The Platinum Channel: Higgs Decays to as many as 8 Leptons

We propose a search for Higgs decays with as many as eight leptons in the final state. This signal can arise in a simple model with a hidden vector ($A_d$) that gets mass via a hidden scalar ($h_d$) vacuum expectation value. The 125 GeV Higgs can then decay $H\rightarrow h_d h_d \rightarrow 4A_d\rightarrow 8f$, where $f$ are Standard Model fermions. We recast current searches and show that a branching ratio of $H\rightarrow h_dh_d$ as large as 10% is allowed. We also describe a dedicated search that could place bounds on BR($H\rightarrow h_dh_d$) as low as $10^{-5}$ using only 36 fb$^{-1}$ of data, with significant improvements coming from greater integrated luminosity.


I. INTRODUCTION
The discovery of the Higgs boson [1,2] completes the Standard Model (SM), but it also opens up a new avenue to look for deviations from the SM. As yet, all measurements of the Higgs have been consistent with the SM [3], but deviations due to beyond the SM physics could have been missed so far if these are at a level below current theoretical and/or experimental uncertainties, or if they manifest in unconventional final states. In this paper we present an as yet unattempted measurement that could be done to probe physics beyond the SM.
The Higgs square operator, H † H, is the only gauge invariant renormalizable scalar operator in the SM. Therefore, it is quite natural to expect that if there is another sector that talks to the SM, its scalars could couple to the SM via this "Higgs portal" operator [4]. In this work, we posit a very simple hidden sector: a new U (1) gauge boson which acquires mass via a hidden sector Higgs mechanism, and the hidden Higgs has a renormalizable coupling to the SM via the Higgs portal. The new gauge boson generically couples to the SM through the "vector portal," [5] B µν F µν d , where B µν is the field strength tensor for SM hypercharge, and F µν d is the field strength for the hidden gauge group. The phenomenology of a hidden abelian gauge group was first studied in [6].
The model with Higgs and vector portal couplings was studied in the ultra-light regime in [7,8]. It was studied for general Higgs phenomenology in [9], and it has been most thoroughly studied in the context of Higgs decays to four leptons [10][11][12][13][14][15], the so called golden channel. With this model, however, there is a large region of parameter space where decays to more than four leptons are possible. If we take the hidden scalar to be lighter than half the Higgs mass, and the hidden photon to be lighter than * izaguirre.eder@gmail.com stolar@physics.carleton.ca half the hidden scalar mass, 1 then the SM Higgs could decay via where H is the SM Higgs at 125 GeV, h d and A d are the hidden sector scalar and vector respectively, and f are SM fermions. The first decay occurs through the Higgs portal operator and current limits allow its branching ratio to be as large as O(10%). The second decay is the dominant decay of the hidden sector Higgs if kinematically allowed because of the minimality of the hidden sector. If there were other hidden sector fields that the hidden Higgs could decay to (for example, a dark matter candidate), then this branching ratio would be reduced, but it is naturally large as long as the hidden gauge coupling is reasonably large. The decay of the hidden photon goes via the vector portal coupling even if it is extremely small. The Higgs portal coupling does not mediate hidden vector decays at tree level. If the hidden vector is parametrically lighter than the Z, then it dominantly couples to the electromagnetic current, thus giving each hidden photon a significant branching ratio to SM leptons, and this branching ratio can be extracted from e + e − scattering data at low masses [14] and from three-loop QCD calculation at higher masses [16]. We call the decay in Eq. (1) the platinum channel because of how spectacular it would be at the LHC.
Higgs decays to lepton jets [17] can also arise from this model [18] (see also [19] for Higgs decays to lepton jets in a different model), and the work of [18] studies Higgs decays to leptons where the mass of the A d is ∼ 1 GeV so that the final state lepton pairs are very collimated and may be treated as a single detector object. In this work we consider the general case as long as the decays in Eq. (1) are kinematically allowed and explore the phenomenology of this scenario. We find that current constraints on this process are dominated by the CMS multi-lepton searches [20] and are quite weak. We also show that there are searches that are very low background and could be performed with current and future data which would explore significant regions of parameter space. We therefore hope that this work will spur future study by our experimental colleagues.
The rest of this paper proceeds as follows. In Section II, we present the details of a simple model that gives rise to this decay. In Section III we explore current constraints on the model including a recast of the CMS multilepton search from [20], and in Section IV we show how a dedicated search could significantly improve the limits. In Section V we briefly explore non-minimal models that give rise to this scenario, and conclusions are given in Section VI.

II. A SIMPLE MODEL
We consider the following Lagrangian with L SM being the usual Standard Model Lagrangian, and where h d is the hidden (or dark) sector Higgs, and F µν is the field strength tensor for the hidden U (1) gauge boson A d . The h d has unit charge under the hidden U (1).
is the usual Mexican hat potential with negative mass squared term so that h d gets a vacuum expectation value (vev) even in the absence of portal operators. The portal Lagrangian is given by the vector portal and the Higgs portal: where H is the SM Higgs and B µν is the field strength for SM hypercharge. Current limits on this model require both λ and to be small as we will see in detail below, so we work to first order in both. The normalization of the vector portal coupling is chosen so that when we go to the mass basis, the mixing between the hidden gauge boson and the photon is . Detailed formulae for the mixings and couplings in this model can be found, for example, in [10,14,18]. Here we state the results for the processes of interest in our study. Both the SM Higgs and the hidden Higgs get vevs in the absence of the portal coupling: with v ≈ 246 GeV. The Higgs portal coupling shifts the vevs by O(λ). That coupling induces mixing between the SM and hidden Higgses, which in turn allows the SM Higgs to decay to two hidden vectors. If kinematically allowed, the tree level width for this decay is given by: to leading order in λ and . The decay of the Higgs to two hidden Higgses is mediated by the Higgs portal coupling with a Higgs vev insertion Therefore the branching ratio to hidden scalars is typically comparable to that to hidden vectors, so the mode to hidden scalars which gives rise to the platinum decay in Eq. (1) can be phenomenologically important in this model. This model can also give Higgs decay to Z and A d which would go through the vector portal. Constraints typically point towards λ, and this decay is further suppressed by m 2 A /m 2 Z , so it is negligible in the parameter space of interest. The Z can also decay as Z → A d h d which was studied in detail in [21]. While the LHC is not presently sensitive to this decay in this model, it may become sensitive in the future.
The branching ratio of the SM-like Higgs decay to hidden scalars is given by: where the first approximation is that the hidden sector does not give a significant contribution to the total width, and the second is assuming that the hidden scalar mass is well below half the Higgs mass.
With this minimal hidden sector, the only decay of the hidden Higgs that is not suppressed by small couplings is that to two hidden vectors as long as it is kinematically allowed. So in that regime One could expand the hidden sector to include, for example, a dark matter candidate [22]. This could change some of the phenomenology, but we leave more complicated models to future work. The hidden vector couples to the electromagnetic current with strength e and thus couples democratically to electromagnetic charge. It also couples to the Z current, but that is suppressed by m 2 A d /m 2 Z which is small in the region of parameter space we are interested in.
The branching ratio of the hidden vector to leptons (e and µ) was calculated very precisely in [14] using e + e − scattering data for lighter hidden vectors m A d 10 GeV, and using a three-loop QCD computation at higher masses [16]. This branching ratio varies from 60% at m A d = 1 GeV to 30% with m A d = 20 GeV, but there are very large variations when the mass is near a QCD resonance. For more details see Fig. 2 of [14], but in this preliminary collider study we use tree-level branching ratios keeping in mind that this will not be a suitable approximation near QCD resonances.
From the computations in [14], we can also compute the lifetime of the A d very precisely, but in the range we are interested, it is approximately given by which translates to a lifetime of so the A d decays promptly as long as 10 −6 , which is the range we will focus on here. If the hidden photon has a macroscopic lifetime, then the current constraints as well as experimental challenges for finding it are quite different, and we leave the small case with displaced decays to future work.

III. CURRENT CONSTRAINTS
We first look at constraints on direct production of the hidden sector fields. If the hidden vector is lighter than the hidden scalar, then dark photon constraints can be straightforwardly applied to this scenario. For 1 GeV m A d 10 GeV, the strongest constraints come from BABAR [23] through resonant produciton of A d and decay into SM leptons, and set a bound on the kinetic mixing parameter , namely The exceptions are regions very close to narrow QCD resonances having much weaker bounds. In this work, we therefore, do not consider masses very close to the mass of the φ, J/ψ and Υ resonances. For larger masses, the leading bounds on come from LHCb [24] through a dilepton resonance analysis, where the bounds are These bounds apply to prompt decays of the hidden vector, the case we consider here, and we see that there are at least two decades of allowed parameter space where the hidden photon is prompt and not excluded.
The above constraints can also be interpreted as the leading limits on this scenario in the case where λ limit. When the hidden scalar h d is kinematically accessible and λ is sufficiently large, the h d can be directly produced via its mixing with the SM Higgs. It will then dominantly decay to two A d , which then each decay to a pair of SM fermions. In the mass range of interest, 10 GeV m h d 60 GeV, the strongest limits come from LEP, but most searches do not look for this particular decay channel, so the bounds all turn out to be quite weak.
In detail, the strongest bound comes from the decay mode independent search at OPAL [25], which places a limit on sin 2 θ h where θ h is the mixing angle between the SM-like and hidden Higgs. This limit varies from ∼ 0.05 at low mass to ∼ 0.6 at high mass. In our model, We could in principle be sensitive to direct production of h d if we identify H 2 = h d and H 1 = A d . These searches, however, do not put any bounds on the scenario, mainly because they require specific final states, and the branching ratio of the A d to any particular SM state is somewhat small. We now move to LHC constraints arising from decays of the 125 GeV Higgs. The mixing of the h d and H can induce the SM-like H to decay to A d A d which can result in the Higgs decay to four leptons [10][11][12][13][14][15] as shown in Eq. (6). This has been searched for at ATLAS [28] and CMS [29,30], with the strongest bounds for m A d > 15 GeV coming from [28], and the strongest bounds for m A d < 2m τ coming from [29]. These limits are shown as the dashed red lines in Fig. 1. The only searches in the region 3.5 GeV < m A d < 15 GeV use the 4τ final state [30] and cannot set a non-trivial limit because of significantly larger background than searches with muons or electrons. In [28][29][30] there are also searches for H → ZA d → 4 , but as discussed previously, this decay is suppressed in the model considered here.
Finally, we consider the cascade process that can give rise to the platinum channel, H → h d h d → 4A d . This can be constrained by the CMS multilepton study from [20], whose signal regions are potentially applicable to this topology as they require low p T leptons as well as no missing energy. In this work, we recast the limit from [20] to set a bound on the model considered here,   (6) and (7). The yellow band parameterizes the uncertainty due to lepton efficiency, see text for details. The solid curve are the projected limits from the proposed platinum channel searches with ≥ 5-8 leptons going from bottom to top. Here the mass of the hidden Higgs h d is set to 55 GeV, but the limits are fairly insensitive to that parameter. The projections use an integrated luminosity of 35.9 fb −1 , and scale down inversely with luminosity. We do not present projections for the hidden photon mass near the φ, J/ψ or Υ resonances.
but we note that because this is a recast, there are significant uncertainties on our limit. We simulate events using the SM + Dark Vector + Dark Higgs model [14] in MadGraph5 aMC@NLO [31] and hadronize events using Pythia8.2 [32]. While our strategies will focus on leptons, we must hadronize the jets in order to reasonably approximate the isolation requirements imposed by experiments. We ignore detector effects in this preliminary study, but we note that these can be important considering the low p T thresholds we use and the high pile-up environment of the LHC. We use the low-/ E T , 4-lepton signal regions from [20]. In order to derive the constraints from the CMS search, we must apply lepton identification efficiencies, which are somewhat small for leptons with low p T . Because [20] only provides the low-p T lepton tagging efficiencies for the most pessimistic working point, we must use the pessimistic values and obtain a conservative result. The true signal efficiency is almost certainly better than what we find, because [20] states that a looser set of lepton identification criteria are used for searches with four leptons, but does not specifically state what these efficiencies are. Therefore, we consider efficiencies of 50% (100%) to set a conservative (aggressive) limit.
We find that the Signal Region (SR) H of [20], which requires 4 leptons and fewer than two opposite-sign, same-flavor (OSSF) lepton pairs, is most sensitive to the hidden sector topology we study. Using the CL s method [33], we estimate a constraint on this scenario at the 95% confidence level, which is shown as the dot-dashed purple line in Fig. 1, with the yellow coloured band showing our uncertainty due to lepton identification efficiencies. All the constraints in Fig. 1 are shown for m h d = 55 GeV, but the limits are mostly insensitive to the value of this parameter. The region of m A d 10 GeV is complicated by the presence of QCD resonances. As discussed above, we use the tree-level branching ratios of the A d to SM fermions, which is a good approximation far away from QCD resonances, but can also be improved [14], and we mask our plots when m A d is near the masses of the φ, J/ψ, and Υ. From Fig. 1, we see that the searches for H → A d A d are more sensitive to this model than the CMS multi-lepton searches, but, as we will show in the next section, a dedicated search could be significantly more sensitive than both.
The CMS multilepton search is sensitive to the process H → h d h d → 4A d , so we also show the constraints placed on BR(H → h d h d ) as a function of m h d in Fig. 2. This branching ratio is sensitive to m A d and the limits vary from 10% to 10 −3 depending on the A d mass and on whether we use aggressive or conservative parameterization for lepton efficiency.

IV. STRATEGIES AND PROJECTIONS
We now comment on potential for improvement with a dedicated analysis. Given the large branching ratio into leptons, we focus on multilepton final states beyond four leptons. In particular, the lesson from the CMS analysis is that a 5 + lepton final state should suffer from very low backgrounds. It is beneficial to use multilepton triggers with low p T thresholds. Currently, the threelepton triggers seem like a good candidate, given the low p T requirements on the leptons. For ATLAS, these are given by [34] • three loose e's: p T ≥ 15, 8, 8 GeV at L1 (17, 10, 10 at HLT), • three µ's: p T > 6 GeV (3 × 6 at HLT).
While these analyses were performed at 8 TeV, the trigger thresholds did not increase significantly in the 13 TeV run [20,36], so we use these thresholds for our estimated projections. For the leptons in addition to those required to pass the trigger, we require p T (µ) > 2 GeV [37] and p T (e) > 5 GeV [38]. For all electrons (muons), we require |η| < 2.5 (2.4). We can then place a projected limit assuming there will be zero background looking for events with ≥ n leptons with n = 5, 6, 7, 8. We require that the leptons are isolated using the p T dependant isolation criteria from [20].
Since we are making the same background assumption about all the different channels, the ≥5 lepton channel will have the best projected limit, but we show all four possible values of n to motivate different possible searches. In particular, an excess in the n = 8 lepton bin is particularly interesting as it allows to potentially fully reconstruct the Higgs invariant mass. We show the projected limit BR(H → h d h d ) in Fig. 2. For low mass A d , a dedicated search along these lines would exceed current limits by about three orders of magnitude, while for moderate mass A d by a factor of a few.
This projected limit assumes a luminosity of 35.9 fb −1 at 13 TeV, the same amount of data used in [20], and much less than the total amount of data presently collected. We see that even with this modest integrated luminosity, branching ratios of H → h d h d as low as O(10 −5 ) can be explored. Because this search is essentially background free, the limit will scale inversely with integrated luminosity as more data is analyzed.
We also show the projected bound on BR(H → A d A d ) in Fig. 1 using Eqs. (6) and (7). For low mass A d , the bound would improve that from searching for H → A d A d by a factor of O(30), while for larger masses it improves only using the 5 and 6 lepton searches by a factor of a few. In the mass range of 2m τ < m A d < 15 GeV, there is no limit from this channel, but this region is complicated by QCD resonances.

V. NON-MINIMAL MODELS
In the simple model presented in Sec. II, the Higgs decay to hidden two vectors and to two hidden scalars have correlated rates as shown in Eq. (6) and Eq. (7). Nature need not realize such a simple model, and, as seen in Fig. 1, the strongest current constraint on this simple model in much of the parameter range is from the Higgs decay to two vectors which then go to four leptons. Therefore, we here present a simple extension where the decay to two hidden photons can be parametrically smaller than the decay to two hidden scalars.
Consider a model with a U (1) as above, but with two hidden scalars that have unit charge under the U (1), h 1 and h 2 , that are still neutral under all SM gauge groups. As in the 2HDM, the Higgs potential now has many more parameters and there are potentially multiple new and interesting processes that can arise. Here we will do a simplified analysis assuming that the mixing between h 1 and h 2 is small, and where m H = 125 GeV is the mass SM-like Higgs, v i is the vev of the ith hidden Higgs, and λ i is the scalar portal coupling of the ith hidden Higgs to the SM-like Higgs.
In this regime, the SM Higgs decay to two hidden vectors through mixing with h 1 (h 2 ) is suppressed by the small parameter v 1 (λ 2 ). The decay to two h 2 's is forbidden by kinematics, while the decay to two h 1 's goes like λ 1 v, where v 246 GeV is the SM Higgs vev. The decay of the h 1 to two hidden vectors is suppressed by the small parameter v 1 , but if there is nothing else that the h 1 can decay to, this will not be a suppression to the rate of the SM Higgs decay to four hidden vectors and the platinum channel decay of Eq. (1).
In this more complicated scenario, the strongest bound will be from the CMS multi-lepton search, and from Fig. 2 we see that the branching ratio of H → h d h d can be as large as 10% for low m h d and m A d . In that scenario, the proposed search of this work would improve bounds even more than in the minimal model. We here stress that the parameter region of Eq. (16) is simply an existence proof of a relatively simple model where the decay to two vectors can be suppressed while the decay to four vectors can be large. We leave a full study of the more complicated models and other extensions to future work.

VI. CONCLUSIONS
Hidden massive photons have recently generated significant interest in the community and spurred significant experimental progress [39]. If such a photon gets mass from a Higgs mechanism, then one naturally expects a Higgs portal coupling between the hidden Higgs and the SM Higgs. In such a scenario, if the dark vector and scalar are near the weak scale, then the SM like Higgs could easily have a decay Since the A d couples to the electromagnetic current, it could in turn decay to a pair of leptons, allowing for Higgs decays with final state with large numbers of leptons. Such a signature, which we call the platinum channel, would be spectacular at the LHC and essentially background free. While there are some searches for many leptons, there is no dedicated search for this platinum channel Higgs decay, and current searches are relatively weak. A dedicated search requiring at least five leptons can significantly increase the reach for such a scenario, with Fig. 2 showing a reach with a branching ratio of the SM Higgs to two hidden scalars as low as 10 −5 using data that has already been analyzed. For a background free search, we expect the reach to scale inversely with luminosity, so we can expect a factor of about 10 (100) improvement in reach with Run 3 (high luminosity) LHC.
Finally, we note that a genuine experimental study is needed to make precise predictions on the reach. The sensitivity depends very strongly on lepton thresholds, the lower the better. At very low thresholds, however, experimental issues such as fakes become significantly more difficult, so we note that with the low thresholds used in this study, the uncertainties on our projections will be relatively large. Yet given the significant gains possible with a dedicated search and the simplicity of the model presented here, we believe that such a search may be well worth the effort.