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

Transcription

1 Studies on Higgs Mass Resolutions and Mass Fitting with Four-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 the decay channel H ZZ l + l l + l, where l,l = e or µ using proton-proton collision data corresponding to an integrated 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 propagating uncertainties in the energy and momentum measurements of the leptons. A validation of the method with the closure test is carried out for Higgs mass varying between GeV. The mass resolutions for all the selected Higgs event candidates are calculated based on the lepton measurement uncertainty propagations. The second main part of the thesis presents the Higgs mass fitting with and without adding event-by-event resolution. The mass of the Higgs-like boson is m H = (stat) (syst) ± 0.42 GeV. 1

2 Contents 1 Introduction 3 2 ATLAS detector 3 3 Event Selection 4 4 Higgs Mass Resolution Study Electron Energy Resolution Muon Momentum Resolution Detector-Induced Resolution Final State Radiation Induced Resolution Results on the MC Study Mass Resolution of the Higgs Candidates 16 6 Final State Radiation Photon Selection 18 7 Higgs Mass Measurements Mass fit of the Z 4l resonant peak Mass fit of the H ZZ 4l Conclusion 22 9 Appendix The sample list of FSR photons found for 2012 Higgs candidates The sample list of Kinematics of 2012 Higgs candidates in mass window GeV The sample list of fitted M ZZ results for various Higgs mass Invariant mass distributions for combined 2011 and 2012 Higgs candidates Invariant mass distributions for combined 2011 and 2012 single Z resonance candidates

3 1 Introduction A historic moment was reached on July 4th last year when the ALTAS and CMS experiments have separately reported the 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 electroweak symmetry breaking. According to the Standard Model, electroweak interactions are mediated by γ, W ±, and Z 0 bosons, which are originally massless. The Lagrangian in the electroweak theory is required to be locally gauge invariant under 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) symmetry group. After the symmetry breaking, a neutral scalar particle, the Higgs boson, appears and the vector bosons, W and Z, become massive, while the photon of electromagnetism remains massless. This theoretical hypothesis has finally confirmed 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 4l, H γγ, and H WW 2l2ν. The cleanest channel for the discovery of the Higgs boson is its decay to four leptons H l + l l + l, where l,l = e or µ. This channel provides an excellent energy resolution and the reconstructed electrons and muons. The signal apears as a narrow 4-lepton invariant mass peak on top of a smooth background. The Standard Model irreducible background mainly comes from the SM ZZ 4l decays. The subsequent measurements of this newly discovered boson properties are essential. The first important measurement is the Higgs mass. Since the experimental signals have been observed in different channels, final determination of 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 4l final state is presented. The analysis is carried out using the s = 8TeV data recorded in 2012 corresponding to an integrated luminosity of 20.7 fb 1. 2 ATLAS detector The ATLAS detector shown in Fig. 1 is a multi-purpose particle physics detector with approximately forward-backward symmetric cylindrical geometry. The inner tracking detector (ID) covers pseudorapidity range η < 2.5 and consists a silicon pixel, a silicon micro-strip detector, and a transition radiation tracker (TRT). The ID is surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field. A lead/liquid-argon (LAr) sampling calorimeter measures the energy and the position of electromagnetic showers within η < 3.2. LAr sampling calorimeter also measures hadronic showers in the end-cap region (1.5 < η < 3.2) and forward region (3.1 < η < 4.9). An iron/scintillator tile 3

4 calorimeter measures hadronic showers in the central region ( η < 1.7). The muon spectrometer (MS) locates at the outer-most part of the detector. It surrounds the calorimeters and consists of three large superconducting air-cool toroid magnets, a system of precision tracking chambers ( η < 2.7), and fast tracking chambers for triggering. A three-level trigger system is used to select events to be recorder for offline analysis. 3 Event Selection In ATLAS Higgs detection program, electron candidates are identified from clusters of energy deposited in the electromagnetic calorimeter associates with an inner detector track. Muon candidates are reconstructed by matching inner detector tracks with tracks reconstructed in the muon spectrometer. If the track reconstructed in the muon spectrometer is a complete track, then the two independent momentum measurements from ID and MS are combined to form combined muons ; if the tracks reconstructed in the muon spectrometer are partial tracks, then the momentum is measured using the ID information only to form segment-tagged muons. The muon reconstruction and identification coverage is extended by using tracks reconstructed in the forward region 2.5 < η < 2.7 of the muon spectrometer, which in this case, there is no inner detector coverage. In the barrel region, where there is no muon spectrometer coverage, the energy deposit profile of inner detector tracks is used to identify muons with η < 0.1 and p T > 15 GeV and this reconstructed muons are labeled as calo-tagged. The Higgs boson candidate quadruplet is formed by selecting two same-flavor, opposite-sign lepton pairs in an event. Electrons are required to have transverse energy E T > 7 GeV and in pseudorapidity range η < Muons are required to have transverse momentum p T > 6 GeV and in pseudorapidity range η < 2.7. The four leptons of the quadruplets are required to separated as R = η 2 + φ 2 > 0.1 for same flavor leponts and as R > 0.2 for different flavor leptons. The di-lepton of the quadruplet with a mass m 12 closest to the nominal Z boson mass is identified as the leading di-lepton and the the second di-lepton of the quadruplet with a mass m 34 is the sub-leading di-lepton. The higher p T lepton in the quadruplet must satisfy p T > 20 GeV, and the second and third leptons in descending p T order must satisfy p T > 15 GeV and p T > 10 GeV respectively. The mass window for the leading di-lepton mass m 12 is required to be between 50 and 106 GeV. The sub-leading di-lepton mass m 34 is required to exceed a threshold of 12 GeV. The event selection criteria described here is presented in Table 1. 4

5 Event Preselection Electrons H4l2011Defs and Multilepton (2012) quality GSF electrons with E T > 7 GeV and η < 2.47 Muons Combined or segment-tagged muons with p T > 7 GeV and η < 2.7 calo-tagged muons with p T > 15 GeV and η < 0.1 stand-alone muons with p T > 6 GeV, 2.5 < η < 2.7 and R > 0.2 Quadraplet selection Event Selection Two pairs of same-flavour opposite-charge leptons. The three leading leptons in the quadruplet have p T > 20, 15, and 10 GeV. Pick the pair that has M Z1 nearest Z-mass, and then M Z2 nearest. Kinematic selection Leading di-lepton mass requirement 50 GeV < m 12 < 106 GeV Sub-leading di-lepton mass requirement 12 < m 34 < 115 GeV No same-flavor opposite-charge di-lepton giving M l + l < 5 GeV (J/ψ veto) R(l,l ) > 0.1(0.2) for all same-flavor (opposite-flavor) leptons in the quadruplet. 4 Higgs Mass Resolution Study Table 1: Summary of the event selection requirements The 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, we will describe the Higgs mass resolution calculation in detail. The Higgs mass resolution depends on both energy and momentum uncertainties of the lepton measurements and the final state radiation. We will first present the energy and momentum resolutions for electrons and muons. The mass resolution due to lepton detections is calculated using the standard error propagations. The final state radiation (FSR) is due to the internal radiations and Bremsstrahlung radiations of leptons. The FSR would cause the Higgs mass peak to shift to a lower value. The FSR photons usually have very low transverse energy E T, so they are very difficult to be detected. The resolution induced by FSR is treated as systematics uncertainties based on MC studies. The final mass resolution is obtained from the quadratic sum of the detector resolution and the FSR systematic. In this study, the NLO generator PowhegBox with NLO PDF set CT10 is used to model Higgs production through the gluon-gluon fusion process. The MC events are fully simulated with ATLAS detector and reconstructions. The MC samples studied ranges from Higgs mass 110 GeV to 200 GeV. The Higgs mass with M = 125 GeV is used to validate the results. 4.1 Electron Energy Resolution The electron energy resolution is calculated from a resolution function from the EnergyRescalar class provided by the ATLAS 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 resolution parametrized by a MC Sampling term, a MC Noise term, an MC Constant term, and a Data Constant term, which all are functions of η. The η corresponds to the end-cap (1.5 < η <3.2) and forward (3.1 < η < 4.9) regions where Liquid-argon (LAr) sampling calorimeter is used to measure the energy and the position of electromagnetic showers. The electron energy resolution is expressed as: σ 2 = Sampling Term2 energy + Noise Term2 energy 2 +Constant Term 2 5

6 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). σ 2 = Sampling Term2 energy + Noise Term2 energy 2 +Constant Term 2 + data Condstant Term 2 The electron relative energy resolution is plotted as a function of momentum for different regions and they are shown in Figure Muon Momentum Resolution The ATLAS Muon Spectrometer (MS) is designed to provide a relative resolution for the momentum measurement better than 3% over a wide transverse momentum p T range. [1] In the MS, the magnetic field is generated by an air-core toroid coils and the deflection of muon trajectory in the field is used to measure the muon momentum. The muon track in the MS is reconstructed from three layers of precision drift tube chambers (MDT) in range η < 2.0 and two layers of MDT chambers in combination of one layer of cathode strip chambers (CSC) in range 2.0 η < 2.7. The muon momentum 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 muons which are muon segments and hits reconstructed in the Muon Spectrometer, CaloTag muons which are inner tracks and calorimeter hits in the Inner Detector, and Combined muons which are muon track formed from the successful combination of an ID track and a MS track. So for muon identification, the tracks are measured separately in ID and MS and then they are combined and reconstructed as a single muon trajectory. 6

7 η region p MS 0 (TeV) p MS 1 (%) p MS 2 (TeV 1 ) barrel transition end-caps CSC/No-TRT η region p ID 0 (TeV) p ID 1 (%) p ID 2 (TeV 1 ) barrel n.a transition n.a end-caps n.a CSC/No-TRT n.a 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 the MS, for a given η, the relative momentum resolution σ(p)/p is parametrized as a function of p T as follows, σ(p) p = pms 0 p T p MS 1 p MS 2 p T (1) where p MS 0 corresponds to the uncertainties in the energy loss in the calorimeter material, p MS 1 corresponds multiple scattering, and p MS 2 corresponds to intrinsic resolution terms. For the ID, the approximate parametrization of the resolution is as follows, σ(p) = p ID 1 p ID 2 p T for η < 1.9 p (2) σ(p) = p ID 1 p ID 1 2 p T p tan 2 for η > 1.9 (θ) where coefficients p ID 1 is associated with the multiple scattering and pid 2 is associated with the intrinsic resolution terms. The combined muon momentum is obtained from combing the ID and MS measurements and is calculated using a weighting function as follows 2σ σ CB MS P P T = σid P (3) PT CB σ 2 MS + σ2 ID 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 listed separately for Data and MC in Table 2 and Table 3 respectively. The coefficients were obtained from the SmearingClass package. Using the coefficients given in Table 2 and Table 3 for Data and MC simulation respectively, we can obtain the resolution curves. For MS and ID in the barrel region η < 1.05 and End-cap region 1.7 < η < 2.0, the relative momentum resolutions are plotted as a function of p T for both data and simulation. For resolution curves from the fitted parameter values of the MS in the collision data and simulation, the results are shown in Figure 3; for resolution curves from the fitted parameter values of the ID in the collision data and simulation, the results are shown in Figure 4. 7

8 η region p MS 0 (TeV) p MS 1 (%) p MS 2 (TeV 1 ) barrel transition end-caps CSC/No-TRT η region p ID 0 (TeV) p ID 1 (%) p ID 2 (TeV 1 ) barrel n.a transition n.a end-caps n.a CSC/No-TRT n.a 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 of muon p T, for the barrel and end-cap regions of the detector. 8

9 Figure 4: Resolution curve from the fitted parameter values of the ID in collision data and simulation as a function of muon p T, for the barrel and end-cap regions of the detector. 4.3 Detector-Induced Resolution In the detector-induced resolution calculation, we use equation (1) for Standalone muons form MS, equation (2) for Calo-Tag muons from ID, and equation (3) for Combined muons. The Higgs mass M for all decaying lepton channels is calculated using M 2 = (E 1 + E 2 + E 3 + E 4 ) 2 ( P 1 + P 2 + P 3 + P 4 ) 2 M 2 = ( 4 i=1 E 2 i i=1 j>i 2E i E j ) ( 4 i=1 Pi i=1 j>i 2 P i Pj ) (4) The masses for electron and muon can be approximate to be zero because they are negligible compared with their momentum in GeV. Then, we have E = M 2 + P 2 P, then equation (4) above becomes M 2 = 3 4 i=1 j>i Now using the standard error propagation formula for function f(x,y), ( ) f 2 ( ) f 2 f (x,y) = dx x 2 + dy 2 y 2P i P j (1 cos(θ i j )) (5) Here we use the fact that the detector s angular resolution is much better that its momentum resolution, we can neglect the dθ term, then we arrive at the mass resolution of the form M Track = 1 M 4 i=1 ] 2 P j (1 cos(θ i j )) P 2 i j=1, j i [ 4 1/2. (6) Using this formula, we are able to calculate the detector-induced resolution for each Higgs decay event in four-lepton final state. As an example, the resolution M Track is plotted for each event in Figure 5 using MC sample with Higgs 9

10 mass equals to 125 GeV. We will show that the mass resolution due to lepton measurement uncertainties cannot totally count for the mass resolution (see Figure 6). This is due to additional final state radition contributions which will be discussed in the next section. Figure 5: Detector-induced resolution from MC simulation with Higgs mass (125 GeV) M Track for each event fit with a Gaussian function. 4.4 Final State Radiation Induced Resolution Photons from final state radiation have very low transverse energy E T and they have large kinematic overlap with the background. 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 be corrected in data. So our approach is to study the MC four-lepton mass distributions to see the effects of FSR and include 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 the low mass region. As already mentioned, this is induced mainly by FSR photons. The effect of this FSR induced low mass tail is that the mass peak from each channel is shifted to lower value. This effect can be seen clearly in Figure 6 where the reconstructed invariant masses from MC samples are fitted with a gaussian function in the peak region for four-lepton decay channels. To a better understanding of the effect induced by the FSR on the mass tail and accurately measure the resolution induced by FSR, we calculate the difference between the reconstructed mass and truth mass in each event as follows, M ZZ M Recon 4l M H ZZ. (7) 10

11 Figure 6: Invariant mass distributions of MC Higgs (M H = 125 GeV) in four 4l final states. 11

12 Figure 7: M ZZ for each channel in the MC sample with M Higgs = 125 GeV We plot the mass difference M ZZ 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 M ZZ and the Gaussian function is used to fit the left tail of the M ZZ. By looking at the mass difference, the natural width of the Higgs boson is removed by subtracting the truth mass. In Figure 7, the M ZZ is fitted using RooFit utility. The signal region or the peak region is described by the Crystal Ball function and the background region or the tail region is described by the Gaussian function. Recall the FSR shift is described by the M ZZ mean, in this case, neither the Crystal Ball function or Gaussian function adequately describe the FSR shift and the resolution since the two regions are overlapped. Instead, we use a weighted average of the two fits to find combined mean and sigma. The weights used are the fractional areas of the signal and background in the total fit. Since the gaussian function fits the tail region and further down the tail region, the gaussian peak does not describe well the mean and sigma of the M ZZ peak, so we only add the percentage of the gaussian that lies under the peak region. The mean and sigma are then described by M Comb CB Area Mean CB + Gaus Area(Gaus Corr ) Fit Area Fit Area σ Comb CB Area σ CB + Gaus Area(Gaus Corr ) Fit Area Fit Area σ Gauss Mean Gaus, (8) where the fit area is the sum of the Crystall and Gaussian areas as shown in Figure 7. The Gaus Corr term here is the estimated percentage of the gaussian area under the peak region. All the parameters in equation 4.8 are obtained directly from RooFit and for M Higgs = 125 GeV, the values are listed in Table 4 and Table 5. The calculated M FSR values for four channels tell us the mass shift induced by FSR photons. The calculated σ Comb in the last line of Tabel 5 gives the 12

13 eeee eeµµ µµ ee µµµµ CB Area Fit Area Gauss Area Fit Area Gaus Corr Table 4: Fitted area eeee eeµµ µµ ee µµµµ Mean CB Mean Gaus M FSR σ CB σ Gaus σ Comb 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 values are much more comparable with results shown in Figure Results on the MC Study As we have discussed in the beginning of this section, the total resolution is a combination of the resolution induced by the detector and the resolution induced by the FSR photons. The mass shift caused by FSR photons has been estimated carefully by using MC samples and by fitting M ZZ for all MC samples. The resolution induced by the detector is treated by using the lepton momentum resolution reported earlier. These errors are then propagated to the Higgs mass resolution using error propagation. The total calculated resolution M Calc is then extracted by a quadratic sum of the detector induced resolution M Track and the FSR shift M FSR as follows M Calc = ( M FSR ) 2 + ( M Track ) 2 (9) Using this technique, we arrived at a good agreement between the measure Higgs resolution and the calculated resolution. The measured Higgs resolution here is the Higgs width σ Comb. Again, using MC sample with M Higss = 125 GeV, we find that the agreement between the measured and calculated resolution is within 6% except the eeµµ channel. The result is listed in Table 6. eeee eeµµ µµee µµµµ M Track M FSR M Calc σ Comb Percent Error (%) Table 6: Comparison of calculated resolution with the measured resolution using MC sample M H = 235 GeV To further test this study, we extend the calculation done for the case with MC sample M Higss = 125GeV to other MC Higgs masses ranging from 110 GeV to 200 GeV. The measured Higgs resolution (or Higgs width) M CB = σ CB and the calculated resolution M Comb = M Calc were plotted together for all MC Higgs masses separately for each channel. If our method is valid, it is expected that the measured M CB and the calculated M Comb to be consistent. The comparisons are shown in Figure 8, from which we see that the measured and calculated resolutions agree reasonably well in which the calculated resolution is within a 10 % window of the measured resolution except for eeee and µµµµ 13

14 Figure 8: The measured Higgs width M CB 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 down in mass region below 160 GeV with 12 % difference at Higgs mass 125 GeV. The mass measurements can be sensitive to event-by-event fluctuations in the muon momentum resolution. The standard deviations between the calculated and measured resolutions defined by σ M = 1 M CB M Comb 2 M CB + M Comb 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 M CB M Higgs and the fraction of the calculated resolution M Comb M Higgs are also plotted in combination of all four channels and the results are shown in Figure 10 and Figure 11. These plots show that the mass resolution calculations for each individual events is fully validated by the MC closure tests. 14

15 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 15

16 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 Candidates The detector induced resolutions for 2012 candidate events are calculated in the same way as used in the MC simulation studies 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 M ZZ to obtain the FSR shift in data. Instead, we use the four-lepton invariant mass value and use the method of linear interpolation based on the M FSR calculated for MC samples to determine the FSR shift. As an example, if a candidate has a mass GeV, then the resolution induced by FSR M FSR is calculated by linear interpolation between the M FSR values found for MC samples with M Higgs = 120 GeV and M Higgs = 123 GeV. In the mass resolution calculations for the Higgs candidates presented here, 16 candidates in the mass window GeV and 20 candidates in the mass window GeV are used. The calculated candidate resolution is within 3% of the Higgs candidate mass. This result is shown in Figure 12. In Figure 12, the plot on the left shows the calculated candidate resolution for Higgs candidate mass in the mass window GeV; the plot on the right shows the fraction of calculated candidate resolution. The calculated resolution for candidates from four-muon decay channel are listed in Table 7. We notice that two candidates from muon channel that are close in mass seems to have a considerable fluctuation in the calculated resolution, which can also be seen from Figure 12. They are candidates with RunNumber , Mass GeV with calculated resolution equals 2.85 GeV and RunNumber , Mass GeV with calculated resolution equals 1.79 GeV. Close investigation shows that the candidate with RunNumber are reconstructed with all four muons coming from barrel regions of the Muon Spectrometer while the candidate with RunNumber are reconstructed from end-cap muons. The calculated FSR shift for these two candidates are very close, however, due to the lack of muon spectrometer hardware coverage and the bending caused by the magnetic field, the detector-induced resolution is higher for the candidate with RunNumber 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. 16

17 RunNumber EventNumber M 4l M Track M FSR M Calc Table 7: Higgs candidates found from 4µ channel in the estimated Higgs mass range with candidate mass, detectorinduced resolution, FSR-induced resolution, and combined resolution Figure 12: Candidate resolution as a function of candidate mass; Fraction of calculated candidate resolution as a function of candidate mass in Higgs mass range Figure 13: Candidate resolution as a function of candidate mass; Fraction of calculated candidate resolution as a function of candidate mass range up to 200 GeV 17

18 6 Final State Radiation Photon Selection In the current H 4l analysis of FSR photons, the candidate FSR photon clusters are selected by following requirements: 1. the cone between the cluster and the muon R cluster,µ = η 2 + φ 2 < 0.15, 2. the transverse energy of the cluster E T > 3.5 GeV, 3. the fraction f 1 > 0.1. If more than one clusters are found in the cone, then the one with the smallest R cluster,µ is selected. [3] The FSR photon candidates are added at the the 4-lepton candidate level and after all cuts. The FSR candidates found using this selection for 2012 s = 8 TeV with an integrated luminosity 20 fb 1 are reconstructed and listed in the Appendix. 7 Higgs Mass Measurements The 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 the cleanest signal from the background. To begin with, we first look at the mass fit for the single resonant peak from Z 4l. The single resonance from Z boson provides a good calibration on the Higgs mass measurements since the Z boson mass and width have been properly measured and it receive detector response in a similar regime to the newly discovered Higgs-like boson resonance decaying to four leptons at around 125 GeV. 7.1 Mass fit of the Z 4l resonant peak In this study, in order to allow a good comparison of data to MC, the MC events are produced with a minimum dilepton mass of 0.25 GeV. Compared with the singlez selection described in section 6, the M ll cut is lowered to 1 GeV from the original 5 GeV cut. In the process of fitting the mass peak, we first fit the reconstructed invariant mass peak for all four 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 Γ Z = 2.49 GeV from PDG value. During the initial Gaussian fit, the Gaussian σ is set to the Z boson width value. Then we fit the mass spectra from all four channels to both data and MC events using a convoluted probability density function of Breit-Wigner distribution and Gaussian distribution, BW(x,M Z,Γ Z ) Gauss(x,m 4l,σ 4l ) where M Z in the Breit-Wigner distribution is set to the fitted mass peak from the initial Gaussian function on the MC events M Z = 91.2 GeV and Γ Z is set to the PDG Z boson width value Γ Z = 2.48 GeV. We fit the mass spectra separately in different lepton final states to obtain a better understanding of the mass peak value. Since the 4µ channel has the largest statistics, so it becomes a critical channel for calibrating and determining the Higgs mass peak. The fitted 4µ mass for data and MC simulations are shown in Figure 14. The fitted mass peak here is M Z = 90.8 and m 4l M Z shows the shift of the mass fit compared to the data sample. Here the fitted mass peak in data is lowered by 100 MeV and the mass peak fit error is about 290 MeV. This fit tells us that the reconstructed 4µ mass is accurate to about 0.1% around the Z mass. The eeµµ also prove reasonably good statistics compared to other channels for mass fitting. The result for data and MC events are shown in Figure 15 and it shows that the statistics of the fitted mass peak is consistent for data and MC events. 7.2 Mass fit of the H ZZ 4l From the single resonant Z boson study, we see that the fit using a Breit Wigner convoluted with a Gaussian distribution provides 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 Z boson width. In this case, the width of the Breit Wigner distribution should be a very small number. Therefore, we see that Breit Wigner distribution does not contribute much in the mass peak determination. Instead, we use the Crystal Ball function to fit the mass peak. Full data obtained from 2011 collisions corresponding to an integrated luminosity 4.6 fb 1 and 2012 collisions corresponding to an integrated luminosity 20 fb 1 are used to fit the Higgs mass peak. 18

19 Figure 14: Invariant mass distributions and fitting for the reconstructed 4µ events for data and MC within the Z mass window of 80 to 100 GeV Figure 15: Invariant mass distributions and fitting for the reconstructed 2µ2e events for data and MC within the Z mass window of 80 to 100 GeV 19

20 We selected 14, 14, 11, and 21 events within the Higgs mass window from 110 to 140 GeV in 4e, eeµµ, µµee, and 4µ channels respectively. We can see that the statistics for the Higgs candidate events are considerably lower than that of the single Z candidate events. The mass fit for eeµµ and µµee channels will not give significant results since the statistics 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 then add the per-event resolution calculated using the method described in Section 4 by constructing a conditional probability distribution function with two observables M 4l and M4l err where M4l 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 procedure used in the single Z mass peak fitting described in Section 7.1. The resulting fit of data and MC events for the inclusive channel are shown in Figure 16. We can see that the fitted mass peak given by the Crystal Ball function is about GeV 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 m H = 125 GeV from gluon-gluon fusion process. Using the MC sample, we see that the Crystal Ball describes the shape reasonable well except 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 probability distribution function model, P (m 4l σ m4l ) P(σ m4l ) where P (m 4l σ m4l ) is the conditional PDF of m 4l given the mass resolution σ m4l and P (σ m4l ) is the PDF describing the event-by-event mass error. The conditional PDF P (m 4l σ m4l ) is modeled using a Gaussian distribution whose sigma is the event-by-event mass error. Gauss(x,m 4l σ m4l ) The resulting fit for inclusive channel is shown in Figure 17. In constructing the model PDF, the per-event mass error PDF is directly obtained from the histogram contains the mass error distribution. The per-event error PDF replaces the global resolution parameter σ of the Gaussian function by a global scale factor parameter. The model is then combined from the conditional Gaussian pdf and the per-event error pdf. We notice that the shape of the distribution does not appear to change significantly. This is due to the mean values of the event-by-event error pdf used in the fitting are small compared to the statistical uncertainties in the measurements. The result shows that the Higgs mass resolution to be about 2.19 GeV which is way larger compared to the ATLAS fitted result around 0.2 GeV.[4] If we examine the Figure 6 closely, we see that the mass peaks for all four channels are different since the mean values lie on both sides of m H = 125 GeV. In the mass fitting process, the data used is combined using data from all four lepton final states since the individual channel does not provide enough statistics to provide a good fit result in the mass window GeV. As a result, since the uncertainty from each channel is not considered in the fitting process, the fitted σ not only accounts for the Higgs mass resolution, but also the uncertainties caused by combing all the lepton final states. 20

21 Figure 16: Invariant mass distributions and fitting for the reconstructed events from all lepton final states for data and MC 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 within the Higgs mass window of 120 to 130 GeV with event-by-event mass error included 21

22 8 Conclusion In this thesis study, the Higgs mass resolution calculations are done on the MC samples first using the quadratic sum of the detector-induced resolutions and the mass shift due to FSR systematics. With the closure test performed on the method, a good agreement between the measured resolutions from the MC events and the final calculated resolutions are established. This method is then used to perform the resolution calculations on the Higgs candidates with the FSR shifts obtained from linear interpolation based the FSR shifts for MC events. The next topic we have presented is the Higgs mass fitting using the data collected by the ATLAS detector in 2011 and 2012 which have an integrated luminosity 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 GeV. The mass fitting done in the mass window GeV suggests the Higgs mass to be at about m H = ± 0.42 GeV. With the statistical and systematics uncertainties included, the mass of the Higgs-like boson is measured to b m H = (stat) (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 M 4l M f sr 4l M 12 M f sr 12 M 34 M f sr 34 2µ2e µ µ2e µ µ2e 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 GeV Run Event p 1 T p 2 T p 3 T p 4 T M 4l [GeV] M Z1 M Z2 channel e e e e e e e2µ e2µ e2µ µ2e µ2e µ2e µ µ µ µ µ µ µ µ 22

23 9.3 The sample list of fitted M ZZ results for various Higgs mass 23

24 9.4 Invariant mass distributions for combined 2011 and 2012 Higgs candidates Figure 18: The distributions of the four-lepton invariant mass, m 4l, 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 GeV. The signal expectation for m H = 125 GeV is shown for comparison. 24

25 Figure 19: The distribution of the four-lepton invariant mass, m 4l, 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 GeV. The signal expectation for m H = 125 GeV is shown for comparison. 25

26 9.5 Invariant mass distributions for combined 2011 and 2012 single Z resonance candidates Event / 3 GeV 10 ATLAS Internal s = 7 TeV: s = 8 TeV: Ldt = 4.6 fb 1 1 Ldt = 20.7 fb ZZ (*) Data (*) ZZ Z+jets,tt + e e e + e Event / 3 GeV 35 ATLAS Internal s = 7 TeV: s = 8 TeV: Ldt = 4.6 fb 1 1 Ldt = 20.7 fb ZZ (*) Data (*) ZZ Z+jets,tt + e e µ + µ m 4l [GeV] m 4l [GeV] Event / 3 GeV 16 ATLAS Internal s = 7 TeV: s = 8 TeV: Ldt = 4.6 fb 1 Data (*) ZZ Z+jets,tt 1 Ldt = 20.7 fb (*) + + ZZ µ µ e e Event / 3 GeV ATLAS Internal s = 7 TeV: s = 8 TeV: Ldt = 4.6 fb 1 Data (*) ZZ Z+jets,tt 1 Ldt = 20.7 fb (*) + + ZZ µ µ µ µ m 4l [GeV] m 4l [GeV] Figure 20: Invariant mass distributions for four leptons, m 4l, for 2011 s = 7 TeV and 2012 s = 8 TeV single Z resonance candidates combined compared to the background expectation in the mass range GeV. 26

27 Event / 3 GeV ATLAS Internal s = 7 TeV: Ldt = 4.6 fb 1 s = 8 TeV: Ldt = 20.7 fb 1 ZZ Data (*) ZZ Z+jets,tt (*) + l l l + l m 4l [GeV] Figure 21: Invariant mass distribution for four leptons, m 4l, for 2011 s = 7 TeV and 2012 s = 8 TeV single Z resonance candidates combined for inclusive final state compared to the background expectation in the mass range GeV. 27

28 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 Collision Data at s = 7 TeV, ATLAS-CONF [3] ATLAS Collaboration, Reconstruction of collinear final-state-radiation photons in Z decays to muons in s = 7 TeV proton-proton collisions, ATLAS-CONF [4] ATLAS Collaboration, Measurements of the properties of the Higgs-like boson in the four lepton decay channel with the ATLAS detector using 25 fb 1 of proton-proton collision data., ATLAS-CONF