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Probing AdS/CFT with Heavy Quarks

arXiv:0706.2336  (LHC predictions) arXiv:0710.0703 (RHIC predictions). Probing AdS/CFT with Heavy Quarks. William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 26, 2007. With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev. Introduction.

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Probing AdS/CFT with Heavy Quarks

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  1. arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) Probing AdS/CFT with Heavy Quarks William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 26, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev AdS Strings Intersect with Nuclear Beams at Columbia

  2. Introduction • AdS/CFT looks promising, pQCD also has its successes • Desire a robust probe that can cleanly falsify one or both formalisms: • Try Heavy Quarks! AdS Strings Intersect with Nuclear Beams at Columbia

  3. Quantitative AdS/CFT with Jets • 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! AdS Strings Intersect with Nuclear Beams at Columbia

  4. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • Use future detectors’ identification of c and b to distinguish between pQCD, AdS/CFT • RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) • 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 AdS Strings Intersect with Nuclear Beams at Columbia

  5. Model Inputs for LHC Predictions • 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) AdS Strings Intersect with Nuclear Beams at Columbia

  6. LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 • 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 born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST • LHC Prediction Zoo: What a Mess! • Let’s go through step by step AdS Strings Intersect with Nuclear Beams at Columbia

  7. 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) AdS Strings Intersect with Nuclear Beams at Columbia

  8. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, nucl-th/0706.2336 • 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, nucl-th/0706.2336 AdS Strings Intersect with Nuclear Beams at Columbia

  9. But There’s a Catch x5 “z” • Speed limit estimate for applicability of AdS/CFT drag computation • g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) • Limited by Mcharm ~ 1.2 GeV • Ambiguous T for QGP • smallest gcrit for largest T = T(t0, x=y=0): (O) • largest gcrit for smallest T = Tc: (|) D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane AdS Strings Intersect with Nuclear Beams at Columbia

  10. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH, M. Gyulassy, nucl-th/0706.2336 • T(t0): (O), corrections unlikely for smaller momenta • Tc: (|), corrections likely for higher momenta AdS Strings Intersect with Nuclear Beams at Columbia

  11. 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 AdS Strings Intersect with Nuclear Beams at Columbia

  12. 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, to be published AdS Strings Intersect with Nuclear Beams at Columbia

  13. 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, to be published AdS Strings Intersect with Nuclear Beams at Columbia

  14. Conclusions • Year 1 of LHC could show qualitative differences between energy loss mechanisms: • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST • Ratio of charm to bottom RAA, Rcb, will be an important observable • Ratio is: flat in ST; approaches 1 from below in pQCD partonic E-loss • A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 2-3 times increase in Rcb by 30 GeV—this can be observed in year 1 at LHC • Measurement at RHIC will be possible • AdS/CFT calculations applicable to higher momenta than at LHC due to lower medium temperature • Universality of pQCD and AdS/CFT Dependencies? AdS Strings Intersect with Nuclear Beams at Columbia

  15. Additional Discerning Power • Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1 • Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity AdS Strings Intersect with Nuclear Beams at Columbia

  16. Conclusions (cont’d) • Additional c, b PID Goodies: • Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for RcAA/RbAA with the possibility of breaching 1 and asymptotically approaching 1 from above • Surface emission models (although already unlikely as per v2(pT) data) predict flat in pTc, b RAA, with a ratio of 1 • Moderately suppressed radiative only energy loss shows a dip in the ratio at low pT; convolved loss is monotonic. Caution: in this regime, approximations are violated • Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass • Need for p+A control AdS Strings Intersect with Nuclear Beams at Columbia

  17. Backups AdS Strings Intersect with Nuclear Beams at Columbia

  18. LHC p Predictions • Our predictions show a significant increase in RAA as a function of pT • This rise is robust over the range of predicted dNg/dy for the LHC that we used • This should be compared to the flat in pT curves of AWS-based energy loss (next slide) • We wish to understand the origin of this difference WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation AdS Strings Intersect with Nuclear Beams at Columbia

  19. Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~a3 Log(E/m2L)/E DEel/E ~a2 Log((E T)1/2/mg)/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation AdS Strings Intersect with Nuclear Beams at Columbia

  20. 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: AdS Strings Intersect with Nuclear Beams at Columbia

  21. But There’s a Catch (II) • Limited experimental pT reach? • ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II AdS Strings Intersect with Nuclear Beams at Columbia

  22. 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) AdS Strings Intersect with Nuclear Beams at Columbia

  23. Introduction to Jargon pT f Naïvely: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f Common to Fourier expand RAA: AdS Strings Intersect with Nuclear Beams at Columbia

  24. 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 AdS Strings Intersect with Nuclear Beams at Columbia

  25. pQCD Success at RHIC: Y. Akiba for the PHENIX collaboration, nucl-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 AdS Strings Intersect with Nuclear Beams at Columbia

  26. 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? AdS Strings Intersect with Nuclear Beams at Columbia

  27. 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) AdS Strings Intersect with Nuclear Beams at Columbia

  28. h/s Sensitive to Initial Conditions Diffuse BGK IC => Ideal Hydro, h/s ~ 1/4p Sharp CGC IC => Viscous Hydro Currently no exp. constraint on IC T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys. Lett. B636:299-304,2006 AdS Strings Intersect with Nuclear Beams at Columbia

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