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 January 6, 2010 Jianwei Qiu

January 6, 2010 Jianwei Qiu 2 Outline  QCD and pQCD in hadronic collisions:  Cross sections and asymmetries: Role of the quantum interference or correlation Factorization – predictive power of pQCD calculation Expansion in inverse power of hard scale and in power of α s  Importance of NLO contributions in power of α s : Resummation to all orders in α s 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

January 6, 2010 Jianwei Qiu 3  High energy scattering process: High energy hadronic collisions PP  (Jet, π, γ, J/ ψ,…)X, w/o polarization Momentum transfer Q=(P T, M J/ ψ, …) >> typical hadronic scale ~ 1/fm In-stateOut-state  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,...

January 6, 2010 Jianwei Qiu 4 Scattering amplitude square – Probability – Positive definite A function of in-state and out-state variables: momentum, spin, …  Spin-averaged cross section: Not necessary positive! Chance to see quantum interference directly – Positive definite  Asymmetries or difference of cross sections: Cross sections and asymmetries  Cross section:

January 6, 2010 Jianwei Qiu 5 Connecting hadrons to QCD partons  QCD confinement: QCD parton dynamics  Factorization - approximation: Do not see partons in the detector! Single active parton from each hadron! (Diagrams with more active partons from each hadron!) A Probability ~ A Product of probabilities! 2 2

January 6, 2010 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

January 6, 2010 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  Power correction is process dependent – non-universal!  NLO is necessary

January 6, 2010 Jianwei Qiu 8 Questions  What have we learned from hadronic collisions?  What is special for J-PARC and what J-PARC can contribute to our knowledge of strong interaction in hadronic collisions? NLO pQCD collinear factorization formalism has been very successful in interpreting data from high energy scattering J-PARC could provide crucial tests of QCD in a regime where NLO pQCD collinear factorization formalism has NOT been very successful

January 6, 2010 Jianwei Qiu 9 Unpolarized inclusive DIS – one hadron

January 6, 2010 Jianwei Qiu 10 Jet in hadronic collisions - two hadrons Data and Predictions span 7 orders of magnitude! Inclusive Jet cross section at Tevatron: Run – 1b results

January 6, 2010 Jianwei Qiu 11 Prediction vs CDF Run-II data Highest E T jet !

January 6, 2010 Jianwei Qiu 12 Universal parton distributions  Modern sets of PDFs with uncertainties: Consistently fit almost all data with Q > 2GeV xf(x,Q 2 ) x Q 2 =10 GeV 2 xu xd xS (x0.05) xG (x0.05) NLO

January 6, 2010 Jianwei Qiu 13 Jet production at RHIC - two hadrons  STAR: NLO Calclation: Jäger, Stratmann, Vogelsang PRL97, (2006)

January 6, 2010 Jianwei Qiu 14 Inclusive single hadron at RHIC – 3 hadrons  PHENIX: PRD76, (2007)

January 6, 2010 Jianwei Qiu 15 Extending x coverage and particle type  BRAHMS: PRL98, (2007) Large rapidity ,K,p cross sections for p+p,  s=200 GeV

January 6, 2010 Jianwei Qiu 16 Direct photon at RHIC  PHENIX: Sakaguchi, 2008

January 6, 2010 Jianwei Qiu 17 Polarized inclusive DIS – one hadron  Success of the NLO formalism:

January 6, 2010 Jianwei Qiu 18 RHIC Spin Program  Collider of two 100 (250) GeV polarized proton beam:  The asymmetry:

January 6, 2010 Jianwei Qiu 19 RHIC Measurements on Δ G Star jet Phenix π 0 Small asymmetry leads to small gluon “helicity” distribution

January 6, 2010 Jianwei Qiu 20 Current status on Δ G  Definition:  NLO QCD global fit - DSSV: PRL101,072001(2008) Strong constraint on Δ G from

January 6, 2010 Jianwei Qiu 21 Large SSA in hadronic collisions  Hadronic :

January 6, 2010 Jianwei Qiu 22  One collinear parton per hadron in hard collision:  Helicity – flip quark mass term  Generate the phase from the loop diagram α s SSA in parton model SSA vanishes in the parton model:  spin-dependence of parton’s transverse motion

January 6, 2010 Jianwei Qiu 23  QCD Collinear factorization approach is more relevant – Expansion Cross section with ONE large scale Too large to compete! Three-parton correlation  SSA – difference of two cross sections with spin flip is power suppressed compared to the cross section  Sensitive to twist-3 multi-parton correlation functions  Integrated information on parton’s transverse motion Koike’s talk

January 6, 2010 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

January 6, 2010 Jianwei Qiu 25 Direct photon at fixed target energies  Another long standing problem: Aurenche et al., PRD73, (2007)

January 6, 2010 Jianwei Qiu 26  Higher order corrections beyond NLO: where Threshold logarithms  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 Large high order corrections in power of α s

January 6, 2010 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

January 6, 2010 Jianwei Qiu 28 Threshold resummation – Single scale  Resummation is usually done in a “transformed” space:  Express energy (or momentum) conservation δ -function as  Individual z i -integration transform the function of z i into the “transformed” space Mellin moments of :  Threshold resummation:

January 6, 2010 Jianwei Qiu 29 Resummation for single hadron production de Florian, Vogelsang, 2005  Resummed “coefficient” functions:  “Observed” partons Unobserved recoil jet where  Correction to gg  gg: Big enhancement factor:

January 6, 2010 Jianwei Qiu 30 Improvement from resummation E706 de Florian, Vogelsang, 2005 WA70

January 6, 2010 Jianwei Qiu 31 Improvement to direct photon production  Direct contribution: Relatively small resummation effect: Catani et al.; Sterman, Vogelsang; Kidonakis, Owens for the Compton term  Fragmentation contribution: Similar enhancement for gg  gg, but, gluon fragmentation function to photon is very small!

January 6, 2010 Jianwei Qiu 32 Drell-Yan at low Q T – two scales   Fixed-order collinear pQCD calculation: Note:   “integrated” Q T distribution: Effect of gluon emission Assume this exponentiates   “resummed” Q T distribution – DDT formalism: as Q T →0

January 6, 2010 Jianwei Qiu 33 CSS resummation formalism  Experimental fact:  Why? Particle can receive many finite k T kicks via soft gluon radiation yet still have Q T =0 – Vector sum!  Subleading logarithms are equally important at Q T =0  Solution: impose 4-momentum conservation at each step of soft gluon resummation

January 6, 2010 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

January 6, 2010 Jianwei Qiu 35 Power correction is very small, excellent prediction! Examples with large Q Qiu and Zhang, PRL, 2001

January 6, 2010 Jianwei Qiu 36 Example with low Q large phase space Berger, Qiu, Wang, 2005 CEM with all order resummation of soft gluon shower CDF Run-I D0 Run-II A prediction

January 6, 2010 Jianwei Qiu 37 IF b max ~ 0.3 1/GeV Example with low Q small phase space Qiu and Zhang, PRD, 2001

January 6, 2010 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

January 6, 2010 Jianwei Qiu 39 Resummed “helicity structure functions”  Drell-Yan hadronic tensor:  EM current conservation: where are functions of and the choice of frame for all values of even when  Connection to inclusive cross section:  Difficulty for : No LO perturbative double logs!

January 6, 2010 Jianwei Qiu 40 Lam-Tung relation  Normalized Drell-Yan angular distribution:  Lam-Tung relation: J.C. Peng, 2008 Peng’s talk  TMD Boer-Mulders function: Extending CSS resummation Collins, Qiu and Sterman Boer’s talk

January 6, 2010 Jianwei Qiu 41 Heavy quarkonium production After more than 35 years, since the discovery of J  we still have not been able to fully understand the production mechanism of heavy quarkonia  Fact:  Basic production mechanism: Coherent soft interaction Quarkonium Perturbative Non-perturbative A B Different models  Different assumptions/treatments on how the heavy quark pair becomes a quarkonium?

January 6, 2010 Jianwei Qiu 42 Popular production models  Color singlet model:  Only pairs with right quantum number can become quarkonia  Non-perturbative part ~ decay wave function squared  Color evaporation model:  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:  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 Chang 1974, Einhorn and Ellis (1975), … Fritsch (1978); Halzen; … Bodwin, Braaten, Lapage (1994); …

January 6, 2010 Jianwei Qiu 43 CSM: Huge high order corrections

January 6, 2010 Jianwei Qiu 44 Polarization of quarkonium at Tevatron  Measure angular distribution of μ + μ − in J/ ψ decay  Normalized distribution:

January 6, 2010 Jianwei Qiu 45 Surprises from polarization measurements  Transverse polarization at high p T ? NRQCD: Cho & Wise, Beneke & Rothstein, 1995, … CDF Collaboration, PRL 2007 KT-fact: Baranov, 2002

January 6, 2010 Jianwei Qiu 46 Li, He, and Chao, Braaten and Lee, … LO  Possible resolution for J/ ψ + η c : Exclusive production in e + e -  Double charm production:  NLO correction:  Relativistic Correction: K factor = 1.96 K factor = 1.34 X-section: Wave func: K factor = 1.32 K factor = 4.15 Bodwin et al. hep-ph/ Combined: Zhang, Gao, Chao, PRL

January 6, 2010 Jianwei Qiu 47  Charm associated production: Kiselev, et al 1994, Cho, Leibovich, 1996 Yuan, Qiao, Chao, 1997  Ratio to light flavors: Production rate of is larger than  Message: combined ? all these channels: Inclusive production in e + e - Belle: NRQCD: Belle:

January 6, 2010 Jianwei Qiu 48 Factorization  None of the factorized production models, including NRQCD model, were proved theoretically  Factorization of NRQCD model fails for low p T NRQCD PQCD Quantum inteference  Factorization of NRQCD model might work for large p T Spectator interactions are suppressed by (1/p T ) n Factorization is necessary for the predictive power

January 6, 2010 Jianwei Qiu 49  Fragmentation contribution at large P T   Fragmentation function – gluon to a hadron H (e.g., J/ ψ ): Nayak, Qiu, Stermen, 2005 Factorization: fragmentation contribution Cannot get fragmentation func. from PDFs or decay matrix elements

January 6, 2010 Jianwei Qiu 50 Connection to NRQCD Factorization  Proposed NRQCD factorization:  Proved pQCD factorization for single hadron production:  Prove NRQCD Factorization To prove: with  IR safe  gauge invariant and universal  independent of the direction of the Wilson lines  Status: Have not been able to prove or disprove this!

January 6, 2010 Jianwei Qiu 51 Leading power in M H /P T  Cross section is given by the fragmentation contribution:  partonic part should be infrared safe for all powers in α s :  fragmentation functions obey the DGLAP evolution  Only difference from single pion production is the fragmentation functions  Should only apply to the region where P T >> M H  Can we do better at lower P T ? Power correction in 1/P T – direct production

January 6, 2010 Jianwei Qiu 52 Factorization for heavy quarkonium production  Factorized cross section:  Expect the first two terms to dominate:  H (4) are IR safe and free of large logarithms  D (4) are fragmentation functions of 4-quark operators Kang, Qiu and Sterman Qiu, 1990  Urgent projects: Calculation of H (4) and evolution of D (4)

January 6, 2010 Jianwei Qiu 53 “Direct” production of heavy quark pairs  Removal of fragmentation logarithms:  All partonic hard parts are evaluated at P T : Project the factorized formula to the state H (4) are free of large logarithms – absorbed into the PDFs and fragmentation functions Smooth transition from high P T to P T ~ M H Need “new” non-perturbative fragmentation functions

January 6, 2010 Jianwei Qiu 54 Summary and outlook  QCD has been very successful in interpreting data in high energy collisions  However, the successful collinear factorization formalism has difficulties to explain phenomena at fixed target energies, where high order pQCD corrections, so as new types of QCD dynamics become important.  J-PARC facility could make crucial contributions to our understanding of QCD and strong interaction via measurements of single hadron, photon, dilepton, heavy quarkonium, and etc. as well as asymmetries of these reliable observables Thank you!

55 Backup transparencies January 6, 2010 Jianwei Qiu

56  Matrix elements of parton operators: January 6, 2010 Jianwei Qiu Twist = dimension of the operator – its spin High twist matrix elements  Parton distributions and helicity distributions: Matrix elements of twist-2 operators:, Probability interpretation  Multi-parton correlation functions: Matrix elements of high twist operators: NO simple probability interpretation!, More interesting QCD dynamics!

57 January 6, 2010 Jianwei Qiu  Factorization – connecting partons to hadrons: Twist-n parton distribution/correlation: High twist effects = power corrections  QCD confinement: Experiments measure hadrons and leptons, not partons! Cross section and power corrections  Cross section with a large momentum transfer: Power expansion:

January 6, 2010 Jianwei Qiu 58 “Enhance” the power corrections  Calculable high twist effects are in general “small”: If the 1 st power correction is large, immediate question is what is the size of the next power corrections High twist effects are small for fully inclusive cross section  Observables – leading power term vanishes: Single transverse spin asymmetry: Transverse momentum broadening:  Observables – large power corrections – resummation:,,, …

January 6, 2010 Jianwei Qiu 59  NLO global fitting leads to negative gluon distribution at low x and Q 2 MRST, CTEQ PDF’s have the same features Does it mean that we have no gluon for x < at 1 GeV? No! Negative gluon distribution at low x, Q 2 ?

January 6, 2010 Jianwei Qiu 60 Recombination prevents negative gluon  Small-x gluons are not localized in a Lorentz contracted nucleon Data  Gluon recombination Gribov, Levin, Ryskin, 83 Recombination  Recombination slows down Q 2 -evolution  Prevents the distribution to be negative Mueller, Qiu, 86, McLerran, Venugopalan, 94, … Eskola, et al. 03

61  Hard probe – process with a large momentum transfer:  Size of a hard probe is very localized and much smaller than a typical hadron at rest:  But, it might be larger than a Lorentz contracted hadron: If an active parton x is small enough the hard probe could cover several nucleons in a Lorentz contracted large nucleus! January 6, 2010 Jianwei Qiu Hard probe at low x

January 6, 2010 Jianwei Qiu 62  In target rest frame:  If, the q-qbar state of the virtual photon can interact with whole hadron/nucleus coherently. The conclusion is frame independent Frame dependence?

January 6, 2010 Jianwei Qiu 63  Saturation: Radiation = Recombination Estimate: Gribov, Levin, Ryskin, 83 Mueller, Qiu, 86  Saturation scale: Proton is dilute enough  How to approach the saturation region?  How to treat the saturation in QCD? Use nuclear target! McLerran, Venugopalan, 94, … Parton saturation