Measurement of the ϒ( nS )  μ + μ - Decay Angular Distribution (Upsilon Polarization Analysis)

1. Measurement of the ϒ(nS)μ+μ- Decay Angular Distribution(Upsilon Polarization Analysis) Blessing: CDF Note 10628 Web page with questions and answers: http://www-cdf.fnal.gov/~mjones/internal/Upsilon.html Matthew Jones Purdue University CDF B Group Meeting

2. Analysis Goals • Measure all three parameters simultaneously • Measure in both the Collins-Soperand S-channel helicity frame • Test self-consistency by calculating rotationally invariant combinations of λθ, λφ and λθφ • Minimize sensitivity to modeling the ϒ(nS) resonance line shape • Explicit measurement of angular distribution of di-muon background CDF B Group Meeting

3. Method • Uses 6.7 fb-1 of jbmm dataset • UPSILON_CMUP_CMU and UPSILON_CMUP_CMX trigger paths • Factor acceptance and angular distribution: • A(cosθ,φ) from high statistics Monte Carlo • w(cosθ,φ; λθ, λφ,λθφ ) from angular distribution • Performed binned likelihood fit to observed distribution of (cosθ,φ) to determine λθ, λφ,λθφ. CDF Collaboration Meeting

4. Method • Level 1 trigger efficiency from Bs μ+μ- analysis. • Level 2 CMP trigger efficiency measured using J/ψ μ+μ- sample. • Generated, simulated and reconstructed well over 109 decays on namgrid. • Two component fit: • signal + background CDF Collaboration Meeting

5. Questions CDF B Group Meeting

6. Toy Monte Carlo Studies • Important for several things: • Quantifies statistical uncertainty due to finite Monte Carlo statistics • Evaluates statistical component of highly correlated quantities, eg, in CS and SH frames • Checks on statistical uncertainties from fit • Bias/efficiency checks CDF B Group Meeting

7. Comparison of in CS and SH frames • How much of the difference is statistical? • The toy Monte Carlo simulates in one reference frame and fits in both CS and SH frame • RMS of the difference quantifies the statistical component CDF B Group Meeting

8. Comparison of in CS and SH frames • Much of the observed difference can be explained by statistics. • Remaining difference quantified as a systematic uncertainty CDF B Group Meeting

9. Prompt Scale Factor Fit • Important change to the procedure since pre-blessing motivated by detailed analysis of stability of the fit in low pT bins of the ϒ(3S) • End result is an improved analysis, but with a small (≤ 1 sigma) shift in some parameters • To fully understand this, let’s review the analysis procedure… CDF B Group Meeting

10. Analysis Procedure • In each range of m(μ+μ-), split sample into prompt and displaced muon components • Three fits: • Measure fraction of ϒ(nS) that is present in the displaced muon component • Measure the prompt scale factor: ratio of background yields in prompt and secondary samples. • Fit to angular distribution given signal fraction in prompt sample and angular distribution of background constrained from the displaced sample. CDF B Group Meeting

11. First Fit • Single Gaussian in both prompt and displaced samples • Bias in yield estimates should cancel in the ratio • Corrects for (small) amount of signal in displaced component in fits 2 and 3 • No change since pre-blessing CDF B Group Meeting

12. Second Fit • During pre-blessing the scale factor was also obtained from the first fit: prompt background = displaced background scaled by a quadratic function of mass. • This might introduce a bias because of inadequacies modeling the ϒ(nS) line shape. CDF B Group Meeting

13. Second Fit: a better procedure • Ratio of prompt/displaced distributions really is flat. Does not suggest any need for a quadratic function. • Fit only to sidebands – completely avoids any bias due to line shape description. • Quadratic form studied as a systematic. CDF B Group Meeting

14. How big is the change? • λθ • λφ • λθφ ϒ(1S) Old result (from pre-blessing) in black. New result with new prompt scale factorf fit in red. • λθ • λφ • λθφ CDF B Group Meeting

15. How big is the change? • λθ • λφ • λθφ ϒ(2S) Old result (from pre-blessing) in black. New result with new prompt scale factorf fit in red. • λθ • λφ • λθφ CDF B Group Meeting

16. How big is the change? • λθ • λφ • λθφ ϒ(3S) Old result (from pre-blessing) in black. New result with new prompt scale factorf fit in red. • λθ • λφ • λθφ CDF B Group Meeting

17. Comparison with Quadratic • Difference is not easily visible by eye on these distributions… CDF B Group Meeting

18. Comparison with Quadratic One-sigma confidence intervals calculated as a function of mass given the 2 or 3 fitted coefficients. • Is the quadratic significantly better? • Quantify by calculating χ2/dof from sidebands. CDF B Group Meeting

19. Prompt scale factor goodness of fit No change in many cases. Quadratic function makes agreement in high-mass sideband worse CDF B Group Meeting

20. Systematic uncertainty • Half the difference between quadratic and linear result should bound the systematic uncertainty (might be conservative): FSR from ϒ(1S) True background FSR from ϒ(1S) Linear fit True background Quadratic fit FSR from ϒ(1S) True background CDF B Group Meeting

21. Systematic Uncertainty • This systematic uncertainty is smaller than or sometimes similar to other systematic uncertainties. We should quote it… LINEAR QUADRATIC LINEAR QUADRATIC CDF B Group Meeting

22. Systematic Uncertainty CDF B Group Meeting

23. Comparison with CDF ϒ(1S) publication from Run I • Level of agreement: χ2/dof = 2.13/4, P=0.712 CDF B Group Meeting

24. Comparisons with DØ ϒ(1S) publication • Level of agreement: χ2/dof = 35.2/7, P=1.02x10-5 CDF B Group Meeting

25. Comparisons with DØ ϒ(2S) publication • Level of agreement: χ2/dof = 7.89/7, P=0.342 CDF B Group Meeting

26. Comparisons with blessed CDF ϒ(1S) result • Level of agreement: χ2/dof = 17.0/8, P=0.030 CDF B Group Meeting

27. Comparisons with newer version of the CDF ϒ(1S) result (not blessed) • Level of agreement: χ2/dof = 6.38/8, P=0.604 CDF B Group Meeting

28. Restricted Rapidity Range • Analysis repeated with |y|<0.4 • No significant change in differential cross section • No large systematic changes in angular distributions: |y|<0.6 |y|<0.4 CDF B Group Meeting

29. Summary • First complete analysis of angular distribution of Upsilon decays • All questions since pre-blessing have been addressed – lots of useful discussion. • New treatment of prompt scale factor has improved the analysis • No evidence for significant polarization. CDF B Group Meeting

30. Blessed Material • Temporary location of public web page: http://www-cdf.fnal.gov/~mjones/internal/blessed/ • Includes description of the analysis and links to blessed material with supplementary explanations. CDF B Group Meeting

31. Di-muon mass plots CDF B Group Meeting

32. Di-muon mass plots CDF B Group Meeting

33. Di-muon mass plots CDF B Group Meeting

34. Un-polarized angular acceptanceCollins-Soper frame CDF B Group Meeting

35. Un-polarized angular acceptanceCollins-Soper frame CDF B Group Meeting

36. Un-polarized angular acceptanceCollins-Soper frame CDF B Group Meeting

37. Un-polarized angular acceptanceS-channel helicity frame CDF B Group Meeting

38. Un-polarized angular acceptanceS-channel helicity frame CDF B Group Meeting

39. Un-polarized angular acceptanceS-channel helicity frame CDF B Group Meeting

40. Comparison of prompt/displaced background CDF B Group Meeting

41. Projections of fits in background bins CDF B Group Meeting

42. Projections of fits in the ϒ(1S) signal bin CDF B Group Meeting

43. Triangle plots CDF B Group Meeting

44. Triangle plots CDF B Group Meeting

45. Triangle plots CDF B Group Meeting

46. Rotational Invariants You need to look closely… CDF B Group Meeting

47. Properties of background CDF B Group Meeting

48. Rotational Invariants CDF B Group Meeting

49. Graphs of λθ, λφand λθφ CDF B Group Meeting

50. Graphs of λθ, λφand λθφ CDF B Group Meeting