1. Top mass error predictions with variable JES for projected luminosities Joshua Qualls Centre College josh.qualls@centre.edu Mentor: Michael Wang

2. Contents Motivation - Top mass Theory - Top decay - Matrix Element method - Ensemble tests Analysis - ROOT Macros/plots Conclusion

3. Precise knowledge of M W and m t constrain m h, the Higgs mass Why measure top mass? Consider W boson mass (1+  r) 1 Radiative corrections Radiative corrections to Feynman diagram

4. - tt produced from pp collisions in Tevatron - From dozens to thousands annually - Three decay modes of interest: 1) All jets 2) Dilepton 3) Lepton + Jets Top Quark Production - -

5. Decay channel 1: All Jets p p t t All jets = 44% Pros -Large branching fraction - Jet energy calibration using hadronic W Cons -High background levels - W q q b b W + q q

6. Decay channel 2: Dilepton p p t t b W W + - l l v v All jets = 44% Dilepton = 5% Pros - Low background levels Cons - Low branching fraction - No hadronic W b b

7. Decay channel 3: Lepton + Jets p p t t W - All jets = 44% Dilepton = 5% Lepton + Jets = 29% Other = 22% W - l v Pros - Reasonable branching fraction - Jet energy calibration from hadronic W - Medium background levels - Traditionally yielded best results b W + q q b

8. The General Method Event specified by x i in volume dx i Probability for configuration of N observed events within infinitesimal phase space dx i containing empty finite elements Δx i is: P(x 1,…x N )dx 1 …dx N = Prob(0 events in Δx 1 ) x Prob(1 event in dx 1 ) x … By Poisson statistics, total probability is However, actual events occur in more than one dimension

9. - Extend method to k-dimensional space V - Probability density depends on parameter(s) α - Likelihood function given by - Maximize L(α), OR (due to rapid variations in L(α) ) minimize -ln L(α) Likelihood Function

10. - Event with four jets, electron, and missing E T might not be tt - W + 4 jets - five jets, with one improperly reconstructed - W + 3 jets, with one jet splitting - Correct for this by calculating the Acceptance: - Includes all conditions for accepting or rejecting an event - geometric acceptance - trigger efficiencies - reconstruction efficiencies - selection criteria Detector Complications tt ?

11. Jet Complications 1) Detector sees 4 jets, a lepton, missing E T, interaction vertex - Can’t definitively match jets to quarks - Must try all 12(ish) permutations 2) Determining jet energy scale (JES) - Jet energy determined by scintillator sheets - Numerous effects spoil the accuracy of conversion of light into jet energy - Consider two situations: 1) fixed JES 2) variable JES b? u?

12. - Event probabilities calculated directly - Have signal and probability component - For good detector, P sig is proportional to the cross section: Where the cross section is given by And |M| corresponds to the matrix element Matrix Element Method

13. Event n Event n-1Event 3 Event 2 Event 1 To extract m top from a sample of n events, probabilities are calculated for each individual event as a function of m top : From these we build the likelihood function The best estimate of the top mass is then determined by minimizing: 0.5 And the statistical error can be estimated from: Matrix Element Method (2)

14. From a large pool of M monte carlo events, we perform ensemble tests by randomly drawing n events N number of times to form N pseudo-experiments: Expt NExpt 1Expt N-1 Expt 3 Expt 2 min σσσσσ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20..................... M A. The error is estimated for each experiment and entered into the “Mass Error” histogram B. The mass at the minimum for each experiment is entered into the “Top Mass” histogram C. The pulls are calculated for each experiment by dividing the deviation of the mass at the minimum from the mean of this mass for all experiments by the estimated error Ensemble tests

15. 1) Writing numerous scripts to streamline the process of performing probability calculations - Creating job submission template files - Writing out generated events - Scanning output files for errors, and creating new submission files 2) Modifying ROOT macros to create ensemble test histograms and compare mass error vs. beam luminosity My Projects

16. - Theory predicts scaling of mass error with increased luminosity for fixed JES ≈ 1 - Beam luminosity corresponds to the number of simulated events - - Observed events should scale with luminosity - - 150 events corresponds to 0.4 fb -1 - Theory had only predicted (accurately) the situation with fixed JES - Mass error scales as 1/x 2 - My mentor (among others) made theoretical calculations saying that the mass error for variable JES should scale as a constant times the fixed JES Variable JES

17. 1)Modified code to perform n pseudo experiments - - n ranges from 150 to 2400 2) Generated likelihood histograms for fixed and variable JES 3) Generate the three histograms mentioned previously: -mass error -top mass -mass pull 4) Debug this endlessly ROOT Macros

18. 1-D Likelihood

19. 2-D Likelihood

20. Sample Histogram

21. Mass Error Plot

22. Top Mass Plot

23. - Evidence that variable JES mass errors will scale at approximately 1.5 times fixed JES mass errors - Calculations for the exact theoretical value are still being performed - Tentative value of 1.5 does not account for W mass - This will lower the value, hopefully to the experimentally determined ~1.4 - Scripts for job submission are still being used, both to submit jobs locally and to the Open Science Grid Results

24. Acknowledgements: Michael Wang, Gaston Gutierrez, FNAL, D0 Collaboration, DOE, etc. Thank You Questions?

25. Epilogue