1. W Mass From LEP Fermilab Wine and Cheese Seminar Fermilab Wine and Cheese Seminar 6th October, 2006 Ambreesh Gupta, University of Chicago

2. Ambreesh GuptaFermilab Wine & Cheese2 Outline 1. Introduction - W Boson in the Standard Model of Particle Physics 2. W mass Measurement - Identifying and reconstructing W’s. - Mass extraction techniques used by LEP experiments 3. Systematic Uncertainties on W mass measurement 5. Summary I will show results from all the four experiments with details on OPAL analyses.

3. Ambreesh GuptaFermilab Wine & Cheese3 Standard Model of Particle Physics Our picture of the fundamental constituents of nature There are about 19 (+10) free parameters in the theory to be determined experimentally Standard Model predicts relationship between these parameters.

4. Ambreesh GuptaFermilab Wine & Cheese4 Standard Model Relations Standard Model predicts relation between the parameters; W boson mass(M W ) and Fermi constant(G F ), fine structure constant(  ), Z boson mass (M Z )  : electron g-2 0.004 ppm G F : muon life-time 9 ppm M Z : LEP 1 lineshape 23 ppm Precision measurements require higher order terms in the theory and help constraint the unknown pieces. (running of  ) f W H W t W W

5. Ambreesh GuptaFermilab Wine & Cheese5 Precision EW top-quark mass “predicted” by electroweak corrections prior to direct discovery  The measured W mass precision is such that Top and Higgs loops required for consistency in the Standard Model (SM)  This gives an indirect inference on the Higgs.  Better precision on W mass constraints the Higgs  Indirect measurement of W mass - W mass known to 20 MeV from indirect measurement (LEP1 + SLD +Tevatron). - A direct measurement of W mass with similar precision is of great interest.  Measurement of the width of W boson can also be carried out at LEP providing further checks on consistency of the SM.

6. Ambreesh GuptaFermilab Wine & Cheese6 Large Electron Positron Collider (LEP) LEP I (1989-1993) : Z physics. 18 million Z bosons produced LEP II (1996-2000) : W physics. 80,000 W’s produced. (Energies from 161 GeV – 209 GeV) W’s produced in pairs.

7. Ambreesh GuptaFermilab Wine & Cheese7 The Four LEP Experiments ALEPH L3

8. Ambreesh GuptaFermilab Wine & Cheese8 WW Production and Decay at LEP W’s produced in pairs at LEP - 700 pb -1 /experiment; 40,000 WW BR ~ 44% BR ~ 46% BR ~ 10% WW  l l WW  qql WW  qqqq Efficiency Purity l l 70% 90% qql 85% 90% qqqq 85% 80% Backgrounds

9. Ambreesh GuptaFermilab Wine & Cheese9 Event Selection Very good agreement between expected and observed.  Event selection primarily based on multivariate relative likelihood discriminants OPAL

10. Ambreesh GuptaFermilab Wine & Cheese10 W Mass at LEP The WW cross section at  s = 2Mw sensitive to W mass LEP experiments collected 10 pb -1 data at  s = 161 GeV Combined Result : Mw = 80.40  0.21 GeV  Most of LEP 2 data at higher energies - use direct reconstruction  There are two main steps in measuring W mass and width 1. Reconstruct event-by-event mass of W’s 2. Fit mass distribution  Extract M W and  W.  However, jet energies poorly measured (  /E ~ 12% ), neutrinos unobserved.  Kinematic fitting plays vital role

11. Ambreesh GuptaFermilab Wine & Cheese11 Kinematic Fitting  Mass Reconstruction - Identify lepton and jets (DURHAM) -- Energy flow techniques - Kinematic fitting -- Use LEP beam energy as constraint -- Total Energy =  s; Total Momem. = 0; -- Additionally, apply equal mass constraint m w+ - m w- = 0;  Significantly improved mass resolution  Caveat - Photon radiation will change  s   s’ (photon energy)  Need good WW  4f theory model (~0.5% theory error )

12. Ambreesh GuptaFermilab Wine & Cheese12 Mass Reconstruction  qql channel - 1 or 2 constraint kinematics fit - Golden channel  qqqq channel - Well constrained events - But, ambiguity in assigning jets to W’s  Combinatorial Background - 5-jet event: 10 comb., 4-jet: 3-comb.

13. Ambreesh GuptaFermilab Wine & Cheese13 Fit Methods  Re-weighting - Weight fully simulated events to create sample with new W mass and width parameter - No external bias correction needed - Need large event sample to derive stable weights 80.3381.33  LEP experiments used three likelihood methods to extract W mass and width from the reconstructed mass spectrum. 1. Re-weighting 2. Breit-Wigner 3. Convolution The primary difference between the methods is the amount of information they try to use for the best measurement.

14. Ambreesh GuptaFermilab Wine & Cheese14 Fit Methods (continued)  Breit-Wigner - Fit to W mass spectrum with Breit-Wigner function - Width adjusted to account for resolution and ISR effects. - Bias corrected by comparing to fully simulated MC. Fitted Function (70-88) GeV mass  Convolution - P(m1,m2|Mw,Gw)  R(m1,m2) - Build event-by-event Likelihood - Maximize statistical sensitivity - Need bias correction as in BW

15. Ambreesh GuptaFermilab Wine & Cheese15 Likelihood Variables - Likelihood built using three variables -- both in qqlv, qqqq channels - ~ 400 events per bin for stable fit - Fit for eight energy point, four channels, then combine => lots of MC needed. 5C fit mass error 5C fit mass Hadronic 4C mass 5C fit mass error5C fit mass 4C fit mass difference - OPAL variables - ALEPH also 3-d fit

16. Ambreesh GuptaFermilab Wine & Cheese16 Performance of Likelihood Fucntion  Test the central value modeling with bias plot  Test the uncertainty on central value with pull distribution. OPAL  Check bias and pulls distributions...below a typical example

17. Ambreesh GuptaFermilab Wine & Cheese17 OPAL W mass  Very good agreement between three methods in channel and year  Strong correlation between methods => Combining them had only small stat. gain  CV, which has the smallest expected statistical uncertainty is used as the main method.  Use of momentum cut analysis makes significant reduction in FSI uncertainty.  Final W mass and total uncertainty from the three methods on OPAL - M w   M w (Stat.+Syst.) CV 80.416  0.053 RW 80.405  0.052 BW 80.390  0.058

18. Ambreesh GuptaFermilab Wine & Cheese18 LEP W Mass  The combined preliminary LEP W mass M W = 80.376  0.025 (stat)  0.022 (syst) GeV  Systematics on W mass Source Hadronisation QED(ISR/FSR) Detector Colour Reconnection Bose-Einstein Correlation LEP Beam Energy Other Total Systematics Statistical Total qql qqqqcombined 14 7 10 9 2 10 4 19 5 8 35 7 9 11 13 8 10 0 9 3 21 30 36 44 40 59 22 25 33 Channel weights qqlv : 76% qqqq : 22% xs : 2% (MeV)

19. Ambreesh GuptaFermilab Wine & Cheese19 LEP W Width  The combined preliminary LEP W width  W = 2.196  0.063(stat)  0.055(syst) GeV  Systematics on W width Source Hadronisation QED(ISR/FSR) Detector Colour Reconnection Bose-Einstein Correlation LEP Beam Energy Other Total Systematics Statistical Total qql + qqqq (MeV) 40 6 22 27 3 5 19 55 63 84

20. Ambreesh GuptaFermilab Wine & Cheese20 LEP Beam Energy LEP beam energy used in event kinematics fit   M W /M W   E LEP /E LEP Beam energy calibrated using - Resonant De-Polarization (41- 60 GeV.) - Extrapolated to LEP II energies NMR probes - Main systematic error due to extrapolation Extrapolation checked with 1. Flux Loop 2. Spectrometer 3. Synchrotron Oscillation Final results on LEP beam energy ( Eur. Phys. J., C 39 (2005), 253 ) - Reduction of beam energy uncertainty used in earlier W mass combination - old  E beam = 20-25 MeV   M W = 17 Mev - new :  E beam = 10-20 MeV   M W ~ 10 Mev -- OPAL Final 9 MeV

21. Ambreesh GuptaFermilab Wine & Cheese21 LEP Beam Energy Cross Check with Data  LEP beam energy can be estimated using radiavtive return events - Z mass precisely known - Measured mass in radiative events sensitive to beam energy  Result consistent with zero within experimental errors

22. Ambreesh GuptaFermilab Wine & Cheese22 Detector MC modeled to represent data; Disagreements  Systematic error Systematics from MC Modeling Main Sources - QED/EW radiative effects - Detector Modeling - Hadronisation Modeling - Background Modeling - Final State Interaction

23. Ambreesh GuptaFermilab Wine & Cheese23 KoralW’s O(  3 ) implementation adequate, but misses - WSR - interference between ISR,WSR & FSR KandY includes - O(  ) corrections - Screened Coulomb Correction Error ~ 7 MeV Photon Radiation

24. Ambreesh GuptaFermilab Wine & Cheese24 Z0 calibration data recorded annually provides a control sample of leptons and jets (~ 45 GeV). Data/Mc comparison used to estimate corrections for - Jet/Lepton energy scale/resolution - Jet/Lepton energy linearity - Jet/Lepton angular resolution/biases - Jet mass Error is assigned from the error on correction qqlv qqqq Combined 10 MeV 8 MeV 10 MeV Detector Systematics Raw  Corrected LEP Combined: Jet energy scale Jet energy resolution

25. Ambreesh GuptaFermilab Wine & Cheese25 Detector Systematics: Breakdown OPAL

26. Ambreesh GuptaFermilab Wine & Cheese26 MC programs (JETSET,HERWIG,ARIADNE) model production of hadrons  but difference in particles and their distributions The difference interplays with detector response - particle assignment to jets - cuts applied to low momentum particles - low resolution for neutral particles - assumptions made on particle masses at reco. JETSET used by all LEP experiment with parameters tuned with Z peak data  systematic shift estimated from shift with other hadronization models. qqlv qqqq Combined 13 MeV 19 MeV 14 MeV LEP Combined: Hadronization Modeling

27. Ambreesh GuptaFermilab Wine & Cheese27 Final State Interactions Two known sources that could potentially bias W mass and width measurement 1. Color Reconnection - color flow between W’s could bias their masses - only phenomenological models exist. - Most sensitive variable to CR is W mass itself 2. Bose-Einstein Correlation. - coherently produced identical pions are closer in phase space. - BE correlation between decay products of same W established - Does the effect exist between W’s? The Basic Problem: If products of hadronically decaying W’s (~0.1 fm) interact before hadronization (~1.0 fm)  Can create a mass bias.

28. Ambreesh GuptaFermilab Wine & Cheese28 Color reconnection  Only phenomenological models exist. - SK1 model produces largest shift  CR strength parameter (k i )  LEP experiments estimate effect of color reconnection  Measure particle flow in the inter-jet regions of the W’s - Extreme values of CR disfavored by data  but it does not rule out CR - A 68% upper limit on k i is used to set a data driven uncertainty on W mass. - Combined LEP value of k i = 2.13  For this Reco. Prob., CR error ~ 120 MeV (OPAL)

29. Ambreesh GuptaFermilab Wine & Cheese29  A,D,L,O use varations of below - OPAL Uses P-cut 2.5 GeV for qqqq - ~18% loss in statistics. - Much reduced CR systematics 125  41 MeV (k i =2.3) OPAL - A worthwhile tradeoff! - ALEPH 28 MeV, L3 38 MeV Cuts and Cones: Reducing CR effect  CR affects mostly soft particles between jets  changes jet direction  Re-calculate Jet direction 1. Within cone of radius R 2. Cut on particle momentum P 3. Weighted particle momentum |P|  Final CR error in qqqq 35 MeV

30. Ambreesh GuptaFermilab Wine & Cheese30  2.5 GeV P-cut to redefine jet direction also reduces BEC W mass bias - OPAL (default) 46 MeV  (P-cut) 24 MeV.  LEP experiments have measured BEC between W’s - Using “mixing method” - A,D,L,O: only a fraction of Full BEC seen in data (0.17  13) BEC in WW events  A 68% upper limit on BEC fraction seen in data (OPAL), used to set W mass systematics  M W = ( 0.33 + 044)   M W (Full BEC) = 19 MeV  L3 18 MeV, ALEPH 2 MeV Final BEC error in qqqq 7 MeV

31. Ambreesh GuptaFermilab Wine & Cheese31 Results: qqqq and qqlv channels

32. Ambreesh GuptaFermilab Wine & Cheese32 Results: LEP W mass and Width m W (LEP) = 80.376 ± 0.033 GeV  W (LEP) = 2.196 ± 0.083 GeV

33. Ambreesh GuptaFermilab Wine & Cheese33 W’s as Calibration Sample at LHC “Yesterdays sensation is today’s calibration and tomorrows background” - Telegdi - W’s from top decay are foreseen to provide the absolute jet scale. - Fast simulation studies in the past showed feasibility - Select samples with a four jets and lepton (electron,muon) with two jets b-tagged. - estimated 45K events from 10 fb-1 - Cross check with Z/  +Jet sample - Sattistics not the issue but understanding the physics of the events.

34. Ambreesh GuptaFermilab Wine & Cheese34 Summary  Final results from all the four LEP experiments  Final LEP combination will use combined FSI error  Much reduced FSI error in final results  A new preliminary LEP combination  Total LEP W mass uncertainty decreased to 33 MeV It took about five years after LEP shut down to get final W mass results from all the four experiment. Now it is up to Tevatron to better the W mass precision before LHC turns on.