Consistency of Jet Quenching Predictions at the LHC

1. [ “The hot, the heavy and the cold” ] Consistency of Jet Quenching Predictions at the LHC Ivan Vitev, T-16 and P-25, LANL “High PT Physics at the LHC” workshop, March 23-27, Jyvaskyla, Finland

2. Outline of the Talk • The problem of predictions versus fits for QGP suppression • Consistency between hard and soft observables • Entropy density, energy-momentum conservation, … • Examples from RHIC and LHC • The problem of applicability of the jet-quenching approaches • Light hadrons versus heavy quarks – the issue of formation time • New approach to D- and B-mesons suppression in the QGP • Results for the LHC • The problem of completeness in jet quenching phenomenology • Inclusion of cold nuclear matter effects • Understanding initial- versus final-state radiative energy loss • Example at the LHC • Conclusions

3. Part I [ The Hot ] • Can you live without 11 dimensions in the QGP?

4. --- Wang dE/dx =0.25 GeV/fm --- Vitev dNg/dy = 900 --- Levai L/λ = 4 Few Real Predictions • Before the real high pT • data appeared • Afterwards – many fits from various models with parameter tuning Require consistency Entropy rapidity density: QGP formation time: Saskia Mioduszewski, QM 2002

5. Light Hadron Quenching in A+A (E-Loss) • Theoretical reason: the only way • to formulate energy loss without unphysical sensitivity to the formation time Significantly different values are indicative a theoretical inconsistency I.V., Phys.Lett.B 639 (2006)

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

7. The Cause of the Inconsistency A useful table Difference Realistic Typical gluon energy GLV • Note that the region of PT at RHIC is • 10-20 GeV and at the LHC 100-500 GeV C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003) Consistent, energy-momentum conserving calculations should be used before one looks at string theory for help Energy momentum violation

8. Gluon Feedback to Single Inclusives • High pT suppression at the LHC can be • comparable and smaller than at RHIC • LHC quenching follows the steepness • of the partonic spectra. There is a • constant suppression region • The redistribution of the lost energy is • very important at the LHC. 100% • correction and pT<15 GeV affected I.V., Phys. Lett. B 639 (2006) Ivan Vitev,LANL

9. Part II [ The Heavy ] • Can you really quench heavy flavor?

10. Heavy Quark Mass and Radiative Energy Loss For massive quarks - "dead cone effect" Cuts part of phase space M.Djordjevic, M.Gyulassy, Nucl.Phys.A (2004)

11. Non-Photonic Electron / Heavy Flavor Quenching Proceed to A+A collisions • Single electron measurements • (presumably from heavy quarks) • may be problematic for mainstream • theory • Radiative Energy Loss using • (D)GLV (both c + b) • Radiative + Collisional + Geometry • (both c + b) (overestimated) • Deviation by a factor of two • Is it accidental or is it symptomatic? S. Wicks et al., nucl-th/0512076

12. Hadron Parton QGP extent B D 25 fm 0.4 fm 1.6 fm Conceptually Different Approach to D / B • Problem: treated in the same way as light quarks + • Fragmentation and dissociation of hadrons from heavy quarks inside the QGP C.Y.Wong, Phys.Rev.C 72, (2005)

13. Light Cone Wave Functions S.Brodsky, D.S.Hwang, B.Q.Ma, I.Schmidt, Nucl.Phys.B 592 (2001) Fix two momentum scales • Find dissociation time

14. Heavy Meson Dissociation at RHIC and LHC Coupled rate equations A.Adil, I.V., hep-ph/0611109 • The asymptotic solution in the QGP - • sensitive to t0~0.6 fm and expansion • dynamics • Features ofenergy loss • B-mesons as suppressedas D-mesons • at pT~ 10 GeV (unique feature)

15. Similar to light , however, • different physics mechanism Quenching of Non-Photonic Electrons A.Adil, I.V., hep-ph/0611109 • PYTHIA used to decay all B- and • D-mesons / baryons into (e++e-) • SuppressionRAA(pT) ~ 0.25is • large • B-mesons are included. They give • a major contribution to (e++e-) • Predictions also made for Cu+Cu (RHIC) and Pb+Pb (LHC)

16. Example at the LHC What can we learn from Heavy Flavor at the LHC? • For the same t0~0.6 fm • the suppression is similar • to RHIC since the larger • parton densityis compen- • sated by the stiffer spectra • Sensitivity to the formation • time t0 – QGP formation time

17. Part III [ The Cold ] • How about cold nuclear matter effects?

18. preliminary When One ≠ One • Theoretical results:cancellation between factor of 4 Cronin enhancement and 2- to 3-fold quenching • Experimental findings: Ncoll,Pb+Pb = 807 ± 81 S.Bathe., LANL seminar I.V., Phys.Lett.B 632 (2005) • With any multiple scattering effect there is no reason to expect • If one understands this in A+A collisions one should also accept this is • p+A collisions

19. Regimes of QCD Radiative Energy Loss G.Bertsch, F.Gunion., Phys.Rev.D (1982) Limited applicability (no hard scattering) I.V., hep-ph/0703002 Best studied QGP applications • Bertsch-Gunion Energy Loss • Initial-State Energy Loss • Final-State Energy Loss I.V., hep-ph/0703002 R.Baier et al., Nucl.Phys.B (1997) New result Dominant cold nuclear matter effect M.Gyulassy, P.Levai, I.V., Phys.Rev.Lett. (2000) E.K.Wang, X.N.Wang, Phys.Rev.Lett. (2002) P.Arnold,G.Moore, L.Yaffe, JHEP (2003)

20. Quantitative Behavior of E-loss • Bertsch-Gunion Energy Loss • Initial-State Energy Loss << • Final-State Energy Loss Correct way to study E-loss in nuclei: in the rest frame of the nucleus I.V., hep-ph/0703002

21. Consistency of Cold Nuclear Matter Tomography • Dynamical shadowing (coherent • final-state scattering) HT/LT? • Cronin effect (initial-state transverse momentum diffusion) • Initial state energy loss (final state at these energies - negligible) Consistency in the extracted cold nuclear matter properties

22. Evidence at all Rapidities Experimental y = 1.4-2.2 Very similar behavior of charm quarks (D-mesons) to light hadrons Even at mid-rapidity seemingly small modification 10% - 25% may arise from cancellation of nuclear effects as large as a factor of 2 I.V., T.Goldman, M.Johnson, J.W.Qiu, Phys. Rev. D 74 (2006)

23. Example at the LHC • At the expected larger medium • density and stiffer spectra at the • LHC there is reduced sensitivity • to the medium density 0-10% central Pb+Pb • How important is cold nuclear • matter energy loss? – Has the • same effect as doubling the parton • rapidity density 0-10% central Pb+Pb • Consistent inclusion of cold nuclear matter energy loss may be more important at the LHC (Y=0) I.V. in preparation

24. Summary • Light flavor quenching • Requires consistency: already a RHIC models sacrifice this consistency • At LHC: regions of less suppression than at RHIC, new effects • Collisional QGP-induced B- / D-meson dissociation • Derived formation and dissociation times in the QGP. They are short • B-mesons are as suppressedasD-mesons at pT ~ 10 GeV,unique • At the LHC obtain the same qualitative behavior as at RHIC • Cold nuclear matter effects • Calculated dynamical shadowing, Cronin and initial-state energy los • Quantitatively important both in p+A and A+A recations • Affect in a major way the extractionof the QGP properties at the LHC

25. Energy Loss in QCD Establishing the E-loss mechanism • Radiative: Important: mass dependence Qualitatively: • Collisional: Important: no mass dependence Qualitatively:

26. Strategy for Calculating HF Suppression • Calculatethe baseline D- and B-meson cross sections • in p+p collisions • Calculatethe fragmentation probability of heavy quarks • Calculatethe QGP-induced dissociation probability • for heavy mesons • Solvethe system of coupled rate equations and predict • the heavy quark (single electron) suppression

27. Detailed Analysis to LO Single inclusive D - mesons D - meson triggered back-to-back correlations Flavor excitation Flavor creation Faster convergence of the perturbative series Slower convergence of the perturbative series F.Olness et al., Phys.Rev.D59 (1999) Two different expansions

28. Heavy Quark Production in p+p Collisions • Gluon fusion is not • the dominant process • in single inclusive • open charm (bottom) • production I.V.,T.Goldman,M.Johnson,J.W.Qiu, Phys.Rev.D74 (2006) • Comparable to “NLO” results: (under-predicts the • cross section by 30% - x 2 )

29. B-mesons Fragmentation Probability for Heavy Quarks Recall • Fragmentation probability K.Cheung,T.Z.Yuan, Phys.Rev.D53 (1996) • Time-dependent implementation

30. Light Cone Wave Functions • Results for heavy flavor • Longitudinal momentum fractions Meson boost – equal quark rapidity Begin to understand hadron structure / parton distributions from first principles From general theory of LCWF for the lowest-lying Fock state

31. ()n Heavy Meson Propagation in Dense Matter • Solve for the color and kinematic • structure of this operator (automatically • ensures unitarity) • Single scattering in the medium q q’ q q’

32. q, g Light Cone Wave Functions Fix two momentum scales • Expansion in Fock components • Transverse momentum scale Cornell potential M. Avila, Phys.Rev.D49 (1994) Fourier transform to momentum space S.Brodsky, D.S.Hwang, B.Q.Ma, I.Schmidt, Nucl.Phys.B 592 (2001) Typical transverse momentum squared

33. Light Cone Wave Functions • Results for heavy flavor • Longitudinal momentum fractions Meson boost – equal quark rapidity Begin to understand hadron structure / parton distributions from first principles From general theory of LCWF for the lowest-lying Fock state

34. ()n Heavy Meson Propagation in Dense Matter • Solve for the color and kinematic • structure of this operator (automatically • ensures unitarity) • Single scattering in the medium q q’ q q’

35. Heavy Meson Propagation in Dense Matter II Initial distribution: Resum multiple scattering in impact parameter (B,b) space • Heavy meson acoplanarity: • Broaden (separate)the q q-bar pair:

36. Deriving Heavy Meson Dissociation • Distortion of the light cone wave function leads to meson decay Meson survival probability: Properties of survival probabilities: Dissociation time:

37. Langevin Simulation of Heavy Quark Diffusion Input in a Langevin simulation of heavy quark diffusion H. van Hees, I.V., R. Rapp, in preparation • Drag coefficient: • Diffusion coefficient: Equilibration is imposed by Einstein’s fluctuation-dissipation relation: Radiative energy loss is dominantexcept for b-quarks and very small systems

38. Transport + Quenching Approach Numerical results for heavy quark diffusion Results arepreliminary H. van Hees, I.V., R. Rapp, in preparation • The suppression and v2 are large when e-loss and q-resonance interactions are • combined • Normal hierarchy: c quarks are significantly more suppressed than b-quarks

39. Experimental Tools • LDRD DR proposal • Used to leverage full scale • detector upgrade (FVTX) Experimentally validate / disprove theories Collisional dissociation Mainstream approach • Best reason to measure D- and B-mesons separately

41. Comparison to Other Models Wang Wicks et al. How do you build from T = 400 MeV LHC: from T = 1 GeV Ivan Vitev,LANL

42. Come to your one conclusions • One should use adequate energy-momentum conserving formalism • Instead authors scurry around to seek for justification - Argued that transverse expansion leads to 4 times energy loss, Armesto, Salgado, Wiedeman (2005) – wrong on the basis of elementary physics (translational invariance) - Killed even by the original authors, Baier et al. (2006) - Found comfort in String theory, Rajagopal, Wiedeman (2006)

43. - drag ~ - diffusion ~ Langevin Simulations of C- / B-Quark Diffusion • Model of quark-resonance interaction • near the QCD phase transition Fokker-Plank diffusion equation • Expansion of gain / loss terms tosecond • order Equilibration is imposed by Einstein’s fluctuation-dissipation relation: H. van Hees, R. Rapp, Phys.Rev.C71 (2005) • Efficient at • Include e-loss at high pT

44. High Twist Shadowing Theory (Dynamical) Shadowing is the ratio of DIS reduced cross sections – structure functions Coherent final state scattering theory • QCD factorization approach, background • color magnetic field J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004) • Dynamical parton mass (QED analogy): S.Brodsky et al, Phys.Rev.D65 (2002) Calculate versus parameterize

45. Regimes of QCD Radiative Energy Loss • Bertsch-Gunion Energy Loss • Initial-State Energy Loss • Final-State Energy Loss I.V., in preparation

46. Nuclear Effects at Forward Rapidity (Light H) • Dynamical shadowing (FS) • Cronin effect (IS) • Initial state energy loss (IS) • Consistency in the extracted cold • nuclear matter properties I.V., in preparation • The most detailed calculation so far at forward rapidity • Now apply for heavy quarks

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

48. Cold Nuclear Matter Effects on D- Production Experimental y = 1.4-2.2 E-loss plays a similarly important role Very similar behavior of charm quarks (D-mesons) to light hadrons Nuclear suppression in d+A reactions I.V., T.Goldman, M.Johnson, J.W.Qiu, Phys. Rev. D 74 (2006) Important at forward Y. Not so important at Y = 0

49. Outline of the Talk Based upon: I.V., work in progress A.Adil and I.V., hep-ph/0611109 H. van Hees I.V. and R. Rapp, work in progress • Energy loss in QCD • Radiative and collisional energy loss, recent developments • Application to A+A collisions and p+A collisions • Applications to heavy quarks • Discrepancy between PQCD and c- and b-quark quenching • Transport+quenching approach to D- and B mesons • Alternative theory of heavy flavor suppression • In-medium formation and dissociation of D- and B- mesons • Suppression of non-photonic electrons • Conclusions

50. Types of Energy Loss • Collisional: Arises from the acceleration of the charges in the target. No significant mass dependence • Radiative: Arises from the acceleration of the incident charge. Can have significant mass dependence Much more efficient