Cross Sections and Spin Asymmetries in Hadronic Collisions

1. Cross Sections and Spin Asymmetries in Hadronic Collisions Jianwei Qiu Brookhaven National Laboratory KEK theory center workshop on high-energy hadron physics with hadron beams KEK, Japan, January 6-8, 2010 Jianwei Qiu

2. Outline • Cross sections and asymmetries: Role of the quantum interference or correlation • QCD and pQCD in hadronic collisions: Factorization – predictive power of pQCD calculation Expansion in inverse power of hard scale and in power of αs • Importance of NLO contributions in power of αs: Resummation to all orders in αs Resummation to all powers in power corrections • Asymmetries – leading power does not contribute: Single spin asymmetry, transverse momentum broadening, … • Role of J-PARC facility in hadron physics Jianwei Qiu

3. High energy hadronic collisions • High energy scattering process: PP (Jet, π, γ, J/ψ,…)X, w/o polarization In-state Out-state Momentum transfer Q=(PT, MJ/ψ, …) >> typical hadronic scale ~ 1/fm • Why these reactions? • Short-distance interaction – use of QCD perturbation theory • Important tests of our understanding of QCD • – role of high orders, resummation, power corrections, … • Important insights into proton structure • – parton densities, helicity distributions, multiparton correlations, … • Baseline for heavy-ion collisions, ... Jianwei Qiu

4. Cross sections and asymmetries • Cross section: Scattering amplitude square – Probability – Positive definite A function of in-state and out-state variables: momentum, spin, … • Spin-averaged cross section: • Asymmetries or difference of cross sections: – Positive definite Not necessary positive! Chance to see quantum interference directly Jianwei Qiu

5. Connecting hadrons to QCD partons • QCD confinement: Do not see partons in the detector! • Factorization - approximation: QCD parton dynamics Single active parton from each hadron! 2 2 (Diagrams with more active partons from each hadron!) A Probability ~ A Product of probabilities! Jianwei Qiu

6. PQCD factorization • Collinear factorization: Collinear on-shell active partons • Transverse-momentum dependent (TMD) factorization: On-shell active partons Not generally proved, but, used phenomenologically Jianwei Qiu

7. Predictive power of pQCD factorization • Prompt photon production as an example: Hard part: • Predictive power: • Short-distance part is Infrared-Safe, and calculable • Long-distance part can be defined to be Universal • Scale dependence – artifact of pQCD calculation • NLO is necessary • Power correction is process dependent – non-universal! Jianwei Qiu

8. Questions • What have we learned from hadronic collisions? NLO pQCD collinear factorization formalism has been very successful in interpreting data from high energy scattering • What is special for J-PARC and what J-PARC • can contribute to our knowledge of strong • interaction in hadronic collisions? J-PARC could provide crucial tests of QCD in a regime where NLO pQCD collinear factorization formalism has NOT been very successful Jianwei Qiu

9. Unpolarized inclusive DIS – one hadron Jianwei Qiu

10. Jet in hadronic collisions - two hadrons Inclusive Jet cross section at Tevatron: Run – 1b results Data and Predictions span 7 orders of magnitude! Jianwei Qiu

11. Prediction vs CDF Run-II data Highest ET jet ! Jianwei Qiu

12. Q2=10 GeV2 NLO Q2=10 GeV2 xf(x,Q2) xu xG(x0.05) xd xS(x0.05) x Universal parton distributions • Modern sets of PDFs with uncertainties: Consistently fit almost all data with Q > 2GeV Jianwei Qiu

13. Jet production at RHIC - two hadrons • STAR: PRL97, 252001 (2006) NLO Calclation: Jäger, Stratmann, Vogelsang Jianwei Qiu

14. Inclusive single hadron at RHIC – 3 hadrons • PHENIX: PRD76, 051106 (2007) Jianwei Qiu

15. Extending x coverage and particle type Large rapidity p,K,p cross sections for p+p, s=200 GeV • BRAHMS: PRL98, 252001 (2007) Jianwei Qiu

16. Direct photon at RHIC • PHENIX: Sakaguchi, 2008 Jianwei Qiu

17. Polarized inclusive DIS – one hadron • Success of the NLO formalism: Jianwei Qiu

18. RHIC Spin Program • Collider of two 100 (250) GeV polarized proton beam: • The asymmetry: Jianwei Qiu

19. RHIC Measurements on ΔG Star jet Phenix π0 Small asymmetry leads to small gluon “helicity” distribution Jianwei Qiu

20. Current status on ΔG • Definition: • NLO QCD global fit - DSSV: PRL101,072001(2008) Strong constraint on ΔG from Jianwei Qiu

21. Large SSA in hadronic collisions • Hadronic : Jianwei Qiu

22. SSA in parton model • One collinear parton per hadron in hard collision: • Helicity – flip quark mass term • Generate the phase from the loop diagram αs SSA vanishes in the parton model: • spin-dependence of parton’stransverse motion Jianwei Qiu

23. Cross section with ONE large scale Too large to compete! Three-parton correlation • QCD Collinear factorization approach is more relevant • SSA – difference of two cross sections with spin flip • is power suppressed compared to the cross section – Expansion • Sensitive to twist-3 multi-parton correlation functions • Integrated information on parton’s transverse motion Koike’s talk Jianwei Qiu

24. Pion production at fixed target energies • A long standing problem: Data is much higher than NLO at fixed-target energies! Aurenche et al.; Bourrely, Soffer Jianwei Qiu

25. Direct photon at fixed target energies • Another long standing problem: Aurenche et al., PRD73, 094007(2007) Jianwei Qiu

26. Large high order corrections in power of αs • Higher order corrections beyond NLO: Threshold logarithms where • Threshold logarithm is a consequence of the rapidity • integration of the generic perturbative term: with The limit: inhibits the real emission while the soft /collinear gluon emission is still allowed Jianwei Qiu

27. Enhanced by steep falling parton flux • Convolution with parton distributions: where • Partonic flux: The product of parton distributions strongly favor the region where xx’ small, that is, enhances the region where • Solution: Threshold resummation – resum to all powers. Sterman; Catani, Trentadue; … • Threshold resummation is particularly important for • J-PARC energy Chance to probe QCD high order dynamics Jianwei Qiu

28. Threshold resummation – Single scale • Resummation is usually done in a “transformed” space: • Express energy (or momentum) conservation δ-function as • Individual zi-integration transform the function of ziinto the • “transformed” space • Threshold resummation: Mellin moments of : Jianwei Qiu

29.  Resummation for single hadron production • Resummed “coefficient” functions: de Florian,Vogelsang, 2005 “Observed” partons Unobserved recoil jet where • Correction to gggg: Big enhancement factor: Jianwei Qiu

30. Improvement from resummation E706 WA70 de Florian,Vogelsang, 2005 Jianwei Qiu

31. Improvement to direct photon production • Direct contribution: Relatively small resummation effect: for the Compton term Catani et al.; Sterman, Vogelsang; Kidonakis, Owens • Fragmentation contribution: Similar enhancement for gggg, but, gluon fragmentation function to photon is very small! Jianwei Qiu

32. Drell-Yan at low QT – two scales • Fixed-order collinear pQCD calculation: Note: • “integrated” QT distribution: Effect of gluon emission Assume this exponentiates • “resummed” QTdistribution – DDT formalism: as QT→0 Jianwei Qiu

33. CSS resummation formalism • Experimental fact: • Why? Particle can receive many finite kT kicks via soft gluon radiation yet still have QT=0 – Vector sum! • Subleading logarithms are equally important at QT=0 • Solution: impose 4-momentum conservation at each step of soft gluon resummation Jianwei Qiu

34. “b”-space resummation • The formula: • “b”-space distribution – perturbative at small b: • Predictive power: IF long b-space tail is not important for the b-integration Large Q Large phase space for the shower = large s Jianwei Qiu

35. Examples with large Q Qiu and Zhang, PRL, 2001 Power correction is very small, excellent prediction! Jianwei Qiu

36. Example with low Q large phase space CDF Run-I D0 Run-II A prediction CEM with all order resummation of soft gluon shower Berger, Qiu, Wang, 2005 Jianwei Qiu

37. Example with low Q small phase space Qiu and Zhang, PRD, 2001 IF bmax ~ 0.3 1/GeV Jianwei Qiu

38. Drell-Yan lepton angular distributions • The observable: • “Helicity structure functions”: NO CSS resummation proved for these “structure functions”! The CSS formalism only proved for inclusive Drell-Yan • Idea: Connect the resummation of these structure functions to the resummation of the inclusive Drell-Yan cross section – helper: EM gauge invariance Berger, Qiu, Rodriguez, 2007 Jianwei Qiu

39. Resummed “helicity structure functions” • Drell-Yan hadronic tensor: where are functions of and the choice of frame • EM current conservation: for all values of even when • Connection to inclusive cross section: • Difficulty for : No LO perturbative double logs! Jianwei Qiu

40. Lam-Tung relation Peng’s talk • Normalized Drell-Yan angular distribution: • Lam-Tung relation: • TMD Boer-Mulders function: Boer’s talk J.C. Peng, 2008 Extending CSS resummation Collins, Qiu and Sterman Jianwei Qiu

41. Coherent soft interaction A Quarkonium B Perturbative Non-perturbative Different models Different assumptions/treatments on how the heavy quark pair becomes a quarkonium? Heavy quarkonium production • Fact: After more than 35 years, since the discovery of J/y, we still have not been able to fully understand the production mechanism of heavy quarkonia • Basic production mechanism: Jianwei Qiu

42. Popular production models • Color singlet model: Chang 1974, Einhornand Ellis (1975), … • Only pairs with right quantum number can become quarkonia • Non-perturbative part ~ decay wave function squared • Color evaporation model: Fritsch (1978); Halzen; … • All colored or color singlet pairs with invariant mass less then open charm threshold could become bound quarkonia • Non-perturbative part = one constant per quarkonium state • NRQCD model: Bodwin, Braaten, Lapage (1994); … • All colored or color singlet pairs could become quarkonia • Power expansion in relative velocity of heavy quark pairs • Non-perturbative part = one matrix element per QQ state Jianwei Qiu

43. CSM: Huge high order corrections Jianwei Qiu

44. Polarization of quarkonium at Tevatron • Measure angular distribution of μ+μ− in J/ψ decay • Normalized distribution: Jianwei Qiu

45. Surprises from polarization measurements • Transverse polarization at high pT? NRQCD: Cho & Wise, Beneke & Rothstein, 1995, … KT-fact: Baranov, 2002 CDF Collaboration, PRL 2007 Jianwei Qiu

46. Exclusive production in e+e- Li, He, and Chao, Braaten and Lee, … • Double charm production: LO • Possible resolution for J/ψ+ηc: Zhang, Gao, Chao, PRL Kfactor = 1.96 • NLO correction: • Relativistic Correction: Kfactor = 1.34 X-section: Wave func: Kfactor = 1.32 Combined: Kfactor = 4.15 Bodwin et al. hep-ph/0611002 Jianwei Qiu

47. Belle: NRQCD: Belle: Production rate of is larger than all these channels: combined ? Inclusive production in e+e- • Charm associated production: Kiselev, et al 1994, Cho, Leibovich, 1996 Yuan, Qiao, Chao, 1997 • Ratio to light flavors: • Message: Jianwei Qiu

48. PQCD Quantum inteference NRQCD Factorization • None of the factorized production models, including NRQCD model, were proved theoretically • Factorization of NRQCD model fails for low pT • Factorization of NRQCD model might work for large pT Spectator interactions are suppressed by (1/pT)n Factorization is necessary for the predictive power Jianwei Qiu

49. 2 2 2 Factorization: fragmentation contribution Nayak, Qiu, Stermen, 2005 • Fragmentation contribution at large PT  • Fragmentation function – gluon to a hadron H (e.g., J/ψ): Cannot get fragmentation func. from PDFs or decay matrix elements Jianwei Qiu

50. IR safe • gauge invariant and universal • independent of the direction of the Wilson lines with Connection to NRQCD Factorization • Proposed NRQCD factorization: • Proved pQCD factorization for single hadron production: • Prove NRQCD Factorization To prove: • Status: Have not been able to prove or disprove this! Jianwei Qiu