The Z lineshape using data from ALEPH

Transcription

1 The Z lineshape using data from ALEPH

2 Standard Model Building blocks of matter Leptons and Quarks Fundamental interactions Coupling between matter ( ν e ) e ν µ µ ( ) ν τ τ ( ) Interaction Carrier ( u ) d ( c ) s ( t ) b elektromagnetic weak strong gravitation Photon (γ) W and Z Gluon (g) Graviton (G) Fermions, Spin 1/2 Bosons, Spin 1 (2) We will focus on Z couplings to fermions 2

3 Standard Model Building blocks of matter Leptons and Quarks Fundamental interactions Coupling between matter ( ν e ) e ν µ µ ( ) ν τ τ ( ) Interaction Carrier ( u ) d ( c ) s ( t ) b elektromagnetic weak strong gravitation Photon (γ) W and Z Gluon (g) Graviton (G) Fermions, Spin 1/2 Bosons, Spin 1 (2) We will focus on Z couplings to fermions 2

4 The e + e - cross-section fermion pair production: f=e,µ,τ,u,d,s,c,b,ν e,ν µ,ν τ e + f e - Z/γ* f background e + e +! " f! " f e - e - 3

5 The Z resonance 4

6 The Z resonance the total Z with: 4

7 Radiative corrections e + γ f e - Z/ γ * f Initial state photon radiation: enhances cross section above the resonance and reduces it below Energy [GeV] Born cross section [nb] : no QED corrections for initial and final state radiation Total cross section [nb] : with initial and final state radiation

8 Radiative corrections e + γ f e - Z/ γ * f Initial state photon radiation: enhances cross section above the resonance and reduces it below Energy [GeV] Born cross section [nb] : no QED corrections for initial and final state radiation Total cross section [nb] : with initial and final state radiation

9 Radiative corrections e + γ f e - Z/ γ * f true Breit-Wigner Initial state photon radiation: enhances cross section above the resonance and reduces it below Energy [GeV] Born cross section [nb] : no QED corrections for initial and final state radiation Total cross section [nb] : with initial and final state radiation

10 Radiative corrections e + γ f e - Z/ γ * f true Breit-Wigner Initial state photon radiation: enhances cross section above the resonance and reduces it below We will apply correction factors Energy [GeV] Born cross section [nb] : no QED corrections for initial and final state radiation Total cross section [nb] : with initial and final state radiation

11 Cross-section measurement The basic formula to extract cross-section from a selected signal sample is N sel = σ(signal) * L int * ε + N bckg 6

12 Cross-section measurement The basic formula to extract cross-section from a selected signal sample is N sel = σ(signal) * L int * ε + N bckg cross section we want to measure 6

13 Cross-section measurement The basic formula to extract cross-section from a selected signal sample is N sel = σ(signal) * L int * ε + N bckg cross section we want to measure integrated luminosity 6

14 Cross-section measurement The basic formula to extract cross-section from a selected signal sample is N sel = σ(signal) * L int * ε + N bckg cross section we want to measure selection efficiency integrated luminosity 6

15 Luminosity Measured using Bhabha scattering e + e + γ* Energy [GeV] Events Integrated Luminosity [nb] e - e - Mainly a QED process: can be calculated with very good precision

16 Signal selection cuts 8

17 Signal selection cuts Try to minimize error on cross section measurement 8

18 Signal selection cuts Try to minimize error on cross section measurement 8

19 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error 8

20 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error too loose cut high efficiency, small purity large number of events (N sel ), but also large background most likely large systematic uncertainty (from limited theoretical knowledge of the background distributions) 8

21 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error too loose cut high efficiency, small purity large number of events (N sel ), but also large background most likely large systematic uncertainty (from limited theoretical knowledge of the background distributions) 8

22 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error too loose cut high efficiency, small purity large number of events (N sel ), but also large background most likely large systematic uncertainty (from limited theoretical knowledge of the background distributions) The efficiency must be estimated using MC events 8

23 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error too loose cut high efficiency, small purity large number of events (N sel ), but also large background most likely large systematic uncertainty (from limited theoretical knowledge of the background distributions) The efficiency must be estimated using MC events 8

24 Signal selection cuts Try to minimize error on cross section measurement too strong cut low efficiency, high purity small number of events (N sel ) large statistical error too loose cut high efficiency, small purity large number of events (N sel ), but also large background most likely large systematic uncertainty (from limited theoretical knowledge of the background distributions) The efficiency must be estimated using MC events 8

25 Background Main background process are Z decays to electrons, muons and taus two clearly identified muons and electrons of high energy few tracks with low total energy in case of taus (neutrino from tau decay is not detected) To design selection, scan the displays of Z decay events : 9

26 background e + e + Two-photon scattering: γ γ f f Characteristics: I. low multiplicities II. low visible energy (a lot lost into the beam pipe) III. boosted along the beam direction e - e - Cross-sections: had: nb leptons: nb 10

27 A simple analysis: measure BR(Z µ + µ ) at LEP Measure: BR(Z µ + µ ) = Number ofµ+ µ events Total number of events Take a sample of events, and count those with a µ + µ final state. Two tracks, approximately back-to-back with the expected p Empirically, other kinds of events have more tracks Right number of muon hits in outer layers Muons are very penetrating, travel through entire detector Expected energy in calorimeter Electrons will deposit most of their energy early in the calorimeter; muons leave little 11

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44 Summary so far We have a result: BR(Z µ + µ ) = 2/15 Let s have now a closer look... 28

45 Statistical error We saw 2 events, but it could easily have been 1 or 3 Those fluctuations go like the square-root of the number of events (for large number of events...): BR(Z µ + µ ) = N µµ N total ± Nµµ N total To reduce that uncertainty needs many events Can not process them by eye if thousands or millions of events Need to select events using some algorithm based on measured quantities like p, the number of charged tracks or the number of hits in the muon chambers... (more later on) 29

46 What if you only see 50% of the µ + µ events? Efficiency because of detector imperfections, poor understanding, etc... where ε is the efficiency of our selection, say We need therefore to correct our result: BR(Z µ + µ ) = N seen ɛn total 30

47 Are all µ + µ tagged events really Z µ + µ? Background Say N not µ+µ is the background to our µ + µ sample, then BR(Z µ + µ ) = N seen N not µµ ɛn total 31

48 Z τ + τ µ + νµ ν 32

49 Uncertainties σ BR(Z µ+ µ ) = Nseen ɛn total ɛ ɛ N seen ɛn total N not µµ ɛn total Statistical uncertainty Systematic uncertainties Do not change with more data... 33

50 Further uncertainties This is not the full story... What about the denominator? How many Z events are lost? It would be probably better to measure a ratio like BR(Z µ + µ ) BR(Z qˆq) = Number of µ + µ events Total number of hadronic events 34

51 Esercizio Oggi e settimana prossima 35

52 Esercizio Scan events and classify them as being hadronic, electrons, muons, taus cross-check your selection by estimating the partial Z widths Oggi e settimana prossima 35

53 Esercizio Scan events and classify them as being hadronic, electrons, muons, taus cross-check your selection by estimating the partial Z widths Study selection cuts and measure σ had (s) Oggi e settimana prossima 35

54 Esercizio Scan events and classify them as being hadronic, electrons, muons, taus cross-check your selection by estimating the partial Z widths Study selection cuts and measure σ had (s) Oggi e settimana prossima Fit the line shape, and determine the Z- parameters M Z, Γ Z, σ peak 35

55 Esercizio Scan events and classify them as being hadronic, electrons, muons, taus cross-check your selection by estimating the partial Z widths Study selection cuts and measure σ had (s) Fit the line shape, and determine the Z- parameters M Z, Γ Z, σ peak Oggi e settimana prossima Measure Γ µ /Γ had, Γ τ /Γ had 35

56 Esercizio Scan events and classify them as being hadronic, electrons, muons, taus cross-check your selection by estimating the partial Z widths Study selection cuts and measure σ had (s) Fit the line shape, and determine the Z- parameters M Z, Γ Z, σ peak Oggi e settimana prossima Measure Γ µ /Γ had, Γ τ /Γ had Determine number of light neutrinos N ν 35

57 Data are available in ~v_ciulli/zpeak Aleph Data Here is a short description of variables (ask for more informations): clas Clas bit : preclassification of event. Example: Clas 16 = hadronic event cthr Cosine of the thrust axis polar angle (angle from the beam (+z) to the thrust axis), [-1,1]. d0 minimum distance of track to interaction point in plane transverse to beam axis (cm). Vector of length nch (number of charged tracks) ech Energy sum (GeV) of all charged tracks (no selection) eec Energy sum (GeV) of all objects in ECAL (no selection). eecal energy of the ECAL object (GeV). vector of length nec (number of ECAL objects) egood sum of energy (GeV) of good charged tracks, see variable ngood 36

58 Aleph Data ehc Energy sum (GeV) of all objects in HCAL (no selection). ehcal energy of the HCAL object (GeV). vector of length nhc (number of HCAL objects) elep evt nch centre-of-mass energy (GeV) Event number Number of all charged tracks (no selection) nec Number of all objects in ECAL (no selection) nefl Number of energy flow objects ngood Number of good charged tracks. according to standard ALEPH selection: Ntpc>4, abs (costheta)<0.95, d0<2., z0<20. nhc Number of all objects in HCAL (no selection) 37

59 Aleph Data nhits number of hits of the track in the tracking system (TPC in ALEPH). Vector of length nch (number of charged tracks) njet number of jets found [0,10]. Jets found by Durham E-scheme, Ycut=0.04; jets are found with "good" charged tracks (see standard ALEPH definition in description of variable ngood) nplanes number of hits in the last planes of HCAL (for muon identification) [0,11] Vector of length nch (number of charged tracks) pcha pcha(3): Track momentum (px,py,pz) (GeV/c). Vector of length nch*3 (number of charged tracks) Example: pcha[1][2] gives the third (z) component of the second charged track of each event (note the C notation of vector components). pecal Phi of the ECAL object (radians) [0, 2], vector of length nec (number of ECAL objects) pefl pefl(4): Four momentum (px,py,pz,e) (GeV/c). Vector of length nefl*4 (number of energy flow objects) phcal Phi of the HCAL object (radians) [0, 2], vector of length nhc (number of ECAL objects) 38

60 Aleph Data pjet pjet(4): jet four momentum (px,py,pz,e) (GeV). vector of length njet*4 qcha Charge of the track [-1 or 1], vector of length nch*2 (number of charged tracks) run Run number. The runs are selected to be good runs where all the subdetecteors of the apparatus work well. tecal Theta of the ECAL object (radians) [0,1], vector of length nec (number of ECAL objects) thcal Theta of the HCAL object (radians) [0,1], vector of length nhc (number of HCAL objects) thruv Thrustvalue typeefl z0 Type of energy flow object [0-9] 0-2:charged track, 0:hadron, 1:electron, 2: muon, 3:electromagnetic object (ECAL),photon, 4:neutral hadron (HCAL), 6:LCAL, 7:SICAL (luminometers) Vector of length nefl (number of energy flow objects) minimum distance of track to interaction point along beam axis (cm). Vector of length nch (number of charged tracks) 39