Constraints on the Higgs boson width from off-shell production and decay to Z-boson pairs

Constraints are presented on the total width of the recently discovered Higgs boson, Γ H , using its relative on-shell and off-shell production and decay rates to a pair of Z bosons, where one Z boson decays to an electron or muon pair, and the other to an electron, muon, or neutrino pair. The analysis is based on the data collected by the CMS experiment at the LHC in 2011 and 2012, corresponding to integrated luminosities of 5 . 1 fb − 1 at a center-of-mass energy √ s = 7 TeV and 19 . 7 fb − 1 at √ s = 8 TeV. A simultaneous maximum likelihood ﬁt to the measured kinematic distributions near the resonance peak and above the Z-boson pair production threshold leads to an upper limit on the Higgs boson width of Γ H < 22 MeV at a 95% conﬁdence level, which is 5.4 times the expected value in the standard model at the measured mass of m H = 125 . 6 GeV.

The gluon fusion production cross section depends on Γ H through the Higgs boson propagator dσ gg→H→ZZ where g ggH and g HZZ From Eq. (2), it is clear that a measurement of the relative off-shell and on-shell production in the H → ZZ channel provides direct information on Γ H , as long as the coupling ratios remain unchanged, i.e. the gluon fusion production is dominated by the top-quark loop and there are no new particles contributing. In particular, the on-shell production cross section is unchanged under a common scaling of the squared product of the couplings and of the total width Γ H , while the off-shell production cross section increases linearly with this scaling factor. The dominant contribution for the production of a pair of Z bosons comes from the quark-initiated process, qq → ZZ, the diagram for which is displayed in Fig. 1(left). The gluon-induced diboson production involves the gg → ZZ continuum background production from the box diagrams, as illustrated in Fig. 1  Lowest order contributions to the main ZZ production processes: (left) quark-initiated production, qq → ZZ, (center) gg continuum background production, gg → ZZ, and (right) Higgs-mediated gg production, gg → H → ZZ, the signal.
example of the signal production diagram is shown in Fig. 1(right). The interference between the two gluon-induced contributions is significant at high m ZZ [15], and is taken into account in the analysis of the off-shell signal. Vector boson fusion (VBF) production, which contributes at the level of about 7% to the on-shell cross section, is expected to increase above 2m Z . The above formalism describing the ratio of off-shell and on-shell cross sections is applicable to the VBF production mode. In this analysis we constrain the fraction of VBF production using the properties of the events in the on-shell region. The other main Higgs boson production mechanisms, ttH and VH (V = Z, W), which contribute at the level of about 5% to the on-shell signal, are not expected to produce a significant off-shell contribution as they are suppressed at high mass [8,9]. They are therefore neglected in the off-shell analysis.
In this Letter, we present constraints on the Higgs boson width using its off-shell production and decay to Z-boson pairs, in the final states where one Z boson decays to an electron or a muon pair and the other to either an electron or a muon pair, H → ZZ → 4 (4 channel), or a pair of neutrinos, H → ZZ → 2 2ν (2 2ν channel). Relying on the observed Higgs boson signal in the resonance peak region [7], the simultaneous measurement of the signal in the high-mass region leads to constraints on the Higgs boson width Γ H in the 4 decay channel. The 2 2ν decay channel, which benefits from a higher branching fraction [16,17], is used in the highmass region to further increase the sensitivity to the Higgs boson width. The analysis is performed for the tree-level HVV coupling of a scalar Higgs boson, consistent with our observations [4,7], and implications for the anomalous HVV interactions are discussed. The Higgs boson mass is set to the measured value in the 4 decay channel of m H = 125.6 GeV [7] and the Higgs boson width is set to the corresponding expected value in the SM of Γ SM H = 4.15 MeV [8,9]. The measurement is based on pp collision data collected with the CMS detector at the LHC in 2011, corresponding to an integrated luminosity of 5.1 fb −1 at the center-of-mass energy of √ s = 7 TeV (4 channel), and in 2012, corresponding to an integrated luminosity of 19.7 fb −1 at √ s = 8 TeV (4 and 2 2ν channels). The CMS detector, described in detail elsewhere [18], provides excellent resolution for the measurement of electron and muon transverse momenta (p T ) over a wide range. The signal candidates are selected using well-identified and isolated prompt leptons. The online selection and event reconstruction are described elsewhere [2,3,7,16]. The analysis presented here is based on the same event selection as used in Refs. [7,16]. The analysis in the 4 channel uses the four-lepton invariant mass distribution as well as a matrix element likelihood discriminant to separate the ZZ components originating from gluonand quark-initiated processes. We define the on-shell signal region as 105.6 < m 4 < 140.6 GeV and the off-shell signal region as m 4 > 220 GeV. The analysis in the 2 2ν channel relies on the transverse mass distribution m T , where p T,2 and m 2 are the measured transverse momentum and invariant mass of the dilepton system, respectively. The missing transverse energy, E miss T , is defined as the magnitude of the transverse momentum imbalance evaluated as the negative of the vectorial sum of transverse momenta of all the reconstructed particles in the event. In the 2 2ν channel, the off-shell signal region is defined as m T > 180 GeV. The choice of the off-shell regions in both channels is done prior to looking at the data, based on the expected sensitivity.
Simulated Monte Carlo (MC) samples of gg → 4 and gg → 2 2ν events are generated at leading order (LO) in perturbative quantum chromodynamics (QCD), including the Higgs boson signal, the continuum background, and the interference contributions using recent versions of two different MC generators, gg2VV 3.1.5 [11,19] and mcfm 6.7 [20], in order to cross-check theoretical inputs. The QCD renormalization and factorization scales are set to m ZZ /2 (dynamic scales) and MSTW2008 LO parton distribution functions (PDFs) [21] are used. Higher-order QCD corrections for the gluon fusion signal process are known to an accuracy of next-to-next-to-leading order (NNLO) and next-to-next-to-leading logarithms for the total cross section [8,9] and to NNLO as a function of m ZZ [14]. These correction factors to the LO cross section (K factors) are typically in the range of 2.0 to 2.5. After the application of the m ZZ -dependent K factors, the event yield is normalized to the cross section from Refs. [8,9]. For the gg → ZZ continuum background, although no exact calculation exists beyond LO, it has been recently shown [22] that the soft collinear approximation is able to describe the background cross section and therefore the interference term at NNLO. Following this calculation, we assign to the LO background cross section (and, consequently, to the interference contribution) a K factor equal to that used for the signal [14]. The limited theoretical knowledge of the background K factor at NNLO is taken into account by including an additional systematic uncertainty, the impact of which on the measurement is nevertheless small.
Vector boson fusion events are generated with phantom [23]. Off-shell and interference effects with the nonresonant production are included at LO in these simulations. The event yield is normalized to the cross section at NNLO QCD and next-to-leading order (NLO) electroweak (EW) [8,9] accuracy, with a normalization factor shown to be independent of m ZZ .
In order to parameterize and validate the distributions of all the components for both gluon fusion and VBF processes, specific simulated samples are also produced that describe only the signal or the continuum background, as well as several scenarios with scaled couplings and width. For the on-shell analysis, signal events are generated either with powheg [24][25][26][27] production at NLO in QCD and JHUGen [28,29] decay (gluon fusion and VBF), or with pythia 6.4 [30] (VH and ttH production).
In both the 4 and 2 2ν channels the dominant background is qq → ZZ. We assume SM production rates for this background, the contribution of which is evaluated by powheg simulation at NLO in QCD [31]. Next-to-leading order EW calculations [32,33], which predict negative and m ZZ -dependent corrections to the qq → ZZ process for on-shell Z-boson pairs, are taken into account. All simulated events undergo parton showering and hadronization using pythia. As is done in Ref. [7] for LO samples, the parton  [7]. In this region, the contribution of the ttH and VH production processes is added to the dominant gluon fusion and VBF contributions.
showering settings are tuned to approximately reproduce the ZZ p T spectrum predicted at NNLO for the Higgs boson production [34].
Generated events are then processed with the detailed CMS detector simulation based on Geant4 [35,36], and reconstructed using the same algorithms as used for the observed events.
The final state in the 4 channel is characterized by four wellidentified and isolated leptons forming two pairs of opposite-sign and same-flavor leptons consistent with two Z bosons. This channel benefits from a precise reconstruction of all final state leptons and from a very low instrumental background. The event selection and the reducible background evaluation are performed following the methods described in Ref. [7]. After the selection, the 4 data sample is dominated by the quark-initiated qq → ZZ → 4 (qq → 4 ) and gg → 4 productions. In order to enhance the sensitivity to the gg production in the off-shell region, a likelihood discriminant D gg is used, which characterizes the event topology in the 4 center-of-mass frame using the observables (m Z 1 , m Z 2 , Ω) for a given value of m 4 , where Ω denotes the five angles defined in Ref. [28]. The discriminant is built from the probabilities P gg tot and P qq bkg for an event to originate from either the gg → 4 or the qq → 4 process. We use the matrix element likelihood approach (MELA) [2,29] for the probability computation using the mcfm matrix elements for both gg → 4 and qq → 4 processes. The probability P gg tot for the gg → 4 process includes the signal (P gg sig ), the background (P gg bkg ), and their interference (P gg int ), as introduced for the discriminant computation in Ref. [37]. The discriminant is defined as where the parameter a is the strength of the unknown anomalous gg contribution with respect to the expected SM contribution (a = 1). We set a = 10 in the definition of D gg according to the expected sensitivity. Studies show that the expected sensitivity does not change substantially when a is varied up or down by a factor of 2. It should be stressed that fixing the parameter a to a given value only affects the sensitivity of the analysis. To suppress the dominant qq → 4 background in the on-shell region, the analysis also employs a MELA likelihood discriminant D kin bkg based on the JHUGen and mcfm matrix element calculations for the signal and Table 1 Expected and observed numbers of events in the 4 and 2 2ν channels in gg-enriched regions, defined by m 4 ≥ 330 GeV and D gg > 0.65 (4 ), and by m T > 350 GeV and E miss T > 100 GeV (2 2ν). The numbers of expected events are given separately for the gg and VBF processes, and for a SM Higgs boson (Γ H = Γ SM H ) and a Higgs boson width and squared product of the couplings scaled by a factor 10 with respect to their SM values. The unphysical expected contributions for the signal and background components are also reported separately, for the gg and VBF processes. For both processes, the sum of the signal and background components differs from the total due to the negative interferences. The quoted uncertainties include only the systematic sources. 4 2 2ν (a) the background, as illustrated by the inset in Fig. 2 and used in Ref. [7].
The 2 2ν analysis is performed on the 8 TeV data set only. The final state in the 2 2ν channel is characterized by two oppositelycharged leptons of the same flavor compatible with a Z boson, together with a large E miss T from the undetectable neutrinos. We require E miss T > 80 GeV. The event selection and background estimation is performed as described in Ref. [16], with the exception that the jet categories defined in Ref. [16] are here grouped into a single category, i.e. the analysis is performed in an inclusive way.
The m T distribution in the off-shell signal region (m T > 180 GeV) is shown in Fig. 4. The expected and observed event yields in a gg-enriched region defined by m T > 350 GeV and E miss T > 100 GeV are reported in Table 1.
Systematic uncertainties comprise experimental uncertainties on the signal efficiency and background yield evaluation, as well as uncertainties on the signal and background from theoretical predictions. Since the measurement is performed in wide m ZZ regions, there are sources of systematic uncertainties that only affect the total normalization and others that affect both the normalization and the shape of the observables used in this analysis. In the 4 final state, only the latter type of systematic uncertainty affects the measurement of Γ H , since normalization uncertainties change the on-shell and off-shell yields by the same amount. Among the signal uncertainties, experimental systematic uncertainties are evaluated from observed events for the trigger efficiency (1.5%), and combined object reconstruction, identification and isolation efficiencies (3-4% for muons, 5-11% for electrons) [7]. In the 2 2ν final state, the effects of the lepton momentum scale (1-2%) and jet energy scale (1%) are taken into account and propagated to the evaluation of E miss T . The uncertainty in the b-jet veto (1-3%) is estimated from simulation using correction factors for the b-tagging and b-misidentification efficiencies as measured from the dijet and tt decay control samples [38].
Theoretical uncertainties from QCD scales in the qq background contribution are within 4-10% depending on m ZZ [7]. An additional uncertainty of 2-6% is included to account for missing higher order contributions with respect to a full NLO QCD and NLO EW evaluation. The systematic uncertainty in the normal-ization of the reducible backgrounds is evaluated following the methods described in Refs. [7,16]. In the 2 2ν channel, for which these contributions are not negligible at high mass, the estimation from control samples for the Z + jets and for the sum of the tt, tW and WW contributions leads to uncertainties of 25% and 15% in the respective background yields. Theoretical uncertainties in the high mass contribution from the gluon-induced processes, which affect both the normalization and the shape, are especially important in this analysis (in particular for the signal and interference contributions that are scaled by large factors). However, these uncertainties partially cancel when measuring simultaneously the yield from the same process in the on-shell signal region. The remaining m ZZ -dependent uncertainties in the QCD renormalization and factorization scales are derived using the K factor variations from Ref. [14], corresponding to a factor of two up or down from the nominal m ZZ /2 values, and amount to 2-4%. For the gg → ZZ continuum background production, we assign a 10% additional uncertainty on the K factor, following Ref. [22] and taking into account the different mass ranges and selections on the specific final state. This uncertainty also affects the interference with the signal. The PDF uncertainties are estimated following Refs. [39,40] by changing the NLO PDF set from MSTW2008 to CT10 [41] and NNPDF2.1 [42], and the residual contribution is about 1%. For the VBF processes, no significant m ZZ -dependence is found regarding the QCD scales and PDF uncertainties, which are in general much smaller than for the gluon fusion processes [8,9]. In the 2 2ν final state, additional uncertainties on the yield arising from the theoretical description of the parton shower and underlying event are taken into account (6%).
We perform a simultaneous unbinned maximum likelihood fit of a signal-plus-background model to the measured distributions in the 4 and 2 2ν channels. In the 4 channel the analysis is performed in the on-shell and off-shell signal regions defined above. In the on-shell region, a three-dimensional distribution x = (m 4 , D kin bkg , p T 4 or D jet ) is analyzed, following the methodology described in Ref. [7], where the quantity D jet is a discriminant used to separate VBF from gluon fusion production. In the off-shell region, a two-dimensional distribution x = (m 4 , D gg ) is analyzed.
In the 2 2ν channel, only the off-shell Higgs boson production is analyzed, using the x = m T distribution.
The probability distribution functions are built using the full detector simulation or data control regions, and are defined for the signal, the background, or the interference between the two contributions, P sig , P bkg , or P int , respectively, as a function of the observables x discussed above. Several production mechanisms are considered for the signal and the background, such as gluon fusion (gg), VBF, and quark-antiquark annihilation (qq). The total probability distribution function for the off-shell region includes the interference of two contributions in each production process: The list of background processes is extended beyond those quoted depending on the final state (Z + X, top, W + jets, WW, WZ). The parameters μ ggH and μ VBF are the scale factors which modify the signal strength with respect to the reference parameterization in each production mechanism independently. The parameter (Γ H /Γ 0 ) is the scale factor which modifies the observed width with respect to the Γ 0 value used in the reference parameterization.
In the on-shell region, the parameterization includes the small contribution of the ttH and VH Higgs boson production mechanisms, which are related to the gluon fusion and VBF processes, respectively, because either the quark or the vector boson coupling to the Higgs boson is in common among those processes. Interference effects are negligible in the on-shell region. The total probability distribution function for the on-shell region is written as The above parameterizations in Eqs. (5,6) are performed for the tree-level HVV coupling of a scalar Higgs boson, consistent with our observations [4,7]. We find that the presence of anomalous couplings in the HVV interaction would lead to enhanced off-shell production and a more stringent constraint on the width. It is evident that the parameterization in Eq. (5) relies on the modeling of the gluon fusion production with the dominant top-quark loop, therefore no possible new particles are considered in the loop. Further discussion can also be found in Refs. [43][44][45].
The three parameters Γ H , μ ggH , and μ VBF are left unconstrained in the fit. The μ ggH and μ VBF fitted values are found to be almost identical to those obtained in Ref. [7]. Systematic uncertainties are included as nuisance parameters and are treated according to the frequentist paradigm [46]. The shapes and normalizations of the signal and of each background component are allowed to vary within their uncertainties, and the correlations in the sources of systematic uncertainty are taken into account.
The fit results are shown in Fig. 5  MeV for the 4 analysis and for the analysis combining the 4 on-shell and 2 2ν off-shell regions, respectively.
The expected limit for the two channels combined without including the systematic uncertainties is Γ H < 28 MeV at a 95% CL.
The effect of systematic uncertainties is driven by the 2 2ν channel with larger experimental uncertainties in signal efficiencies and background estimation from control samples in data, while the result in the 4 channel is largely dominated by the statistical uncertainty.
The statistical compatibility of the observed results with the expectation under the SM hypothesis corresponds to a p-value of 0.24. The statistical coverage of the results obtained in the likelihood scan has also been tested with the Feldman-Cousins approach [47] for the combined analysis leading to consistent although slightly tighter constraints. The analysis in the 4 channel has also been performed in a one-dimensional fit using either m 4 or D gg and consistent results are found. The expected limit without using the MELA likelihood discriminant D gg is 40% larger in the 4 channel.
In summary, we have presented constraints on the total Higgs boson width using its relative on-shell and off-shell production and decay rates to four leptons or two leptons and two neutrinos. The analysis is based on the 2011 and 2012 data sets corresponding to integrated luminosities of 5.1 fb −1 at √ s = 7 TeV and 19.7 fb −1 at √ s = 8 TeV. The four-lepton analysis uses the measured invariant mass distribution near the peak and above the Z-boson pair production threshold, as well as a likelihood discriminant to separate the gluon fusion ZZ production from the qq → ZZ background, while the two-lepton plus two-neutrino off-shell analysis relies on the transverse mass distribution. The presented analysis determines the independent contributions of the gluon fusion and VBF production mechanisms from the data in the on-shell region. It relies nevertheless on the knowledge of the coupling ratios between the off-shell and on-shell production, i.e. the dominance of the top quark loop in the gluon fusion production mechanism and the absence of new particle contribution in the loop. The presence of anomalous couplings in the HVV interaction would lead to enhanced off-shell production and would make our constraint tighter.