QCD Factorization and Universality of Nuclear Parton Distribution Functions

1. QCD Factorization and Universality of Nuclear Parton Distribution Functions Jianwei Qiu Iowa State University CERN Workshop on Proton-Nucleus Collisions at the LHC CERN, May 25-27, 2005 Jianwei Qiu, ISU

2. Outline of the Talk • QCD factorization at leading power (twist), and universality of parton distribution functions (PDFs) • What happens to the factorization formalism when a proton is replaced by a nucleus? • Quantum coherent multiple scattering and power corrections in QCD • Resummed power corrections to cross sections • Modified nuclear PDFs with coherent power corrections • Summary and outlook Jianwei Qiu, ISU

3. Bench mark tests: Exp: Observables can be readily measured Thy: Calculations/predictions have to be reliable No predictions No tests • QCD asymptotic freedom pQCD works for processes with large momentum exchange hard probes Bench mark tests and Hard probes Jianwei Qiu, ISU

4. Multiple scales in hadronic collisions (3) (2) (1) • Hard collision: Q >> ΛQCD • Gluon shower: <kT>dynamic ~ F[Q2,log(s/Q2)] • Hadron wave function: <kT>intrinsic ~ 1/fm ~ ΛQCD • PQCD factorization: (1) Perturbative IR safe single hard partonic “cross section” (2) Leading log DGLAP evolution of PDFs (3) Nonperturbative PDFs Jianwei Qiu, ISU

5. Predictive power of QCD factorization • Short-distance dynamics (process dependent) • DGLAP evolution of PDFs (process independent) • Universality of PDFs (gauge invariant matrix elements with renormalization prescription) Jianwei Qiu, ISU

6. For pQCD factorization to work, PDFs are required to have the same parton-level collinear divergences as those in partonic scattering amplitudes CO and IR safe for How factorization works in practice? Partonic “cross section”: Partonic scattering Jianwei Qiu, ISU

7. CO divergent as kT → 0 • The divergence is not a part of DGLAP evolved PDFs • multiparton matrix elements • Collinear part: power corrections to DGALP evolution modified evolution equations • Short-distance part: power corrections to Corrections to leading twist factorization • DGLAP evolved PDFs do not remove all CO divergences of partonic scattering [GLR,MQ, …] • Consequences: Jianwei Qiu, ISU

8. Success of QCD factorization approach • Successful QCD global fits to obtain PDFs consistent with all data for Q2 > 5 GeV2 • DGLAP evolution works very well for PDFs for a wide range of x and Q2 • Strong scaling violation for low x region Jianwei Qiu, ISU

9. same process dependent hard parts: • replace nucleon PDFs, by nuclear PDFs, defined in terms of same operators with • same operatorssame DGLAP evolution • different state different input PDFs at Change a proton to a nucleus (I) • No effect to the short-distance physics at Q • No effect on the DGLAP evolution kernels Leading twist factorization formalism holds • Only source of A-dependence for the leading twist nPDFs is from the input nPDFs: Jianwei Qiu, ISU

10. Change a proton to a nucleus (II) • No theoretical input for A-dependence of nPDFs within the leading twist factorization formalism! • The scale of input nPDFs, μ0, becomes special, above which no input for A-dependence • Extract by fitting data on nuclear targets with the factorized formalism and DGLAP evolution for nPDFs precise data might have to choose a very large μ0 [EKS98, …] • Model/calculate the input nPDFs, evolve them with DGLAP need power corrections to fit DIS data [FGS, …] • Fix a scale independent ratio between nPDFs and PDFs not consistent with LT factorization[HIJING, …] • CGC input + its own quantum evolution [RV’s talk] • Go beyond the normal LT formalism, because power corrections are enhanced by nuclear size and small x[GLR,MQ,QV,…] Jianwei Qiu, ISU

11. 2 + + + … Multiple scattering, power corrections • Incoherent/independent (each scattering is localized): Redistributes parton momentum spectrum, but, not the total production rate • Coherent (the probe interacts coherently with all scattering centers): • Interference: suppress/enhance the production rate • Penalty: (1/Q2)N suppressed, large number of unknown multi-field matrix elements • Helper: large A, large gluon density at small x Jianwei Qiu, ISU

12. Hard probes are not localized at small x • 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: • low x: uncertainty in locating the parton is much larger than the size of the boosted hadron (a nucleon) If the active x is small enough a hard probe could cover several nucleons In a Lorentz contracted large nucleus! Jianwei Qiu, ISU

13. + + ≈ Coherent multiparton interactions At small x, the hard probe covers several nucleons, coherent multiple scattering could be equally important at relatively low Q To take care of the coherence, we need to sum over all cuts for a given forward scattering amplitude Summing over all cuts is also necessary for IR cancellation Jianwei Qiu, ISU

14. ≠ Collinear approximation is important With collinear approximation: IR safe  = In general, matrix elements with different cuts are not equal: Jianwei Qiu, ISU

15.  Leading contribution in medium length Parton momentum convolution: All coordinate space integrals are localized if x is large Leading pole approximation for dxi integrals : • dxi integrals are fixed by the poles (no pinched poles) • xi=0 removes the exponentials • dy integrals can be extended to the size of nuclear matter Leading pole leads to highest powers in medium length, a much small number of diagrams to worry about Jianwei Qiu, ISU

16. xs Different from the CGC approach • Experiments measure cross sections, not PDFs • PDFs are extracted based on • factorization • truncation of perturbative expansion CGF CGC • How to probe the boundary between different regions? pQCD factorization Look for where pQCD factorization approach fails Jianwei Qiu, ISU

17. Power corrections to partonic x-sections • Coherent multiple scattering leads to dynamical power corrections: • Characteristic scale for the power corrections: • For a hard probe: • To extract the universal matrix element, we need new observables more sensitive to Jianwei Qiu, ISU

18. Resummed power corrections to SF’s • LO contribution toDIS cross section: • NLO contribution: • Nth order contribution: Infrared safe! Jianwei Qiu, ISU

19. Multiparton correlation functions • Potential medium length enhancement: • Approximation: • nuclear state: • constant nuclear density only one parameter: a well-defined universal matrix element Jianwei Qiu, ISU

20. Contributions to DIS structure functions Qiu and Vitev, PRL2004 • Transverse structure function: Similar expression of FL Single parameter for the power correction, and is proportional to the same characteristic scale Jianwei Qiu, ISU

21. Neglect LT shadowingupper limit of x2 Jianwei Qiu, ISU

22. Power Corrections in Neutrino-Nucleus DIS Qiu and Vitev, Phys.Lett.B 587 (2004) • Coherent power corrections are process dependent: • Power of factorization: Same nonperturbative ξ2 Predict high twist shadowing in neutrino-nucleus structure functions: Consistent with new NTeV data (DIS2005) Jianwei Qiu, ISU

23. No A1/3-enhancement + ≈ ● ● ● ≈ + + + ● ● ● Factorization argument similar to DIS Factorization in p-nucleus collisions • A-enhanced power corrections, A1/3/Q2, are factorizable: • But, power corrections to hard parts are process-dependent, and they aredifferent from DIS Jianwei Qiu, ISU

24. Power Corrections in p+A Collisions • Hadronic factorization fails for power corrections of the order of 1/Q4 and beyond • Medium size enhanced dynamical power corrections in p+A are factorizable to make predictions for p+A collisions, but, multiple hard scales, s, t, u. • Single hadron inclusive production: • Once we fix the incoming parton momentum from the beam • and outgoing fragmentation parton, we uniquely fix the • momentum exchange, qμ, and the probe size • coherence along the direction of qμ – pμ • only t relevant. smaller t, larger coherent effect Ivan Vitev, ISU Jianwei Qiu, ISU

25. Numerical results for power corrections Qiu and Vitev, hep-ph/0405068 • Similar power correction modification to single and double inclusive hadron production • increases with centrality and increase with rapidity • disappears at high pT because of the power suppression Power corrections to evolution equations will flatten the pT dependence – slower evolution Jianwei Qiu, ISU

26. On-shell Fixed On-shell Intuition for the power corrections • DIS with a space-like hard scale: LO Resum all powers • DY with a time-like hard scale: Fixed Resum all powers LO Jianwei Qiu, ISU

27. + ... + + Coherent power corrections to PDFs Hard probe sees only one effective parton: Pinched poles in the ladder diagrams – corrections to evolution    Jianwei Qiu, ISU

28. Modified ladder diagrams … … … … Jianwei Qiu, ISU

29. Modifications to DGLAP equation Z. Kang and J. Qiu in preparation DGLAP equation: What were done: • resum all powers of leading pole coherent power corrections to all particles entering final-state • derive a set of generalized ladder diagrams • derive a modified DGLAP equation with the power corrections Modifications: • shift the parton momentum fraction in PDFs in the integral part • shift the 1/x pole by 1/(x+Δx) • naturally generates the shadowing at low Q2, if we evolve from high Q2. Jianwei Qiu, ISU

30. PDF x Shadowing in nPDFs • Shadowing in nPDFs: shadowing in input nPDFs, plus power corrections to evolution equations • Power corrections complement to the shadowing in nPDFs: • Shadowingin nPDFs changes the x- and Q-, as well as A-dependence of the parton distributions • Power correctionsto the DIS structure functions (or cross sections) are effectively equivalent to a shift in x • Power corrections vanish quickly as hard scale Q increases while theshadowingin nPDFsgoes away much slower • If shadowing in nPDFs is so strong that x-dependence of parton distributions saturates for x< xc, additional power corrections, the shift in x, should have no effect to the cross section! xc Jianwei Qiu, ISU

31. DGLAP evolution Net effect of shadowed nPDFs DGLAP + process independent power corrections nPDFs + process dependent power corrections CGC? Role of coherent power corrections • Ratio of physical observables: RA Jianwei Qiu, ISU

32. Our approach to multiparton interactions • Advantage: • factorization approach enables us to quantify the high order corrections • express non-perturbative quantities in terms of matrix elements of well-defined operators – universality • better predictive power • Disadvantage: • Rely on the factorization theorem – not easy to prove • Hard probe might limit the region of coherence – small target • Helper: • Hard probe at small x could cover a large nuclear target Jianwei Qiu, ISU

33. Identify a characteristic scale for the QCD rescattering: in cold nuclear matter Summary and outlook • Introduce a systematic factorization approach to coherent QCD multiparton interactions – power corrections • Leading medium size enhanced nuclear effects due to power corrections can be systematically calculated • Derive coherent power corrections to DGLAP evolution equation (numerical evaluation of nPDFs is underway) • Should be relevant for physics approaching to saturation • Many applications: jet broadening, suppression of jet correlation in p-A, … Jianwei Qiu, ISU

34. Backup transparencies Jianwei Qiu, ISU

35. Factorization in hadron-hadron collisions • Soft-gluon interactions take place all the time: • Factorization = Soft-gluon interactions are powerly suppressed • Factorization breaks beyond 1/Q2 term: Doria, et al (1980) Basu et al. (1984) Brandt, et al (1989) Jianwei Qiu, ISU

36. Acoplanarity and power corrections • Consider di-hadron correlations associated with hard (approximately) back-to-back scattering • Coherent scattering reduces: • Incoherent scattering broadens: Jianwei Qiu, ISU

37. Only small broadening • versus centrality • Looks rather similar at • forward rapidity of 2 • The reduction of the area • is rather modest • Apparently broader • distribution • Even at midrapidity a small • reduction of the area • Factor of 2-3reduction of the • area at forward rapidity of 4 Dihadron Correlation Broadening and Attenuation Mid-rapidity and moderate pT J.Adams et al., Phys.Rev.Lett. 91 (2003) Forward rapidity and small pT Trigger bias can also affect: Qiu and Vitev, Phys.Lett.B 570 (2003); hep-ph/0405068 Jianwei Qiu, ISU