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Upsilon Polarization at CDF

Upsilon Polarization at CDF. Matthew Jones Purdue University. Brookhaven, 1968. PDP-6 – 36 bit processor. First observation of charmonium. Second observation of charmonium. SLAC Mark I. BNL E-598. Bottomonium. Fermilab E288: CFS collaboration. Over 30 years later….

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Upsilon Polarization at CDF

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  1. Upsilon Polarization at CDF Matthew Jones Purdue University Fermilab W&C Seminar

  2. Brookhaven, 1968 PDP-6 – 36 bit processor Fermilab W&C Seminar

  3. First observation of charmonium Fermilab W&C Seminar

  4. Second observation of charmonium SLAC Mark I BNL E-598 Fermilab W&C Seminar

  5. Bottomonium Fermilab E288: CFS collaboration Fermilab W&C Seminar

  6. Over 30 years later… CESR/CUSB (1980’s) BB threshold PEP II/BaBar (2008) Fermilab W&C Seminar

  7. Quarkonium Production Einhorn & Ellis: Phys. Rev. D12, 2007 (1975). Glover, Martin & Stirling: Z. Phys. C38, 473 (1988). Comparison with UA1 at Or not… Fermilab W&C Seminar

  8. Color-Singlet Production Model • Production/decay via : • Production at hadron colliders: • Definite prediction for polarization! Fermilab W&C Seminar

  9. Color Evaporation Model • pairs produced with must eventually form a bound state. Halzen - Phys. Lett. B 69, 105 (1977) Fritzsch- Phys. Lett. B 67, 217 (1977) • Unable to predict polarization… Fermilab W&C Seminar

  10. The CDF Detector in Run Ia Fermilab W&C Seminar

  11. 1992 measurement: No prompt/secondary separation Assumptions: Fraction from B decays? Feed-down from excited states? J/ψ Cross Section – Run Ia PRL 69, 3704 (1992) Fermilab W&C Seminar

  12. Muon upgrades: CMX (|η|<1) + CMP (|ηmax| ~ 0.4) Muon triggers: Level 1 trigger: Muon stubs Level 2 trigger: Association with tracks The CDF Detector in Run Ib Fermilab W&C Seminar

  13. 1997 measurement: Silicon detector allows measurement of prompt fraction Excess and shape not explained by Structure functions Production in B decays Feed-down from states J/ψ Cross Section – Run Ib PRL 79, 572 (1997) X 30 Fermilab W&C Seminar

  14. 1995 measurement: No feed-down from B decays Also a significant excess! Run I ϒ(nS)Cross Section PRL 75, 4358 (1995) |y| < 0.4 Direct + feed-down from decays Direct Fermilab W&C Seminar

  15. Non-Relativistic QCD Caswell & Lepage – Phys. Lett. 167B, 437 (1986) Bodwin, Braaten & Lepage – Phys. Rev. D 51, 1125 (1995) • Expansion in powers of and • Factorization hypothesis applied to ϒ: • Color-octet terms are important! pQCD NRQCD matrix elements Fermilab W&C Seminar

  16. Octet Sum Singlet NRQCD + Color-Octet Models • Matrix elements tuned to accommodate Tevatron results • Apparently not needed to explain J/ψ cross section measurements from HERA: Cho & Leibovich, PRD 53, 6203 (1996). • Predicted transverseϒpolarization for Fermilab W&C Seminar

  17. “Polarization” Transverse: Longitudinal: Phys. Rev. Lett. 88, 161802 (2002). Longitudinal Fit yield in 8 bins of cosθ* Transverse Fermilab W&C Seminar

  18. Another Approach: “kT factorization” “un-integrated gluon density” Initial state gluon polarization related to kT • No need for color-octet terms… • Some criticism of the method (not gauge invariant) • Predicted longitudinal ϒpolarization for Fermilab W&C Seminar

  19. Higher-order QCD calculations • Partial calculation including terms up to … • Large increase in cross section compared with LO calculation • No need for color-octet contributions • Predicts longitudinalϒpolarization for Artoisenet, et al – Phys. Rev. Lett. 101, 152001 (2008). Fermilab W&C Seminar

  20. ϒ(1S) Polarization in Run I • No strong polarization observed in ϒ(1S) decays... • What happens at high pT? • Feed-down from χb states? • Expect better comparison with ϒ(2S) and ϒ(3S)? CDF Run I: Phys. Rev. Lett. 88, 161802 (2002). NRQCD: Phys. Rev. D63, 071501(R) (2001). kT-factorization: JETP Lett. 86, 435 (2007). NNLO*: Phys. Rev. Lett. 101, 152001 (2008). Fermilab W&C Seminar

  21. Tevatron Run II The end! New CDFϒ(nS) polarization Preliminary CDFϒ(1S) polarization DØ ϒ(1S), ϒ(2S) polarization CDFψ(2S) cross section CDF J/ψ, ψ(2S) polarization (CDF Run Iϒ(1S) polarization) Run I Fermilab W&C Seminar

  22. ϒ Polarization from DØ in Run II DØ Run II: Phys. Rev. Lett. 101, 182004 (2008). CDF Run I: Phys. Rev. Lett. 88, 161802 (2002). NRQCD: Phys. Rev. D63, 071501(R) (2001). kT-factorization: JETP Lett. 86, 435 (2007). NNLO*: Phys. Rev. Lett. 101, 152001 (2008). • Not sure what to make of this… • Inconsistent with any model • Inconsistent with CDF result • Different rapidity coverage? Fermilab W&C Seminar

  23. Suggested New Paradigm • Faccioli, et al remind us… Phys. Rev. Lett. 102, 151802 (2009). • General spin-1 state: • Angular distribution when decaying to fermions: … • A pure state cannot have all simultaneously. • Incoherence due to feed-down from multiple sources? • Choice of reference frame is important. • Collins-Soper frame may be more appropriate. Fermilab W&C Seminar

  24. Fixed Target Experiments? • J/ψ polarization measurements in fixed-target experiments apparently inconsistent • Consistent picture might emerge when taking into account the full 3-d nature of the angular distributions Fermilab W&C Seminar

  25. Transverse: Longitudinal: Transverse/Longitudinal Insufficient But an arbitrary rotation will preserve the transverse/longitudinal shape... Fermilab W&C Seminar

  26. 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. • Invariant under rotations: Fermilab W&C Seminar

  27. Helicity (HX) – J/ψmomentum vector in C.M. frame of colliding beams (natural for production in gluon fragmentation) Gottfried-Jackson (GJ) – Direction of beam momentum in J/ψrest frame (better suited for spin transferred from initial hadron) Collins-Soper (CS) – Bisector of beam momentum vectors in J/ψrest frame (~C.M. frame of colliding partons) Which polarization axis? Fermilab W&C Seminar

  28. Could it be possible? S-channel helicity frame Fermilab W&C Seminar

  29. Could it be possible? Collins-Soper frame Fermilab W&C Seminar

  30. New CDF Analysis • Goals: • Use both central and forward muon systems • Measure all three parameters simultaneously • Measure in Collins-Soper and 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-muonbackground Fermilab W&C Seminar

  31. The CDF II Detector Central Muon Upgrade CMP Central Muon Extension CMX 0.6<|η|<1 6 layers of double-sided silicon SVX-II • Two triggers used: • CMUP (4 GeV) + CMU (3 GeV) • CMUP (4 GeV) + CMX (3 GeV) • Both require: • opposite charge • 8 < m(μ+μ-) < 12 GeV/c2 Drift chamber 1.4 Tesla field COT • Integrated luminosity: 6.7 fb-1 • Sample size: 550,000 ϒ(1S) • 150,000 ϒ(2S) • 76,000 ϒ(3S) Central Muon System CMU |η|<0.6 Fermilab W&C Seminar

  32. Analysis Method • Previous analysis techniques do not generalize well to fits in both cosθ and φ. • Instead, we factor the acceptance and angular distribution: • A(cosθ,φ) from high statistics Monte Carlo • w(cosθ,φ; λθ, λφ,λθφ ) from angular distribution • Use binned likelihood fit to observed distribution of (cosθ,φ) to determine λθ, λφ,λθφ. • Bins are large compared to angular and pTresolution • Bins are small compared to variations in w(cosθ,φ) Fermilab W&C Seminar

  33. Analysis Method • Trigger and reconstruction efficiencies measured using J/ψμ+μ- and B+J/ψK+ control samples • Geometric acceptance calculated using full detector simulation • Two component fit: • signal + background Fermilab W&C Seminar

  34. The Background is Complicated • Dominant background: correlated production • Triggered sample is very non-isotropic • pT(b) spectrum falls rapidly with pT • Angular distribution evolves rapidly with pT and m(μ+μ-) • Very simple toy Monte Carlo: peaking backgrounds may be present in some pT ranges. 5-6 GeV/c 6-7 GeV/c 4-5 GeV/c m(μ+μ- ) Fermilab W&C Seminar

  35. A New Approach – by example Phys. Rev. Lett. 106, 121804 (2011) • lifetime analysis: • We do not fit m(J/ψK+) in bins of ct(J/ψK+)… • Instead, we expect the background decay time distribution to be independent of mass • Mass sidebands constrain its shape Fermilab W&C Seminar

  36. New Approach • Use muon impact parameter to isolate a background-enhanced (displaced) sample • Complimentary sample (prompt) contains most of the ϒ(nS) signal. • Impact parameter requirement must not bias angular distributions • Fit to invariant mass distribution: • Measure fraction of ϒ(nS) signal present in displaced sample • Fit to displaced sample + prompt sidebands: • Measures ratio of prompt/displaced backgrounds • Not biased by signal line shape model • Allows us to predict the level of prompt background under the ϒ(nS) • Two component fit to (cosθ,φ) distribution • Determines λθ, λφ,λθφfor signal and background • Purely empirical parameterization of background – helpful to add additional term Fermilab W&C Seminar

  37. Background Proxy Sample • Measure fraction of signal in displaced sample: This fit measures the fraction of the ϒ signal that is present in the displaced sample (1-4%) Fermilab W&C Seminar

  38. Background Proxy Sample • Measure prompt scale factor: The ratio of prompt/secondary distributions is almost constant. Simultaneous fit to displaced sample and ϒ sidebands. Avoids possible bias from modeling theϒline shape. Quadratic scale factor function considered in systematic studies. Fermilab W&C Seminar

  39. Angular distributions in sidebands • The sub-sample containing a displaced track (|d0| > 150 μm) is a good description of the background under the ϒ(nS): • Prompt (histogram) and displaced (error bars) angular distributions match in the sidebands. • We use the displaced muon sample to constrain the angular distribution of background under the ϒ(nS) peaks. Fermilab W&C Seminar

  40. Fits to signal + background • The fit provides a good description of the angular distribution in both background and in signal + background mass bins. Only background Signal + background Fermilab W&C Seminar

  41. Fitted Parameters Signal and background have very different angular distributions. Background is highly “polarized” but the signal is not. mass bin numbers Fermilab W&C Seminar

  42. Consistency Tests It can be shown that the expression is the same in all reference frames. We observe that indeed it is. Fermilab W&C Seminar

  43. Frame Invariance Tests • Differences generally consistent with expected size of statistical fluctuations • Differences used to quantify systematic uncertainties on λθ, λφ and λθφ Fermilab W&C Seminar

  44. Results for ϒ(1S) state • λθ • λφ • λθφ • What about the ϒ(2S) and ϒ(3S) states? • λθ • λφ • λθφ Fermilab W&C Seminar

  45. Results for ϒ(2S) state • λθ • λφ • λθφ • Looks quite isotropic, even at high pT… • λθ • λφ • λθφ Fermilab W&C Seminar

  46. First measurement of ϒ(3S) spin alignment • λθ • λφ • λθφ • No evidence for significant polarization. Statistical Stat+syst. • λθ • λφ • λθφ Fermilab W&C Seminar

  47. Comparison with Models • Previous predictions for in the S-channel helicity frame: Fermilab W&C Seminar

  48. Comparison with previous results Agrees with previous CDF publication from Run I • NRQCD – Braaten & Lee, Phys. Rev. D63, 071501(R) (2001) • kT – Baranov & Zotov, JETP Lett. 86, 435 (2007) Fermilab W&C Seminar

  49. Comparison with previous results • Does not agree with result from DØ at about the 4.5σ level • Different rapidity coverage? • Subtraction of highly polarized background? • NRQCD – Braaten & Lee, Phys. Rev. D63, 071501(R) (2001) • kT – Baranov & Zotov, JETP Lett. 86, 435 (2007) Fermilab W&C Seminar

  50. Comparisons with newer calculations CDF Run II preliminary – 6.7 fb-1 Nucl. Phys. B 214, 3 (2011) summary: • NLO NRQCD – Gong, Wang & Zhang, Phys. Rev. D83, 114021 (2011) • Color-singlet NLO and NNLO* - Artoisenent, et al. Phys. Rev. Lett. 101, 152001 (2008) NLO NRQCD with color-octet matrix elements Significant uncertainty due to feed-down from states (conservative assumptions) NLO color- singlet Fermilab W&C Seminar

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