Measurements of the Total and Differential Higgs Boson Production Cross Sections Combining the $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ Decay Channels at $\sqrt{s}=8$ TeV with the ATLAS Detector

Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3 fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions.


Measurements of the Total and Differential Higgs Boson Production Cross Sections
Combining the H → γγ and H → ZZ * → 4 Decay Channels at √ s = 8 TeV with the ATLAS Detector The ATLAS Collaboration (Dated: April 23, 2015) Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3 fb −1 of pp collisions produced by the Large Hadron Collider at a center-of-mass energy of √ s = 8 TeV and recorded by the ATLAS detector. Cross sections are obtained from measured H → γγ and H → ZZ * → 4 event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be σpp→H = 33.0 ± 5.3 (stat) ± 1.6 (sys) pb. The measurements are compared to state-of-the-art predictions.
PACS numbers: 13.85.Lg,13.85.Qk, 14.80.Bn This Letter presents measurements of the total and differential cross sections of inclusive Higgs boson production using 20.3 fb −1 of pp collisions produced by the Large Hadron Collider (LHC) [1] at a center-of-mass energy of √ s = 8 TeV and recorded by the ATLAS detector [2]. The measured cross sections probe the properties of the Higgs boson and can be directly compared to the theoretical modeling of different Higgs boson production mechanisms, such as the most recent gluon fusion (ggF) QCD calculations. They can also be used to constrain new physics scenarios, for example using the effective field theory framework as proposed in Refs. [3][4][5][6][7]. The analysis uses event yields measured in the H → γγ and H → ZZ * → 4 decays and detector efficiencies, both determined as described in Refs. [8,9]. The statistical uncertainties on the Higgs boson signal yields in both channels are larger than the systematic uncertainties, while the total uncertainties in the two channels are similar. Combining the analyses improves the precision of the cross-section measurements by up to 40%, and by 25-30% on average, with respect to the corresponding measurements in the most precise individual channel.
Distributions of the differential pp → H cross sections are reported as a function of the transverse momentum p H T and the rapidity |y H | of the Higgs boson, the jet multiplicity N jets , and the transverse momentum of the leading jet p j1 T . The observables p H T and |y H | describe the kinematics of the Higgs boson. They are sensitive to perturbative QCD modeling in ggF production, which is the dominant Higgs boson production mechanism in the Standard Model (SM). The |y H | distribution furthermore offers a clean probe of the gluon parton distribution function (PDF) and will play a role in future PDF fits. The N jets distribution is sensitive to the relative contributions of different production mechanisms. The observable p j1 T probes the theoretical modeling of partonic radiation in ggF production as well as the modeling of jets in events with Higgs boson production by vector-boson fusion (VBF) and associated production (VH). Jets pro-duced in VBF and VH processes tend to have higher transverse momenta than those produced in the ggF production mode.
Cross sections are extracted using a combined likelihood that takes into account the signal yields in the H → γγ channel and the data and background yields in the H → ZZ * → 4 channel, as well as detector efficiencies, fiducial acceptances and SM branching fractions [10]. A complementary approach, using a separate likelihood, combines the differential distributions normalized to unity, referred to as shapes, which removes the implicit SM assumption on the branching fractions. For the extraction of the yields, the detector efficiencies, fiducial acceptances, and branching fractions, the Higgs boson mass is set to the value measured by the ATLAS Collaboration of m H = 125.36 ± 0.41 GeV [11]. The signal yield in the H → γγ channel is obtained from fits to the diphoton mass spectra [8], while in the H → ZZ * → 4 channel, the estimated background is subtracted from the data yields in each bin in a mass window around m H , defined by the reconstructed four-lepton mass [9]. The fiducial acceptance in both channels [8,9] is derived using a set of Monte Carlo (MC) event generators. Powhegbox [12][13][14], interfaced with Pythia8 [15] for showering, is used to generate ggF and VBF events, while Pythia8 is used to simulate VH and associated production with top quarks (ttH) and b-quarks (bbH). The fiducial acceptance for events with |y H | < 1.2 is approximately 72% for H → γγ, and 55-59% for H → ZZ * → 4 . For higher |y H |, the acceptance decreases to 35-38% in both channels. The fiducial acceptance is more constant as a function of the other variables and is in the range 56-62% for the H → γγ channel and 44-53% for the H → ZZ * → 4 channel.
After correcting the differential cross sections and normalized shapes for fiducial acceptance and branching fractions, the corresponding measurements in both channels are found to be in good agreement with each other; p-values obtained from χ 2 compatibility tests are in the range 56-99%.
In the binned maximum-likelihood fit, the statistical uncertainty of the H → γγ event yield is modeled using a Gaussian distribution, while the event yield in the H → ZZ * → 4 channel follows a Poisson distribution due to the small sample size. Experimental and theoretical systematic uncertainties affecting the signal yields, detector efficiencies, branching fractions and fiducial acceptance corrections are taken into account in the likelihood as constrained nuisance parameters. Nuisance parameters describing the same uncertainty sources are treated as fully correlated between bins and channels. Systematic uncertainties on the H → γγ and H → ZZ * → 4 background estimates and efficiency correction factors, as well as the uncertainty on the integrated luminosity, are described in detail in Refs. [8,9]. The branching fraction uncertainty due to the assumed quark masses and other theoretical uncertainties are evaluated following the recommendations of Ref. [16], considering uncertainty correlations between the H → γγ and H → ZZ * → 4 decay channels. Uncertainties on the acceptance correction related to the choice of PDF set are evaluated by taking the envelope of the sum in quadratures of eigenvector variations of the baseline (CT10 [17]) and the central values of alternative (MSTW2008NLO [18] and NNPDF2.3 [19]) PDF sets. Uncertainties on the acceptance correction associated with missing higher-order corrections are evaluated by varying the renormalization and factorization scales coherently and individually by factors of 0.5 and 2 from their nominal values, and by reweighting the p H T distribution from Powheg-box to the prediction of the HRes 2.2 calculation [20,21]. The envelope of the maximum deviation of the combined scale variations and the p H T reweighting is used as the systematic variation. To account for the uncertainty in the mass measurement, the Higgs boson mass is varied by ±0.4 GeV. To assess the systematic uncertainty due to the assumption of SM cross-section fractions of the Higgs boson production modes, the VBF and VH fractions are varied by factors of 0.5 and 2 from the SM prediction and the fraction of ttH is varied by factors of 0 and 5. These factors are based on current experimental bounds [22][23][24][25][26]. The total uncertainties on the acceptance correction range from 1% to 6%, depending on the channel, distribution and bin.
The total systematic uncertainties on the combined differential cross sections range from 4% to 12%, depending on the distribution and bin. For the kinematic variables p H T and |y H |, the largest systematic uncertainties on the differential cross sections are due to the luminosity and the background estimates in both channels. For the jet variables N jets and p j1 T , the largest systematic uncertainties on the differential cross sections are due to the jet energy scale and resolution. In the shape combination, the normalization uncertainties including luminosity, branching fractions, and efficiency uncertainties do not apply.   Table I.

ATLAS
Statistical uncertainties dominate all resulting distributions, ranging from 23% to 75%. 1.8 (sys) pb. Combining the analyses yields σ pp→H = 33.0 ± 5.3 (stat) ± 1.6 (sys) pb. Figure 1 presents a comparison of these measurements with two ggF predictions to which contributions from other relevant Higgs boson production modes (VBF, VH, ttH, bbH) are added using cross sections and uncertainties from Ref.
[10], is accurate to next-to-next-to-leading order (NNLO) in QCD and utilises threshold resummation accurate to next-tonext-to-leading logarithms (NNLL). A significant effort has been undertaken by the theory community to provide ggF cross sections beyond this precision through various improvements in the perturbative calculations [31,[47][48][49][50][51]. Recently, the ADDFGHLM group has provided a fixed-order calculation accurate to next-to-next-to-nextleading order (N 3 LO) [27][28][29][30]. A PDF uncertainty of +7.5 −6.9 % is assigned to the LHC-XS prediction, derived following the recommendations in Ref. [16]. This uncertainty is increased by +0.3 −0.1 % for the ADDFGHLM prediction corresponding to the change in uncertainty of the MSTW2008nnlo PDF set when changing the calculation from NNLO to N 3 LO. The PDF uncertainty is treated as uncorrelated with the QCD scale uncertainty.
The central value of the measured total cross section is larger than the SM predictions presented in Fig. 1. A likelihood-ratio test statistic is used to quantify the agreement, using a bifurcated Gaussian to model the asymmetric theory uncertainties. The resulting p-values are 5.5% and 9.0% for the agreement between data and the predictions from LHC-XS and ADDFGHLM, respectively. The ratio of the measured cross section to the LHC-XS prediction is higher than the results presented in Refs. [22,23], which use an event categorization based on the expected SM yields in the different Higgs boson production modes. Figure 2 shows the comparison of the combined cross sections in different inclusive and exclusive jet multiplicity bins with state-of-the-art predictions, including NLOaccurate multi-leg (ML) merged ggF MC event generators (further details are given in Table I). Jets are reconstructed using the anti-k t algorithm [52] with a radius parameter R = 0.4 [53], and are required to have p T > 30 GeV and |y| < 4.4. Simulated particle-level jets are built from all particles with cτ > 10 mm excluding neutrinos, electrons and muons that do not originate from hadronic decays. Photons are excluded from jetfinding if they lie inside a cone of radius ∆R < 0.1 of an electron or muon, and neither the photon nor lepton originate from a hadron decay. To allow comparisons with the unfolded measurements, the analytical calculations are corrected for effects of hadronization and multiple particle interactions. These correction factors and their associated uncertainties are obtained using the Pythia8 and Herwig [54] Measured Higgs boson production cross sections in inclusive and exclusive jet multiplicity bins compared to different theoretical predictions (see Table I for details and references).
NNLO+NNLL calculations. However, for N jets ≥ 1, the MC predictions formally have NLO accuracy, which is the same as the analytical calculations. Contributions from other relevant Higgs boson production modes are generated using Powheg for VBF and Pythia8 for VH, ttH, and bbH, and are scaled to the cross sections in Ref.
[10]. Uncertainties are assigned to all MC predictions from QCD scale and PDF variations. The ML-merged ggF predictions also have uncertainties due to the choice of merging scale. The SHERPA uncertainties further include resummation scale variations. The measured cross sections are higher than the predictions for all measured jet multiplicities. The poorest agreement with data can be found in the inclusive and exclusive 1-jet bins, with p-values ranging between 0.1% and 3.6%.
The combined differential cross sections as a function of p H T , |y H |, and p j1 T are shown in Fig. 3 (left). The measured p H T and |y H | distributions are compared to the HRes calculation and the p j1 T measurement is compared to STWZ and JetVHeto predictions. Figure 3 (right) shows the comparisons of the normalized shapes to predictions from the MC event generators NNLOPS, SHERPA 2.1.1, and MG5 aMC@NLO, as well as the HRes calculation. The uncertainties on the predicted shapes are evaluated following the same approach as for the differential cross-section predictions. They are derived from the impact of QCD scale, merging scale and PDF variations. The mean of the measured p H T distribution is 40.1 ± 3.0 GeV, while the means of the MC predictions range from 34 to 37 GeV.    The p-values quantifying the compatibility of the measured shapes and the predictions range from 8% to 88%. For the calculation of these values, the theory uncertainties are assumed to be Gaussian distributed and fully correlated between bins.
In conclusion, this Letter presents the first measurements of total and differential cross sections and shapes for inclusive pp → H production. The measurements were performed in the H → γγ and H → ZZ * → 4 channels using the full 2012 dataset, which consists of 20.3 fb −1 of pp collisions produced by the LHC at a center-of-mass energy of √ s = 8 TeV and recorded by the ATLAS detector. While the measured total cross section is higher than the tested predictions, p-values indicate fair agreement between the current best predictions and the data for all studied differential cross sections and shapes.
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
aj Also at Department of Physics, The University of Michigan, Ann Arbor MI, United States of America ak Also at Discipline of Physics, University of KwaZulu-Natal, Durban, South Africa al Also at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia * Deceased

SUPPLEMENTAL MATERIAL
The fiducial cross section σ i in a given bin i can be expressed as where n i is the measured Higgs boson signal yield, L is the integrated luminosity (20.3 fb −1 for this analysis), B is the branching ratio (0.228% for H → γγ and 0.0129% for H → ZZ * → 4 , = e or µ), α i is the fiducial acceptance and c i is a correction factor for detector effects, primarily accounting for reconstruction efficiency but also for bin-to-bin migration. For H → ZZ * → 4 , the signal yield is defined as the number of observed events n data in a window around the Higgs boson mass peak minus the background estimate: n i = n data,i − n bkg,i , while for H → γγ, the signal yield is extracted from a simultaneous signal+background fit of the m γγ distribution. The correction factors for detector effects c i , along with their systematic uncertainties are taken from the differential cross section measurements in the individual channels [8,9]. The differential cross section is defined as the fiducial cross section divided by the bin width. The binning is the same as in Fig. 4.

Fiducial acceptance
For each bin i, the acceptance factor for each decay channel is defined as The fiducial acceptances for both channels and all measured distributions are presented in Fig. 4 and Tables II  and III. They are based on Eq. 2 and derived using the Higgs MC samples described in the text. For p H T and |y H |, α i is the probability for an event to pass the fiducial requirements. The acceptance is lower for H → ZZ * → 4 than for H → γγ since it is less likely for four decay products to fulfill the fiducial requirements. For the jet variables p j1 T and N jets , an additional migration effect enters due to overlap between jets and the Higgs boson decay products, which affects the fiducial regions differently than the total phase space, where no Higgs boson decay products need to be considered. The fiducial acceptance falls off steeply as the Higgs boson rapidity increases, as both fiducial definitions include pseudo-rapidity requirements on the Higgs boson decay products. Figure 5 presents the measured jet multiplicity distributions. The lower two subfigures include the individual H → γγ and H → ZZ * → 4 measurements. Figure 6 presents the same six distributions as shown in Fig. 3, but with the individual channel measurements overlaid.  Tables IV-VII present the measured differential cross  sections and Tables VIII-XI report the corresponding  shape measurements.   TABLE IV. Measured cross section in bins of p H T . The first uncertainty is statistical, the second is systematic.

Additional figures
dσ/dp H    Tables XII-XV contain the correlation matrices of the  differential cross section measurements and Tables XVI-XIX those of the differential shape measurements.   TABLE XII