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Upsilon Polarization at CDF

Upsilon Polarization at CDF. Matthew Jones Purdue University. Heavy Quarkonium : and . BB threshold. Very simple system – non-relativistic QM works:. Bottomonium Spectroscopy. cheat sheet radial excitations; can decay to P-wave states ( );

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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. Heavy Quarkonium: and BB threshold • Very simple system – non-relativistic QM works: Fermilab W&C Seminar

  3. Bottomonium Spectroscopy cheat sheet radial excitations; can decay to P-wave states (); The decays feed down to lower mass states The ground state; not yet observed at hadron colliders The states are vector mesons (spin 1) – they can be polarized! Transverse: Longitudinal: The system is similar, except that the charm quark is lighter. Fermilab W&C Seminar

  4. 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

  5. 1997 measurement: Silicon detector allows measurement of prompt fraction Not explained by Structure functions Production in B decays Feed-down from states What about the ϒsystem? No secondary component Calculations more reliable for heavy quarks? J/ψ Cross Section – Run I PRL 79, 572 (1997) X 30 Fermilab W&C Seminar

  6. 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

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

  8. 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: • Bound states are “color singlets” – no net color charge. • Color-octet terms might be really important! pQCD NRQCD matrix elements Fermilab W&C Seminar

  9. 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

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

  11. 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

  12. 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

  13. 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

  14. CDF Measurement Phys. Rev. Lett. 88, 161802 (2002). Template distributions for transverse/longitudinal polarization strongly influenced by detector acceptance. Fit yield in 8 bins of cosθ* Longitudinal Transverse Transverse: Longitudinal: • Observed distribution is isotropic - neither longitudinal nor transverse. Fermilab W&C Seminar

  15. 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… Different feed-down assumptions in kT calculations: decays preserve polarization destroy all polarization 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

  16. 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

  17. 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? elements of the spin-density matrix Fermilab W&C Seminar

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

  19. 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

  20. 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

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

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

  23. 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

  24. The CDF II Detector CENTRAL MUON SYSTEM CMP FORWARD MUON SYSTEM CMX 0.6<|η|<1 6 layers of double-sided silicon SVX-II • Two triggers used: • CMU*CMP (4 GeV) + CMU (3 GeV) • CMU*CMP (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

  25. The CDF Upsilon Sample • Two trigger scenarios: • Two central (CC) • Central+forward (CF) • Rapidity coverage: • CC: • CF: • Good signal separation: • Yields in : 550,000 ϒ(1S) 150,000 ϒ(2S) 76,000 ϒ(3S) CENTRAL-CENTRAL CENTRAL-FORWARD

  26. Analysis Method • Previous analysis techniques do not generalize well to fits in both cosθ and φ. • We can factor the detector acceptance and the underlying angular distribution: • A(cosθ,φ) from high statistics Monte Carlo • w(cosθ,φ; λθ, λφ,λθφ ) from the 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

  27. Geometric Acceptance • Geometric acceptance calculated with full detector simulation for each pT range analyzed • Muon detectors simulated with 100% efficiency Central + Forward Central + Central Fermilab W&C Seminar

  28. Trigger Efficiency Matched with muon • sample: • Selects J/ψ from B decays • Trigger requires that only one is a muon • Measures efficiency of muon trigger • sample: • Fully reconstructed decays • Kaon is unbiased • Measures efficiency of track trigger … not matched. matched with trigger track. … not matched. Fermilab W&C Seminar

  29. Analysis Method … 11 1 10 0 … • Two components in each mass range: signal + background Fermilab W&C Seminar

  30. 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. Fermilab W&C Seminar

  31. Background Structure This is just all toy Monte Carlo but it makes us worried… A polynomial may not describe the mass distribution under the signal when fitted using just the sidebands. Fermilab W&C Seminar

  32. Need for a New 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

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

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

  41. 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

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

  43. 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

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

  45. 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

  46. 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 • The decays really look isotropic… • As they did in Run I • Even when pT is large • Even for the ϒ(3S) Suggestive of significant feed-down/multiple incoherent production mechanisms. Fermilab W&C Seminar

  47. arXiv:1112.1591 Accepted for publication in Phys. Rev. Letters Fermilab W&C Seminar

  48. Additional Material Fermilab W&C Seminar

  49. 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

  50. 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

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