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Open Questions in Jet Quenching Theory

Open Questions in Jet Quenching Theory. Ivan Vitev. QCD Workshop, Brookhaven National Laboratory July 17-21, 2006 , Upton, NY. Outline of the Talk. Based on :. I.V., Phys.Lett.B 639 (2006), I.V. in preparation. I.V., T.Goldman, M.B.Johnson, J.W.Qiu , hep-ph/0605200.

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Open Questions in Jet Quenching Theory

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  1. Open Questions in Jet Quenching Theory Ivan Vitev QCD Workshop, Brookhaven National Laboratory July 17-21, 2006 , Upton, NY

  2. Outline of the Talk Based on: I.V.,Phys.Lett.B 639 (2006), I.V. in preparation I.V.,T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200 • Final state interactions in the QGP: •  Radiative energy loss •  Recursive solutions for multiple parton scattering •  Energy, system size dependence and QGP properties • Initial state energy loss: •  Evidence for energy loss in cold nuclei in p+A •  Differential distributions for medium-induced initial state • gluon bremsstrahlung •  Phenomenological implications • Heavy versus light quarks in p+p and p+A: •  Heavy quark correlations •  Cold nuclear matter effects for heavy versus light quarks • Conclusions:

  3. In-Medium Modification of the PQCD Cross Sections • The way to understand medium effects on hadron cross sections in the framework of PQCD • is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron • wave function (FF) Scattering in the medium Range of the interaction in matter QGP: Cold nuclear matter: Calculated in the Born approximation

  4. Understanding the LPM Effect • Bremsstrahlung is the most efficient way to lose energy since it carries a fraction of the energy LPM = Landau- Pomeranchuk-Migdal • Formation time: coherence effects • Acceleration: radiation • Onset of coherence • Full coherence

  5. Building up Multiple Scattering Approximations that allow to treat many scatterings: Double Born scattering Single Born scattering

  6. Momentum transfers Number of scatterings Color current propagators Coherence phases (LPM effect) + + Medium-InducedRadiation in the Final State • Includes interference with the radiation from hard scattering M.Gyulassy,P.Levai,I.V., Nucl.Phys.B 594 (2001)

  7. 0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb Analytic Approximations and Numerical Results mean number of scatterings Landau-Pomeranchuk -Migdal (LPM) effect J.D.Bjorken, Phys.Rev.D 27 (1983)

  8. P xaP xbP’ P’ Jets and Hadrons from PQCD Can also incorporate Cronin effect: Pd X Pd / zd Pc / zc X Pc Nuclear medium Kinematic modifications

  9. In classes with the same we find • numerically the same suppression System Size Dependence of Jet Quenching Reduction of the hard scattering cross section Probability density - • Absolute scale comparisons can and • should be done at large pT • Similar pT dependence (flat) in Au+Au • and Cu+Cu (For example central Cu+Cu and mid central Au+Au) I.V., Phys.Lett.B 639 (2006)

  10. Tomographic Summary LHC SPS RHIC F.Karsch, Nucl.Phys.A698 (2002) D. d’Enterria, Eur.Phys.J C (2005)

  11. Transport Coefficients in Thermalized QGP • Experimental: Bjorken expansion • Theoretical: Gluon dominated plasma • Energy density • Transport coefficients (not a good measure for expanding medium) • Define the average for Bjorken

  12. New Directions for Energy Loss Calculations • One possible discussion Provide simulations including the geometry, combination of elastic and radiative E-loss, jet topologies … • A new direction: energy loss in cold nuclear matter, initial state • It is a challenging theoretical • problem that has not been solved • (you will see the solution) • Of immediate relevance to pQCD • effects in cold nuclear matter p+A • High twist shadowing only • Initial state energy loss + HTS Implementation of initial state E-loss S.S.Adler et al., nucl-ex/0603017

  13. High Twist Shadowing in DIS Final state coherent scattering • Dynamical parton mass (QED analogy): x = energy = mass J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)

  14. Cold Nuclear Matter Energy Loss • Shadowing parameterizations: • (not) • Dynamical calculations of high • twist shadowing: (not) • Energy loss: in combination • with HTS (yes) T.Alber et al., E.Phys.J.C 2 (1998) • Circular arguments should be avoided • Nigh statistics 200 GeV p+A measurements will certainly reduce error • bars, however … • Most useful measurement – low energy p+A run (only at RHIC II)

  15. Medium-InducedRadiation in the Initial State Asymptotic Asymptotic Large Q2 • Bertsch-Gunion case with interference • Realistic initial state medium induced radiation I.V. in preparation

  16. Energy Loss to First Order in Opacity • Bertsch-Gunion Energy Loss Qualitatively • Initial-State Energy Loss New • Final-State Energy Loss Old

  17. Numerical Results For Quark Energy Loss • Initial state E-loss is much smaller than • the incoherent Bertsch-Gunion limit At any order in opacity we require • Energetic quark jets can easily lose 20-30% • of their energy, gluon jetsx • Initial state E-loss is much larger than • final state energy loss in cold nuclei • Coherence effects lead to cancellation of • the medium-induced radiation M.Djordgevic, M.Gyulassy, Nucl.Phys.A (2004) Radiation intensity Fractional energy loss

  18. Path Length Dependence of E-Loss • Bertsch-Gunion – linear dependence on L by definition • Final state E-loss – approaches quadratic dependence on L, important for • the centrality dependence and elliptic flow • Initial state E-loss – approaches linear dependence on L, important for the • centrality dependence in p+A reactions

  19. pQCD Calculations of Heavy Quarks Schematic NLO and NNL LO, NLO, NNLO expansion LL, NLL, NNLL expansion m/pT, (m/pT)2 power corrections Will return to power corrections • The new scale, mass, implies large • logarithms, but … • The contribution of logarithms is small in • measurable pT ranges • The quarks are treated as “heavy” – in the fixed • order calculation. Implies that NLO generates • the PDF for charm and bottom (mostly) M.Cacciari, P.Nason, JHEP 9805 (1998)

  20. Phenomenological Results Comparison to the Tevatron data Comparison to the RHIC data Scales: R.Vogt et al., Phys.Rev.Lett.95 (2005) M.Cacciari, P.Nason, JHEP 0309 (2003) • Description of open charm at the Tevatron is within uncertainties but not perfect • Residual large scale uncertainties – should be careful with consistent choices • At RHIC perturbative calculations under predict the data by factor of 2 – 4. Whether • it is experimental systematic, incomplete theory or both – open question

  21. Numerical Results and Partonic Sub-Processes Partonic sub-processes FFs: Braaten et al., Phys.Rev.D51 (1995) PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002) • Meaningful K-factors (otherwise K>4) • Anti-correlation between K and the • hardness of fragmentation r • If (LO,c-PDF) ~(NLO,no c-PDF) what are • the corrections from (NLO,c-PDF)?

  22. D (B) meson D (B) meson “Few” hadrons “Many” soft hadrons Hadron Composition of C (B) Triggered Jets Possibility for new measurements of heavy flavor production at RHIC • Can clarify the underlying hard scattering • processes and open charm production • mechanisms • Can constrain the hardness of D and B • meson fragmentation Robust

  23. HTS for Light Hadrons and Open Charm Single inclusive particles Away-side correlations • Very similar dynamical shadowing • for light hadrons and heavy quarks • Insufficient to explain the forward • rapidity data • Single and double inclusive cross • sections are similarly suppressed I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200 J.W.Qiu, I.V., Phys.Lett.B632 (2006)

  24. Energy Loss and High Twist Shadowing Double inclusive yields (away-side) Single inclusive particles I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200 • Main difference is much more pT independent suppression as compared to high twist • shadowing • Very similar e-loss effects for light hadron and heavy quark spectra • Single and double inclusive cross sections are similarly suppressed Same

  25. Effects of Medium-Induced Radiation I.V., Phys.Lett.B630 (2005) • Cancellation of collinear radiation – large angle soft gluons and • correspondingly soft hadrons • Beyond the cancellation region - well defined power • dependence • The importance – hard scattering has the • same power dependence

  26. Phenomenological Implications Correlated! PHENIX Collaboration, Phys.Rev.Lett. (2005) • Suppression at forward rapidity – from energy loss of the incoming partons • Enhancement at backward rapidity – comes from the redistribution of the lost • energy • Consistent pQCD code is still to be developed

  27. Conclusions • In-medim interactions can be understood following the history of a jet in a hard scatter: • Radiative energy loss in the QGP: •  Predicted supession for Cu+Cu versus centrality and pT •  QGP suppression is consistent with perturbative interaction of jets • in the medium • Coherent final state interactions: •  Shadowing is dynamically generated and arises from the final state •  Shadowing for D mesons and light pions is similar • Initial state interactions: •  Transverse momentum diffusion and Cronin effect •  Energy loss and rapidity asymmetry in p+A – new theoretical results • Modification of di-jets: •  Gluon feedback is important for di-hadrons at large angle •  Flow leads to deflection of the jet+gluons, so be exp. determined

  28. + + (Neglect and ) Initial StateElasticScatterings a) Initial state elastic scattering Unitarization of multiple scattering = Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system Initial condition Mean number of scatterings Solution The approximate solution is that of a 2D diffusion = Elastic scattering cross section Implemented in the PQCD approach as broadening of the initial state partons

  29. Cronin Effect Good description at mid rapidity Default Wrong sign at forward rapidity Cronin effect: enhancement of cross sections at intermediate transverse momenta relative to the binary scaled p+p I.V., Phys.Lett.B526 (2003) A.Accardi, CERN yellow report, references therein Data

  30. Robust Heavy Quarks in p+p and p+A New possibility: hadron composition of heavy quark triggered jets FFs: Braaten et al., Phys.Rev.D51 (1995) PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002) • Anti-correlation between K and the • hardness of fragmentation r • Non-trivial hadron composition of c and b • triggered jets

  31. In-Medium Modification of the PQCD Cross Sections • The way to understand medium effects on hadron cross sections in the framework of PQCD • is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron • wave function (FF) a) Initial state interactions Elastic scattering and Cronin effect d) Final state interactions in the QGP Jet quenching b) Initial state interactions Energy loss and forward Y suppression e) Final state interactions in the QGP Large angle correlations, Di-Jet suppression, Deflection of jets by flow c) Final state interactions Dynamical shadowing, Generalization to heavy quarks Cold nuclear matter effects are present at times • Jet interactions in the medium result in kinematic modifications to the hard scattering cross • section that are process dependent

  32. Process Dependence of Power Corrections (For example forward rapidity) Suppression ( ) • The function F(xb) contains the small xb dependence (For example DY) Enhancement ( ) • Power corrections are process dependent and not separable in PDFs and FFs S.Brodsky et al, Phys.Rev.D65 (2002) • Similar process dependence in single spin asymmetries S.Brodsky et al, Phys.Lett.B530 (2002) • Shadowing is dynamically generated in the hadronic collision

  33. Universal Features of Jet Quenching Approximately universal behavior Baseline: Prediction: Scalings: Natural variables Fractional energy loss: Suppression: I.V., Phys.Lett.B in press, hep-ph/0603010

  34. Numerical Results for Jet E-Loss 0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb … … M.Gyulassy, P.Levai, I.V., Phys.Lett.B (2002) • Small probability not to radiate • Small fractional energy loss at large ET • Scales in the QGP Initial parameters

  35. System Size Dependence of Jet Quenching • Absolute scale comparisons can and should be done at large pT • Similar pT dependence (flat) in Au+Au and Cu+Cu • In classes with the same we find • numerically the same suppression For example central Cu+Cu and mid central Au+Au • Future tests of high energy nuclear • physics at the LHC I.V., Phys.Lett.B in press, hep-ph/0603010

  36. Energy Loss and Di-Jets e) QGP effects on di-jet production One way of incorporating energy loss: • “Standard” quenching of leading • hadrons • Redistribution of the lost energy • in “soft” hadrons Satisfies the momentum sum rule A+A Single inclusive particles Away-side yields RHIC LHC I.V., Phys.Lett.B630 (2005)

  37. Radiation Distribution and Flow Effects q0 Gluon number distribution without or withq0 = 1 GeV • Mechanical analogy, Theoretical derivation Problem Result: same energy loss and shifted reference frame Solution: expand about Show that vanishes • We cannot confirm the prescription N.Armesto et al., Phys.Rev.C (2005) • Important for deflected jets, to be seen in • experiment

  38. Cancellation of collinear radiation

  39. Energy Loss to First Order in Opacity Qualitatively • Bertsch-Gunion Energy Loss • Initial-State Energy Loss • Final-State Energy Loss

  40. Non-Perturbative Scales • Chiral perturbation theory • (Generalized) vector dominance model • Bertsch-Gunion • QCD evolution of FFs and PDFs • Coherent high twist shadowing Implementation J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)

  41. Numerical Results For Quark Energy Loss At any order in opacity we require • Initial state E-loss is much smaller than • the incoherent Bertsch-Gunion limit • Energetic quark jets can easily lose 20-30% • of their energy, gluon jetsx • Initial state E-loss is much larger than • final state energy loss in cold nuclei • Coherence effects lead to cancellation of • the medium-induced radiation Fractional energy loss Radiation intensity

  42. Longitudinal size: Shadowing Transverse size: If then If then exceed the parton size Deviation from A-scaling: II. Coherent Power Corrections What remains for theory: power corrections in DIS - suppression Data from: NMC FSI are always present: S.Brodsky et al. Ivan Vitev,LANL

  43. Vacuum DGLAP type Calculate everything else + + + + + + + + + + ... + Medium-Induced Bremsstrahlung • Calculating the multiple scatterings in the plasma p 2 p Example of hard scattering Medium M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001) Reaction operator: (Cross section level ) Potential Advantage: applicable for elastic, inelastic and coherent scattering controlled approach to coherent radiation (LPM)

  44. Comparison to Other Models • Strong coupling used as a parameter • Find T = 370 MeV (OK) S.Turbide et al., Phs.Rev.C. (2005) • Find (NOT OK) G.Paic et al., Euro Phys.J C (2005) K.Eskola et al., Phys.Rev.D (2005) • Find dNg/dy = 1200 (OK) I.V., M.Gyulassy, Phys.Rev.Lett. (2002) I.V. Phys.Lett.B in press B.Cole, QM 2005 proceedings • These are not equivalent descriptions – the medium properties differ by more than • an order of magnitude (sometimes close to two) • How do you build from T = 400 MeV LHC: from T = 1 GeV

  45. Energy momentum violation The Source of the Problem C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003) A useful table Problem Realistic Typical gluon energy GLV • Note that the region of PT at RHIC is • 10-20 GeV and at the LHC 100-200 GeV Negative gluon number and jet enhancement from energy loss Problem Problem Negative probability density • Symptomatic of problems in the underlying model of energy loss

  46. Analytic Limits of Delta E • Controlled approach to coherence GLV • Average implementations in the large • number of scatterings limit BDMPS, AMY • Includes the fluctuations of the gluon • momentum and energy • Calculate differential spectra in • Calculate the energy loss Different dynamics REQUIRES different solutions M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86 (2001) - transport coefficient - effective gluon rapidity density Static: BJ expansion: BJ+2D

  47. Energy Loss and High Twist Shadowing Double inclusive yields (away-side) Single inclusive particles I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200 • Main difference is much more pT independent suppression as compared to high twist • shadowing • Very similar e-loss effects for light hadron and heavy quark spectra • Single and double inclusive cross sections are similarly suppressed Same

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