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Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

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. A Talk in Two Parts. pQCD vs. AdS/CFT Drag

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Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

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  1. Zeroth 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 WWND 2008

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

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

  4. (Proper) Subset of Mechanisms • DGLV, AdS/CFT Drag, Diffusion… • Use heavy quark RAA to test these two LPM: dpT/dt ~ -LT3 log(pT/Mq) dpT/dt ~ -(T2/Mq) pT WWND 2008

  5. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 • 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 RAA(pT) for pQCD Rad+El • Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST WWND 2008

  6. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • 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 pT WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] WWND 2008

  7. RHIC Rcb 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 pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 WWND 2008

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

  9. Some Investigations of 0th Order Production Radiation WWND 2008

  10. Motivation • Previous work: test pQCD or AdS/CFT energy loss • Heavy quark RQAA and RcAA/RbAA • Future goal: additional energy loss test using photon bremsstrahlung • Zeroth Order Calculation • Recent p + p fragmentation g data • Good warm-up and test problem • Investigate running a, low-pT, etc. • Reevaluate magnitude of Ter-Mikayelian WWND 2008

  11. New Fragmentation g Data A. Hanks, QM2008 WWND 2008

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

  13. Quark and Gluon/Photon Mass Effects q ~ Mq/E • 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 • Y. Dokshitzer and D. Kharzeev, Phys.Lett.B519:199-206,2001 M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 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 mg = m∞ • Small-x pQCD 0th Order result: M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 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 WWND 2008

  16. Classical/QFT Inconsistency • For mQ = mg = 0 and in the small x, large E+ limit, both are equal: • For mQ, mg ≠ 0 and the small x, large E+ limit, they differ: 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 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 WWND 2008

  19. Resulting Expression • To lowest order in 1/E+ • New: • (1-x)2 prefactor: naturally kills hard gluons • mg2 in numerator: fills in the dead cone!?! • What are the sizes of these effects? Call this LO 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 kT and x limits • x large enough to create mg • x small enough that EJet > Mq • Fixed m = .5 GeV and as = .5 • Similar to Magda full HTL propagator with running as 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 mg = 0 and pT → 0 WWND 2008

  22. Conclusions • No single satisfactory energy loss model • Search for tests sensitive to mechanism • Ratio of charm to bottom RAA 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? WWND 2008

  23. Backups WWND 2008

  24. Reasonable Consistency with Magda c b M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 WWND 2008

  25. 0th Order % Differences WWND 2008

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

  28. pQCD Success at RHIC: Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005) • Consistency: RAA(h)~RAA(p) • Null Control: RAA(g)~1 • GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy WWND 2008

  29. Trouble for wQGP Picture • e- RAA too small • Hydro h/s too small • v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) • wQGP not ruled out, but what if we try strong coupling? WWND 2008

  30. Intro to AdS/CFT Large Nc 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 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 WWND 2008

  32. Qualitative AdS/CFT Successes: AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • Mach wave-like structures • sstrong=(3/4) sweak, similar to Lattice • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) WWND 2008

  33. AdS/CFT Energy Loss Models • Langevin model • Collisional energy loss for heavy quarks • Restricted to low pT • 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! WWND 2008

  34. AdS/CFT Drag • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2T2/2Mq WWND 2008

  35. Energy Loss Comparison D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 D3 Black Brane (horizon) zh = pT Black Hole z = 0 • AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT • Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) WWND 2008

  36. RAA Approximation y=0 RHIC LHC • Above a few GeV, quark production spectrum is approximately power law: • dN/dpT ~ 1/pT(n+1), where n(pT) has some momentum dependence • We can approximate RAA(pT): • RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) WWND 2008

  37. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT • Asymptotic pQCD momentum loss: • String theory drag momentum loss: • Independent of pT and strongly dependent on Mq! • T2 dependence in exponent makes for a very sensitive probe • Expect: epQCD 0 vs. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST eST~ 1 - Exp(-m L), m = pl1/2T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 WWND 2008

  38. Model Inputs • AdS/CFT Drag: nontrivial mapping of QCD to SYM • “Obvious”: as = aSYM = const., TSYM = TQCD • D 2pT = 3 inspired: as = .05 • pQCD/Hydro inspired: as = .3 (D 2pT ~ 1) • “Alternative”: l = 5.5, TSYM = TQCD/31/4 • Start loss at thermalization time t0; end loss at Tc • WHDG convolved radiative and elastic energy loss • as = .3 • WHDG radiative energy loss (similar to ASW) • = 40, 100 • Use realistic, diffuse medium with Bjorken expansion • PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900) WWND 2008

  39. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 • 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 RAA(pT) for pQCD Rad+El • Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST WWND 2008

  40. An Enhanced Signal • But what about the interplay between mass and momentum? • Take ratio of c to b RAA(pT) • pQCD: Mass effects die out with increasing pT • Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching • ST: drag independent of pT, inversely proportional to mass. Simple analytic approx. of uniform medium gives RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27 • Ratio starts below 1; independent of pT RcbpQCD(pT) ~ 1 - asn(pT) L2 log(Mb/Mc) ( /pT) WWND 2008

  41. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • 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 pT WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] WWND 2008

  42. Not So Fast! x5 “z” • Speed limit estimate for applicability of AdS drag • g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) • Limited by Mcharm ~ 1.2 GeV • Similar to BH LPM • gcrit ~ Mq/(lT) • No Single T for QGP • smallest gcrit for largest T T = T(t0, x=y=0): “(” • largest gcrit for smallest T T = Tc: “]” D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane WWND 2008

  43. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • T(t0): (O), corrections unlikely for smaller momenta • Tc: (|), corrections likely for higher momenta WWND 2008

  44. Measurement at RHIC y=0 RHIC LHC • Future detector upgrades will allow for identified c and b quark measurements • RHIC production spectrum significantly harder than LHC • NOT slowly varying • No longer expect pQCD dRAA/dpT > 0 • Large n requires corrections to naïve Rcb ~ Mc/Mb WWND 2008

  45. RHIC c, b RAA pT Dependence • Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] WWND 2008

  46. RHIC Rcb 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 pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] WWND 2008

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

  48. Backups WWND 2008

  49. Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007 1D Hubble flow => r(t) ~ 1/t => T(t) ~ 1/t1/3 M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 WWND 2008

  50. Langevin Model AdS/CFT here • Langevin equations (assumes gv ~ 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: WWND 2008

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