevant comparison to the H cascade search for this benchmark. As can be seen from Fig. 9, the 3 σ exclusion of the H cascade search reaches m H ∼ 650 GeVwithin two standard deviations of the SM limit. The direct H search is not as sensitive as the cascade search, as it suffers from the SM ZZ background.
The theory makes no prediction for the value of m H , and therefore the lookelsewhere effect should be considered. However, considering the optimized selection criteria for m + − + − bb in the most sensitive channel, we estimate that the number of independent m H bins in the region this analysis is sensitive is only about three. Thus, the look-elsewhere effect is not expected to significantly affect the projected sensitivity of this search.

Conclusions
In this paper, we demonstrate that the search gg → H → AZ → ZZh can be a discovery mode for additional Higgs boson at the 14 TeV LHC. For a benchmark with m A = 250 GeV and m H = 450 GeV we find that the significance with 300 fb −1 is over 10σ in the "golden channel" ( + − )( + − )(bb), and that the most signal abundant channel ( + − )(jj)(bb) may reach 5σ significance with a boosted decision tree analysis. At the high-luminosity LHC (3000 fb −1 ) the prospects are even better, with five channels having over 5σ significance. We emphasize that this benchmark will not be probed by other search channels or Higgs coupling measurements. The reach also persists for values of m H up to 650 GeV, again in models that are not probed by existing searches. We conclude that searches for ZZh final state are highly motivated at the 14 TeV LHC.   The most important backgrounds are Zbb and tt. We use MadGraph5 to generate both signal and background and perform hadronization and the detector simulation with PYTHIA8 and Delphes3. The A → Zh → + − bb benchmark cross section we used here is 50 fb.
We are interested in one OSSF lepton pair and two b-tagged jets. Our requirements are as follows: • Two OSSF leptons with p T > 10 GeV, |η| < 2.5 The dominant background is ZZ. We use MadGraph5 to generate both signal and background and perform hadronization and the detector simulation with PYTHIA8 and Delphes3. The H → ZZ → + − + − benchmark cross section is set to be 0.875 fb.