Upsilon Polarization Analysis: dealing with the di- muon backgrounds

1. Upsilon Polarization Analysis:dealing with the di-muon backgrounds Matthew Jones Purdue University B Production and Decay Meeting

2. Overview of Polarization Analyses • The usual method: • Fit m(μ+μ-) to get ϒ(nS) yields in bins of some angular variable • Fit the yields to measure parameters that characterize the angular distribution • Drawbacks: • Poor use of statistics if sample is divided into many small bins in polar angles • Non-trivial background shape varies significantly with pT and with decay angle B Production and Decay Meeting

3. Overview of Polarization Analyses • This analysis: • Select ranges of m(μ+μ-) that contain theϒ(nS) signals (and background) • Constrain the angular distribution of the background (using sidebands or control samples) • Fit the angular distribution of signal + background • Binned likelihood fit makes efficient use of statistics • Easier to parameterize angular distribution of background than invariant mass • These truths we hold to be self evident – at least until we learn otherwise… B Production and Decay Meeting

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

5. Background Properties • Angular distribution depends on invariant mass – it is not constant, it is not even linear. • Angular distribution is not consistent with the decay of a primary spin-1 object • Significant momentum-dependent structure: 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

6. Toy background model • Suppose the background is dominated by production with semi-leptonic decays • Pythia and Herwig are too inefficient to generate high statistics samples • Simulate main properties of correlated production using a toy Monte Carlo. • Eyeball the shapes of the distributions described in PRD 65, 094006 (2002): R.D. Field, “The sources of b-quarks at the Tevatron and their Correlations”. B Production and Decay Meeting

7. Toy Monte Carlo • pT of the b-quark • Δφ between b-quarks • Δy between b-quarks • pT asymmetry • E(μ)in B rest frame • Peterson fragmentation • Boost muons into lab frame • Full cdfSim, trigsim, production chain • Same analysis cuts applied to data pT(b) Δφ Δy ApT E(μ) B Production and Decay Meeting

8. Simulated background properties • This reproduces, at least qualitatively, most of the properties of the background • Parameters in the model have not been eye-balled, not fit… difficult to quantify systematic uncertainties. Component that peaks at large ΔpT Kinematic limit B Production and Decay Meeting

9. Background mass distributions • Background shape is complicated. • Could explain the strange longitudinal polarization seen by DØ at low pT… B Production and Decay Meeting

10. Background Control Sample • If the background is dominated by , then we can select a pure background sample by requiring displaced tracks Require at least one track has more than 2 r-φ silicon hits and has |d0|>150 μm. Dominated by background. Complementary sample is everything that fails this selection. B Production and Decay Meeting

11. Angular distribution in side-bands • The displaced and non-displaced track samples have similar angular distributions: Error bars: displaced (scaled) Histogram: non-displaced P(Kolmogorov) = 89% P(Kolmogorov) = 67% B Production and Decay Meeting

12. Fit in background mass ranges • Five parameters: • Angular distribution coefficients: • Control sample cross section, • Non-displaced background scale factor, • Simultaneous fit to displaced and non-displaced track samples and to CMUP+CMU and CMUP+CMX samples. • Background is not spin-1: no reason to constrain to the physical range for spin-1 decays. B Production and Decay Meeting

13. Background fits B Production and Decay Meeting

14. Backgrounds under signals • The non-displaced background scale factor varies slightly with mass. • Fit it with a quadratic and interpolate into signal mass bins. Also calculate scale factor uncertainty in signal bins. Gaussian constraint applied to non-displaced background scale factor in signal fits. B Production and Decay Meeting

15. Signal Fits • Simultaneous fit to displaced track sample and non-displaced signal + background. • Fits are generally stable, although some fail to converge without some help with initial parameters. • Probably need to account for some additional systematic effects. • Very low statistics in displaced track sample at high pT… • Leads to additional instability • But the background is smoother here… B Production and Decay Meeting

16. ϒ(1S) results S-channel helicity frame Collins-Soper frame Background B Production and Decay Meeting

17. ϒ(2S) results S-channel helicity frame Collins-Soper frame Background B Production and Decay Meeting

18. ϒ(3S) results S-channel helicity frame Collins-Soper frame Background B Production and Decay Meeting

19. Observations • Behavior is still not perfect • Surprisingly large jumps between some pT bins • Occasional convergence issues in some bins • Next steps • Need to quantify possible difference between angular distributions in displaced and non-displaced track samples • Use wider mass range to get more statistics for displaced track sample at high pTwhere things are smoother? • Examine different pT binning. • Work on lowest pT bins (which are even less interesting). • Further discussion is welcome… B Production and Decay Meeting