Measurement of the Higgs boson mass from the $H\to \gamma \gamma$ and $H\to Z{Z}^{*}\to 4\ell$ channels in $pp$ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector

An improved measurement of the mass of the Higgs boson is derived from a combined fit to the reconstructed invariant mass spectra of the decay channels $H\to \gamma \gamma$ and $H\to Z{Z}^{*}\to 4\ell$. The analysis uses the $pp$ collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at center-of-mass energies of 7 TeV and 8 TeV, corresponding to an integrated luminosity of $25{\mathrm{fb}}^{-1}$. The measured value of the Higgs boson mass is $m_H=125.36\pm 0.37(\text{stat})\pm 0.18(\text{syst})\mathrm{GeV}$. This result is based on improved energy-scale calibrations for photons, electrons, and muons as well as other analysis improvements, and supersedes the previous result from ATLAS. Upper limits on the total width of the Higgs boson are derived from fits to the invariant mass spectra of the $H\to \gamma \gamma$ and $H\to Z{Z}^{*}\to 4\ell$ decay channels.

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Figure 1

Relative scale difference, $\mathrm{\Delta }$ Scale, between the measured electron energy scale and the nominal energy scale, as a function of $E_{\mathrm{T}}$ using $J/\psi \to e^{+}{e}^{-}$ and $Z\to e^{+}{e}^{-}$ events (points with error bars), for four different $\eta$ regions: (a) $|\eta |<0.6$, (b) $0.6<|\eta |<1.37$, (c) $1.37<|\eta |<1.82$ and (d) $1.82<|\eta |<2.37$. The uncertainty on the nominal energy scale for electrons is shown as the shaded area. The error bars include the systematic uncertainties specific to the $J/\psi \to e^{+}{e}^{-}$ measurement.

Figure 2

Relative scale difference, $\mathrm{\Delta }$ Scale, between the measured photon energy scale using $Z\to \ell \ell \gamma$ events and the nominal energy scale: (a) as a function of $E_{\mathrm{T}}$ for unconverted photons, (b) as a function of $\eta$ for unconverted photons, (c) as a function of $E_{\mathrm{T}}$ for converted photons and (d) as a function of $\eta$ for converted photons. Photons reconstructed in the transition region between the barrel and end-cap calorimeters are not considered. The $Z\to \ell \ell \gamma$ measurements are the points with error bars. The uncertainty on the nominal energy scale for photons is shown as the shaded area. The error bars include the systematic uncertainties specific to the $Z\to \ell \ell \gamma$ measurement.

Figure 3

Ratio of the reconstructed dimuon invariant mass for data to the corrected mass in simulation for $J/\psi$, $\mathrm{\Upsilon }$ and $Z$ events: (a) as a function of $\eta$ of the higher-$p_{\mathrm{T}}$ muon and (b) as a function of $⟨p_{\mathrm{T}}⟩$ of the two muons, as defined in the text. The shaded areas show the systematic uncertainty on the simulation corrections for each of the three samples. The error bars on the points show the combined statistical and systematic uncertainties as explained in the text. In (a), the two large $|\eta |$ bins have measurements only from $Z$ events due to trigger limitations above $|\eta |=2.4$.

Figure 4

Invariant mass distribution in the $H\to \gamma \gamma$ analysis for data (7 TeV and 8 TeV samples combined), showing weighted data points with errors, and the result of the simultaneous fit to all categories. The fitted signal plus background is shown, along with the background-only component of this fit. The different categories are summed together with a weight given by the $s/b$ ratio in each category. The bottom plot shows the difference between the summed weights and the background component of the fit.

Figure 5

Difference, ${\mathrm{\Delta }}_i$, between the mass measured in a given $\gamma \gamma$ subsample and the combined $\gamma \gamma$ mass, using three different alternative categorizations to define the subsamples. The top three points show a categorization based on the photon conversion status: $UU$ is the subsample with both photons unconverted, $UC$ the subsample with one converted and one unconverted photon, and $CC$ the subsample with two converted photons. The middle three points show a categorization based on the number of reconstructed primary vertices ($N_{\mathrm{PV}}$) in the event. The bottom three points show a categorization based on the photon impact points on the calorimeter: $BB$ is the subsample with both photons detected in the barrel calorimeter, $BE$ the subsample with one photon in the barrel calorimeter and one photon in the end-cap calorimeter and $EE$ the subsample with both photons in the end-cap calorimeter.

Figure 6

(a) Distribution of the four-lepton invariant mass for the selected candidates in the $m_{4\ell }$ range 80–170 GeV for the combined 7 TeV and 8 TeV data samples. Superimposed are the expected distributions of a SM Higgs boson signal for $m_H=124.5\mathrm{GeV}$ normalized to the measured signal strength, as well as the expected $Z{Z}^{*}$ and reducible backgrounds. (b) Distribution of the ${\mathrm{BDT}}_{Z{Z}^{*}}$ output versus $m_{4\ell }$ for the selected candidates in the 110–140 GeV $m_{4\ell }$ range for the combined 7 TeV and 8 TeV data samples. The expected distribution for a SM Higgs with $m_H=124.5\mathrm{GeV}$ is indicated by the size of the blue boxes, and the total background is indicated by the intensity of the red shading.

Figure 7

The profile likelihood as a function of $m_H$ for the combination of all $H\to Z{Z}^{*}\to 4\ell$ channels and for the individual channels for the combined 7 TeV and 8 TeV data samples. The combined result is shown both with (solid line) and without (dashed line) systematic uncertainties, and the two results are almost indistinguishable.

Figure 8

Value of $-2\ln \mathrm{\Lambda }$ as a function of $m_H$ for the individual $H\to \gamma \gamma$ and $H\to Z{Z}^{*}\to 4\ell$ channels and their combination, where the signal strengths ${\mu }_{\gamma \gamma }$ and ${\mu }_{4\ell }$ are allowed to vary independently. The dashed lines show the statistical component of the mass measurements. For the $H\to Z{Z}^{*}\to 4\ell$ channel, this is indistinguishable from the solid line that includes the systematic uncertainties.

Figure 9

Likelihood contours $-2\ln \mathrm{\Lambda }(S,m_H)$ as a function of the normalized signal yield $S=\sigma /{\sigma }_{\mathrm{SM}}(m_H=125.36\mathrm{GeV})$ and $m_H$ for the $H\to \gamma \gamma$ and $H\to Z{Z}^{*}\to 4\ell$ channels and their combination, including all systematic uncertainties. For the combined contour, a common normalized signal yield $S$ is used. The markers indicate the maximum likelihood estimates in the corresponding channels.