1. 4/9/08 William Horowitz WWND 2008 1 Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) April 9, 2008 With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Hendrik van Hees

2. 4/9/08 William Horowitz WWND 2008 2 A Talk in Two Parts pQCD vs. AdS/CFT Drag 0 th Order Production Radiation

3. 4/9/08 William Horowitz WWND 2008 3 Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms (In Five Slides) arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions)

4. 4/9/08 William Horowitz WWND 2008 4 (Proper) Subset of Mechanisms DGLV, AdS/CFT Drag, Diffusion… Use heavy quark R AA to test these two dp T /dt ~ -(T 2 /M q ) p T LPM: dp T /dt ~ -LT 3 log(p T /M q )

5. 4/9/08 William Horowitz WWND 2008 5 –LHC Prediction Zoo: What a Mess! –Let’s go through step by step –Unfortunately, large suppression pQCD similar to AdS/CFT–Large suppression leads to flattening –Use of realistic geometry and Bjorken expansion allows saturation below.2 –Significant rise in R AA (p T ) for pQCD Rad+El–Naïve expectations met in full numerical calculation: dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST LHC c, b R AA p T Dependence WH, M. Gyulassy, arXiv:0706.2336

6. 4/9/08 William Horowitz WWND 2008 6 LHC R c AA (p T )/R b AA (p T ) Prediction Recall the Zoo: –Taking the ratio cancels most normalization differences seen previously –pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) –AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p T WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

7. 4/9/08 William Horowitz WWND 2008 7 RHIC R cb Ratio Wider distribution of AdS/CFT curves at RHIC due to large n power law production: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits WH, M. Gyulassy, arXiv:0710.0703 pQCD AdS/CFT pQCD AdS/CFT

8. 4/9/08 William Horowitz WWND 2008 8 Conclusions AdS/CFT Drag observables calculated Generic differences (pQCD vs. AdS/CFT Drag) seen in R AA –Masked by extreme pQCD Enhancement from ratio of c to b R AA –Discovery potential in Year 1 LHC Run Understanding regions of self- consistency crucial RHIC measurement possible

9. 4/9/08 William Horowitz WWND 2008 9 Some Investigations of 0 th Order Production Radiation

10. 4/9/08 William Horowitz WWND 2008 10 Motivation Previous work: test pQCD or AdS/CFT energy loss –Heavy quark R Q AA and R c AA /R b AA Future goal: additional energy loss test using photon bremsstrahlung Zero th Order Calculation –Recent p + p fragmentation  data –Good warm-up and test problem Investigate running , low-p T, etc. –Reevaluate magnitude of Ter-Mikayelian

11. 4/9/08 William Horowitz WWND 2008 11 New Fragmentation  Data A. Hanks, QM2008

12. 4/9/08 William Horowitz WWND 2008 12 Motivating Example: Running  s –Fixed  s is simplification to speed up code Not a free parameter –Running  s will most likely introduce a large error –Want to understand systematics in 0 th Order S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl.Phys. A783 :493-496,2007

13. 4/9/08 William Horowitz WWND 2008 13 Quark mass => Dead cone –Ultrarelativistic “searchlight” rad. pattern Gluon mass => Longitudinal modes, QCD Ter-Mikayelian –Reduction of production radiation compared to vacuum Alters DGLAP kernel Quark and Gluon/Photon Mass Effects  ~ M q /E Y. Dokshitzer and D. Kharzeev, Phys.Lett. B519 :199-206,2001 M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

14. 4/9/08 William Horowitz WWND 2008 14 Previous Calculation of Ter-Mikayelian Reduction of E-loss for charm quarks by ~ 30% E-loss from full HTL well approx. by fixed m g = m ∞ Small- x pQCD 0 th Order result: M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

15. 4/9/08 William Horowitz WWND 2008 15 Compare Classical E&M to “pQCD” –Classical E&M Recall Jackson: Soft photon limit => –Note charge conserved –Usual pQCD approach –Charge explicitly not conserved => Ward identity ( ) violated

16. 4/9/08 William Horowitz WWND 2008 16 Classical/QFT Inconsistency –For m Q = m g = 0 and in the small x, large E + limit, both are equal: –For m Q, m g ≠ 0 and the small x, large E + limit, they differ:

17. 4/9/08 William Horowitz WWND 2008 17 Not a Classical Error –Wrong classical calculation? Plugged in massive 4-vectors into massless formulae Rederive classical result using Proca Lagrangian –After several pages of work… Identical to

18. 4/9/08 William Horowitz WWND 2008 18 Error from QFT Ward Violation Identical expressions are not a surprise QFT Calculation –Photon momentum carried away crucial for cancellation of photon mass Classical case neglects both; effects cancel

19. 4/9/08 William Horowitz WWND 2008 19 Resulting Expression –To lowest order in 1/E + –New: (1- x ) 2 prefactor: naturally kills hard gluons m g 2 in numerator: fills in the dead cone!?! –What are the sizes of these effects? Call this LO

20. 4/9/08 William Horowitz WWND 2008 20 LO Gluon Production Radiation Prefactor => 50-150% effect –Implications for in-medium radiative loss? Filling in dead code => 5-20% –Numerics includes k T and x limits » x large enough to create m g » x small enough that E Jet > M q –Fixed  =.5 GeV and  s =.5 »Similar to Magda full HTL propagator with running  s

21. 4/9/08 William Horowitz WWND 2008 21 LO vs. All Orders Production Rad. Ter-Mikayelian similar for both Different normalizations –0-60% effect All orders calculation self-regulates for m g = 0 and p T → 0

22. 4/9/08 William Horowitz WWND 2008 22 Conclusions No single satisfactory energy loss model Search for tests sensitive to mechanism –Ratio of charm to bottom R AA for pQCD vs. AdS/CFT –Future tests using photon bremsstrahlung Inclusion of away-side jet fills in dead cone –Ultimately leads to a relatively small (5-20%) effect Radiative calculations integrate over all x ; importance of large x behavior?

23. 4/9/08 William Horowitz WWND 2008 23 Backups

24. 4/9/08 William Horowitz WWND 2008 24 Reasonable Consistency with Magda b c M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

25. 4/9/08 William Horowitz WWND 2008 25 0 th Order % Differences

26. 4/9/08 William Horowitz WWND 2008 26 Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) February 9, 2008 With many thanks to Miklos Gyulassy and Simon Wicks arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions)

27. 4/9/08 William Horowitz WWND 2008 27 Motivation –Many heavy quark energy loss models –Hope to distinguish between two broad classes: Standard Model pQCD AdS/CFT Drag –Comparison difficult: nontrivial mapping of AdS/CFT to QCD predictions for LHC –Look for robust signal

28. 4/9/08 William Horowitz WWND 2008 28 pQCD Success at RHIC: –Consistency: R AA (  )~R AA (  ) –Null Control: R AA (  )~1 –GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g /dy~dN  /dy Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005)

29. 4/9/08 William Horowitz WWND 2008 29 e - R AA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632 :81-86 (2006) wQGP not ruled out, but what if we try strong coupling? D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro  /s too small v 2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71 :034909 (2005) (first by E. Shuryak, Phys. Rev. C66 :027902 (2002)) Trouble for wQGP Picture

30. 4/9/08 William Horowitz WWND 2008 30 Intro to AdS/CFT Large N c limit of d -dimensional conformal field theory dual to string theory on the product of d +1-dimensional Anti-de Sitter space with a compact manifold 3+1 SYM z = 0

31. 4/9/08 William Horowitz WWND 2008 31 Strong Coupling Calculation The supergravity double conjecture: QCD  SYM  IIB – IF super Yang-Mills (SYM) is not too different from QCD, & – IF Maldacena conjecture is true –Then a tool exists to calculate strongly- coupled QCD in classical SUGRA

32. 4/9/08 William Horowitz WWND 2008 32 Mach wave-like structures s strong =(3/4) s weak, similar to Lattice  /s AdS/CFT ~ 1/4  << 1 ~  /s pQCD e - R AA ~ ,  R AA ; e - R AA (  ) T. Hirano and M. Gyulassy, Nucl. Phys. A69 :71-94 (2006) Qualitative AdS/CFT Successes: PHENIX, Phys. Rev. Lett. 98, 172301 (2007) J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213

33. 4/9/08 William Horowitz WWND 2008 33 AdS/CFT Energy Loss Models Langevin model –Collisional energy loss for heavy quarks –Restricted to low p T –pQCD vs. AdS/CFT computation of D, the diffusion coefficient ASW model –Radiative energy loss model for all parton species –pQCD vs. AdS/CFT computation of –Debate over its predicted magnitude ST drag calculation –Drag coefficient for a massive quark moving through a strongly coupled SYM plasma at uniform T –not yet used to calculate observables: let’s do it!

34. 4/9/08 William Horowitz WWND 2008 34 AdS/CFT Drag Model heavy quark jet energy loss by embedding string in AdS space dp T /dt = -  p T  =    T 2 /2M q

35. 4/9/08 William Horowitz WWND 2008 35 Energy Loss Comparison –AdS/CFT Drag: dp T /dt ~ -(T 2 /M q ) p T –Similar to Bethe-Heitler dp T /dt ~ -(T 3 /M q 2 ) p T –Very different from LPM dp T /dt ~ -LT 3 log(p T /M q ) t x Q, m v D7 Probe Brane D3 Black Brane (horizon) 3+1D Brane Boundary Black Hole z = 0 z h =  T z m = 2  m / 1/2

36. 4/9/08 William Horowitz WWND 2008 36 R AA Approximation –Above a few GeV, quark production spectrum is approximately power law: dN/dp T ~ 1/p T (n+1), where n(p T ) has some momentum dependence –We can approximate R AA (p T ): R AA ~ (1-  (p T )) n(p T ), where p f = (1-  )p i (i.e.  = 1-p f /p i ) y=0 RHIC LHC

37. 4/9/08 William Horowitz WWND 2008 37 –Use LHC’s large p T reach and identification of c and b to distinguish between pQCD, AdS/CFT Asymptotic pQCD momentum loss: String theory drag momentum loss: –Independent of p T and strongly dependent on M q ! –T 2 dependence in exponent makes for a very sensitive probe –Expect:  pQCD 0 vs.  AdS indep of p T !! dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST  rad   s L 2 log(p T /M q )/p T Looking for a Robust, Detectable Signal  ST  1 - Exp(-  L),  =    T 2 /2M q S. Gubser, Phys.Rev. D74 :126005 (2006); C. Herzog et al. JHEP 0607:013,2006

38. 4/9/08 William Horowitz WWND 2008 38 Model Inputs –AdS/CFT Drag: nontrivial mapping of QCD to SYM “Obvious”:  s =  SYM = const., T SYM = T QCD –D 2  T = 3 inspired:  s =.05 –pQCD/Hydro inspired:  s =.3 (D 2  T ~ 1) “Alternative”: = 5.5, T SYM = T QCD /3 1/4 Start loss at thermalization time  0 ; end loss at T c –WHDG convolved radiative and elastic energy loss  s =.3 –WHDG radiative energy loss (similar to ASW) = 40, 100 –Use realistic, diffuse medium with Bjorken expansion –PHOBOS (dN g /dy = 1750); KLN model of CGC (dN g /dy = 2900)

39. 4/9/08 William Horowitz WWND 2008 39 –LHC Prediction Zoo: What a Mess! –Let’s go through step by step –Unfortunately, large suppression pQCD similar to AdS/CFT–Large suppression leads to flattening –Use of realistic geometry and Bjorken expansion allows saturation below.2 –Significant rise in R AA (p T ) for pQCD Rad+El–Naïve expectations met in full numerical calculation: dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST LHC c, b R AA p T Dependence WH, M. Gyulassy, arXiv:0706.2336

40. 4/9/08 William Horowitz WWND 2008 40 But what about the interplay between mass and momentum? –Take ratio of c to b R AA (p T ) pQCD: Mass effects die out with increasing p T –Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching ST: drag independent of p T, inversely proportional to mass. Simple analytic approx. of uniform medium gives R cb pQCD (p T ) ~ n b M c / n c M b ~ M c /M b ~.27 –Ratio starts below 1; independent of p T An Enhanced Signal R cb pQCD (p T )  1 -  s n (p T ) L 2 log(M b /M c ) ( /p T )

41. 4/9/08 William Horowitz WWND 2008 41 LHC R c AA (p T )/R b AA (p T ) Prediction Recall the Zoo: –Taking the ratio cancels most normalization differences seen previously –pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) –AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p T WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

42. 4/9/08 William Horowitz WWND 2008 42 –Speed limit estimate for applicability of AdS drag  <  crit = (1 + 2M q / 1/2 T) 2 ~ 4M q 2 /(  T 2 ) –Limited by M charm ~ 1.2 GeV Similar to BH LPM –  crit ~ M q /( T) –No Single T for QGP smallest  crit for largest T T = T(  0, x=y=0): “(” largest  crit for smallest T T = T c : “]” Not So Fast! D3 Black Brane D7 Probe Brane Q Worldsheet boundary Spacelike  if  >  crit Trailing String “Brachistochrone” “z” x5x5

43. 4/9/08 William Horowitz WWND 2008 43 LHC R c AA (p T )/R b AA (p T ) Prediction (with speed limits) –T(  0 ): (O), corrections unlikely for smaller momenta –T c : (|), corrections likely for higher momenta WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

44. 4/9/08 William Horowitz WWND 2008 44 Measurement at RHIC –Future detector upgrades will allow for identified c and b quark measurements y=0 RHIC LHC NOT slowly varying –No longer expect pQCD dR AA /dp T > 0 Large n requires corrections to naïve R cb ~ M c /M b –RHIC production spectrum significantly harder than LHC

45. 4/9/08 William Horowitz WWND 2008 45 RHIC c, b R AA p T Dependence Large increase in n (p T ) overcomes reduction in E-loss and makes pQCD dR AA /dp T < 0, as well WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]

46. 4/9/08 William Horowitz WWND 2008 46 RHIC R cb Ratio Wider distribution of AdS/CFT curves due to large n : increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] pQCD AdS/CFT pQCD AdS/CFT

47. 4/9/08 William Horowitz WWND 2008 47 Conclusions AdS/CFT Drag observables calculated Generic differences (pQCD vs. AdS/CFT Drag) seen in R AA –Masked by extreme pQCD Enhancement from ratio of c to b R AA –Discovery potential in Year 1 LHC Run Understanding regions of self- consistency crucial RHIC measurement possible

48. 4/9/08 William Horowitz WWND 2008 48 Backups

49. 4/9/08 William Horowitz WWND 2008 49 Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 1D Hubble flow =>  (  ) ~ 1/  => T(  ) ~ 1/  1/3 S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007

50. 4/9/08 William Horowitz WWND 2008 50 Langevin Model –Langevin equations (assumes  v ~ 1 to neglect radiative effects): –Relate drag coef. to diffusion coef.: –IIB Calculation: Use of Langevin requires relaxation time be large compared to the inverse temperature: AdS/CFT here

51. 4/9/08 William Horowitz WWND 2008 51 But There’s a Catch (II) Limited experimental p T reach? –ATLAS and CMS do not seem to be limited in this way (claims of year 1 p T reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II

52. 4/9/08 William Horowitz WWND 2008 52 LHC  Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Our predictions show a significant increase in R AA as a function of p T This rise is robust over the range of predicted dN g /dy for the LHC that we used This should be compared to the flat in p T curves of AWS- based energy loss (next slide) We wish to understand the origin of this difference

53. 4/9/08 William Horowitz WWND 2008 53 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Asymptopia at the LHC Asymptotic pocket formulae:  E rad /E   3 Log(E/  2 L)/E  E el /E   2 Log((E T) 1/2 /m g )/E

54. 4/9/08 William Horowitz WWND 2008 54 K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005)

55. 4/9/08 William Horowitz WWND 2008 55 Pion R AA Is it a good measurement for tomography? –Yes: small experimental error Claim: we should not be so immediately dis- missive of the pion R AA as a tomographic tool –Maybe not: some models appear “fragile”

56. 4/9/08 William Horowitz WWND 2008 56 Fragility: A Poor Descriptor All energy loss models with a formation time saturate at some R min AA > 0 The questions asked should be quantitative : –Where is R data AA compared to R min AA ? –How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? –Define sensitivity, s = min. param/max. param that is consistent with data within error

57. 4/9/08 William Horowitz WWND 2008 57 Different Models have Different Sensitivities to the Pion R AA GLV: s < 2 Higher Twist: s < 2 DGLV+El+Geom: s < 2 AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

58. 4/9/08 William Horowitz WWND 2008 58 T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

59. 4/9/08 William Horowitz WWND 2008 59 A Closer Look at ASW K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005) The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a)(b)

60. 4/9/08 William Horowitz WWND 2008 60 –Surface Emission: one phrase explanation of fragility All models become surface emitting with infinite E loss –Surface Bias occurs in all energy loss models Expansion + Realistic geometry => model probes a large portion of medium Surface Bias vs. Surface Emission A. Majumder, HP2006S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

61. 4/9/08 William Horowitz WWND 2008 61 A Closer Look at ASW –Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: No Bjorken expansion Glue and light quark contributions not disentangled Plotted against L input (complicated mapping from L input to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005)