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Upsilon Polarization at CDF

Upsilon Polarization at CDF. Matthew Jones Purdue University. Quarkonium Production. Einhorn & Ellis: Phys. Rev. D12, 2007 (1975). Glover, Martin & Stirling : Z. Phys. C38, 473 (1988). Comparison with UA1 at. Or not…. 1997 measurement:

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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. 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

  3. 1997 measurement: Silicon detector allows measurement of prompt fraction Discrepancy between measurement and theory and not explained by Structure functions Production in B decays Feed-down from states J/ψ Cross Section – Run I PRL 79, 572 (1997) X 30 Fermilab W&C Seminar

  4. Color-Singlet Production Model • Production/decay via : • Production at hadron colliders: • Matrix elements also predict polarization. Fermilab W&C Seminar

  5. 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

  6. 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

  7. Octet Sum Singlet NRQCD + Color-Octet Models • Matrix elements tuned to accommodate Tevatron results Unknown NRQCD Matrix Elements adjusted to match data. Agreement with cross section is not too surprising now. We need an independent observable to really test the model. Cho & Leibovich, PRD 53, 6203 (1996). • Predicted transverseϒpolarization for Fermilab W&C Seminar

  8. Measuring “Polarization” • We don’t really measure polarization… • We actually measure the direction () of the in the ϒ rest frame. Boost into rest frame Fermilab W&C Seminar

  9. Measuring “Polarization” • Angular distributions depend on: • Spin and direction of initial state (ϒ is spin 1) • Spins of final state particles ( are spin ½) • Transverse polarization (helicityλ= ±1): • Longitudinal polarization (helicityλ= 0): • Fit data using Fermilab W&C Seminar

  10. CDF Measurement Phys. Rev. Lett. 88, 161802 (2002). Transverse: Longitudinal: Fit yield in 8 bins of cosθ* Longitudinal Transverse • Observed distribution is isotropic - neither longitudinal nor transverse. Fermilab W&C Seminar

  11. Another Model: “kT factorization” “un-integrated gluon density” Initial state gluon polarization related to kT • No need for color-octet terms… • Predicted longitudinalϒpolarization for Fermilab W&C Seminar

  12. 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

  13. ϒ(1S) Polarization in Run I • No strong polarization observed in ϒ(1S) decays... • What happens at high pT? • Feed-down from χb states? • Less feed-down for ϒ(2S) and ϒ(3S) states… 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

  14. 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). Fermilab W&C Seminar

  15. 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? • Which coordinate system is best? Fermilab W&C Seminar

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

  17. 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

  18. S-channel Helicity (SH) – ϒmomentum vector defines the z-axis, the x-axis is in the production plane Collins-Soper(CS) – z-axis bisects beam momentum vectors in ϒrest frame, x-axis in the production plane: Which coordinate system? Fermilab W&C Seminar

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

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

  21. 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-muon background Fermilab W&C Seminar

  22. 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

  23. 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 pT resolution • Bins are small compared to variations in w(cosθ,φ) Fermilab W&C Seminar

  24. Analysis Method • Two components in each mass range: signal + background Fermilab W&C Seminar

  25. Acceptance Calculation • Geometric acceptance calculated with full detector simulation for each pT range analyzed • Trigger and reconstruction efficiencies measured using J/ψμ+μ- and B+J/ψK+ control samples Central + Central Central + Forward Fermilab W&C Seminar

  26. The Background is Complicated • Dominant background: correlated production • Triggered sample is very non-isotropic • spectrum falls very rapidly • Angular distribution evolves rapidly with and • Very simple toy Monte Carlo shows that 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

  27. Need for aNew Approach Angular distributions in low-mass and high-mass sidebands are not the same as in background under the ϒ(nS) signals. • Sideband subtraction won’t work: • Dominant background is semi-leptonic B decays • Angular distributions not correlated with decay time • Muons with large impact parameters provides an almost pure background sample with the same angular distribution Beam spot Fermilab W&C Seminar

  28. Does it work? • We can check using the sidebands… • Displaced sample: one muon has impact parameter Beam spot Displaced sample: one muon has impact parameter Prompt sample: neithermuon has impact parameter Angular distributions in prompt and displaced samples are the same, both forand for . (CS frame) Fermilab W&C Seminar

  29. Measuring Background Fraction • The ratio of prompt/secondary distributions is almost constant. • Simultaneous fit to displaced sample and ϒ sidebands. • Avoids possible bias from modeling theϒline shape. Fermilab W&C Seminar

  30. Fits to signal + background mass bin, • The fit provides a good description of the angular distribution in both background and in signal+background samples. Collins-Soper frame S-channel helicity frame Fermilab W&C Seminar

  31. 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

  32. 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

  33. 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

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

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

  36. 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

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

  38. 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

  39. Comparison with previous results • Does not agree with result from DØ at about the 4.5σlevel • Unaccounted for systematics associated with 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

  40. 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

  41. Summary • Which formalism best describes J/ψ and ϒ production in hadron collisions is still debatable… • Angular distributions provides useful tests • New result from CDF: • First complete measurement of angular distribution of ϒ(nS) decays at a hadron collider. • First analysis of any aspect angular distributions of ϒ(3S) decays. • First demonstration of consistency in two reference frames • But the decays really look isotropic… • Even when pT is large • Even for the ϒ(3S) Suggestive of significant feed-down/multiple incoherent production mechanisms. Fermilab W&C Seminar

  42. Additional Material Fermilab W&C Seminar

  43. 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

  44. Toy Monte Carlo for correlated production Phys. Rev. D65, 094006 (2002): R.D. Field, “The sources of b-quarks at the Tevatron and their Correlations”. • 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 detector simulation and event reconstruction • Same analysis cuts applied to data pT(b) Δφ Δy E(μ) ApT Fermilab W&C Seminar

  45. 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

  46. Not much polarization... Maybe becomes slightly longitudinal at high pT. Not completely consistent with Run I result... What about the ϒ(1S)? CDF J/ψ Polarization Fermilab W&C Seminar

  47. J/ψ polarization at ALICE • Extract parameters from 1-dimensional projections: where • Iteratively tune Monte Carlo to calculate polarized acceptance • Hard to make it converge: • Assume that λθφ=0. • Impose invariance of as a constraint. Fermilab W&C Seminar

  48. J/ψ polarization at ALICE • Expect to extend measurement to higher pT using 2011 data. • No measurement in Collins-Soper frame from other collider experiments. Fermilab W&C Seminar

  49. Other Rotational Invariants This is the part that is invariant under rotations. Fermilab W&C Seminar

  50. General proof Fermilab W&C Seminar

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