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) Pre-blessing: CDF Note 10628 Matthew Jones Purdue University CDF B Group Meeting

2. The ϒ Polarization Puzzle • No satisfactory agreement with any calculation • Incompatible results from CDF and DØ • No significant signs of strong polarization NRQCD Braaten & Lee, PRD 63, 071501R ( 2001) CDF B Group Meeting

3. Basic Quantum Mechanics • The decay of a pure spin-1 state cannot be isotropic • Back to the fundamentals: • General state for a spin-1 particle: • Angular distribution when decaying to μ+μ-: No choice of a1, a0 and a-1 can make all coefficients vanish simultaneously. CDF B Group Meeting

4. “Transverse”: “Longitudinal”: Transverse/Longitudinal is not sufficient But an arbitrary rotation will preserve the transverse/longitudinal shape... CDF B Group Meeting

5. Need for full polarization analysis • The templates for dN/dΩ are more complicated than simply 1 ± cos2θ. • Need to measure λθ, λφ and λθφ simultaneously. CDF B Group Meeting

6. Reference Frames • Angular distributions measured with respect to some coordinate system • S-channel helicity frame ( is in direction of ) • Collins-Soper frame (approximates rest frame of colliding partons) • Regardless of the coordinate system, the shape should be the same • Some combinations of λθ, λφ, λθφ should be invariant • +3λφ)/(1-λφ) • Fancy F • Important to demonstrate consistency in multiple reference frames CDF B Group Meeting

7. Analysis Goals • Use both the CMUP+CMU and CMUP+CMX trigger paths (nominally 6726 pb-1) • Measure λθ, λφ, λθφas a function of pT for all three ϒ(nS) resonances • Perform measurement in both Collins-Soper frame and S-channel helicity frame • Compare angular invariants measured in both frames. • Measure differential production cross section CDF B Group Meeting

8. Previous Work • CDF Notes 10385, 10387: feasibility studies • BPD meeting: January 25th, 2011 • Applied to CDF data in one pTbin • BPD meetings: March 8th, March 22nd, April 5th • Cross section studies • BPD meetings: May 24th • Background studies • BPD meeting, June 21st • CDF Note 10628: full analysis • BPD meetings, August 23rd, 30th CDF B Group Meeting

9. Upsilon Candidate Selection • Data sets: jbmm* up to period 28 (0d to 0m) • Trigger paths: UPSILON_CMUP_CMU/CMX: • 4 GeV/c CMUP muon, 3 GeV/c CMU/CMX muon • 8 < m(μ+μ-) < 12 GeV/c2 • Good run list: v.34 • Offline selection: • 25+25 COT hits • No silicon hit requirements • COT/XFT fiducial cuts • Muon track matched with XFT trigger track CDF B Group Meeting

10. Upsilon Candidate Selection Offline fiducial and trigger match cuts CMUP muon requirement CMU muon CMX muon CDF B Group Meeting

11. One of many invariant mass distributions 0 1 2 3 4 5 6 7 8 9 10 11 ϒ(1S) (2S) (3S) • Divide into 12 ranges classified as “signal” and “sideband”. • Measure angular distribution within each mass bin. • Some bins contain only background, some are signal+background. CDF B Group Meeting

12. Acceptance Cuts • With no acceptance cuts the distribution of (θ,ϕ) remains unchanged. • Cuts on and η restrict the accepted range of angles. • Example: • pT > 4 GeV/c • η < 1 Isotropic without acceptance cuts CDF B Group Meeting

13. Acceptance Cuts • With no acceptance cuts the distribution of (θ,ϕ) remains unchanged. • Cuts on and η restrict the accepted range of angles. • Example: • pT > 4 GeV/c • η < 1 Very non-isotropic CDF B Group Meeting

14. Acceptance Templates • Generate isotropic μ+μ- pairs (about a billion) • Signal at fixed masses • Continuous mass distribution • pT dependence of signal and background tuned to match the data • Simulate using cdfSim release 6.1.4mc.m patch t • Luminosity file from good run list + DFCLuminosityTool • Offline requirements: • Just require CdfMuon objects • Apply rejection using parameterized trigger/reconstruction/selection efficiencies when generating angular distribution templates. CDF B Group Meeting

15. Trigger Efficiencies • CMU/CMX trigger efficiency calculated using MuonLoPtEfficiency tool (Bsμ+μ- search) • CMP efficiency measured using the unbiased jpmm J/ψ μ+μ- sample • Lots of variation in the amount of material • Separate fits in 24 azimuthal “wedges” • Parameterized by run range, pT and zCMP CDF B Group Meeting

16. CMP Efficiency Parameterization CDF B Group Meeting

17. CMP Efficiency Fits Complete set of plots is in the appendix of note 10628. CDF B Group Meeting

18. Muonχ2 matching cuts • Described in CDF Note 6201. • Parameterization is convenient • Easily applied offline • Unfortunately, the efficiency depends on pT • Measure efficiency using unbiased leg of J/ψ in the μ+SVT sample: CDF B Group Meeting

19. |z|<60 cm vertex cut • From CDF Note 7935 (Nov 2005): • 95.50 ± 0.35% • Cross-checked using the J/ψ sample to fit the luminous region: CDF B Group Meeting

20. Low pTMuon Scale Factors • Measure relative efficiency for finding CdfMuon objects in data/MC: • Fiducial track efficiency from CDF Note 6394 • Use unbiased leg of J/ψin μ+SVT • XFT efficiency measured using unbiased track in B+J/ψK+… CDF B Group Meeting

21. Low pTMuon Scale Factors Kaon-XFT not matched Kaon-XFT match • Scale factors: • Mainly an issue for a cross section measurement. Does not affect polarization analysis. CDF B Group Meeting

22. Data/MC comparison Hole made bigger in data to match mistake in Monte Carlo. CDF B Group Meeting

23. Various Cross-checks • Checked ϒ(nS) yield in various subsamples • East/west, top/bottom, north/south • Checked XFT and muon efficiencies in 1st half and 2nd half of the data • Checked J/ψ yield vs time • No obvious problems in control samples CDF B Group Meeting

24. Upsilon cross section • Reasonable agreement with Run I results • Still think there is about a 10% systematic disagreement • Possibly implicit SVX requirement in CharmMods? • No evidence for biases that would affect angular distribution analysis. CDF B Group Meeting

25. Background Properties • Signal and background expected to have different angular distributions • To subtract the background component you need to know • The amount of background (from mass fit) • The angular distribution of the background • The background is complicated: • Its properties change rapidly with mass and pT • Two possible ways to sort this out: • Interpolate background into signal region • Isolate background component in the signal region CDF B Group Meeting

26. Background Properties • Why does background at high mass look “transverse” (1 + cos2θ) while the background at low mass looks more “longitudinal” (1-cos2θ)? Bin 0 Bin 11 Bin 4 – ϒ(1S) CDF B Group Meeting

27. Background Properties • Look at pT asymmetry: |pT(μ+)-pT(μ-)| This feature corresponds to back-to-back muons: lowest possible pT that still satisfies the trigger and pT(μ+μ-) cuts  large |cosθ| If this came from bb events, we would need to generate a LARGE Monte Carlo sample to study it in detail. Test the hypothesis that the background is dominated by bb production using a toy Monte Carlo… CDF B Group Meeting

28. Toy Background Model • Parameterized distributions from tuned Pythia[R.D.Field, PRD 65, 094006 (2002)] • pT(b), pT asymmetry: • Δφ, Δy • Peterson fragmentation, • Semi-leptonic B decay E(μ) spectrum • Compare with data… CDF B Group Meeting

29. Simulated background properties Kinematic limit Kinematic limit Component that peaks at large ΔpT B Production and Decay Meeting

30. Displaced Track Sample • Isolate background component by requiring one of the tracks to have ≥3 silicon hits and to have |d0|> 150 μm. • Measure signal fraction in displaced track sample. • Measure relative prompt/displaced background yields. CDF B Group Meeting

31. Background Angular Distribution • Is the angular distribution in the displaced sample the same as in the complementary prompt sample? Displaced Prompt It apparently seems to be more or less indistinguishable… CDF B Group Meeting

32. Background Angular Distribution • Quasi-chi-squared statistic: S-channel helicity frame Collins-Soper frame CDF B Group Meeting

33. Fits to signal+background bins • Binned likelihood fit to observed (cosθ,φ) distribution: • Integrated luminosity: L • Signal cross section: • Displaced background cross section: (from mass fit) • Prompt background cross section: (from mass fit) • sp is a Gaussian constraint from the mass fit. • Fraction of signal in displaced track sample: (from mass fit) • Acceptance from Monte Carlo: and • Weight function: CDF B Group Meeting

34. Fits to signal+background bins Example: Prompt Displaced Another quasi-χ2 goodness-of-fit statistic: CDF B Group Meeting

35. Fits to signal+background bins Example: Prompt Displaced Another quasi-χ2 goodness-of-fit statistic: CDF B Group Meeting

36. Goodness-of-fit Prompt CS frame Displaced mass Prompt SH frame pT Displaced CDF B Group Meeting

37. Fit quality is worse at low pT • Add an additional term to background angular distribution: • Improvement is significant in most pT bins. CDF B Group Meeting

38. Fit Parameters Background bins ϒ(1S) ϒ(2S) ϒ(3S) Gaussian error ellipse + 1-sigma contour CDF B Group Meeting

39. Fit Parameters Background bins ϒ(1S) ϒ(2S) ϒ(3S) Gaussian error ellipse + 1-sigma contour CDF B Group Meeting

40. Systematic Uncertainty from • Ideally, would be the same in both reference frames: • Generally good agreement, but the difference indicates the presence of an (unknown) bias. We use this to quantify the systematic uncertainty on … CS frame SH frame CDF B Group Meeting

41. Systematic Uncertainty from Suppose the shift is a one-sigma effect. Propagate this back into covariance matrix for : Add this to Cov( CDF B Group Meeting

42. Fitted Parameters: ϒ(1S) Stat + syst CDF B Group Meeting

43. Fitted Parameters: ϒ(2S) Stat + syst CDF B Group Meeting

44. Fitted Parameters: ϒ(3S) Stat + syst CDF B Group Meeting

45. Analysis Goals • Use both the CMUP+CMU and CMUP+CMX trigger paths (nominally 6726 pb-1) • Measure λθ, λφ, λθφas a function of pT for all three ϒ(nS) resonances • Perform measurement in both Collins-Soper frame and S-channel helicity frame • Compare angular invariants measured in both frames. • Measure differential production cross section (we don’t propose to bless this result yet) X CDF B Group Meeting

46. Summary • First complete analysis of angular distribution of Upsilon decays • Can’t cheat statistics – sometimes there is never enough data • Important to quantify systematic biases or instabilities in the fit– self consistent cross-checks are essential • Lots of minor additions/studies possible, but we think it is important to move it closer to publication on a short time scale. CDF B Group Meeting

47. List of stuff to bless • Di-muon mass plot • Examples of angular acceptance calculated with Monte Carlo • Data/Monte Carlo acceptance comparisons • Prompt/displaced projection comparisons • Prompt/displaced sideband fits • Prompt/displaced di-muon mass distribution fit • Prompt/displaced signal bin fits • A couple of “Triangle plots” • Graphs of vspT in CS and SH frames • Graphs of vspT in CS and SH frames • Others? CDF B Group Meeting