Upsilon Polarization Analysis Status CDF note 10628 v1.1

1. Upsilon Polarization AnalysisStatusCDF note 10628 v1.1 Matthew Jones Purdue University B Production and Decay Meeting

2. Overview of Polarization Analysis • Angular distribution of muons is the superposition of signal + background • Background dominated by heavy flavor • Requiring one displaced track enhances background • In sideband regions, the angular distribution of displaced track sample agrees well with angular distribution in complementary sample • Level of background calculated from fits to invariant mass distribution • Sufficient information to subtract angular distribution of background in a mass range that contains the ϒ(nS) signal B Production and Decay Meeting

3. Example: 6.5 < pT < 8.5 GeV/c Background only Background only Signal + background B Production and Decay Meeting

4. Some of the Recent Changes • Efficiency for muon matching cut found to depend on pT… • Peaking co-linear background suppressed by cut on • Revert to classic binned log-likelihood fit since Monte Carlo samples are large • Measure signal fraction in displaced track sample – accounted for in simultaneous fit. B Production and Decay Meeting

5. Muonχ2<9 cut efficiency • Measured using μ+SVT sample • Simulated in Monte Carlo template generation CMU CMX B Production and Decay Meeting

6. Background Properties • Peaking background suppressed by the cut • Included in Monte Carlo acceptance calculation • No loss of signal efficiency for Component that peaks at large ΔpT Kinematic limit Also contributes to peaking in cosθ distribution in the S-channel helicity frame. B Production and Decay Meeting

7. Invariant mass fits • Components: • Background: exponential or gamma function • Signal: single Gaussians • Fit for: • Prompt background scale factor • Signal fraction in displaced track sample (typically between 1 and 4%) • Mass shift and resolution B Production and Decay Meeting

8. Angular distribution in side-bands • The displaced and non-displaced track samples have similar angular distributions: Error bars: displaced (scaled) Histogram: non-displaced • Drell-Yan contribution expected to be small (few %) • Not surprising if dominated by heavy flavor decays B Production and Decay Meeting

9. Sideband fits using unpolarized templates • Predicted yield in bin i,j: • is the unpolarized acceptance and efficiency from the Monte Carlo. • Background parameters are not limited to physical range for a spin-1 particle decay. B Production and Decay Meeting

10. Projections of sideband fits • First in Collins-Soper frame: B Production and Decay Meeting

11. Projections of sideband fits • Now in S-channel helicity frame: B Production and Decay Meeting

12. Signal + Background fit • Mass bin contains signal + background • Relative fractions constrained from fit to mass distribution • Displaced track sample constrains background angular distribution B Production and Decay Meeting

13. Projections from ϒ(1S) bin Collins-Soperframe Displaced track sample B Production and Decay Meeting

14. Projections from ϒ(1S) bin S-channel helicity frame B Production and Decay Meeting

15. Angular variables Background mass bins 1S 2S 3S • Angular distribution of signal is quite different from background shape. • Parabolic errors approximate confidence intervals from mncont() quite well. B Production and Decay Meeting

16. Angular Invariant, • Similar in both reference frames • Would like to use difference to quantify systematic uncertainties on Black: CS frame Red: SH frame B Production and Decay Meeting

17. ϒ(1S) Results B Production and Decay Meeting

18. ϒ(2S) Results B Production and Decay Meeting

19. ϒ(3S) Results Getting ugly – may want to combine some adjacent bins. B Production and Decay Meeting

20. Differential Cross Section • Only a cross check at this point • pT-dependent efficiencies included in unpolarized templates • pT-independent quantities: • Muon scale factors • Vertex cuts (suspicious old result) • Final state radiation B Production and Decay Meeting

21. Final State Radiation • The fit scales the signal yield by the fraction of the single Gaussian in mass range • FSR simulated using PHOTOS • A Gaussian fit to the line shape with FSR accounts for only about 92% of the events • In Run I, this was determined to be (93±2)% Final correction factor: B Production and Decay Meeting

22. Differential Cross Section B Production and Decay Meeting

23. Time Dependence in J/ψ datasets B Production and Decay Meeting

24. No time-dependent efficiencies found • Track reconstruction efficiency: • XFT efficiency for fiducial tracks: • Difficult to pin down CMU efficiency… claimed to be well understood for • No evidence for bias in angular distributions B Production and Decay Meeting

25. Systematic Uncertainties • Proposal: • Trivial stuff: uncertainties in efficiencies used to generate templates • Monte Carlo statistics: samples are generally large, but statistical precision should be quantified • Background model: compare ϒ decay angular distribution with background shape constrained using the sideband regions. • Alternative treatments: • parameterization with additional ad-hoc shape component • wider mass range for displaced track background proxy • This is the remaining work in progress. B Production and Decay Meeting

26. Summary • Complete, self-consistent analysis of angular distribution • No strong evidence for significant polarization • Difficult to see how this would agree with NRQCD or kT factorization models. • Systematic uncertainties to be evaluated • These studies might provide ways to demonstrably reduce possible bias B Production and Decay Meeting