1. Chris Hays Duke University TEV4LHC Workshop Fermilab 2004 W Mass Measurement at the Tevatron CDF DØDØ

2. Past, Present, and Future C. Hays, Duke University, TEV4LHC Precision of direct measurements: x x x x 2004: LEP 42 MeV Tevatron 59 MeV 1983: UA1 5 GeV 1989: UA1 2.9 GeV 1990: UA2 900 MeV 1995: CDF 180 MeV 2000: D Ø 91 MeV xx W mass now known to better than 5 parts in 10,000 Looking forward: * Tevatron Run 2 has quadrupled Run 1 CDF, D Ø data sets * CDF has analyzed first 200 pb -1 of data and determined uncertainties CDF: 79 MeV D Ø : 84 MeV x x x 2011: Tevatron <15 MeV LHC <15 MeV 2004: CDF 76 MeV 2005: CDF/D Ø <59 MeV 2006: CDF/D Ø <34 MeV 2008: CDF/D Ø <20 MeV 2010: ATLAS/CMS <20 MeV x x ~1 fb - 1 ~0.4 fb - 1 ~0.2 fb - 1 (  M W =34 MeV) ~4 fb - 1 x ~10 fb - 1

3. W Mass Fit Distributions Transverse mass * m T 2 = 2p T E T (1-cos(  )) * m ~ 2 p T + u || * Low sensitivity to p T W * Recoil modelling crucial Lepton p T * m ~ 2 p T * Insensitive to recoil * p T W modelling crucial u^u^ u || (u)(u) E T = -(p T + u) mTmT pTpT CDF RUN II PRELIMINARY CDF RUN II PRELIMINARY C. Hays, Duke University, TEV4LHC

4. CDF Run 2 Uncertainties Scale and resolution:  :  W = + 30 MeV e:  W = + 70 MeV Scale and resolution: ,e:  W = + 50 MeV C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY Tower removal:  :  W = + 10 MeV e:  W = + 20 MeV Production and decay model: ,e:  W = + 30 MeV Backgrounds: ,e:  W = + 20 MeV Statistics:  :  W = + 50 MeV e:  W = + 45 MeV Transverse mass fit

5. Production and Decay Model Uncertainties C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY l + Parton Distribution FunctionsQED Radiative Corrections e Uncertainty determined from CTEQ eigenvectors + MRST e W charge asymmetry will reduce uncertainty  W ~ 5 MeV with 4 fb -1 v LHC: No charge asymmetry v Constrain PDFs with lepton h distributions from W and Z  W ~ 10 MeV achievable e Single-photon FSR modelled e 2-photon FSR needs to be added  W ~ 5 MeV with 4 fb -1 (also at LHC)

6. Production and Decay Model Uncertainties C. Hays, Duke University, TEV4LHC p T W Model e Uncertainties determined from RESBOS parameters g 1, g 2, g 3 e Parameters constrained by Run 1 Z p T distribution p T fit:  W = + 27 MeV m T fit:  W = + 13 MeV g 2 = 0.68 + 0.12 GeV 2 g 3 = -0.60 + 0.30  W ~ 5 MeV with 4 fb -1 (p T fit: 10 MeV) v LHC: Large Z statistics  W ~ 5 MeV achievable (also for p T fit) CDF RUN II PRELIMINARY WW e 70 MeV uncertainty from world average of direct measurements  W ~ 5 MeV with 4 fb -1 (also at LHC)

7. CDF Run 2 Muon Momentum Calibration Set momentum scale using J/  and upsilon decays to muons  W = + 15 MeV CDF RUN II PRELIMINARY CDF RUN II PRELIMINARY (GeV -1 )  p/p CDF RUN II PRELIMINARY e Uncertainty from difference in scales: C. Hays, Duke University, TEV4LHC J/  Upsilon  W = + 20 MeV e Post-alignment-correction uncertainty: e Resolution uncertainty (from Z decays):  W = + 12 MeV Z  W ~ 5 MeV with 4 fb -1 (also at LHC)

8. CDF Run 2 Electron Calibration Tune upstream passive material using tail of E/p distribution Set energy scale using E/p peak  W = +55 MeV  W = +35 MeV Correct for non-linearity  W = +25 MeV C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY CDF RUN II PRELIMINARY CDF RUN II PRELIMINARY  W ~ 15 MeV with 4 fb -1 (also at LHC) e Resolution uncertainty (from Z decays):  W = + 12 MeV

9. CDF Run 2 Recoil Measurement Estimate removed recoil energy using towers separated in  Measure hadronic recoil by summing over all calorimeter towers * Remove towers with energy deposited by lepton C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY  W = +10 MeV e:  W = + 20 MeV Removed muon towers 0.1 x 0.25  438 1243 92 9 MeV  W ~ 5 MeV with 4 fb -1 (also at LHC)

10. CDF Run 2 Recoil Model * Parametrize hadronic response: R = u meas /u true * Resolution model incorporates terms from underlying event and jet resolution Resolution at low p T (Z) dominated by underlying event Resolution at high p T (Z) dominated by jet resolution Tune parameters using Z  events Model underlying event with minimum-bias data (inelastic collisions)  W = +42 MeV u true given by p T (Z)  W = +20 MeV    u C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY  W ~ 10 MeV with 4 fb -1 (also at LHC)

11. CDF Run 2 Backgrounds C. Hays, Duke University, TEV4LHC Electrons Muons  W = + 20 MeV CDF RUN II PRELIMINARY Muons  W ~ 5 MeV with 4 fb -1 (also at LHC)

12. Milestones C. Hays, Duke University, TEV4LHC CDF RUN II PRELIMINARY * Improve understanding of passive material (E/p tail) * Improve COT alignment * Understand W/Z differences in recoil model * W p T constrained with Z p T * Detailed understanding of upsilon/Z systematics * PDF constrained with W charge asymmetry * Include 2-photon FSR

13. Ratio Method Can also measure mass by measuring Z transverse mass for each lepton Lower Z statistics (not an issue at LHC) Are there additional systematics? Potentially removes energy calibration uncertainty C. Hays, Duke University, TEV4LHC W transverse mass measurement gives ratio of W to Z masses p T W uncertainty could be larger than m T measurement D Ø Run 1 Experience (82 pb -1 )

14. Summary Now have Run 2 experience (first milestone hit) Recoil differences between W's and Z's Electron energy calibration (passive material) Should be soluble (still early) Modelling 2-photon FSR (in progress) Experimental issues (CDF) Theoretical issues Update PDFs (need input from W charge asymmetry measurement) C. Hays, Duke University, TEV4LHC Update p T W parameters (need input from Z p T measurement) Preliminary Run 2 results available Potential Improvements at the LHC Can large Z statistics get recoil model below 10 MeV uncertainty? Can PDF uncertainty get below 10 MeV? Most systematics shrinking with increasing data