Looking for an Invisible Higgs Signal at the LHC

While the recent discovery of a Higgs-like boson at the LHC is an extremely important and encouraging step towards the discovery of the {\it complete} standard model(SM), the current information on this state does not rule out possibility of beyond standard model (BSM) physics. In fact the current data can still accommodate reasonable values of the branching fractions of the Higgs into a channel with `invisible' decay products, such a channel being also well motivated theoretically. In this study we revisit the possibility of detecting the Higgs in this invisible channel for both choices of the LHC energies, 8 and 14 TeV, for two production channels; vector boson fusion(VBF) and associated production($ZH$). In the latter case we consider decays of the $Z$ boson into a pair of leptons as well as a $b \bar b$ pair. For the VBF channel the sensitivity is found to be more than $5 \sigma$ at both the energies up to an invisible branching ratio ${\cal B}r_{invis} \sim 0.80$, with luminosities $\sim 20/30 {\rm fb}^{-1}$. The sensitivity is further extended to values of ${\cal B}r_{invis} \sim 0.25$ for $300 {\rm fb}^{-1}$ at 14 TeV. However the reach is found to be more modest for the $ZH$ mode with leptonic final state; with about $3.5 \sigma$ for the planned luminosity at 8 TeV, reaching $8 \sigma$ only for 14 TeV for $50 {\rm fb}^{-1}$. In spite of the much larger branching ratio of the $Z$ into a $b \bar b$ channel compared to the dilepton case, the former channel, can provide useful reach upto ${\cal B}r_{invis} \gsim 0.75$, only for the higher luminosity ($300{\rm fb}^{-1}$) option using jet-substructure and jet clustering methods for $b$-jet identification.


I. INTRODUCTION
The unprecedented high precision to which the Standard Model (SM) [1][2][3] has been tested as well as the discovery of a Higgs like boson at both the ATLAS and CMS [4,5] notwithstanding, the deficiencies of the Standard model (SM) both of the observational [6,7] and aesthetic justify the existence of physics beyond the Standard Model (BSM). For example, the instability of the electroweak scale under radiative corrections is cured by several BSM models. So far the Large Hadron Collider (LHC) has not given us any evidence of BSM physics. The recent discovery of a Higgs like boson at both the ATLAS and CMS [4,5] experiments has opened up new avenues for discovering or restricting the possibility of various BSM scenarios. Since many of the extensions of the SM have been suggested to address the issue of stability of the electroweak symmetry breaking scale against radiative corrections, all of them have implications for properties of the Higgs sector such as the number of the Higgs bosons and their couplings and CP properties. Hence it is very likely that a study of the properties of this boson can also yield information about BSM physics. A clear understanding of the characteristics of the Higgs will elucidate not only the nature of electroweak symmetry breaking (EWSB), but also help in our understanding of how a BSM spectrum may generate or be part of EWSB. The lack of appearance at the LHC of any other particle, not expected in the SM, so far in fact means that the properties of the Higgs may therefore, give us our first glimpse at BSM physics.
Of course the first important step in establishing the new boson which we have discovered as 'a' Higgs boson, will be to have some pointers to the spin and CP of the state. However, finally, the identification of this boson as the particle responsible for EWSB requires the determination of its coupling to fermions and gauge bosons. Let us note that the tree level couplings of the Higgs to the fermions and the electroweak gauge bosons, are completely determined by the details of the EWSB. On the other hand the loop induced couplings of the Higgs to a pair of gg and γγ, as well as the higher dimensional operators in other couplings can receive contributions from BSM physics as well. Hence, the measurement of the relative decay widths of the Higgs into different final states will not only provide information about the EWSB mechanism but may also carry with it information about BSM particle spectra. For example, the apparent excess of events seen in the H → γγ channel coupled with non observation in the H → τ τ channel [4,5], if confirmed, will have strong implications for various BSM models.
Strong cosmological evidence supporting the existence of Dark Matter (DM) means that almost all extensions of SM must include in their spectra a candidate for it which is supposed to be neutral and weakly interacting.
A large number of such models allow for a significant branching fraction for the decay of the Higgs to DM, thus providing a channel where the Higgs decay is "invisible" to the detector. In the SM the Higgs can decay invisibly through H → ZZ * → 4ν, which can only contribute to roughly 0.1% of the branching ratio [8]. Therefore, the observation of a sizable invisible branching ratio (Br inv ) of the Higgs will be a strong indication for BSM physics. There exist several examples of BSM physics models where the Higgs can have an invisible decay, such as, the decay of the Higgs to the lightest supersymmetric particle (LSP) [9], decay to graviscalars in extra-dimensional models [10,11] in gauge extensions of the SM [12,13] and in models for neutrino masses [14][15][16]. It has been noticed in various analysis [17][18][19][20] that if this resonance is interpreted as a Higgs boson, the currently available information on its properties can allow non trivial values of Br inv .
In fact a recent analysis by the CMS collaboration performing a global fit to the LHC data, suggests that an invisible branching ratio in non SM channel as large as 62% at 95% confidence level of the Higgs of mass ∼125 GeV is still allowed [21] 1 . In fact detailed analysis of LEP data showed no evidence for an invisibly decaying Higgs of mass less than 112.1 GeV [23].
The feasibility of determining an invisible branching fraction of the Higgs for √ s = 7 TeV,8 TeV and 14 TeV at the LHC has been studied in various production modes of the Higgs [24][25][26][27][28][29][30][31][32][33][34] which is described very briefly in the next section. We look at the production of Higgs in association with a electroweak gauge boson as well as through Vector Boson Fusion (VBF) in detail. In earlier studies, the leptonic decay of the Z boson was used to identify the invisible decay of a Higgs produced in association with a Z boson [27]. In the present study we update the analysis in the leptonic channel and also probe the possibility of detecting an invisible decay of the Higgs by identifying the associated Z boson through b-tagged jets both for 8 TeV and as well as 14 TeV LHC. We also apply the jet-substructure algorithm [35] for b-tagged final states which marginally help in improving signal acceptance efficiencies. In addition, we study how the invisible decay channel can be probed in the production of the Higgs via vector boson fusion for both 8 TeV and 14 TeV LHC energy.
We organize our work as follows. In section 2, we discuss very briefly about the invisible decay of Higgs. In the subsequent sections 3 and 4, we describe simulation of invisible Higgs signal for VBF and ZH channels.
Finally, we summarize our observations in section 5.

II. SIGNATURES OF AN INVISIBLY DECAYING HIGGS
There are four main production mechanisms of the Higgs boson in a hadron collider. The most dominant one is gluon-gluon fusion via a top quark loop (ggF) (gg → H) followed by VBF (qq → qqH), then Higgs production in association with vector bosons (VH) (qq → ZH/W H) and finally in association with top quark pairs (ttH) (gg/qq → ttH) with the lowest cross section . The various production channels are shown in Fig. 1. Needless to say that the signatures of the Higgs particle are characterized by the pattern of the Higgs decay channels [76]. Recall that the BR of the Higgs decay in the invisible channel in the framework of SM is too low to be observed, therefore, any observation of invisible decay channel of the Higgs will shed some light about BSM physics. On the other hand the production cross section of the Higgs can vary in various models due to the presence of new particles inside loops and modified couplings of Higgs with 1 Similarly ATLAS also obtained a lower bound of 84% at 95 % confidence level on the invisible branching ratio of the Higgs without any assumption on the total decay width [22]. in ggF channel [77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94]. Consequently signal in the invisible decay channel will be a combined effect due to the modified Higgs production cross section and its branching ratio in the invisible channel. Hence this makes it difficult to constrain only the invisible decay branching ratio of the Higgs BR inv (H → inv). Instead what can be constrained is in fact where σ BSM H and σ SM H stand for the Higgs production cross sections in the framework of corresponding BSM and SM respectively. At leading order, the Higgs produced through ggF and decaying invisibly would be hard to detect because of soft missing transverse momentum (p / T ). However, at higher orders in QCD for ggF, the Higgs can be produced in association with a single jet and one can then look for a considerably large missing transverse momentum along with a jet. Interestingly, such final states with a mono-jet have been analyzed with 1 fb −1 of data at √ s = 7 TeV for both CMS [95] and ATLAS [96]. Using those results, R inv in eq. 1 can be constrained and is found to be more than 10 at 95% CL with 1fb −1 data [31]. Moreover, the mono-jet search has also been analyzed by including a second hard jet [95] thus also including events from VBF and VH processes in the signal. It has been argued recently that at 4.7 fb −1 data at √ s = 7 TeV, this can be reduced to R inv < 2 and for 15 fb −1 of data at 8 TeV this can be further reduced to R inv < 0.9 [32]. One should note here that even though the production cross-section is large the mono-jet searches are plagued by large V +jets (V = W, Z) background (Bg).
The most promising channel for the detection of an invisibly decaying Higgs is VBF since it has a relatively large cross section and has an unique event topology that can be used to effectively remove backgrounds [26,29,33]. The signal consists of jets moving in opposite directions with large rapidity gaps. A recent study has shown that R inv as low as 0.21 can be probed with 30 fb −1 data at √ s = 14 TeV and for √ s = 7 TeV with 20 fb −1 it can be probed to as low as 0.4 with 95% CL [34].
We revisit this analysis for 8 TeV and 14 TeV energies. In our current analysis we employ a different set of kinematic selection cut values to that used in Ref [34]. Moreover, in this analysis a precise method of jet reconstruction with anti − k T [97] algorithm built in the FastJet [98] package is implemented. It has to be noted that in our analysis we consider the additional W/Z+3 jets backgrounds which were not considered in earlier works [34,99]. These additional modes do contribute a sizable fraction to the total background cross section, in particular Z+3 jets channel. As a consequence, our conclusion appears to be different than previous works [34,99] which is discussed in Sec.3. However, the main drawback of VBF channels is that it has large systematic uncertainties and it is difficult to estimate the QCD background [29,33].
The ttH channel has been studied in detail [100] for √ s = 14 TeV LHC in both the semileptonic, In this section we study the feasibility of finding the invisible Higgs signal through the VBF process which is the sub dominant process for the Higgs production in hadron colliders. This channel has been studied previously for 14 TeV LHC [26,29,32,101] and very recently for 7 TeV and 8 TeV [34]. We also revisit this analysis for 8 TeV and 14 TeV LHC energy for the Higgs mass of 125 GeV using a different set of selection cut values. In this channel, the Higgs is produced through vector boson fusion, where vector bosons originate by radiating off two initial quarks along with two jets, The final state consists of two jets in the forward and backward directions with a wide separation in rapidity and a reasonably large p / T due to the presence of non-interacting particles from Higgs decay. In addition to this pure VBF processes, there are some non VBF processes which also provide the same final state consisting of 2 jets and p / T . For instance, higher order QCD effects in ggF process can give rise to two jets in the final states because of a hard emission of partons from the initial states with a non negligible cross Therefore, a leptonic veto might help to eliminate certain fraction of backgrounds. Leptons are selected with p ℓ T >10 GeV, |η ℓ | <2.5. We compute missing transverse energy from the momenta of all visible particles.
The following set of cuts are used in the simulation : 1. VBF selections: The leading jets in Higgs production through the VBF process are produced in the forward and backward direction and hence is expected to have a large rapidity gap. Therefore, we select events where the absolute rapidity difference between the two leading jets is |η j1 − η j2 | = |∆η| >4. To ensure that the two jets are in the opposite direction, the product of rapidity of two jets are required to be, η j1 × η j2 <0.    We notice that p / T and M jj cuts are extremely useful to suppress the backgrounds with a marginal effect in the signal cross section. We have also checked that the background contribution due to QCD is negligible because of a strong p / T and a large di-jet invariant mass cut(M jj ); this is why results for QCD are not presented here. In our simulation, the rejection efficiencies due to the central jet veto for QCD Wjj and QCD Zjj are about 20% for both energies. Note that this efficiency depends crucially on the detector effects like calibrations, electronic noise, pile up effects etc. [99], which are not taken into account in this analysis.
In Table I we present the event summary for signal and all background processes subjected to the above set of cuts. The first column represents the production cross section at the leading order obtained from In our estimation the signal purity S/(S+B) is approximately 40% lower than the results obtained by the Ref. [34]. As mentioned earlier, we use a more reliable method of jet reconstruction by using FastJet [98] with anti − K T algorithm [97], and consider an additional W/Z+3jets background. It is to be noted that in our calculation we used LO cross sections for both signal and backgrounds. However the K-factor for the signal is ∼0.95 [106] and for W/Z+jets it is also very close to 1(∼1.1) [107,108]. Therefore, inclusion of K-factors in the above calculation will not alter the conclusions significantly.

IV. INVISIBLE HIGGS SIGNAL VIA ZH
Here we study the signature of the invisible decay of Higgs via the ZH channel, where Z can decay both leptonically and hadronically, Z → ℓl, bb. It is well known from an experimental point of view that the leptonic channel is comparatively cleaner than the hadronic channel consisting of b-jets. However we simulate both these channels to find the detectability of an invisible Higgs decay. In the following, we describe our simulation for both the final states.

(a) Z → ℓl
Here the final states consist of two leptons with opposite charge and same flavor and with a considerable amount of missing transverse momentum due to the Higgs decay into invisible particles.
The main dominant SM backgrounds are expected from the following processes, 1. ZZ production with one Z decaying to neutrinos and the other Z decaying leptonically. Clearly, this background has exactly identical characteristics to the signal.
2. W Z production followed by the leptonic decays of both the W and Z, giving rise to ℓν ℓl ℓ where one of the leptons is lost.
4. Top pair production, tt → W W bb → lν llνl bb which may appear signal-like if the b-jets escape detection.
The Higgs being heavier in comparison to the particles in the background processes other than the top quark, gives rise to a harder p / T . Therefore, by demanding a large p / T one can efficiently reduce backgrounds.
In the signal topology, an added advantage is that the invariant mass of two leptons peaks around the mass of the Z boson. Hence requiring the di-lepton invariant mass to be around the mass of the Z boson, it is possible to suppress backgrounds partially except for the ZZ process. Since the Z boson and the Higgs are more likely to be produced back to back, the transverse mass of the di-lepton system and the p / T , defined as, has a softer distribution for all background processes. Therefore, demanding a large value for this variable enables us to eliminate backgrounds substantially.
As before, we use MadGraph [102] to generate both the signal and background processes which are subsequently passed through PYTHIA6 [103] for event generation including showering. We apply the following set of cuts in our simulation for the event selection and as well as suppressing the background events.
1. Select leptons with p ℓ T > 10 GeV and |η l | < 3. The isolation of lepton is ensured by looking at the total transverse energy E ac T ≤ 20% of the p T of lepton, where E ac T is the scalar sum of the transverse energies of jets within a cone of size ∆R(l, j) ≤ 0.2 between the jet and the lepton.  Table II, we display cross sections for both signal and backgrounds for 8 and 14 TeV energies before and after cuts. In each column, numbers on left stand for the production cross sections corresponding to energies as shown in the respective columns. For both energies, we find that M ll T and p / T play a very useful role in suppressing the backgrounds. The kinematics of ZZ process is identical to that of the signal process although there is a moderate mass difference (35 GeV) between the Z and the Higgs boson, resulting in a similar effect of cuts on both signal and ZZ background. As a consequence, ZZ turns out to be the dominant irreducible background. This channel was studied extensively in an earlier study for 14 TeV LHC energy [27]. Here we have revisited the analysis for 14 TeV LHC energy and performed an optimization of cuts. The numbers on the right hand side of each column show the final cross sections after being multiplied by acceptance efficiencies. For 8 TeV energy with an integrated luminosity of L=20 fb −1 we find S/ √ B ∼ 3.5 which implies a hint of the invisible Higgs signal. However, for 14 TeV energy with  based on LO cross sections. However, we note that the K-factors for vector boson production and tt are 1.6-1.7 [109,110] while for the signal process it is 1.3 [60,63,64] respectively. Hence we do not expect any major changes in our results.

(b)Z → bb
In this section we explore the possibility of detecting invisible Higgs decay channel by identifying two b-jets arising from Z boson decay. We analyze this channel following two methods. In the first method, b-jets are identified by using the standard jet clustering algorithm and in the second method, the jet substructure technique [35] is used to reconstruct . However, in both cases the dominant SM backgrounds arise from: 1. irreducible background from ZZ production with one Z decaying to neutrinos and the other Z decaying to b quarks.
2. The production of Z boson in association with two b quarks and the Z boson decaying to neutrinos, (Zbb → ννbb).
3. W Z production with the W decaying leptonically, and the Z decaying to b-quarks and the lepton is lost, (W Z → lν l bb).
4. tt production where two b-jet from top decays are identified and rest of the event objects are lost.
5. W boson produced in association with b quarks (W bb) where W decays leptonically and the lepton is not identified.
The event topology of this channel is not significantly different from the di-lepton final state as discussed above, and hence we apply similar type of cuts. Absence of any detectable hard lepton in the final state leads us to apply a lepton veto to reduce backgrounds, in particular from tt, W Z and W bb production. As before, M bb T , the transverse mass between two b-jets and p / T distributions of the backgrounds are soft. Therefore, selection of signal events corresponding to large values of these kinematic variables helps to remove significant fraction of the backgrounds. Moreover, we construct another useful variable, R T , to remove large amount of the QCD. [111][112][113][114][115]. This variable is defined as, where H T is the scalar sum of the transverse momenta of all detected jets including all non-tagged jets.
Since one expects less non-tagged jet activity in the signal, R T would tend to have larger values (∼ 1) as compared to the events arising from QCD and other backgrounds. Naturally, requiring R T to have a large value(∼ 1), leads to a substantial suppression of backgrounds, particularly for those due to QCD processes.
We simulate as before the signal and backgrounds using MadGraph [102] applying the following set of selection cuts: 1. Select b-jets by performing a matching between b quarks and jets using matching cone ∆R = 0.3 and finally multiply a b-tagging efficiency of 0.6 [116] for each of the b-jets. In the jet substructure method we employ mass drop techniques described in [35] to find the subjets which are also identified as a b-like jets by flavor matching.
3. Select dijet events with both jets b-like and ensure that |M bb − M Z | < 30 GeV.
In Table III we present the final results of the simulation for both methods for 8 TeV energy. The second column presents the total production cross sections corresponding to each processes and subsequent columns show cross sections after applying the above set of cuts. However, in both cases, for an integrated luminosity of L = 20 fb −1 the best we can achieve is S/ √ B ∼ 2. In Table IV    indirectly probe BSM physics. In this note we revisit the possibility of looking for a Higgs boson decaying invisibly, for two production channels of the Higgs : the vector boson fusion channel (VBF) as well as the associated production of Higgs with Z (ZH), for two different LHC energies: 8 and 14 TeV. In the ZH case, we also investigate the possibility of using the Z → bb channel. In Table V we summarize the lower limits of BR inv for various channels and for different energy and luminosity options. We find that for the Z(→ bb)H channel we fail to set any limits for 8 TeV with 20 fb −1 and 14 TeV with 30 fb −1 luminosity. We note that in the VBF channel the sensitivity is more than 5σ for both the energies