M. Bauce, K. Knoepfel, D. Lucchesi, C. Principato, G. Punzi, C. Vellidis,
[Contact]

## Abstract

We present the first search at the Tevatron for a Higgs boson decaying to an invisible final state. We use the full CDF Run II data set corresponding to $9.7fb^{-1}$ of integrated luminosity. We search in the associated $ZH$ production mode and require two same-flavor, oppositely charged leptons and a significant value of missing transverse energy to be in the final state. We exclude values of $\sigma_{ZH}\times\mathcal{B}(H \to$invisible$)$ greater than 90 fb at 95% credibility level for a Higgs boson mass of 125 $GeV/c^2$. We perform this analysis across a Higgs boson mass range of 115 to 150 $GeV/c^{2}$. We are able to exclude a $\mathcal{B}(H \to$invisible$)$ = 100% assumption at Higgs boson masses lower than 120 $GeV/c^{2}$.

Further details may be found in CDF Note 11068.

## Introduction

The simplest $H\to$invisible process is highly suppressed in the SM. However, beyond-the-SM scenarios allow for enhanced $H\to$invisible decay rates that are potentially observable by collider experiments. In this analysis, we search for a $H\to$invisible process in the $ZH$ associated production mode. Despite the suppressed cross section relative to gluon fusion, the $ZH$ production mode allows one to trigger on leptonic decays of the $Z$. For this analysis, we reconstruct $Z$ candidates by combining $e^+e^-$ and $\mu^+\mu^-$ dilepton four-momenta. We do not explicitly reconstruct $Z\to\tau^+\tau^-$ processes, but as we are not able to infer the missing energy from neutrinos, we gain some acceptance from $\tau^+\tau^-$ decays to same-flavor final states. Events with $e^\pm\mu^\mp$ pairs are used as a control region to test background modeling, as well as events with same-sign, same-flavor lepton pairs. The event selection is described below.

## Event selection

Events are collected using high-$p_T$ muon and high-$E_T$ electron triggers. We require the final state in the signal region to have exactly two same-flavor, oppositely charged leptons. Electrons are identified as objects that have a high-momentum track that deposits almost all of its energy in the electromagnetic compartment of the calorimeter. Muons are identified by matching signatures in the outer muon detectors with tracks made in the inner tracking detector. We consider many combinations of leptons based on which subdetector recorded them; as well as combinations of reconstructed leptons with reconstructed tracks that could not be unambiguously identified as electrons or muons.

In order to suppress backgrounds, we require various event-selection criteria:

• The dilepton transverse momentum must be at least 45 GeV/c
• We accept no events where a reconstructed jet with $E_{T} \geq 15$ GeV satisfies $\Delta \phi (\ell\ell,J) \geq 2.0$ radians
• The azimuthal separation between the $\met$ and closest leading lepton must be at least 0.5 radians

Additional requirements, described below, are imposed depending on the control region or signal region.

## Background model validation

The background model is constructed primarily using Monte Carlo simulation programs: the $ZZ$, $WZ$, $Z$+jets, and $t\bar{t}$ processes are simulated by PYTHIA; $WW$ events are simulated using MC@NLO; the $W\gamma$ background is modeled using BAUR, and $W$+jets is data driven. For the $Z$+jets background, we normalize the prediction to the data (subtracted of all other backgrounds) in the region from $0 < \met < 40$ GeV, where all event selection requirements have been made except the $\met > 60$ GeV criterion. After this multiplicative correction is made, a +3-GeV correction in the $\met$ value is applied only for $Z$+jets events, to bring the corresponding $\met$ distribution into better agreement with that of background-subtracted data.

This model is tested and validated in three control regions:

• An opposite flavor, opposite sign ($e^\pm\mu^\mp$) control region
• A same-sign, same-flavor control region
• A same-flavor, opposite-sign, sideband (in dilepton invariant mass) control region

For each of these control regions, we provide validation plots for six variables:

• The missing transverse energy of the event - $\met$
• The azimuthal angle between the $\met$ vector and the closest leading lepton $\ell$ - $\Delta \phi (\met, \ell)$
• $\Delta R(\ell\ell)$ between the leading leptons
• Dilepton transverse momentum - $p_{T} (\ell\ell)$

The control regions are defined more explicitly below. For each control region including the signal region, the default event-selection requirements as mentioned above are imposed. As can be seen, the background model agrees well with data.

#### Opposite-flavor, opposite-sign control region

For the opposite flavor, opposite control region, we additionally require:

• Reconstructed $e^{\pm}\mu^{\mp}$ dilepton pair
• Dilepton invariant mass within the range $40 \leq M_{\ell\ell} \leq 140\:GeV/c^2$
• Missing transverse energy of at least 20 GeV ($\met$ plot below truncates at 40 GeV, including lower-\met events in the first bin of the plot)

The event yields in the opposite-flavor, opposite-sign control region are:

The uncertainties on the total prediction include the correlations between the various systematic uncertainties that are taken into account (and described below).

#### Same-sign control region

For the same sign control region, we additionally require:

• Reconstructed $\ell^{\pm}\ell^{\pm}$ dilepton pair, where $\ell$ is an electron or muon
• Dilepton invariant mass within the range $40 \leq M_{\ell\ell} \leq 140\:GeV/c^2$
• Missing transverse energy of at least 40 GeV

The event yields in the same-sign, same-flavor control region are:

The uncertainties on the total prediction include the correlations between the various systematic uncertainties that are taken into account (and described below).

#### Sideband control region

For the sideband control region, we additionally require

• Reconstructed $\ell^{\pm}\ell^{\mp}$ dilepton pair, where $\ell$ is an electron or muon
• Dilepton invariant mass that lies in the union $[50,82] \cup [100, 132]\:GeV/c^2$
• Missing transverse energy of at least 50 GeV

The event yields in the sideband control region are:

The uncertainties on the total prediction include the correlations between the various systematic uncertainties that are taken into account (and described below).

#### Signal region

For the signal region, we additionally require

• Reconstructed $\ell^{\pm}\ell^{\mp}$ dilepton pair, where $\ell$ is an electron or muon
• Dilepton invariant mass that lies in the range $82 < M_{\ell\ell} < 100\:GeV/c^2$
• Azimuthal separation between the $\met$ and closest leading lepton to be at least 0.5 radians
• Missing transverse energy of at least 60 GeV

The event yields in the signal region are:

The uncertainties on the total prediction include the correlations between the various systematic uncertainties that are taken into account (and described below).

## Systematic uncertainties

We take into account various systematic uncertainties by introducing nuisance parameters that are typically described using Gaussian distributions, centered at the central value of the systematic correction, with a root-mean-square width equal to its one-standard-deviation value. If necessary, the Gaussian is truncated at zero to avoid negative event yields when running pseudo-experiments. The values of the uncertainties used are shown here:

As the W/Z+jets samples are largely derived from data, many of the systematic uncertainties common to the other samples are not applicable. Note also that the primary effects that could cause a shape variation in the final discriminant are the jet-energy scale, and initial- and final-state radiation. Because we do not cut explicitly on the number of jets in the final state, but rather we veto an event if a jet is in relative proximity with the $\met$ vector, the jet-energy scale and gluon radiation effects translate to rate uncertainties. Therefore, we include no variations in the $\Delta R(\ell\ell)$ shape in our treatment of the systematic uncertainties.

## Results

Results are obtained by constructing a likelihood function that is the product of Poisson probabilities for each bin of the $\Delta R(\ell\ell)$ distribution. The sensitivity of the analysis to excluding the Higgs boson signal is degraded by accounting for systematic uncertainties, as described above. This is included by scaling the likelihood by each of the nuisance-parameter prior probability densities, which are truncated when necessary to ensure non-negative event yields. To estimate the sensitivity of the analysis, we run many pseudo-experiments by drawing random combinations of nuisance parameter values from the prior probability densities. As we are testing to exclude a hypothesis (the presence of $ZH$, where $H\to$invisible), we include no signal contributions to the mean values of the Poisson probabilities. We use a non-negative uniform prior for the signal strength $R$, which is the ratio between the observed and assumed signal cross sections. The upper limit $R_{95}$ is obtained by integrating over all nuisance parameters except for $R$ and finding location of the posterior probability that corresponds to an integral of 95%.

This procedure is repeated for each pseudo-experiment, and the median and 1- and 2-standard deviation variations of the resulting $R_{95}$ distribution are extracted, where the median represents the expected overall sensitivity to excluding the signal hypothesis. Finally, this procedure is performed for data, where a single value of $R_{95}$ is determined. This process is done for each assumed Higgs boson mass.

The upper limits, given relative to the assumed cross section, are shown in the table below:

The $\pm 1$- and $\pm 2$-s.d. columns refer to the $\pm 1$- and $\pm 2$-standard deviation bands as described above. The normalization of the signal is chosen such that $\mathcal{B}(H\to$invisible$) = 100\%$. Hence any observed limit that lies below a limit of 1 excludes $\mathcal{B}(H\to$invisible$) = 100\%$ at 95% credibility level. The same results are plotted here:

The limits can be renormalized such that the $\mathcal{B}(H\to$invisible$) = 100\%$ assumption is removed, and we place a upper limits on $\mathcal{B}(H\to$invisible$)$ itself. To do this, we do not include the uncertainty on the $ZH$ theoretical uncertainty as the $ZH$ signal no longer serves as the normalization factor:

We therefore exclude cross section values of $H\to$invisible, produced in association with $Z\to\ell^+\ell^-$, smaller than 90 fb at a Higgs boson mass of 125 $GeV/c^2$.