Photon Efficiency Measurements using Radiative Z Decays with the ATLAS Detector

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1 Photon Efficiency Measurements using Radiative Z Decays with the ALAS Detector Fionn Bishop, University of Cambridge September, 08 Abstract Modifications to the method of measuring photon efficiencies in radiative Z decays are proposed and the results of their implementation are presented. hese efficiencies are calculated in bins of photon transverse momentum p and pseudorapidity η, and separately for converted and unconverted photons, and electrons and muons. he backgrounds Z ττj, t t and W Z are considered in addition to the dominant background Z llj. he inclusion of Z ττj may significantly affect the efficiency measurement, whereas t t and W Z are insignificant. A missing irreducible background is located at p < 0 GeV and three-body invariant mass m ll < 80 GeV. It is suggested that this is Z ττ, and that the exclusion of this background may result in a significant error on the efficiency. he reducible background template from Monte Carlo is replaced with a template from data in an anti-isolation, anti-id control region, with η bins grouped, which is fitted to a double sided crystal ball function. his improves the statistical power of the template in most regions, particularly 0 < p < 0 GeV, but statistics are very poor in the region p > 0 GeV, m ll < 80 GeV. he use of only unprescaled triggers, and associated p l cuts to mitigate the effects of turn-on, are included in event selection cuts to significantly improve data-monte Carlo agreement. his modified method led to the successful evaluation of the ID efficiency (number of events passing ID and isolation cuts/number of events passing isolation cuts) and the total efficiency (number of events passing ID and isolation cuts/total number of events). Introduction Photons are present in many important physics processes which are studied in the ALAS detector, including H [] and BSM processes such as the decay of supersymmetric particles [, ]. In studying these processes, photon isolation and identification (ID) selection criteria applied to data samples are necessary to exclude the reducible backgrounds that arise as a result of photons from hadronic decays or the reconstruction of jets or leptons as photons. hese selection criteria (cuts) are very effective at reducing background, but also exclude some signal events. o accurately study the processes described above, it is necessary to know the fraction of signal photons that are excluded by these cuts. his is the efficiency: ɛ = N S[cut] N S () It is possible to estimate this quantity using Monte Carlo (MC) simulation, but this leads to large uncertainties as a result of an imperfect description of showering in the detector [] and ultimately, it is important to have a measurement from data. hree methods of obtaining a

2 data-driven measurement of ɛ exist [, ], which are each useful in a different photon transverse momentum (p ) range. he method considered in this report measures photon efficiencies in the radiative Z decay Z ll. A Z boson formed in a Drell-Yan process decays to two sameflavour leptons, and a photon is emitted either as ISR (by one of the initial state quarks; figure ) or FSR (by one of the final state leptons; figure ). his process is used because it is wellunderstood and has a reasonably high cross section. It is useful in the range 0 < p < 00 GeV, because photons with p < 0 GeV cannot be accurately reconstructed in the detector, and the the cross section for Z ll events with p > 00 GeV is too small to produce a sufficient number of events to analyse. q l + q l Z q l Z q l + Figure : he radiative Z decay with an ISR photon. A photon is annihilated by an initial state quark. hen two same-flavour quarks annihilate in a Drell-Yan process to form a Z boson, which decays to two same-flavour leptons. Figure : he radiative Z decay with an FSR photon. wo same-flavour quarks annihilate in a Drell-Yan process to form a Z boson, which decays to two same-flavour leptons. hen one final state lepton radiates a photon. his measurement has been made before [,, 9], but with fractional uncertainties of up to 0%, so there is the potential for improvement. his report discusses several ways in which modifications to the measurement have been implemented with a view to improving precision. he two main modifications are the inclusion of additional backgrounds (ττj, W Z and t t), and the use of data from an anti-isolation, anti-id control region as a background template to reduce background statistical uncertainty. Additionally, the total efficiency (ɛ O ), which is the number of signal events passing both ID and isolation cuts divided by the total number of signal events, is calculated, in addition to the ID efficiency ɛ ID, as an alternative to the combination of the correlated isolation and ID efficiencies. Sections and describe the data and Monte Carlo samples used in this analysis and the selection cuts made. Section defines the cuts related to isolation and ID which are made. he relative importance of the different sources of background are discussed in section. Section explains the current method and the modifications implemented. Section discusses sources of uncertainty. Section 8 presents efficiency measurements and section 9 suggests further improvements to the method. Data and Monte Carlo samples. Data samples he 0 data set was used in this study. integrated luminosity of. fb. his was collected at s = ev and has an

3 . Monte Carlo samples Version ntuples of the Monte Carlo samples described in table were used. All slices of each process were included. Cuts were made to samples of the processes Z ll and Z llj to avoid overlap: In Z ll, only events with isolated or non-isolated photons were used and in Z llj, FSR photons were excluded. Process Name DSID Cuts Z ee Sherpa C0 Z ee 0- ph.truth type == (IsoPhoton) Z µµ Sherpa C0 Z µµ or (NonIsoPhoton) Sherpa.. Z eej Z eej ph.truth origin!= 0 (FSR (Z+jet)(MAXHPV) 00- photon Sherpa.. Z µµj Z µµj (Z+jet)(MAXHPV) Z ττj Sherpa.. Z ττj (Z+jet)(MAXHPV) 8- W Z PowhegPy8EG C0 W Z lνll 0 t t MadgraphPythia8 t t nonallhad 089 able : MC samples used in the analysis Event selection he following selection criteria were applied to all MC and data samples. he Z ll selection criteria are identical to those applied in previous measurements [, 9, ]. he trigger-based selection criteria are an addition and their importance will be discussed.. Z ll selection All events used in this analysis satisfy: Contain at least one primary vertex with at least three associated tracks; and two sameflavour, opposite-sign leptons and one photon 0 < m ll < 8 GeV Electrons: R min > 0. Muons: R min > 0. [ ] where R min = min (ηl η ) + (φ l φ ). he m ll cut excludes the majority of the ISR background Z llj. he R min cuts reduce the effect on photon isolation of lepton energy deposition inside the photon isolation cone.. riggers ables and list the unprescaled triggers saved in the version ntuples, and tables and list the prescaled triggers. Only events that pass at least one of these unprescaled triggers are used. urn-on is an effect where some leptons below the trigger threshold are included and some leptons above the trigger threshold are excluded. his effect is a result of mis-measurement at the trigger level and is poorly modelled in MC. herefore p l cuts are made at values slightly above the trigger threshold to avoid this effect and improve data-mc agreement. Produced using analysis code described in

4 rigger HL e0 lhmedium nod0 HL e0 lhloose nod0 HL e lhvloose nod0 p e HL e lhvloose nod0 LEMVHI p e able : Unprescaled electron triggers p l cut > GeV > GeV rigger HL mu0 HL mu p µ HL mu ivarmedium p µ p l cut > GeV > 8 GeV able : Unprescaled muon triggers rigger HL e0 lhmedium nod0 match HL e0 lhloose nod0 match HL e lhvloose nod0 match HL e lhvloose nod0 LEMVHI match able : Prescaled electron triggers rigger HL mu0 match HL mu0 0eta0 msonly HL mu0 0eta0 msonly match HL mu match HL mu imedium HL mu imedium match HL mu ivarmedium OR HL mu0 HL mu ivarmedium OR HL mu0 match HL mu ivarmedium HL mu ivarmedium match able : Prescaled muon triggers HL e lhtight nod0 ivarloose and HL mu mu8nol are unprescaled triggers which are missing from the version ntuples. his leads to a 0% loss in data. Figures - demonstrate the importance of making p l cuts. Although the use of only unprescaled triggers does not noticeably affect the data, the implementation of associated p l cuts significantly improves the data-mc agreement for p µ < 0 GeV, pµ < 0 GeV, pl < 0 GeV and p l 0 GeV. herefore the use of these cuts improves the quality of subsequent fits and increases the visibility of other inconsistencies between data and MC. Accidentally prescaled in periods B-B8 (runs 8-89 with an effective reduction of 0. fb ) but was used anyway to avoid loss of statistical power

5 s= ev,. fb No ID cut No iso cut All triggers Z µµ Z µµj Z ττj tt WZ Data µ Figure : p l distribution of the leading muon in events with a converted photon. passing any trigger saved in the ntuples are used and no p l cuts are applied. No ID or isolation cuts are applied to the photon s= ev,. fb No ID cut No iso cut All triggers Z µµ Z µµj Z ττj tt WZ Data µ 0 Figure : p l distribution of the subleading muon in events with a converted photon. passing any trigger saved in the ntuples are used and no p l cuts are applied. No ID or isolation cuts are applied to the photon s= ev,. fb No ID cut No iso cut Only unprescaled triggers l No p cuts Z µµ Z µµj Z ττj tt WZ Data µ s= ev,. fb No ID cut No iso cut Only unprescaled triggers l No p cuts Z µµ Z µµj Z ττj tt WZ Data µ 0 Figure : p l distribution of the leading muon in events with a converted photon. Only events passing an unprescaled trigger saved in the ntuples are used but no p l cuts are applied. No ID or isolation cuts are applied to the photon. Figure : p l distribution of the subleading muon in events with an unconverted photon. Only events passing an unprescaled triggers saved in the ntuples are used but no p l cuts are applied. No ID or isolation cuts are applied to the photon.

6 s= ev,. fb No ID cut No iso cut Only unprescaled triggers l With p cuts Z µµ Z µµj Z ττj tt WZ Data µ s= ev,. fb No ID cut No iso cut Only unprescaled triggers l With p cuts Z µµ Z µµj Z ττj tt WZ Data µ 0 Figure : p l distribution of the leading muon in events with an unconverted photon. Only events passing an unprescaled trigger saved in the ntuples are used and p l cuts are applied. No ID or isolation cuts are applied to the photon. Figure 8: p l distribution of the subleading muon in events with an unconverted photon. Only events passing an unprescaled trigger saved in the ntuple are used and p l cuts are applied. No ID or isolation cuts are applied to the photon s= ev,. fb No ID cut No iso cut All triggers Z ee Z eej Z ττj tt WZ Data s= ev,. fb No ID cut No iso cut All triggers Z ee Z eej Z ττj tt WZ Data p e p e Figure 9: p l distribution of the leading electron in events with an unconverted photon. passing any trigger saved in the ntuples are used and no p l cuts are applied. No ID or isolation cuts are applied to the photon. Figure 0: p l distribution of the subleading electron in events with an unconverted photon. passing any trigger saved in the ntuples are used and no p l cuts are applied. No ID or isolation cuts are applied to the photon.

7 s= ev,. fb No ID cut No iso cut Only unprescaled triggers l No p cuts Z ee Z eej Z ττj tt WZ Data s= ev,. fb No ID cut No iso cut Only unprescaled triggers l No p cuts Z ee Z eej Z ττj tt WZ Data p e p e Figure : p l distribution of the leading electron in events with an unconverted photon. Only events passing an unprescaled trigger saved in the ntuples are used but no p l cuts are applied. No ID or isolation cuts are applied to the photon. Figure : p l distribution of the subleading electron in events with an unconverted photon. Only events passing an unprescaled triggers saved in the ntuples are used but no p l cuts are applied. No ID or isolation cuts are applied to the photon s= ev,. fb No ID cut No iso cut Only unprescaled triggers l With p cuts Z ee Z eej Z ττj tt WZ Data s= ev,. fb No ID cut No iso cut Only unprescaled triggers l With p cuts Z ee Z eej Z ττj tt WZ Data p e p e Figure : p l distribution of the leading electron in events with an unconverted photon. Only events passing an unprescaled trigger saved in the ntuples are used and p l cuts are applied. No ID or isolation cuts are applied to the photon. Figure : p l distribution of the subleading electron in events with an unconverted photon. Only events passing an unprescaled trigger saved in the ntuple are used and p l cuts are applied. No ID or isolation cuts are applied to the photon.

8 ID and isolation criteria In all cases, the tight ID criteria are used to define ID cuts. Isolated photons are those that pass the FixedCutLoose working point: E cone0 /p < 0.0 () p cone0 /p < 0.00 () where E cone0 /p measures the calorimeter isolation and p cone0 /p the track isolation. o effectively exclude signal, the anti-isolation region is much tighter than the inverse of the isolation region. It also has an upper limit to avoid biasing the m ll shape: Backgrounds 0.0 < E cone0 /p <.00 () 0. < p cone0 /p <.00 () Figure shows the p distribution of the signal channel and all backgrounds, compared to the distribution of data events. Z llj is a significant background everywhere. Z ττj may be significant at p < 0 GeV. t t and W Z are small everywhere, but are most significant at p > 0 GeV. he method described in this report treats reducible and irreducible backgrounds differently. Reducible backgrounds are those that contain a fake or non-isolated photon, so can be reduced by making an isolation or ID cut. he reducible backgrounds here are Z llj and Z ττj. t t is an irreducible background. W Z is treated as an irreducible background, although it does not fall into either category. here is a significant discrepancy between data and MC at p 0 GeV. his suggests that a background channel is missing from the MC description. his is discussed further in section 9.. 8

9 s= ev,. fb No ID cut No iso cut Z µµ Z µµj Z ττj tt WZ Data Figure : p distribution of events with muons and an unconverted photon which satisfy selection cuts (markers). he signal is Z µµ (red) and the dominant background is Z µµj (dark blue). he next largest background is Z ττj (green), which is mainly in the region p < 0 GeV. t t (pink) and W Z (light blue) are small everywhere. Agreement between data and Monte Carlo is generally good but there is a deficit of Monte Carlo compared to data at p 0 GeV. able provides estimates on the maximum fractional errors on ɛ ID and ɛ O as a result of ignoring backgrounds. hese were evaluated by calculating ɛ when the number of signal events N s was increased by the number of background events, in the p bin with the highest fraction of background. his demonstrates that Z ττj is significant and so must be accurately modelled, whereas t t and W Z do not need to be modelled as accurately. ττj t t W Z ɛ ID /ɛ ID 0.% 0.0% 0.0% ɛ O /ɛ O % 0.% 0.0% Bin 0 < p < GeV 0 < p < 80 GeV able : Estimate of the maximum fractional error on ɛ ID and ɛ O as a result of ignoring the backgrounds Z ττj, t t and W Z. Method Efficiencies are calculated using the events which pass the selection criteria in section. Photon tight identification efficiency ɛ ID is the fraction of isolated photons which pass the tight identification criteria: ɛ ID = N S[ID&iso] () N s [iso] Photon total efficiency ɛ O is the fraction of photons which pass the tight identification and FixedCutLoose isolation criteria: ɛ O = N S[ID&iso] N s () 9

10 Both efficiencies are evaluated in the range m ll = [80,00] GeV. he lower bound on this range was chosen because most events outside of this range were a result of mismeasurement, and so were considered low-quality events. Low-quality would not generally be used in analysis, and so the efficiency of only high-quality events was calculated. Photon efficiencies depend on whether the photon is converted (undergoes e + e pair production before ECAL) or unconverted (undergoes pair production in ECAL); absolute photon pseudorapidity η ; and p, so are calculated separately for converted and unconverted photons, and in the following bins of η and p. hey are also calculated separately for events with electrons and muons. p : [0,, 0,, 0,, 0,, 0, 0, 80] GeV (8) η : [0.00, 0.0,.,.,.8,.] (9) Excluding the range. < η <. due to a lack of detector coverage. he following sections explain the current method of measuring ɛ ID and the modifications to the method which have been tested.. Existing method For p < GeV, background contamination is large and is estimated using a template fit. Only the dominant background Z llj is considered. emplates for signal and background are taken from Monte Carlo and fitted to the data distribution to obtain the purity (P). he efficiency is then evaluated as: ɛ = P cut N data,cut P N data (0) For p > GeV, the background contamination is small and is not evaluated. Instead, the effect of contamination is treated as a systematic uncertainty on ɛ. For more detail, see [, 9, ].. Reducible background template he reducible background template is now taken from data in an anti-isolation, anti-id control region (CR, see section for definition), rather than from Monte Carlo in the signal region. Figures and show the calorimeter and track isolation distribution of all channels. his demonstrates that almost all signal events have calorimeter isolation < 0. and track isolation < 0.. he CR is looser than the inversion of this region to maintain high available statistics. his produces a data set with a large number of reducible background events and only a small fraction (up to %) of signal and irreducible background contamination. 0

11 s= ev,. fb No ID cut No iso cut Z µµ Z µµj Z ττj tt WZ Data cone0 /p E s= ev,. fb No ID cut No iso cut Z µµ Z µµj Z ττj tt WZ Data p cone0 /p Figure : Calorimeter isolation E cone0 /p distribution of events with muons and an unconverted photon. he number of signal events rapidly decreases, so there are almost none with E cone0 /p > 0.. he number of reducible background events decreases slowly with respect to isolation but is large everywhere. Data-MC agreement is much worse at high E cone0 /p. Figure : rack isolation p cone0 /p distribution of events with muons and an unconverted photon. he number of signal events rapidly decreases, so there are almost none with p cone0 /p > 0.. he number of reducible background events decreases slowly with respect to isolation but is large everywhere. Data-MC agreement is much worse at high p cone0 /p. he use of an anti-isolation control region relies on the m ll distribution being independent of isolation. Figure 8 compares the agreement in shape between CR data and MC (with no cuts) in four different parts of the control region. It shows that the m ll distribution of the background is not independent of isolation: As the photons become less isolated (E cone0 /p and p cone0 /p increase), the distribution becomes more skewed towards large m ll. his indicates that it is necessary to exlcude events with E cone0 /p >.00 or pcone0 /p >.00 in the background template, as this would bias the shape. herefore these values are chosen as the upper bound on the control region. Comparisons in all bins are shown in the supplementary appendix. Due to low available statistics, it is difficult to determine if there is a bias at p > 0 GeV. If there is no bias, it may be possible to increase the upper bound on the control region for p > 0 GeV, which would improve the statistical power of the reducible background template.

12 Normalised Z ττj MC, no iso cuts Z eej MC, no iso cuts Control Region a Data 0 < p < GeV Normalised Z ττj MC, no iso cuts Z eej MC, no iso cuts Control Region b Data 0 < p < GeV m ll m ll (a) Comparison using control region a: 0.0 < E cone0 /p < 0.0 & 0. < pcone0 /p < 0.0. here is good agreement between the distributions. (b) Comparison using control region b: 0.0 < E cone0 /p <.00 & 0.0 < pcone0 /p <.00. here is good agreement between the distributions. Normalised Z ττj MC, no iso cuts Z eej MC, no iso cuts Control Region c Data 0 < p < GeV Normalised Z ττj MC, no iso cuts Z eej MC, no iso cuts Control Region d Data 0 < p < GeV m ll m ll (c) Comparison using control region c:.00 < E cone0 /p <.00 &.00 < pcone0 /p <.00. he CR data distribution is slightly more skewed towards large m ll than the MC distribution. (d) Comparison using control region d:.00 < E cone0 /p &.00 < p cone0 /p. he CR data distribution is significantly more skewed towards large m ll than the MC distribution. Figure 8: Comparison of m ll distribution between data in control region (markers) and reducible background MC with no isolation cuts (blue+green), for background to Z ee with an unconverted photon. Skew towards large m ll increases as photons become less isolated (from CRa to CRd). Figure 9 compares the reducible background templates when using data from the selected CR (section ) and Monte Carlo (with no isolation or ID cuts), for background to Z µµ with a converted photon. he template shapes are consistent in all cases. At p < 0 GeV, both templates have good statistics. At 0 < p < 0 GeV, the CR data template has better

13 statistics than the MC, but above this, its statistical power decreases significantly, particularly for m ll < 80 GeV. Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < GeV Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data < p < 0 GeV m ll m ll (a) Comparison in the bin 0 < p < GeV. Both CR data and MC have good statistics. (b) Comparison in the bin < p < 0 GeV. Both CR data and MC have good statistics. Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < GeV Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data < p < 0 GeV m ll (c) Comparison in the bin 0 < p < GeV. he CR data template has better statistical power than the MC m ll (d) Comparison in the bin < p < 0 GeV. he CR data template has better statistical power than the MC.

14 Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < GeV m ll (e) Comparison in the bin 0 < p < GeV. he CR data template has better statistical power than the MC. Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data < p < 0 GeV m ll (f) Comparison in the bin < p < 0 GeV. he CR data template has better statistical power than the MC. Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < GeV Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data < p < 0 GeV m ll (g) Comparison in the bin 0 < p < GeV. he CR data has poor statistical power for m ll < 80 GeV m ll (h) Comparison in the bin < p < 0 GeV. he CR data has poor statistical power for m ll < 80 GeV.

15 Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < 0 GeV Normalised Z ττj MC, no iso cuts Z µµj MC, no iso cuts Control Region Data 0 < p < 80 GeV m ll (i) Comparison in the bin 0 < p < 0 GeV. he CR data has poor statistical power for m ll < 80 GeV m ll (j) Comparison in the bin 0 < p < 80 GeV. he CR data has poor statistical power for m ll < 80 GeV. Figure 9: Comparison of m ll distribution between data in control region (markers) and reducible background MC with no isolation cuts (blue+green), for background to Z µµ with an unconverted photon. here is agreement between the two templates at all p. o further improve the statistical power of the background template, all η bins are used to produce the template. his relies on the m ll distribution being unbiased with respect to η, which is illustrated in figures 0 and. hese show the ratio between the m ll distribution in one bin of η and the m ll distribution in all bins of η for two cases. Plots for all cases are provided in the supplementary appendix. he ratio between the two distributions is consistent with a constant value, which demonstrates that the shape of the m ll distribution is independent of η.

16 0 - s= ev,. fb Background to Z µµ 0 < p < GeV CR Data, 0.00 < η < 0.0 CR Data, all η s= ev,. fb Background to Z ee 0 < p < GeV CR Data, 0.0 < η <. CR Data, all η m µµ m ee Figure 0: m ll distribution of control region events in the range 0 < p < GeV which are reducible background to Z µµ with an unconverted photon, in the bin 0.00 < η < 0.0 (blue markers) and for all η (red markers). he ratio between the two is consistent with a constant value with respect to m ll. Figure : m ll distribution of control region events in the range 0 < p < GeV which are reducible background to Z ee with an unconverted photon, in the bin 0.0 < η <. (blue markers) and for all η (red markers). he ratio between the two is consistent with a constant value with respect to m ll. he improvement in statistical power is particularly noticeable in bins with p where there are only a small number of MC events. his is illustrated in figure. > GeV,

17 0 - s= ev,. fb Background to Z ee < p < 0 GeV CR Data,.8 < η <. CR Data, all η m ee Figure : Comparison between m ll distribution from CR data in the bin.8 < η <. (blue) and in all η bins combined (red), for events in the range < p < 0 GeV which include electrons and a converted photon. he two data sets have approximately the same shape, but the data set using all η has much better statistics. Another benefit of using data as a reducible background template is that it includes any reducible bacgkrounds which are missing in the Monte Carlo description of the data. he CR data is then fitted to a double-sided crystal ball function (DSCB) to reduce statistical fluctuations. his is implemented as an unbinned maximum likelihood fit in RooFit [0]. he fit excludes the range [88,9] GeV to reduce the impact of signal and irreducible background contamination. he DSCB is an asymmetric function with a Gaussian core and power-law tails (figure ). Figures and illustrate the fit in two bins. he fits for all bins are shown in the supplementary appendix. Figure : Plot of a double-sided crystal ball function. he core is Gaussian (blue) and the tails follow a power law (red).

18 0 - s= ev,. fb Fit to DSCB Control Region Data - s= ev,. fb Fit to DSCB Control Region Data 0 < p < GeV 0 0 < p < GeV 0 Data/Fit m ee Data/Fit m ee Figure : Fit of a DSCB to the m ll distribution of the CR data in the 0 < p < GeV, electrons and converted photon bin. Figure : Fit of a DSCB to the m ll distribution of the CR data in the 0 < p < GeV, electrons and converted photon bin.. Efficiency Measurement An extended maximum likelihood fit is implemented in RooFit [0] to fit the signal and background templates to data to determine the number of signal events. he signal and irreducible background templates are taken from Monte Carlo. he irreducible background is treated as a fixed template, so its scaling is not allowed to vary from the value σ data /σ MC. his is for t t and.8 for WZ []. η bins are also grouped in this fit to increase statistical power. he fit is carried out in the range m ll = [0,] GeV to utilise the sidebands to accurately determine the size of the background component. he upper limit on this range was set by the upper limit of m ll in the data and Monte Carlo samples. he lower limit was selected due to the presence of a kinematic edge at m ll 8 GeV. Once the number of signal events before and after a cut had been obtained, the efficiency was calculated in the range m ll = [80,00] GeV. Uncertainties. Statistical Statistical uncertainties were evaluated using the binomial approximation where N s has the Poissonian uncertainty N s. his leads to the uncertainty ɛ( ɛ) ɛ = () N S However, this is not a good approximation for ɛ []. his leads to statistical uncertainties of up to % for p < 0 GeV and up to % for p > 0 GeV.. Background modelling A systematic uncertainty arises due to inaccurate modelling of the background shape. his is due to a poor fit of the DSCB to the CR data, primarily at p < 0GeV and p > 0 8

19 GeV; dependence of the background shape on isolation; and missing irreducible backgrounds. his uncertainty could be estimated by performing a high and low-tail fit of the signal and background templates to data.. Detector geometry Mismodelling of detector geometry in MC leads to a systematic uncertainty. his uncertainty is estimated by evaluating the change in efficiency when an MC sample generated using distorted geometry is used. he maximum fractional uncertainty is % and is assumed to be negligible for p > GeV [9].. Irreducible background cross section Inaccuracies in the scaling factor σ data /σ MC of the irreducible backgrounds affect the fit to determine N S. his uncertainty would be extremely small as the irreducible backgrounds constitute < % of the signal region. It could be estimated by varying the scaling factors within their uncertainties. 8 Results his section presents measurements of ɛ ID and ɛ O in all bins. Measured efficiencies approximately show the expected smooth, monotonic curve with higher efficiencies at higher p. here is agreement between data and Monte Carlo in most cases. Systematic errors would need to be evaluated to fully determine the extent of the agreement. 9

20 8. ID Efficiency Measurements ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z ee 0.00 < η < (a) 0.0 < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z ee 0.0 < η < (b) 0. < η <. ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z ee. < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z ee.8 < η < (c). < η <.8 (d).8 < η <. Figure : Comparison of data-driven and MC ID efficiency measurements for events with electrons and a converted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only. 0

21 ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z ee 0.00 < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z ee 0.0 < η < (a) 0.0 < η < (b) 0. < η <. ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z ee. < η < (c). < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z ee.8 < η < (d).8 < η <. Figure : Comparison of data-driven and MC ID efficiency measurements for events with electrons and an unconverted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

22 ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ 0.00 < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ 0.0 < η < (a) 0.0 < η < (b) 0. < η <. ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ. < η < (c). < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ.8 < η < (d).8 < η <. Figure 8: Comparison of data-driven and MC ID efficiency measurements for events with muons and a converted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

23 ID ID data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ 0.00 < η < data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ 0.0 < η <. ID (a) 0.0 < η < 0. data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ. < η < (c). < η <.8 ID (b) 0. < η <. data mcd - s= ev,. fb FixedCutLoose Isolation Z µµ.8 < η < (d).8 < η <. Figure 9: Comparison of data-driven and MC ID efficiency measurements for events with muons and an unconverted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

24 8. otal Efficiency Measurements O data mcd - s= ev,. fb Z ee 0.00 < η < O data mcd - s= ev,. fb Z ee 0.0 < η < (a) 0.0 < η < 0. (b) 0. < η <. O O data mcd - s= ev,. fb Z ee. < η < data mcd - s= ev,. fb Z ee.8 < η < (c). < η <.8 (d).8 < η <. Figure 0: Comparison of data-driven and MC total efficiency measurements for events with electrons and a converted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

25 O O data mcd - s= ev,. fb Z ee 0.00 < η < data mcd - s= ev,. fb Z ee 0.0 < η < (a) 0.0 < η < 0. (b) 0. < η <. O O data mcd - s= ev,. fb Z ee. < η < data mcd - s= ev,. fb Z ee.8 < η < (c). < η < (d).8 < η <. Figure : Comparison of data-driven and MC total efficiency measurements for events with electrons and an unconverted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

26 O O data mcd - s= ev,. fb Z µµ 0.00 < η < data mcd - s= ev,. fb Z µµ 0.0 < η < (a) 0.0 < η < 0. (b) 0. < η <. O O data mcd - s= ev,. fb Z µµ. < η < data mcd - s= ev,. fb Z µµ.8 < η < (c). < η < (d).8 < η <. Figure : Comparison of data-driven and MC total efficiency measurements for events with muons and a converted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only.

27 O O data mcd - s= ev,. fb Z µµ 0.00 < η < (a) 0.0 < η < data mcd - s= ev,. fb Z µµ 0.0 < η < (b) 0. < η <. O data mcd - s= ev,. fb Z µµ. < η <.8 O data mcd - s= ev,. fb Z µµ.8 < η < (c). < η < (d).8 < η <. Figure : Comparison of data-driven and MC total efficiency measurements for events with muons and an unconverted photon as a function of p, for the four pseudorapidity bins. he error bars show statistical uncertainty only. 9 Further work 9. Reducible background modelling Figures and demonstrate the poor quality of the DSCB fit to the CR data for p < 0 GeV. he DSCB does not approximate the data shape well at m ll < 90 GeV. he fit is better for p > 0 GeV, but could still be improved. his could be achieved by fitting the data to an alternative function. Functions that could be tested are Bernstein polynomials and a triple Gaussian.

28 0 - s= ev,. fb Fit to DSCB Control Region Data - s= ev,. fb Fit to DSCB Control Region Data 0 < p < GeV < p < 0 GeV 0 0 Data/Fit m ee Data/Fit m µµ Figure : Fit of a DSCB to the m ll distribution of the CR data in the 0 < p < GeV, electrons and unconverted photon bin. here is a significant difference between the data and the DSCB fit for m ll < 90 GeV. Figure : Fit of a DSCB to the m ll distribution of the CR data in the 0 < p < GeV, electrons and unconverted photon bin. here is a significant difference between the data and the DSCB fit for m ll < 90 GeV. 9. Missing background identification Figure demonstrates the large deficit in the Monte Carlo description of the data at m ll < 80 GeV, p < 0 GeV. his discrepancy is too large to be explained by the poor fitting of the DSCB (section 9.). A likely cause is the lack of an irreducible background in the Monte Carlo description of the data, of which the most likely candidate is ττ. his channel is expected to have % of the number of events as Z ll (excluding the effects of event selection cuts) [8], which are expected to have m ll and p values in the range where background is missing. Another possible missing irreducible background is W W, but this has a much smaller crosssection, so is not expected to be significant. 8

29 s= ev,. fb No ID cut No iso cut 0 < p < GeV 0.0 < η <. N sig = 8 ± N bkg = 88 ± Z ee Z eej tt WZ + Z ττj Data m ee Figure : m ll distribution of events in the 0 < p < GeV, 0.0 < η <., electrons and unconverted photon bin. he reducible background shape (dark blue) is from the DSCB fit. All templates are scaled as determined by the extended maximum likelihood fit. here is a large discrepancy between data and Monte Carlo at m ll < 80 GeV. 9. Signal modelling Statistical fluctuations in the signal template could be reduced by fitting the signal Monte Carlo to a PDF. he signal channel consists of two components: A large FSR component and the small tail of an ISR component. herefore the PDF would have to be a sum of two functions; one to model the shape of each component. Figure depicts the evolution of the FSR and ISR components as minimum p is increased: he FSR component moves to slightly lower m ll values and the ISR component moves to significantly higher m ll values. he progression of the FSR component suggests that the 0 < m ll < 8 GeV selection cut is only optimised for p < 0 GeV and reducing the upper bound on this cut at p > 0 GeV may improve exclusion of background here. 9

30 m ll Z ee, mcd 0 < p < 80 GeV 0 0 m ll Z ee, mcd 0 < p < 80 GeV m ll m ll (a) 0 < p < 80 GeV. he vertical component at m ll 90 GeV is FSR and the horizontal component at m ll 90 GeV is ISR. m ll Z ee, mcd 0 < p < 80 GeV (b) 0 < p < 80 GeV. When the minimum p is increased, the minimum m ll of ISR events also increases. m ll Z ee, mcd 0 < p < 80 GeV m ll m ll (c) 0 < p < 80 GeV. (d) 0 < p < 80 GeV. As a result of the minimum p cut, almost no ISR events with m ll < GeV remain, and the FSR component has moved to lower m ll values. Figure : Distribution of Z ee events with an unconverted photon in m ll -m ll space in different p regions. above the line at m ll = 8 GeV are excluded by selection cuts. 0 Conclusions his report discusses potential improvements to the measurement of photon efficiencies using radiative Z decays, and presents the results of their implementation. Measurements of photon ID and total efficiencies approximately show the expected smooth, monotonic curve with higher efficiencies at higher p. here is reasonable agreement between efficiencies derived from data and MC, but more comprehensive error estimates are required to make a full comparison. he background channel Z ττj is a significant contribution to the data set, and there is a fractional error of up to 0.% on the ID efficiency and % on the total efficiency if it is not included. herefore it is important to consider this channel in future measurements. he effects of the background channels W Z and t t are not significant compared to statistical and other systematic uncertainties, so do not need to be considered carefully in this measurement. here is a deficit in the Monte Carlo description of the data in the region p < 0 GeV, 0

31 m ll < 80 GeV and this may be resolved by including the irreducible bacgkround Z ττ. his channel is expected to be % of the size of Z ll and have events primarily in this region. herefore it is important to test this measurement with the inclusion of Z ττ. he statistical power of the reducible background template can be improved by using data from an anti-isolation, anti-id control region rather than Monte Carlo and grouping all η bins. his is effective for 0 < p < 0 GeV, but the statistical power of the template is not good at higher p, particularly for m ll < 80 GeV. Statistical fluctuations can further be reduced by fitting the data to a smooth function. However, the fitting can be improved on what has been demonstrated here, particularly at p < 0 GeV. It is possible to calculate the total efficiency directly. However, this leads to large systematic uncertainties as a consequence of the high proportion of background in the denominator. Acknowledgements I am immensely grateful to my supervisor, Kurt Brendlinger, for all of the time, knowledge and encouragement offered throughout the course of this project. I would also like to thank Früd Braren, Daniel Rauch, Julian Schmöckel and Namgyun Jeong for their assistance and for many interesting discussions. he DESY ALAS group have been incredibly welcoming, from the support offered to the many social gatherings. hank you to the Summer Student Program organisers for providing the opportunity to work at DESY, where I have gained so much knowledge and become further inspired by Particle Physics. Finally, thank you to the other summer students for their wonderful friendship and support, and for joining me in some unforgettable experiences. References [] ALAS Collaboration. Measurement of the photon identification efficiencies with the A- LAS detector using LHC Run- data collected in 0 and 0. record/909, Geneva, Oct 0. [] Blocker, Craig. Uncertainties on Efficiencies. statistics/notes/cdf8_eff_uncertainties.ps, Aug 00. [] ALAS Collaboration. Measurement of Higgs boson production in the diphoton decay channel in pp collisions at center-of-mass energies of and 8 ev with the ALAS detector. Physical Review D, 90:0, 0. [] ALAS Collaboration. Search for high-mass diphoton resonances in pp collisions at s = 8eV with the ALAS detector. Physical Review D, 9:000, 0. [] ALAS Collaboration. Search for photonic signatures of gauge-mediated supersymmetry in 8 ev pp collisions with the ALAS detector. Physical Review D, 9:000, 0. [] ALAS Collaboration. Measurement of the photon identification efficiencies with the A- LAS detector using LHC Run- data. European Physical Journal C, :, 0. [] ALAS Collaboration. Measurement of the W ± Z boson pair-production cross section in pp collisions at s = ev with the ALAS detector. Physics Letters B, :, 0. [8] Particle Data Group. Review of Particle Physics. Physical Review D, 9:0000, 08. [9] Nadezda Proklova, Ilaria Luise, Giovanni Marchiori, Evgeny Soldatov, and Gregorio Bernardi. Photon identification efficiency measurements with radiative Z boson decays: Supporting documentation for the Photon identification in 0 and 0 ALAS data. Geneva, Mar 0.

32 [0] W. Verkerke and D. Kirkby. he RooFit toolkit for data modeling. 00.