Study of the mass and spin-parity of the Higgs boson candidate via its decays to Z boson pairs

A study is presented of the mass and spin-parity of the new boson recently observed at the LHC at a mass near 125 GeV. An integrated luminosity of 17.3 inverse femtobarns, collected by the CMS experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, is used. The measured mass in the ZZ channel, where both Z bosons decay to e or mu pairs, is 126.2 +/- 0.6 (stat.) +/- 0.2 (syst.) GeV. The angular distributions of the lepton pairs in this channel are sensitive to the spin-parity of the boson. Under the assumption of spin 0, the present data are consistent with the pure scalar hypothesis, while disfavoring the pure pseudoscalar hypothesis.

struction and momentum measurement algorithms, fine-tuning the electron isolation requirement, and by using a regression technique, as previously used for the H → γγ analysis [2], for the contribution of the ECAL to the electron momentum measurement. For similar reducible background rates, the absolute signal detection efficiency is improved by up to 4% in the 4e channel and up to 2% in the 2e2µ channel. The resolution of the reconstructed mass of the 4 system is improved, relatively, by about 10% in the 4e and 2e2µ channels. Signal candidate masses are measured with a per-event mass precision varying between 1% and 3%. The detection efficiency for a SM Higgs boson of m H = 126 GeV, with leptons within the geometrical acceptance, is 31% in the 4e channel, 42% in the 2e2µ channel, and 59% in the 4µ channel.
Systematic uncertainties are evaluated from the observed data for the trigger efficiency (1.5%) and the combined lepton reconstruction, identification, and isolation efficiencies. These range from 1.2% in the 4µ channel to about 11% in the 4e channel. Systematic uncertainties on energymomentum calibration and energy resolution are incorporated through their effects on the reconstructed mass distributions. Uncertainties of 0.2%, 0.2%, and 0.1%, are assigned on the mass scale for the 4e, 2e2µ, and 4µ channels, respectively. The effect of the energy resolution uncertainties is taken into account by incorporating a 20% uncertainty on the simulated width of the signal mass peak. To validate the level of accuracy with which the absolute mass scale and resolution are known [2,15], we use Z → , Υ → , and J/ψ → events. The limited statistical precision of the control samples is included as a systematic uncertainty on the final results. Since the reducible background is derived from control regions, its prediction is independent of the uncertainties on the integrated luminosity. The integrated luminosity uncertainty (2.2% at 7 TeV [16] and 4.4% at 8 TeV [17]) enters the evaluation of the expected ZZ background and signal rates. Systematic uncertainties on the Higgs boson cross section (about 18%) and branching fraction (2%) are taken from Refs. [18,19]. Further separation between the signal and background is provided by a discriminant K D that incorporates the production and decay kinematics. In this analysis, we make use of observables defined for each event in the 4 center-of-mass frame; the rapidity and transverse momentum of the 4 system depend on the production mechanism and are ignored. We use a matrix element likelihood approach [2,[21][22][23], which combines, for each value of m 4 , the two dilepton masses m Z 1 and m Z 2 and five angular variables denoted Ω. We introduce a kinematic discriminant K D using the probability density in the dilepton masses and angular variables, P (m Z 1 , m Z 2 , Ω|m 4 ). The discriminant is defined as A scalar SM Higgs boson is assumed for the signal. The separation between the signal and background is relatively insensitive to the particular choice of a signal spin-parity hypothesis [22]. The minimum p-value [24], which characterizes the probability for a background fluctuation to be at least as large as the observed maximum excess around m H 126 GeV, is obtained from the measurements of m 4 and K D . It corresponds to a significance of 4.5 standard deviations, which is to be compared to an expected significance of 5.0 standard deviations for the SM Higgs boson.
We measure the mass of the boson using a maximum-likelihood fit to three-dimensional distributions combining for each event the m 4 , the associated per-event uncertainties δm 4 [15] calculated from the individual lepton momentum errors, and K D . The signal strength µ (defined below) is a free parameter in this mass fit. A scalar SM Higgs boson is assumed for the signal lineshape. Figure 1b shows the value of −2∆ ln L, where L is the likelihood, as a function of m H , with and without the effects of systematic uncertainties included. An estimate for the mass of 126.2 ± 0.6 (stat.) ± 0.2 (syst.) GeV is obtained. Combined with the result from the γγ channel [2], we obtain a mass of 125.8 ± 0.4 (stat.) ± 0.4 (syst.) GeV. This value improves upon and supersedes the previous result.
We then compare the observations with the expectation for the SM Higgs boson at the mass value fixed to 125.8 GeV, and obtain a measurement of the signal strength µ = σ/σ SM , the production cross section times the branching fraction relative to the SM expectation. This is evaluated from a scan of a profile likelihood ratio. We perform an unbinned maximumlikelihood fit of the two-dimensional distributions P (m 4 |m H ) × P (K D |m 4 ) for the signal, and P (m 4 ) × P (K D |m 4 ) for the background. The fit is performed simultaneously in the 4e, 2e2µ, and 4µ channels. We obtain a signal strength of µ = 0.80 +0.35 −0.28 , consistent with the expectation for a SM Higgs boson.
The kinematics of the production and decay of the new boson in the ZZ → 4 channel are sensitive to its spin and parity [21-23, 25-35]. To distinguish any two spin-parity hypotheses, we use discriminants of the form D 12 = P 1 /(P 1 + P 2 ), where P 1 and P 2 are the probability densities in m Z 1 , m Z 2 , and Ω corresponding to the two spin parity hypotheses we wish to discriminate and include parametrizations of the m 4 distribution for a resonance at the mass of the new boson. We define two spin-parity discriminants: D PS for the discrimination between a SM Higgs boson and a pure pseudoscalar state J P = 0 − ; D GS for discrimination between a SM Higgs boson and a spin-two tensor state J P = 2 + with the minimal graviton-like coupling to gluons in production and to Z bosons in decay. We also define a discriminant D SB = P sig /(P sig + P bkg ), similar to K D but where the probability densities also include m 4 , for the discrimination between a SM Higgs boson, with J P = 0 + , and the background.
We then fit the observed data in a two-dimensional plane of D PS or D GS versus D SB in the mass range 106 < m 4 < 141 GeV and obtain the likelihood values L 1 and L 2 for two hypotheses of each signal type plus background. Figure 2a shows the observed projections of D SB for events in this mass range, and for a SM Higgs boson signal with m H = 126 GeV. Figures 2b  and 2c show the projections of the D PS and D GS discriminants, for events with D SB > 0.5. In these latter two cases, the distributions for the spin-parity states being distinguished are also illustrated in the plot. More data are needed for significant discrimination of the 0 + from the 2 + hypothesis. Figure 3 shows the distributions of the log-likelihood ratio −2 ln L 0 − /L 0 + from pseudoexperiments under the assumptions of either a pure scalar or a pure pseudoscalar model. The arrow indicates the observed value. Under the assumption of spin 0, the test statistic formed from a profile likelihood ratio λ = L 0 − /L 0 + of the 0 − and 0 + hypotheses yields a p-value of 0.072% for 0 − and a p-value of 0.7 for 0 + , with −2 ln λ = 5.5 favoring 0 + . This corresponds to a CL s [36] value of 2.4%, a more conservative value for judging whether the observed data are compatible with 0 − . The results presented here have been confirmed with independent methods [37] based on leading-order matrix elements [38].
In summary, we have measured the mass of the new boson to be 126.2 ± 0.6 (stat.) ± 0.2 (syst.) GeV in the ZZ channel, where both Z bosons decay to lepton pairs. Combining results from the γγ and ZZ channels, we obtain a mass of 125.8 ± 0.4 (stat.) ± 0.4 (syst.) GeV, which improves upon previously published results. At this mass the signal strength µ = σ/σ SM is measured to be µ = 0.80 +0.35 −0.28 . Under the assumption of spin zero, the observed data are consistent with the pure scalar hypothesis, while disfavoring the pure pseudoscalar hypothesis. This is the first study of the spin-parity of the newly discovered boson. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. [20] CMS Collaboration, "Observation of Z decays to four leptons with the CMS detector at the LHC", (2012