Studies on Higgs Mass Resolutions and Mass Fitting withFour-lepton Final States with the ATLAS Experiment

Yutong Pan

April 2, 2013

Abstract

This thesis presents the mass resolution and measurement of the newly discovered Higgs-like boson particle in thedecay channel H → ZZ∗ → `+`−`′+`′−, where `,`′ = e or µ using proton-proton collision data corresponding to anintegrated luminosity 20.7 fb−1 at

√s = 8 TeV, recorded with the ATLAS detector at the LHC. The first main part

of the thesis reports the study on mass resolution based on each individual event using MC samples by propagatinguncertainties in the energy and momentum measurements of the leptons. A validation of the method with the closuretest is carried out for Higgs mass varying between 110-200 GeV. The mass resolutions for all the selected Higgs eventcandidates are calculated based on the lepton measurement uncertainty propagations. The second main part of thethesis presents the Higgs mass fitting with and without adding event-by-event resolution. The mass of the Higgs-likeboson is mH = 124.58+0.6−0.5(stat)

+0.5−0.3(syst)±0.42 GeV .

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Contents1 Introduction 3

2 ATLAS detector 3

3 Event Selection 4

4 Higgs Mass Resolution Study 54.1 Electron Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2 Muon Momentum Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.3 Detector-Induced Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.4 Final State Radiation Induced Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.5 Results on the MC Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Mass Resolution of the Higgs Candidates 16

6 Final State Radiation Photon Selection 18

7 Higgs Mass Measurements 187.1 Mass fit of the Z→ 4` resonant peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187.2 Mass fit of the H→ ZZ∗→ 4` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

8 Conclusion 22

9 Appendix 229.1 The sample list of FSR photons found for 2012 Higgs candidates . . . . . . . . . . . . . . . . . . . . . 229.2 The sample list of Kinematics of 2012 Higgs candidates in mass window 110-130 GeV . . . . . . . . . 229.3 The sample list of fitted ∆MZZ results for various Higgs mass . . . . . . . . . . . . . . . . . . . . . . . 239.4 Invariant mass distributions for combined 2011 and 2012 Higgs candidates . . . . . . . . . . . . . . . . 249.5 Invariant mass distributions for combined 2011 and 2012 single Z resonance candidates . . . . . . . . . 26

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1 IntroductionA historic moment was reached on July 4th last year when the ALTAS and CMS experiments have separately reportedthe discovery of a new Higgs-like particle. This discovery is a breakthrough in particle physics in the past half century.

In the context of the Standard Model of particle physics, the Higgs mechanism is responsible for the electroweaksymmetry breaking. According to the Standard Model, electroweak interactions are mediated by γ, W±, and Z0 bosons,which are originally massless. The Lagrangian in the electroweak theory is required to be locally gauge invariantunder SU(2)×U(1) transformation. In the symmetry breqking process, a complex scalar field doublet is introduced.The Higgs field then interacts with the gauge fields to cause the spontaneous breaking of the SU(2)×U(1) symmetrygroup. After the symmetry breaking, a neutral scalar particle, the Higgs boson, appears and the vector bosons, W andZ, become massive, while the photon of electromagnetism remains massless. This theoretical hypothesis has finallyconfirmed by experiments at the LHC.

Figure 1: Schematic of the ATLAS detector at the LHC.

The discovery channels of the Higgs boson include processes of H→ ZZ∗→ 4`, H→ γγ, and H→WW ∗→ 2`2ν.The cleanest channel for the discovery of the Higgs boson is its decay to four leptons H→ `+`−`′+`′−, where `,`′ = e orµ. This channel provides an excellent energy resolution and the reconstructed electrons and muons. The signal apearsas a narrow 4-lepton invariant mass peak on top of a smooth background. The Standard Model irreducible backgroundmainly comes from the SM ZZ∗→ 4l decays.

The subsequent measurements of this newly discovered boson properties are essential. The first important measure-ment is the Higgs mass. Since the experimental signals have been observed in different channels, final determinationof the Higgs mass must be carefully taking into account on the detector resultion and possible systmatic uncertainties.In this thesis, the measurement of Higgs boson mass using 4` final state is presented. The analysis is carried out usingthe√

s = 8TeV data recorded in 2012 corresponding to an integrated luminosity of 20.7 fb−1.

2 ATLAS detectorThe ATLAS detector shown in Fig. 1 is a multi-purpose particle physics detector with approximately forward-backwardsymmetric cylindrical geometry. The inner tracking detector (ID) covers pseudorapidity range |η| < 2.5 and consistsa silicon pixel, a silicon micro-strip detector, and a transition radiation tracker (TRT). The ID is surrounded by a thinsuperconducting solenoid providing a 2 T axial magnetic field. A lead/liquid-argon (LAr) sampling calorimeter mea-sures the energy and the position of electromagnetic showers within |η|< 3.2. LAr sampling calorimeter also measureshadronic showers in the end-cap region (1.5 < |η|< 3.2) and forward region (3.1 < |η|< 4.9). An iron/scintillator tile

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calorimeter measures hadronic showers in the central region (|η| < 1.7). The muon spectrometer (MS) locates at theouter-most part of the detector. It surrounds the calorimeters and consists of three large superconducting air-cool toroidmagnets, a system of precision tracking chambers ( |η|< 2.7), and fast tracking chambers for triggering. A three-leveltrigger system is used to select events to be recorder for offline analysis.

3 Event SelectionIn ATLAS Higgs detection program, electron candidates are identified from clusters of energy deposited in the elec-tromagnetic calorimeter associates with an inner detector track. Muon candidates are reconstructed by matching innerdetector tracks with tracks reconstructed in the muon spectrometer. If the track reconstructed in the muon spectrometeris a complete track, then the two independent momentum measurements from ID and MS are combined to form ”com-bined muons”; if the tracks reconstructed in the muon spectrometer are partial tracks, then the momentum is measuredusing the ID information only to form ”segment-tagged muons”. The muon reconstruction and identification coverageis extended by using tracks reconstructed in the forward region 2.5 < |η|< 2.7 of the muon spectrometer, which in thiscase, there is no inner detector coverage. In the barrel region, where there is no muon spectrometer coverage, the energydeposit profile of inner detector tracks is used to identify muons with |η|< 0.1 and pT > 15 GeV and this reconstructedmuons are labeled as ”calo-tagged”.

The Higgs boson candidate quadruplet is formed by selecting two same-flavor, opposite-sign lepton pairs in anevent. Electrons are required to have transverse energy ET > 7 GeV and in pseudorapidity range |η| < 2.47. Muonsare required to have transverse momentum pT > 6 GeV and in pseudorapidity range |η|< 2.7. The four leptons of thequadruplets are required to separated as ∆R =

√∆η2 +∆φ2 > 0.1 for same flavor leponts and as ∆R > 0.2 for different

flavor leptons. The di-lepton of the quadruplet with a mass m12 closest to the nominal Z boson mass is identified asthe leading di-lepton and the the second di-lepton of the quadruplet with a mass m34 is the sub-leading di-lepton. Thehigher pT lepton in the quadruplet must satisfy pT > 20 GeV, and the second and third leptons in descending pT ordermust satisfy pT > 15 GeV and pT > 10 GeV respectively. The mass window for the leading di-lepton mass m12 isrequired to be between 50 and 106 GeV. The sub-leading di-lepton mass m34 is required to exceed a threshold of 12GeV. The event selection criteria described here is presented in Table 1.

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Event Preselection

Electrons H4l2011Defs and Multilepton (2012) quality GSF electronswith ET > 7 GeV and |η|< 2.47

Muons Combined or segment-tagged muons with pT > 7 GeV and |η|< 2.7calo-tagged muons with pT > 15 GeV and |η|< 0.1stand-alone muons with pT > 6 GeV, 2.5 < |η|< 2.7 and ∆R > 0.2

Event Selection

Quadraplet Two pairs of same-flavour opposite-charge leptons.selection The three leading leptons in the quadruplet have pT > 20, 15, and 10 GeV.

Pick the pair that has MZ1 nearest Z-mass, and then MZ2 nearest.

Kinematic Leading di-lepton mass requirement 50 GeV < m12 < 106 GeVselection Sub-leading di-lepton mass requirement 12 < m34 < 115 GeV

No same-flavor opposite-charge di-lepton giving M`+`− < 5 GeV (J/ψ veto)∆R(`,`′)> 0.1(0.2) for all same-flavor (opposite-flavor) leptons in the quadruplet.

Table 1: Summary of the event selection requirements

4 Higgs Mass Resolution StudyThe mass resolution calculation for each channel in the H→ ZZ? → 4l is essential for the Higgs mass measurement.In the mass fitting program in ATLAS, the mass resolution of each event is a required parameter. In this section, wewill describe the Higgs mass resolution calculation in detail. The Higgs mass resolution depends on both energy andmomentum uncertainties of the lepton measurements and the final state radiation. We will first present the energyand momentum resolutions for electrons and muons. The mass resolution due to lepton detections is calculated usingthe standard error propagations. The final state radiation (FSR) is due to the internal radiations and Bremsstrahlungradiations of leptons. The FSR would cause the Higgs mass peak to shift to a lower value. The FSR photons usuallyhave very low transverse energy ET , so they are very difficult to be detected. The resolution induced by FSR is treatedas systematics uncertainties based on MC studies. The final mass resolution is obtained from the quadratic sum of thedetector resolution and the FSR systematic.

In this study, the NLO generator PowhegBox with NLO PDF set CT10 is used to model Higgs production throughthe gluon-gluon fusion process. The MC events are fully simulated with ATLAS detector and reconstructions. The MCsamples studied ranges from Higgs mass 110 GeV to 200 GeV. The Higgs mass with M = 125 GeV is used to validatethe results.

4.1 Electron Energy ResolutionThe electron energy resolution is calculated from a resolution function from the EnergyRescalar class provided by theATLAS Egamma group. In the EgammaAnalysisUtils package, the function is called:

for data : EnergyRescalar : : resolution( Energy, Eta, Data );

for MC : EnergyRescalar : : resolution( Energy, Eta, MC ).

As suggested by the Egamma group, the energy resolution of electrons is a function of energy and η. The resolutionparametrized by a MC Sampling term, a MC Noise term, an MC Constant term, and a Data Constant term, which allare functions of η. The η corresponds to the end-cap (1.5 < |η|

Figure 2: Electron relative energy resolution as a function of momentum for barrel region (top left), transition region(trop right), end-cap region (bottom left), and CSC/NO-TRT region (bottom right).

σ2 =Sampling−Term2

energy+

Noise−Term2

energy2+Constant−Term2 +data−Condstant−Term2

The electron relative energy resolution is plotted as a function of momentum for different regions and they are shownin Figure 2.

4.2 Muon Momentum ResolutionThe ATLAS Muon Spectrometer (MS) is designed to provide a relative resolution for the momentum measurement bet-ter than 3% over a wide transverse momentum pT range. [1] In the MS, the magnetic field is generated by an air-coretoroid coils and the deflection of muon trajectory in the field is used to measure the muon momentum. The muon trackin the MS is reconstructed from three layers of precision drift tube chambers (MDT) in range |η|< 2.0 and two layersof MDT chambers in combination of one layer of cathode strip chambers (CSC) in range 2.0 ≤ |η| < 2.7. The muonmomentum determination is also provided by the Inner Detector (ID) in the range |η|< 2.5.

In calculating momentum resolution, three types of muon are reconstructed and studied. They are: Standalone muonswhich are muon segments and hits reconstructed in the Muon Spectrometer, CaloTag muons which are inner tracks andcalorimeter hits in the Inner Detector, and Combined muons which are muon track formed from the successful combi-nation of an ID track and a MS track. So for muon identification, the tracks are measured separately in ID and MS andthen they are combined and reconstructed as a single muon trajectory.

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η region pMS0 (TeV) pMS1 (%) p

MS2 (TeV

−1)barrel 0.24 3.31 0.144transition 0 6.01 0.51end-caps 0 4.24 0.216CSC/No-TRT 0.14 3.2 0.159η region pID0 (TeV) p

ID1 (%) p

ID2 (TeV

−1)barrel n.a 1.61 0.363transition n.a 2.59 0.412end-caps n.a 3.39 0.662CSC/No-TRT n.a 5.12 0

Table 2: Resolution parametrization for MS and ID for Data

The ATLAS MS measures the muon momentum resolution as a function of the pseudorapidity η and φ. In theMS, for a given η, the relative momentum resolution σ(p)/p is parametrized as a function of pT as follows,

σ(p)p

=pMS0pT⊕ pMS1 ⊕ pMS2 × pT (1)

where pMS0 corresponds to the uncertainties in the energy loss in the calorimeter material, pMS1 corresponds multiple

scattering, and pMS2 corresponds to intrinsic resolution terms. For the ID, the approximate parametrization of theresolution is as follows,

σ(p)p

= pID1 ⊕ pID2 × pT for|η|< 1.9

σ(p)p

= pID1 ⊕ pID2 × pT1

tan2(θ)for|η|> 1.9

(2)

where coefficients pID1 is associated with the multiple scattering and pID2 is associated with the intrinsic resolution terms.

The combined muon momentum is obtained from combing the ID and MS measurements and is calculated using aweighting function as follows

σCBP T =√

2σMSP σIDP

PCBT√

σ2MS +σ2ID

(3)

The four regions in the pseudorapidity are defined as the following:

Barrel : covering0 < |η|< 1.05;Transition : covering1.05 < |η|< 1.7;End-caps : covering1.7 < |η|< 2.0;CSC/No-TRT : covering2.0 < |η|< 2.5.

The coefficients for the resolution parametrization for both MS and ID cases defined in equations (1) - (3) are listedseparately for Data and MC in Table 2 and Table 3 respectively. The coefficients were obtained from the SmearingClasspackage.

Using the coefficients given in Table 2 and Table 3 for Data and MC simulation respectively, we can obtain theresolution curves. For MS and ID in the barrel region |η| < 1.05 and End-cap region 1.7 < |η| < 2.0, the relativemomentum resolutions are plotted as a function of pT for both data and simulation. For resolution curves from thefitted parameter values of the MS in the collision data and simulation, the results are shown in Figure 3; for resolutioncurves from the fitted parameter values of the ID in the collision data and simulation, the results are shown in Figure 4.

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η region pMS0 (TeV) pMS1 (%) p

MS2 (TeV

−1)barrel 0.24 2.68 0.103transition 0 4.52 0.192end-caps 0 3.12 0.08CSC/No-TRT 0.14 2.64 0.051η region pID0 (TeV) p

ID1 (%) p

ID2 (TeV

−1)barrel n.a 1.61 0.307transition n.a 2.59 0.331end-caps n.a 3.39 0.436CSC/No-TRT n.a 5.12 0

Table 3: Resolution parametrization for MS and ID for MC

Figure 3: Resolution curve from the fitted parameter values of the MS in collision data and simulation as a function ofmuon pT , for the barrel and end-cap regions of the detector.

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Figure 4: Resolution curve from the fitted parameter values of the ID in collision data and simulation as a function ofmuon pT , for the barrel and end-cap regions of the detector.

4.3 Detector-Induced ResolutionIn the detector-induced resolution calculation, we use equation (1) for Standalone muons form MS, equation (2) forCalo-Tag muons from ID, and equation (3) for Combined muons.

The Higgs mass M for all decaying lepton channels is calculated using

M2 = (E1 +E2 +E3 +E4)2− (−→P1 +

−→P2 +

−→P3 +

−→P4)2

M2 = (4

∑i=1

E2i +3

∑i=1

4

∑j>i

2EiE j)− (4

∑i=1

−→P2i +

3

∑i=1

4

∑j>i

2−→Pi−→Pj )

(4)

The masses for electron and muon can be approximate to be zero because they are negligible compared with theirmomentum in GeV. Then, we have E =

√M2 +P2 ≈ P, then equation (4) above becomes

M2 =3

∑i=1

4

∑j>i

2PiPj(1− cos(θi j)) (5)

Now using the standard error propagation formula for function f(x,y),

∆ f (x,y) =

√(∂ f∂x

)2dx2 +

(∂ f∂y

)2dy2

Here we use the fact that the detector’s angular resolution is much better that its momentum resolution, we canneglect the dθ term, then we arrive at the mass resolution of the form

∆MTrack =1M

4∑i=1

[4

∑j=1, j 6=i

Pj(1− cos(θi j))

]2∆P2i

1/2 . (6)Using this formula, we are able to calculate the detector-induced resolution for each Higgs decay event in four-leptonfinal state. As an example, the resolution ∆MTrack is plotted for each event in Figure 5 using MC sample with Higgs

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mass equals to 125 GeV. We will show that the mass resolution due to lepton measurement uncertainties cannot totallycount for the mass resolution (see Figure 6). This is due to additional final state radition contributions which will bediscussed in the next section.

Figure 5: Detector-induced resolution from MC simulation with Higgs mass (125 GeV) ∆MTrack for each event fit witha Gaussian function.

4.4 Final State Radiation Induced ResolutionPhotons from final state radiation have very low transverse energy ET and they have large kinematic overlap with thebackground. Therefore, to identify FSR photons from the large number of background per event are very difficult.From our simulation, about 80% of the FSR photons have transverse momentum less than 1 GeV which cannot becorrected in data. So our approach is to study the MC four-lepton mass distributions to see the effects of FSR andinclude this effect into the systematics of the mass resolution.

In the reconstructed invariant mass from four channels, the mass shape appears to have a long tail extended into thelow mass region. As already mentioned, this is induced mainly by FSR photons. The effect of this FSR induced lowmass tail is that the mass peak from each channel is shifted to lower value. This effect can be seen clearly in Figure 6where the reconstructed invariant masses from MC samples are fitted with a gaussian function in the peak region forfour-lepton decay channels. To a better understanding of the effect induced by the FSR on the mass tail and accuratelymeasure the resolution induced by FSR, we calculate the difference between the reconstructed mass and truth mass ineach event as follows,

∆MZZ ≡MRecon4` −MHZZ . (7)

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Figure 6: Invariant mass distributions of MC Higgs (MH = 125 GeV) in four 4` final states.

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Figure 7: ∆MZZ for each channel in the MC sample with MHiggs = 125 GeV

We plot the mass difference ∆MZZ and fit the plot with a combination of a Gaussian function and a Crystal Ball function.The Crystal Ball function is used to fit the peak of ∆MZZ and the Gaussian function is used to fit the left tail of the∆MZZ . By looking at the mass difference, the natural width of the Higgs boson is removed by subtracting the truthmass.

In Figure 7, the ∆MZZ is fitted using RooFit utility. The signal region or the peak region is described by the CrystalBall function and the background region or the tail region is described by the Gaussian function. Recall the FSR shiftis described by the ∆MZZ mean, in this case, neither the Crystal Ball function or Gaussian function adequately describethe FSR shift and the resolution since the two regions are overlapped. Instead, we use a weighted average of the twofits to find combined mean and sigma. The weights used are the fractional areas of the signal and background in thetotal fit. Since the gaussian function fits the tail region and further down the tail region, the gaussian peak does notdescribe well the mean and sigma of the ∆MZZ peak, so we only add the percentage of the gaussian that lies under thepeak region. The mean and sigma are then described by

∆MComb ≡CBAreaFitArea

MeanCB +GausArea(GausCorr)

FitAreaMeanGaus

σComb ≡CBAreaFitArea

σCB +GausArea(GausCorr)

FitAreaσGauss

, (8)

where the fit area is the sum of the Crystall and Gaussian areas as shown in Figure 7. The GausCorr term here is theestimated percentage of the gaussian area under the peak region. All the parameters in equation 4.8 are obtained directlyfrom RooFit and for MHiggs = 125 GeV, the values are listed in Table 4 and Table 5. The calculated ∆MFSR values forfour channels tell us the mass shift induced by FSR photons. The calculated σComb in the last line of Tabel 5 gives the

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eeee eeµµ µµ ee µµµµCBAreaFitArea

0.78 0.77 0.83 0.81GaussArea

FitArea0.22 0.23 0.17 0.19

GausCorr 0.4 0.46 0.4 0.57

Table 4: Fitted area

eeee eeµµ µµ ee µµµµ

MeanCB -1.71 -1.1 -1.05 -0.47MeanGaus -6.1 -5.35 -6.22 -3.7∆MFSR -1.87 -1.41 -1.30 -0.78σCB 2.58 2.08 2.45 1.93σGaus 4.53 4.76 5.46 5.60σComb 2.41 2.11 2.41 1.25

Table 5: Calculated parameters for mass resolution calculations

result of the measured Higgs mass resolution from MC sample for all four channels. These measured resolution valuesare much more comparable with results shown in Figure 6.

4.5 Results on the MC StudyAs we have discussed in the beginning of this section, the total resolution is a combination of the resolution induced bythe detector and the resolution induced by the FSR photons. The mass shift caused by FSR photons has been estimatedcarefully by using MC samples and by fitting ∆MZZ for all MC samples. The resolution induced by the detector istreated by using the lepton momentum resolution reported earlier. These errors are then propagated to the Higgs massresolution using error propagation. The total calculated resolution ∆MCalc is then extracted by a quadratic sum of thedetector induced resolution ∆MTrack and the FSR shift ∆MFSR as follows

∆MCalc =√(∆MFSR)2 +(∆MTrack)2 (9)

Using this technique, we arrived at a good agreement between the measure Higgs resolution and the calculated resolu-tion. The measured Higgs resolution here is the Higgs width σComb. Again, using MC sample with MHigss = 125 GeV,we find that the agreement between the measured and calculated resolution is within 6% except the eeµµ channel. Theresult is listed in Table 6.

eeee eeµµ µµee µµµµ

∆MTrack 1.46 1.42 1.92 1.92∆MFSR -1.87 -1.41 -1.30 -0.78∆MCalc 2.37 2.00 2.32 2.07σComb 2.41 2.11 2.41 2.15Percent Error (%) 1.66 5.21 3.73 3.72

Table 6: Comparison of calculated resolution with the measured resolution using MC sample MH = 235 GeV

To further test this study, we extend the calculation done for the case with MC sample MHigss = 125GeV to otherMC Higgs masses ranging from 110 GeV to 200 GeV. The measured Higgs resolution (or Higgs width) ∆MCB = σCBand the calculated resolution ∆MComb = ∆MCalc were plotted together for all MC Higgs masses separately for eachchannel. If our method is valid, it is expected that the measured ∆MCB and the calculated ∆MComb to be consistent. Thecomparisons are shown in Figure 8, from which we see that the measured and calculated resolutions agree reasonablywell in which the calculated resolution is within a 10 % window of the measured resolution except for eeee and µµµµ

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Figure 8: The measured Higgs width ∆MCB without FSR and the calculated Higgs mass resolution with FSR added in

channels. In µµµµ channel, we see the calculated resolution with FSR photons added in appeasr to shift slightly downin mass region below 160 GeV with 12 % difference at Higgs mass 125 GeV. The mass measurements can be sensitiveto event-by-event fluctuations in the muon momentum resolution. The standard deviations between the calculated andmeasured resolutions defined by

σ∆M =12

∆MCB−∆MComb∆MCB +∆MComb

are also plotted for varying MC Higgs masses for each channel for comparison. The results are shown in Figure 9.The variation between the calculated and measured resolutions lie within 6%. The fraction of the measured resolution∆MCBMHiggs

and the fraction of the calculated resolution ∆MCombMHiggs are also plotted in combination of all four channels and theresults are shown in Figure 10 and Figure 11. These plots show that the mass resolution calculations for each individualevents is fully validated by the MC closure tests.

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Figure 9: Standard deviations for measured and calculated Higgs mass resolution

Figure 10: Fraction of the measured resolution in Higgs mass as a function of varying Higgs masses for all channel

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Figure 11: Fraction of the calculated resolution in Higgs mass as a function of varying Higgs masses for all channel

5 Mass Resolution of the Higgs CandidatesThe detector induced resolutions for 2012 candidate events are calculated in the same way as used in the MC simulationstudies described in the previous sections. Since we cannot obtain a truth mass similar as we do with the MC samples,we are not able to perform combined fit to the ∆MZZ to obtain the FSR shift in data. Instead, we use the four-leptoninvariant mass value and use the method of linear interpolation based on the ∆MFSR calculated for MC samples todetermine the FSR shift. As an example, if a candidate has a mass 122.89 GeV, then the resolution induced by FSR∆MFSR is calculated by linear interpolation between the ∆MFSR values found for MC samples with MHiggs = 120 GeVand MHiggs = 123 GeV.

In the mass resolution calculations for the Higgs candidates presented here, 16 candidates in the mass window110-130 GeV and 20 candidates in the mass window 110-140 GeV are used. The calculated candidate resolution iswithin 3% of the Higgs candidate mass. This result is shown in Figure 12. In Figure 12, the plot on the left showsthe calculated candidate resolution for Higgs candidate mass in the mass window 110-140 GeV; the plot on the rightshows the fraction of calculated candidate resolution. The calculated resolution for candidates from four-muon decaychannel are listed in Table 7. We notice that two candidates from muon channel that are close in mass seems to have aconsiderable fluctuation in the calculated resolution, which can also be seen from Figure 12. They are candidates withRunNumber 209736, Mass 122.89 GeV with calculated resolution equals 2.85 GeV and RunNumber 204769, Mass123.25 GeV with calculated resolution equals 1.79 GeV. Close investigation shows that the candidate with RunNumber209736 are reconstructed with all four muons coming from barrel regions of the Muon Spectrometer while the candidatewith RunNumber 204769 are reconstructed from end-cap muons. The calculated FSR shift for these two candidates arevery close, however, due to the lack of muon spectrometer hardware coverage and the bending caused by the magneticfield, the detector-induced resolution is higher for the candidate with RunNumber 209736.

We then extend the calculation to include all Higgs candidates up to 200 GeV and the result is shown in Figure 13.The calculated resolution is again within 3% of the candidate mass.

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RunNumber EventNumber M4l ∆MTrack ∆MFSR ∆MCalc207934 44607048 113.07 1.89 -0.67 2.01209864 114421896 119.09 2.16 -0.7 2.27209736 135745044 122.887 2.75 -0.73 2.85204769 82599793 123.253 1.63 -0.74 1.79208123 26433470 123.523 2.59 -0.74 2.69204769 71902630 124.09 2.24 -0.74 2.36204564 25416035 128.72 2.31 -0.79 2.44207397 14947270 135.34 2.6 -0.85 2.74

Table 7: Higgs candidates found from 4µ channel in the estimated Higgs mass range with candidate mass, detector-induced resolution, FSR-induced resolution, and combined resolution

Figure 12: Candidate resolution as a function of candidate mass; Fraction of calculated candidate resolution as afunction of candidate mass in Higgs mass range

Figure 13: Candidate resolution as a function of candidate mass; Fraction of calculated candidate resolution as afunction of candidate mass range up to 200 GeV

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6 Final State Radiation Photon SelectionIn the current H→ 4` analysis of FSR photons, the candidate FSR photon clusters are selected by following require-ments:

1. the cone between the cluster and the muon ∆Rcluster,µ =√

∆η2 +∆φ2 < 0.15,

2. the transverse energy of the cluster ET > 3.5 GeV,

3. the fraction f1 > 0.1.

If more than one clusters are found in the cone, then the one with the smallest ∆Rcluster,µ is selected. [3] The FSRphoton candidates are added at the the 4-lepton candidate level and after all cuts. The FSR candidates found using thisselection for 2012

√s = 8 TeV with an integrated luminosity 20 fb−1 are reconstructed and listed in the Appendix.

7 Higgs Mass MeasurementsThe mass of the newly discover Higgs-like boson is difficult to measure due to the low statistics of the data samples.In this study, we investigate the fitting methods for H → ZZ∗ → 4l decaying channel since this channel provides thecleanest signal from the background. To begin with, we first look at the mass fit for the single resonant peak fromZ→ 4l. The single resonance from Z boson provides a good calibration on the Higgs mass measurements since the Zboson mass and width have been properly measured and it receive detector response in a similar regime to the newlydiscovered Higgs-like boson resonance decaying to four leptons at around 125 GeV.

7.1 Mass fit of the Z→ 4` resonant peakIn this study, in order to allow a good comparison of data to MC, the MC events are produced with a minimum dileptonmass of 0.25 GeV. Compared with the singleZ selection described in section 6, the Mll cut is lowered to 1 GeV fromthe original 5 GeV cut. In the process of fitting the mass peak, we first fit the reconstructed invariant mass peak for allfour channels using simple Gaussian function in MC events in the mass windows of 85 to 95 GeV. Since for Z boson,the width is determined to be ΓZ = 2.49 GeV from PDG value. During the initial Gaussian fit, the Gaussian σ is setto the Z boson width value. Then we fit the mass spectra from all four channels to both data and MC events using aconvoluted probability density function of Breit-Wigner distribution and Gaussian distribution,

BW(x,MZ ,ΓZ)∗Gauss(x,m4`,σ4`)

where MZ in the Breit-Wigner distribution is set to the fitted mass peak from the initial Gaussian function on the MCevents MZ = 91.2 GeV and ΓZ is set to the PDG Z boson width value ΓZ = 2.48 GeV.

We fit the mass spectra separately in different lepton final states to obtain a better understanding of the mass peakvalue. Since the 4µ channel has the largest statistics, so it becomes a critical channel for calibrating and determiningthe Higgs mass peak. The fitted 4µ mass for data and MC simulations are shown in Figure 14. The fitted mass peakhere is MZ = 90.8 and m4`−MZ shows the shift of the mass fit compared to the data sample. Here the fitted mass peakin data is lowered by 100 MeV and the mass peak fit error is about 290 MeV. This fit tells us that the reconstructed 4µmass is accurate to about 0.1% around the Z mass. The eeµµ also prove reasonably good statistics compared to otherchannels for mass fitting. The result for data and MC events are shown in Figure 15 and it shows that the statistics ofthe fitted mass peak is consistent for data and MC events.

7.2 Mass fit of the H→ ZZ∗→ 4`From the single resonant Z boson study, we see that the fit using a Breit Wigner convoluted with a Gaussian distributionprovides reasonably good mass peak value. In the Higgs boson resonance, similar method can still be used. However,we know that the Higgs boson width is estimated to be around 40 to 50 MeV, which is very small compared to the Zboson width. In this case, the width of the Breit Wigner distribution should be a very small number. Therefore, we seethat Breit Wigner distribution does not contribute much in the mass peak determination. Instead, we use the CrystalBall function to fit the mass peak. Full data obtained from 2011 collisions corresponding to an integrated luminosity4.6 fb−1and 2012 collisions corresponding to an integrated luminosity 20 fb−1 are used to fit the Higgs mass peak.

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Figure 14: Invariant mass distributions and fitting for the reconstructed 4µ events for data and MC within the Z masswindow of 80 to 100 GeV

Figure 15: Invariant mass distributions and fitting for the reconstructed 2µ2e events for data and MC within the Z masswindow of 80 to 100 GeV

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We selected 14, 14, 11, and 21 events within the Higgs mass window from 110 to 140 GeV in 4e, eeµµ, µµee, and 4µchannels respectively. We can see that the statistics for the Higgs candidate events are considerably lower than thatof the single Z candidate events. The mass fit for eeµµ and µµee channels will not give significant results since thestatistics are too low. Again, the 4µ channel has the largest statistics. However, in order to obtain a good fitting result,the inclusive channel combined from all events in the four channels is used.

In the Higgs mass study, we first fit the spectra for 4e and µ channels with no per-event resolution added; we thenadd the per-event resolution calculated using the method described in Section 4 by constructing a conditional probabil-ity distribution function with two observables M4` and M4`err where M4`err represents the event-by-event resolution.For the fit with no per-event error, we follow two steps in the mass fitting procedure which are the same as the procedureused in the single Z mass peak fitting described in Section 7.1. The resulting fit of data and MC events for the inclusivechannel are shown in Figure 16. We can see that the fitted mass peak given by the Crystal Ball function is about 124.58GeV with a resolution about 2.19 GeV. This is mainly due to the FSR effect. The fitted error is accurate to about 0.3%. The MC events for the inclusive channel are generated by the PowHegPythia generator with mH = 125 GeV fromgluon-gluon fusion process. Using the MC sample, we see that the Crystal Ball describes the shape reasonable wellexcept the mass is shifted to a lower value compared to the result given from the fitting on data.

The next step is to add in the per-event error into the fitting model. In this case, we use a conditional probabil-ity distribution function model,

P (m4`|σm4`)∗P (σm4`)

where P (m4`|σm4`) is the conditional PDF of m4` given the mass resolution σm4` and P (σm4`) is the PDF describing theevent-by-event mass error. The conditional PDF P (m4`|σm4`) is modeled using a Gaussian distribution whose sigma isthe event-by-event mass error.

Gauss(x,m4`|σm4`)

The resulting fit for inclusive channel is shown in Figure 17. In constructing the model PDF, the per-event mass errorPDF is directly obtained from the histogram contains the mass error distribution. The per-event error PDF replaces theglobal resolution parameter σ of the Gaussian function by a global scale factor parameter. The model is then combinedfrom the conditional Gaussian pdf and the per-event error pdf. We notice that the shape of the distribution does notappear to change significantly. This is due to the mean values of the event-by-event error pdf used in the fitting aresmall compared to the statistical uncertainties in the measurements. The result shows that the Higgs mass resolutionto be about 2.19 GeV which is way larger compared to the ATLAS fitted result around 0.2 GeV.[4] If we examine theFigure 6 closely, we see that the mass peaks for all four channels are different since the mean values lie on both sidesof mH = 125 GeV. In the mass fitting process, the data used is combined using data from all four lepton final statessince the individual channel does not provide enough statistics to provide a good fit result in the mass window 120-130GeV. As a result, since the uncertainty from each channel is not considered in the fitting process, the fitted σ not onlyaccounts for the Higgs mass resolution, but also the uncertainties caused by combing all the lepton final states.

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Figure 16: Invariant mass distributions and fitting for the reconstructed events from all lepton final states for data andMC within the Higgs mass window of 120 to 130 GeV

Figure 17: Invariant mass distribution and fitting for the reconstructed events from all lepton final states for data withinthe Higgs mass window of 120 to 130 GeV with event-by-event mass error included

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8 ConclusionIn this thesis study, the Higgs mass resolution calculations are done on the MC samples first using the quadratic sumof the detector-induced resolutions and the mass shift due to FSR systematics. With the closure test performed on themethod, a good agreement between the measured resolutions from the MC events and the final calculated resolutionsare established. This method is then used to perform the resolution calculations on the Higgs candidates with the FSRshifts obtained from linear interpolation based the FSR shifts for MC events. The next topic we have presented isthe Higgs mass fitting using the data collected by the ATLAS detector in 2011 and 2012 which have an integratedluminosity of 4.6 fb−1 for 2011 at

√s = 7 TeV and 20.7 fb−1 for 2012 at

√s = 8 TeV. With all events selection cuts

applied, 60 candidates are observed in the mass window 110-140 GeV. The mass fitting done in the mass window120-130 GeV suggests the Higgs mass to be at about mH = 124.58± 0.42 GeV. With the statistical and systematicsuncertainties included, the mass of the Higgs-like boson is measured to b mH = 124.58+0.6−0.5(stat)

+0.5−0.3(syst)±0.42 GeV

which is consistent with the Standard Model prediction of a resonance at around 125 GeV.

9 Appendix

9.1 The sample list of FSR photons found for 2012 Higgs candidates

Type RunNumber EventNumber M4l Mf sr4l M12 M

f sr12 M34 M

f sr34

2µ2e 203258 114413312 185.43 191.01 88.12 93.93 95.16 100.54µ 203636 34504484 337.53 342.74 88.57 90.64 86.27 103.042µ2e 203680 10638148 175.42 187.8 84.76 98.89 80.02 91.144µ 204564 149682166 281.83 290.83 88.34 91.62 86.99 110.142µ2e 209161 96479632 108.99 123.17 71.63 83.70 34.85 51.28

Table 8: The list of candidates with at least one FSR photon found in 2012 data

9.2 The sample list of Kinematics of 2012 Higgs candidates in mass window 110-130 GeV

Run Event p1T p2T p

3T p

4T M4` [GeV] MZ1 MZ2 channel

207447 130322373 33.72 19.39 14.89 11.25 110.06 63.32 30.99 4e204564 76786292 45.20 15.56 52.81 12.38 114.14 57.28 49.05 4e203602 82614360 53.89 24.90 61.90 17.80 124.49 70.63 44.67 4e204910 22993546 63.64 60.03 67.03 15.53 125.52 88.93 22.28 4e207447 14931244 30.83 29.83 18.98 15.64 131.56 95.73 34.99 4e207490 64048705 37.65 29.63 20.49 11.26 135.63 88.88 34.69 4e

205113 12611816 75.64 18.71 19.56 7.95 122.65 87.96 19.63 2e2µ209736 164575468 46.13 44.25 14.66 6.08 123.04 90.12 27.25 2e2µ203258 105740575 58.59 31.67 25.02 6.57 129.92 86.24 25.44 2e2µ

204763 95056361 58.71 36.35 14.24 13.11 118.83 89.23 27.26 2µ2e206409 103987613 57.18 37.75 15.70 12.36 121.62 88.43 21.80 2µ2e200967 58511923 64.29 33.47 16.16 15.35 136.25 93.06 20.64 2µ2e

207934 44607048 35.81 29.47 15.68 11.49 113.07 67.02 34.95 4µ209864 114421896 43.57 33.52 23.75 17.54 119.09 83.84 22.58 4µ209736 135745044 73.19 27.16 14.62 12.90 122.89 92.16 20.80 4µ204769 82599793 27.77 29.23 32.58 10.26 123.25 84.01 34.21 4µ208123 26433470 64.13 27.81 25.66 12.28 123.52 73.72 25.97 4µ204769 71902630 47.48 36.11 26.42 7.18 124.09 86.34 31.57 4µ204564 25416035 43.05 38.67 16.36 10.01 128.72 90.94 27.48 4µ207397 14947270 26.24 11.60 28.99 9.28 135.34 89.42 32.68 4µ

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9.3 The sample list of fitted ∆MZZ results for various Higgs mass

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9.4 Invariant mass distributions for combined 2011 and 2012 Higgs candidates

Figure 18: The distributions of the four-lepton invariant mass, m4`, for the selected candidates for the combined 2011√s = 7 TeV and 2012

√s = 8 TeV data sets for various lepton final states compared to the background expectation in

the mass window 80-170 GeV. The signal expectation for mH = 125 GeV is shown for comparison.

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Figure 19: The distribution of the four-lepton invariant mass, m4`, for the selected candidates for the combined 2011√s = 7 TeV and 2012

√s = 8 TeV data sets compared to the background expectation in the mass range 80-170 GeV.

The signal expectation for mH = 125 GeV is shown for comparison.

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9.5 Invariant mass distributions for combined 2011 and 2012 single Z resonance candidates

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Figure 20: Invariant mass distributions for four leptons, m4`, for 2011√

s = 7 TeV and 2012√

s = 8 TeV single Zresonance candidates combined compared to the background expectation in the mass range 60-120 GeV.

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[GeV]4lm

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Figure 21: Invariant mass distribution for four leptons, m4`, for 2011√

s = 7 TeV and 2012√

s = 8 TeV single Zresonance candidates combined for inclusive final state compared to the background expectation in the mass range60-120 GeV.

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References[1] ATLAS Collaboration, Commisioning of the ATLAS Muon Spectrometer with Cosmic Rays, Eur.Phy.J. C70,

(2010)875

[2] ATLAS Collaboration, ATLAS Muon Momentum Resolution in the First Pass Reconstruction of the 2012 p-p Col-lision Data at

√s = 7 TeV, ATLAS-CONF-2011-046.

[3] ATLAS Collaboration, Reconstruction of collinear final-state-radiation photons in Z decays to muons in√

s = 7TeV proton-proton collisions, ATLAS-CONF-2012-143.

[4] ATLAS Collaboration, Measurements of the properties of the Higgs-like boson in the four lepton decay channelwith the ATLAS detector using 25 fb−1 of proton-proton collision data., ATLAS-CONF-2013-013.

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