Find a signal. Ldt. N obs (p T, φ, η, z) = B + σa. = B(p T, φ, η,z,l)+ σ(p 0 T, φ 0, η 0 ) L(t, z) A(p 0 T, φ 0, η 0,z 0 )

Transcription

1 Find a signal N obs (p T, φ, η, z) = B + σa Ldt = B(p T, φ, η,z,l)+ σ(p 0 T, φ 0, η 0 ) L(t, z) A(p 0 T, φ 0, η 0,z 0 ) R(p 0 T, φ 0, η 0,z 0 ; p T, φ, η,z,l) (p T, φ, η,z,l)dp 0 T dφ 0 dη 0 dt σ(x α...) is the true cross section as a function of true variables X a... L(t, z) is the luminosity as a function of time. A(X α..) is the geometrical Acceptance as a function of true variables. R(X α..., L; X a...) is the Resolution function which smears true X α... to detected X a... (X a..., L) is the probability that a particle is actually detected by a physical detector. B(X a..., L) is the background

2 Look for Z s In our detector 2 CTEQ2011 Schellman Expect 2 electrons PT ~ MZ/2 Calorimeter energy Shower looks like an electron Track momentum Tracks come from the same point

3 Z ee 3 This Z0 has high transverse momentum! e + e - 10/30/2009 Louisville

4 4 10/30/2009 Louisville

5 What do we expect 5 dσ(gg gg) d cos θ 1 sin 4 θ 2 The leptons are more isotropic than the backgrounds CTEQ2011 Schellman

6 Jacobian peak dσ dp T p T,GeV CTEQ2011 Schellman

7 Now let s do some data analysis 7 I happen to have a di-electron root file lying around. CTEQ2011 Schellman

8 Invariant mass of raw electron pairs 8 z_m {z_m < 200} 100!10 3 htemp Entries Mean RMS z_m CTEQ2011 Schellman Mass, GeV

9 After quality cuts 9 Mass in GeV/c^2 PK mass_pk Entries Mean RMS CTEQ2011 Schellman Mass, GeV

10 Phi 10 phi in radians PK l_phi_pk Entries Mean RMS φ, radians CTEQ2011 Schellman

11 Detector η 11 Detector eta PK l_det_eta_pk Entries Mean RMS η CTEQ2011 Schellman

12 Detector and physics coordinates 12 Detector is designed around z=0 The beam is actually cm long!"# 0 z CTEQ2011 Schellman

13 PT of leptons 13 Momentum of Lepton in GeV/c PK l_pt_pk Entries Mean RMS p T, GeV CTEQ2011 Schellman

14 Z position of vertex in cm 14 l_z0 PK 5000 l_z0_pk Entries Mean RMS z 0, cm CTEQ2011 Schellman

15 The signal

16 Luminosity 16 N obs (p T, φ, η,z) = B + σa Ldt = B(p T, φ, η,z,l)+ σ(p 0 T, φ 0, η 0 ) L(t, z) A(p 0 T, φ 0, η 0,z 0 ) R(p 0 T, φ 0, η 0,z 0 ; p T, φ, η,z,l) (p T, φ, η,z,l)dp 0 T dφ 0 dη 0 dt σ(x α...) is the true cross section as a function of true variables X a... L(t, z) is the luminosity as a function of time. A(X α..) is the geometrical Acceptance as a function of true variables. R(X α..., L; X a...) is the Resolution function which smears true X α... to detected X a... (X a..., L) is the probability that a particle is actually detected by a physical detector. B(X a..., L) is the background CTEQ2011 Schellman 0-2

17 Luminosity 17 Luminosity is a measure of how often protons/antiprotons get close enough to interact f= beam crossing frequency 396 nsec n= protons/bunch s = transverse beam size = m L ~ crossings/cm 2 /sec CTEQ2011 Schellman

18 Typical Cross Sections Total proton/antiproton cross section is 7x10-30 m 2 Unit of Barns (b) = m 2 Cross Section for top production: This is around 1/10 10 of total Run II L ~ crossings/cm 2 /sec N/sec ~ σl = 5x10-4 /sec N/sec ~ σl = 7x10 6 /sec > 3 interactions per beam crossing! A couple were created/hour but we only saw a small % CTEQ2011 Schellman 18

19 Luminosity 19 Rate = L σ int " A" pbars" protons" P int = N prot σ int /A" L = f rev N pbar N prot /A" CTEQ2011

20 Not easy to do this 20 Hard to measure currents accurately the beam density depends on the intrinsic beam lengths and widths and on the local beam optics. L = 2 f rev " ρ 1 ρ 2 dx dy dz d(ct)" ρ(x,y,z,ct) = " N 1" 2π σ x " 1 " 2π σ y " exp[- (x+δx/2) 2 / 2 σ x2 ]" exp[- (y+δy/2) 2 / 2σ y2 ]" 1 " 2π σ z " exp[ -(z+ct-ct 0 ) 2 / 2σ z2 ]" CTEQ2011

21 You can measure the beam spot size as a function of distance along the beam to get σ x (z), σ y (z) 21 CTEQ2011 Also need estimates of beam current σ z can be estimated from beam timing or N(z) Estimates are good to ~10% at the Tevatron. σ x (z), cm The beam position and size vary with time as the beam heats up and cools down z, cm

22 L(z) distribution for beam collisions 22 z(vtx), cm CTEQ2011

23 Alternate method 23 Measure the total inelastic proton antiproton cross section in a special run. Count inelastic collisions as you run your regular experiment. Use those to get an estimate of your integrated luminosity. CTEQ2011

24 D0 Luminosity System 24 Count fraction, P(0), of beam crossings without inelastic interactions.. CTEQ2011

25 Method 25 Measure µ, the average number of interactions/crossing Apply acceptance and efficiency corrections and then compare to the inelastic pbar p total cross section to get the luminosity integrated over the 396 nsec crossing time. Typical µ are 1-10 at the Tevatron CTEQ2011

26 Interactions/crossing 26 Typical running at the Tevatron CTEQ2011

27 Luminosity errors 27 The luminosity measurement has 3 sources of error The inelastic cross section is only known to 3-4% The luminosity detector is not perfect 3-4% Bookkeeping you have to match the luminosity data stream up with your real data. What happens if you lose a data tape? Flag data as bad? We track this by matching luminosity blocks, 1 minute periods of data. CTEQ2011 Schellman

28 So far we 28 Have a signal Have a normalization How do we find backgrounds? How do we correct for detector efficiency and resolution? How do we correct for Acceptance? CTEQ2011 Schellman

29 Estimating backgrounds Simulate and subtract Requires good modeling Hard to normalize absolutely Simulate and fit Template method Vary cuts matrix method

30 Simulated backgrounds Muon channel

31 Background from template fit Do this for Z+γ signal Neural network discriminant for EM vs jet Relative probability γ MC Zee data Zee MC jet MC ann5

32 Vary cuts matrix method Vary cuts N loose = loose N e + f loose N QCD N tight = tight N e + f tight N QCD is efficiency for signal %. f is probability to create a fake % N e f tightn loose f loose N tight loose f tight tight f loose

33 Efficiency 33 N obs (p T, φ, η, z) = B + σa Ldt = B(p T, φ, η,z,l)+ σ(p 0 T, φ 0, η 0 ) L(t, z) A(p 0 T, φ 0, η 0,z 0 ) R(p 0 T, φ 0, η 0,z 0 ; p T, φ, η,z,l) (p T, φ, η, z, L)dp 0 T dφ 0 dη 0 dt σ(x α...) is the true cross section as a function of true variables X a... L(t, z) is the luminosity as a function of time. A(X α..) is the geometrical Acceptance as a function of true variables. R(X α..., L; X a...) is the Resolution function which smears true X α... to detected X a... (X a..., L)is the probability that a particle is actually detected by a physical detector. B(X a..., L) is the background CTEQ2011 Schellman

34 Efficiency First pass Define an acceptance region where you would expect your detector to work (say η <3, p T > 10 GeV) Take a particle level MC like pythia Reweight kinematics to reflect best knowledge Trace particles through detector Overlay noise and interactions from other events Count how often you reconstruct the particle

35 The raw simulation isn t good enough 35 Use scale factors Find two ways of measuring something Compare the two in data and in simulation Correct by the ratio (p T,z)= (P T ) data/t data (P T ) sim /T sim sim (p T,z) CTEQ2011 Schellman

36 Tag and probe 36 CTEQ2011 Schellman TAG PROBE Find a really good electron (TAG) Find a track which might be from a Z decay (PROBE) Did you find a shower Do the same for a shower (PROBE) that might have a track

37 ZVTX 37 η CTEQ2011 Schellman

38 Typical electron efficiencies Efficiency versus Instantaneous Luminosity Efficiency top_loose, P(χ^2) > 0. top_loose, P(χ^2) > 0.01 top_loose, P(χ^2) > Instantaneous Luminosity / tick

39 Resolutions Step 1 Simulate Step 2 Cry in frustration Step 3 use the data Tune to the Z peak width or Compare energy of back to back jets

40 Check the tuned full detector simulation 40 Leading Muon p for Z/γ* µµ Data Entries: T Matrix elements (MC@NLO,ALPGEN,.) 10 4 Parton showering PYTHIA 3 10 HERWIG Detector 10 2 simulation GEANT 3 and 4 10 Overlay additional interactions Data tuning via scale factor weights 1 MC Entries: e+06 K-S test: e p [GeV] T CTEQ2011 Schellman

41 Z vtx check 41 Z of the vertex for Z/γ* µµ Data Entries: MC Entries: e+06 K-S test: e z vxt [cm] CTEQ2011 Schellman

42 Curvature check 42 Trailing Muon Curvature for Z/γ* µµ Data Entries: MC Entries: e+06 K-S test: q/p T CTEQ2011 Schellman

43 Ok, looks like we understand our efficiencies and resolutions pretty well in our simulation Correct data for backgrounds and efficiency Now on to unfolding the resolution effects

44 Unfolding the resolution effects N obs (p T, φ, η, z) = B + σa Ldt = B(p T, φ, η,z,l)+ σ(p 0 T, φ 0, η 0 ) L(t, z) A(p 0 T, φ 0, η 0,z 0 ) R(p 0 T, φ 0, η 0, z 0 ; p T, φ, η, z, L) (p T, φ, η, z, L)dp 0 T dφ 0 dη 0 dt σ(x α...) is the true cross section as a function of true variables X a... L(t, z) is the luminosity as a function of time. A(X α..) is the geometrical Acceptance as a function of true variables. R(X α..., L; X a...) is the Resolution function which smears true X α... to detected X a... (X a..., L)is the probability that a particle is actually detected by a physical detector. B(X a..., L) is the background

45 Resolution Smearing

46 Unfolding method 1 - matrix Invert the resolution matrix N a = B a + a R aα A α σ α Ldt Invert σ α = 1 A α R 1 αa (N a B a ) a Common to regularize the matrix Improved stability Bias towards smoothing the function Ldt

47 Smearing Matrix R(X α ->X a )

48 Unfolding method 2 - Ansatz Convolute a trial unsmeared function with the resolution as a function of (pt, η) Fit this convoluted smeared function to your data Correct data by the ratio of the unsmeared to smeared ansatz function. Smeared(X a ) R(X α X a )=δ αa Unsmeared(X α ) This works if a simple functional form can fit your data well and the resolution function is well understood.

49 Ansatz fit R(X α X a )=δ αa Smeared(X a ) Unsmeared(X α ) dσ/de T dη (fb/gev) Illustration of Unfolding in 0 η < 0.5 chisq /ndf = 1.13 Observed Data Unfolded Data Smeared hypothesis Hypothesis E T (GeV)

50 Now for the final step: Acceptance Correct from the region we cover to the rest of phase space Why do this instead of including in the efficiency? This correction is big factor of 3 for Z production ε 40%, Α 30% Only depends on generator level quantities Can use the best NNLO simulations

51 D0 1 fb -1 sample 51 63,000 Z 0 CTEQ2011

52 Z Rapidity raw and generated 52 γ* µµ µ Data Entries: MC Entries: e Data MC Z y rapidity CTEQ2011

53 We actually define acceptance as η e < 1 or 1.5 < η e <2.4 and p T > 25 GeV 53 Cut cross section in electron rapidity and pt electron rapidity CTEQ2011

54 Fully corrected normalized distributions

55 55 CTEQ2011

56 Theory 56 Parton density functions Hard cross section Higher order QCD is important CTEQ2011 gq Zq, qq Zg etc. Cross section*b(z ee) LO ~ 180 pb NLO ~ 250 pb NNLO ~ 260 pb

57 Z ee Errors 57 Statistical 0.62% Preselection efficiency 0.85% Radiative corrections <0.5% ID eff stat error 0.4% Tag-probe bias 0.3% Noise corrections 0.22% Vertex z 0.6% Cut variations 1.5% Total systematic error 2.0% PDF error on sigma(tot) Luminosity +1.3% -1.7% 6.1% CTEQ2011

58 More fun Radiative corrections Calibration Jet definitions B-tagging My list of things to check is around 80 items long