1. W mass and widthEmily Nurse0

2. W mass and widthEmily Nurse1 Overview Standard Model Precision Measurements –Motivation for W mass and width measurements The Tevatron and CDF –W and Z production –W and Z reconstruction at CDF Analysis Strategy and Measurement steps Results and implications

3. W mass and widthEmily Nurse2 Standard Model The Standard Model (SM) describes the Universe’s fundamental building blocks and their interactions. Comparisons of predictions with experimental data have successfully tested the theory to a high precision but some questions remain un-answered. What’s the origin of particle mass? (SM Higgs?) Is the SM the full story? (SUSY?, extra-dimensions?, …??)

4. W mass and widthEmily Nurse3 Discovering new physics Direct Discovery of New Particles Precision Measurements of SM Parameters 80 180 280 Reconstructed Mass (GeV)

5. W mass and widthEmily Nurse4 Testing the SM - W and Z bosons The W and Z bosons were predicted by Glashow, Salam and Weinberg’s electroweak theory in the 1960s discovered by the UA1/UA2 experiments in 1983, with masses (M W and M Z ) consistent with the tree level predictions. Current SM calculations make very accurate predictions of M W and M Z and the widths (  W and  Z ) including higher order radiative corrections (i.e. through remormalisation of SM parameters). LEP experiments measure M Z =91187.6  2.1 MeV (0.002%) and  Z =2495.2  2.3 MeV (0.09%). LEP2 and Tevatron experiments measure M W =80403  29 MeV (0.04%) and  W =2141  41 MeV (1.9%). prior to these results

6. W mass and widthEmily Nurse5 Testing the SM - W mass  r W : radiative corrections dominated by tb and Higgs loops  we can constrain M H by precisely measuring M W and M t known to 0.015% known to 0.0009% M Z known to 0.002% M W known to 0.036% G F is found from muon lifetime measurements and can be predicted in terms of M W (tree level) Write g in terms of  and cos  w =M W / M Z and rearrange:  r W could also have contributions from new particle loops ++ e+e+ e  W+W+ g g

7. W mass and widthEmily Nurse6 Testing the SM - W width Within the SM  W is predicted by summing leptonic and hadronic partial widths: (Note: Most higher order corrections are absorbed in the experimental values of M W and G F.)  W 0 =  (W  e ) is precisely predicted in terms of M W and G F : PDG: J. Phys. G 33, 1 Measuring  W tests this accurate SM prediction (deviations of which suggest non-SM decay modes).  W is an input to the M W measurement:  M W ~  W / 7.  W = 2091  2 MeV predominantly from  M W

8. W mass and widthEmily Nurse7 The Tevatron The Tevatron currently has ~2.5 fb -1 on tape (6-8fb -1 expected by the end of Run II). The Tevatron is a W/Z factory (as well as many other things!) :  ( W  l ) ~ 2700 pb (currently ~7 million created, ~0.9 million to analyse).  ( Z  ll ) ~ 250 pb (currently 0.7 million created, ~40 thousand to analyse). But : precision measurements are hard! We need a “precision level” calibration of our detector to keep systematics low. These analyses are based on 200/350pb -1 of CDF data.

9. W mass and widthEmily Nurse8 W and Z production at the Tevatron The large masses (~100 GeV ) of W and Z bosons gives their decay products large p T. The electron and muon channels are used to measure W properties, due to their clean experimental signature. LEADING ORDER Similar for Z production (decays into two charged leptons) W events: Charged lepton is detected and momentum directly measured. Neutrino cannot be detected! Transverse momentum (p T ) is inferred by a vector sum of the total “transverse energy (Esin  )” in the detector. The “missing E T (E T miss )” is found by constraining the sum to zero  interpreted as the neutrino p T. Z events: Both charged leptons are detected and their momenta measured.

10. W mass and widthEmily Nurse9 W and Z production at the Tevatron Initial state gluon radiation from incoming quarks gives the W a boost in the transverse direction  W p T The recoiling gluons form hadrons that are detected in the calorimeter  Hadronic recoil HIGHER ORDER CORRECTIONS Final state  radiation affects the kinematics of the charged lepton Goes into E T miss = p T measurement!

11. W mass and widthEmily Nurse10 e  Detecting particles at CDF SILICONSILICON DRIFT CHAMBER SOLENOIDSOLENOID EMHADRONIC MUON CHAMBERS Electrons: detected in central trackers (drift chamber provides p measurement) and EM calorimeter (provides energy measurement). Muons: detected in central trackers (drift chamber provides p measurement), calorimeter (MIP signal) and muon chambers. E T miss : Hadronic recoil found by summing the EM and HADRONIC calorimeter energy. TRACKERSCALORIMETERS

12. W mass and widthEmily Nurse11 Analysis strategy: measuring M W and  W Ideal world: M W and  W would be reconstructed from from the invariant mass of the W decay products (Breit-Wigner lineshape of propagator peaks at the mass and has an intrinsic width). Reality: The neutrino is not detected thus the invariant mass cannot be reconstructed. Instead we reconstruct the transverse mass.  -channel: central tracker e-channel: EM calorimeter inferred from missing transverse energy MWMW WW Breit-Wigner:

13. W mass and widthEmily Nurse12 Analysis strategy: measuring M W and  W M W /  W found from M T MC template fits data. Simulate M T distribution with a dedicated fast parameterised MC. Utilise well understood data samples (Z events used extensively) to calibrate detector simulation to high precision - we need an excellent description of the lineshape! -  W fit range: 90 -200 GeV - M W fit range:65 - 90 GeV  W templates M W templates

14. W mass and widthEmily Nurse13 M W vs  W The M W and  W analyses are very similar - with different dominant uncertainties. They are performed independently using 200(350)pb -1 of data for the M W (  W ) analyses. As I describe the the measurement steps I will discuss the method used in the analysis for which the effect is more important: M W =  W =

15. W mass and widthEmily Nurse14 Measurement Steps Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

16. W mass and widthEmily Nurse15 Measurement Steps : 1 Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

17. W mass and widthEmily Nurse16 Generator effects : PDFs Parton Distribution Functions (PDFs) are parameterised functions that describe the momentum distribution of quarks in the (anti)proton. Different PDFs result in different acceptance and spectra: Use CTEQ6M and the CTEQ6 ensemble of 2x20 error PDFs (20 orthogonal parameters varied up and down within their errors).  M W = 11 MeV,  W = 17 MeV

18. W mass and widthEmily Nurse17 Generator effects : QCD/QED corrections Simulate QCD corrections (initial state gluon radiation) using RESBOS [Balazs et.al. PRD56, 5558]: NLO QCD + resummation + non-perturabtive. Constrain non-perturbative parameter using our own Z data : QED bremsstrahlung reduces l  p T Simulated at NLO (one-  ) using Berends&Kleiss [Berends et.al. ZPhys. C27, 155] / WGRAD [Baur et.al. PRD59, 013002]. PHOTOS [Barberio et.al. Comput. Phys. Comm., 66, 115] used to establish systematic due to neglecting NNLO (two-  ) terms.  M W = 3 MeV,  W = 7 MeV  M W (  ) = 12 MeV,  W (  ) = 1 MeV  M W (e) = 11 MeV,  W (e) = 8 MeV

19. W mass and widthEmily Nurse18 Measurement Steps : 2 Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

20. W mass and widthEmily Nurse19 Momentum scale set with di-muon resonance peaks in data, using well known particle masses: J/   ;  1S  Z   Lepton momentum calibration (p T  ) M  (GeV) Data MC Data MC  M W (  ) = 17 MeV,  W (  ) = 17 MeV p scale known to 0.021% 1/ (GeV -1 )

21. W mass and widthEmily Nurse20 Lepton momentum resolution (p T  )  fullMC = (q/p T ) meas - (q/p T ) gen taken from full GEANT MC. Sample this histogram and multiply by a constant parameter:  fastMC = S res  fullMC S res found by tuning to M  in Z   data.  M W (  ) = 3 MeV,  W (  ) = 26 MeV

22. W mass and widthEmily Nurse21 Measurement Steps : 3 Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

23. W mass and widthEmily Nurse22 The electron’s journey through CDF energy leakage “out the back” of the EM calorimeter energy loss in solenoid bremsstrahlung in silicon track momentum measurement in COT energy measurement in EM calorimeter

24. W mass and widthEmily Nurse23 Scale and  found in two independent ways: 1) Fit to M ee peak in Z  ee data using well known Z mass/width. 2) Fit to E/p in W  e data (since p has already been well calibrated.) Electron energy calibration/resolution (p T e ) electron energy measured in EM calorimeter electron momentum measured in central tracker Fundamentally E = p (electron mass is negligible). Photons are emitted from electron (bremsstrahlung) which reduces p. The photons usually end up in the same calorimeter tower as the electron thus E doesn’t decrease. Calorimeter scale: E meas = scale  E true Calorimeter resolution:  (E) / E = 13.5% / √E T  

25. W mass and widthEmily Nurse24 Bremsstrahlung in tracker E p  M W (e) = 30 MeV,  W (e) = 17 MeV scale: resolution: M ee (GeV) E/p Data MC Data MC E scale known to 0.034% Leakage “out the back” of the EM calorimeter  M W (e) = 11 MeV,  W (e) = 31 MeV Electron energy calibration/resolution (p T e )

26. W mass and widthEmily Nurse25 Measurement Steps : 4 Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

27. W mass and widthEmily Nurse26 Hadronic Recoil: U To get p T we need a good model of the total energy in W events. U=(U x, U y )=  towers Esin  ( cos , sin  ) Vector sum over calorimeter towers Excluding those surrounding lepton Recoil has 3 components: p T = E T miss = -(U + p T lep ) (3) Underlying energy Multiple interactions and remnants from collision. (2) Bremsstrahlung Photons emitted by lepton that do not end up in the excluded region (1) QCD Gluons recoiling off the boson

28. W mass and widthEmily Nurse27 Hadronic Recoil: U U1U1 U2U2 Accurate predictions of U is difficult (and slow) from first principles. U simulated with ad-hoc parameterised model, tuned on Z  ll data. U split into components parallel (U 1 ) and perpendicular (U 2 ) to Z p T 7 parameter model describes the response and resolution in the U 1 and U 2 directions as a function of the Z p T. Systematic comes from parameter uncertainties (limited Z stats). Z  ee responseresolution Data MC  M W (  ) = 12 MeV  W (  ) = 49 MeV  M W (e) = 14 MeV  W (e) = 54 MeV

29. W mass and widthEmily Nurse28 Measurement Steps : 5 Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

30. W mass and widthEmily Nurse29 multijet muon channel only: Jet fakes/contains a lepton E T miss from misconstruction electron and muon channel: Backgrounds Z  ll One lepton lost E T miss from missing lepton WW  decays to e/  intrinsic E T miss Decay In-Flight x x x x x x x x K,  fake high-p T track Kaon/pion decays “In-Flight” to a . Kink in track gives high-p T measurement. E T miss from mis-measured track p T. Need the m T distributions and the normalisations!

31. W mass and widthEmily Nurse30 Dominant background is Z  (it’s easy to lose a muon leg!) - but we can estimate this background very reliably (using full MC). Decay In-Flight (DIF) has large m T tails: problematic for the width! Backgrounds: Muon channel final cut value /NDF The handles we have on DIF are track quality  2 track and impact parameter. Fractional background found from a template fit to the  2 track distribution. Z  provides the signal template High impact parameter cuts provide the DIF template  M W (  ) = 9 MeV,  W (  ) = 33 MeV

32. W mass and widthEmily Nurse31 Backgrounds: Electron channel final cut value Multijet has large m T tails: problematic for the width!  M W (e) = 8 MeV,  W (e) = 32 MeV Fractional multijet background found from a template fit to the E T miss distribution. “Anti-electron” sample provides the mulitjet template

33. W mass and widthEmily Nurse32 Measurement Steps Muon momentum measurement: Electron energy measurement: p T = E T miss = -(U + p T lep ) Hadronic recoil measurement: Generator effects: PDFs, QCD, QED corrections. Backgrounds:

34. W mass and widthEmily Nurse33 Results: M W fits Data MC Data MC Also includes fits to p T l and p T : M W = 80413  48 (stat + syst) MeV M T (  ) (GeV) M T (e ) (GeV)

35. W mass and widthEmily Nurse34 M W systematic uncertainties

36. W mass and widthEmily Nurse35 M W : world average Central value increases by 6 MeV: 80392  80398 MeV Uncertainty reduced by 15%: 29  25 MeV World’s most precise single measurement!

37. W mass and widthEmily Nurse36 M W : Implications Previous World Data : Including New M W : Direct search from LEP II : m H > 114.4 GeV @ 95% C.L. Including New M t :

38. W mass and widthEmily Nurse37 Results:  W fits  W = 2032  71 (stat + syst) MeV

39. W mass and widthEmily Nurse38  W systematic uncertainties

40. W mass and widthEmily Nurse39  W : world average Central value decreases by 44 MeV: 2139  2095 MeV Uncertainty reduced by 22%: 60  47 MeV World’s most precise single measurement!

41. W mass and widthEmily Nurse40 Indirect Width Measurement R = WW ZZ  (Z  ll)  (W  l )  (W)  (Z) XX R exp =   BR (W  l )   BR (Z  ll) Precision LEP Measurements SM Calculation NNLO Calculation CDF Run II INDIRECT width : 2092 ± 42 MeV PRL 94, 091803 CDF Run II DIRECT width : 2032 ± 71 MeV preliminary

42. W mass and widthEmily Nurse41 Projections 20 MeV syst limit 2.5fb -1 : ~25 MeV ~35 MeV Naïve statistical scaling, 20 MeV syst. limit

43. W mass and widthEmily Nurse42 Summary Two new measurements from CDF: –W mass : 80413 ± 48 MeV (stat + syst) –W width : 2032 ± 71 MeV (stat + syst) Both are the world’s most precise single measurements!! Getting to this point requires a “precision” level calibration of the detector. Together with direct Higgs searches we will continue to squeeze the phase space available to the SM Higgs. Analyses utilised 200 pb -1 and 350 pb -1 respectively, both CDF and DØ already have ~2.5 fb -1 on tape. Working on improved mass/width measurements to further test the SM and constrain m H

44. W mass and widthEmily Nurse43 Back-up slides…

45. W mass and widthEmily Nurse44 W mass  e e  GF (fermi-coupling constant) can be predicted in terms of M W W width: W’ analysis excludes W’ < 788 GeV

46. W mass and widthEmily Nurse45 Generator effects : PDFs 9 - highx valence quarks. ∆X W = 0.5* √ ( ∑ i ( [∆  i up -∆  i down ) 2 ))/1.6

47. W mass and widthEmily Nurse46 Generator effects : QCD corrections RESBOS: NLO QCD + resummation + non-perturbative. Collins-Soper-Sterman (CSS) resummation formalism. Sums LL terms + sub-logs Brock-Landry-Nadolsky-Yuan (BLNY) form: exp [-g 1 - g 2 ln(Q/2Q 0 ) - g 1 g 3 ln(100x 1 x 2 )]b 2 g 1 =0.21  0.01; g 1 =0.68 +0.01 -0.02 ; g 3 =-0.6 +0.05 -0.04 ; From fits to R209, E288, E605 fixed target Drell-Yan data (5< shat <18 GeV) + CDF RunI

48. W mass and widthEmily Nurse47 Simulated effects Bremsstrahlung in si (Bethe-Heitler equation) –Migdal suppression Conversions (Bethe-Heitler equation) Compton scattering (for low energy photons: scattering off e ~ conversions) Ionisation energy loss Energy loss in coil Leakge into HAD calorimeter Acceptance Ionisation energy loss Multiple scattering Acceptance Electrons Muons

49. W mass and widthEmily Nurse48 log 10 (incident electron energy) visible EM energy fraction Simulating Electrons (  ) : CAL superconducting coil electromagnetic cal. hadronic calorimeter Soft electrons suffer absorption in the coil Energetic electrons leak into the hadronic compartment

50. W mass and widthEmily Nurse49 W  e Hadronic Recoil: U (p T ) U || U U U split into components parallel (U || ) and perpendicular (U  ) to charged lepton. Many distributions used to cross check the model in W  l data: Data MC W  e

51. W mass and widthEmily Nurse50 Electron m T signed  plot

52. W mass and widthEmily Nurse51 p T and E T miss fits

53. W mass and widthEmily Nurse52 p T and E T miss fits

54. W mass and widthEmily Nurse53 MSSM parameter range Decoupling limit with SUSY masses of order 2 TeV. Moderate splitting between stop and sbottom doublets (m 2 /m 2 <2.5)