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Jet Energy Loss with pQCD and AdS /CFT in Heavy Ion Collisions

Explore the dynamics of energy loss in Heavy Ion Collisions through the lens of perturbative Quantum Chromodynamics (pQCD) and the AdS/CFT correspondence. Gain insights into the Strong Force theory using various computational techniques and theoretical frameworks. Investigate the mechanisms of Energy Loss in the Quark-Gluon Plasma, with a focus on High-pT Jets and observables in heavy ion experiments like RHIC and LHC.

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Jet Energy Loss with pQCD and AdS /CFT in Heavy Ion Collisions

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  1. Jet Energy Loss with pQCD and AdS/CFT in Heavy Ion Collisions W. A. Horowitz The Ohio State University February 11, 2010 With many thanks to Brian Cole, MiklosGyulassy, Ulrich Heinz, and Yuri Kovchegov HIP Seminar

  2. QCD: Theory of the Strong Force • Running as • -b-fcn • SU(Nc = 3) • Nf(E) • Nf(RHIC) ≈ 2.5 PDG ALEPH, PLB284, (1992) Griffiths Particle Physics HIP Seminar

  3. Bulk QCD and Phase Diagram Long Range Plan, 2008 HIP Seminar

  4. Present and Future QGP Experiments • RHIC • BRAHMS • PHENIX • PHOBOS • STAR • LHC • ALICE • ATLAS • CMS • LHCb ATLAS PHENIX HIP Seminar

  5. Evolution of a HI Collision STAR T Hirano, Colliding Nuclei from AMeV to ATeV HIP Seminar

  6. Past, Present, and Future Questions • Bulk properties • Deconfinement • Thermalization, density • EOS, h/s • QGP DOF • Weakly vs. Strongly coupled plasma • G = U/T: <<1 or >>1? • Weakly vs. Strongly coupled theories • as ~ 0.3 << 1? l = √(gYM2Nc) ~ 3.5 >> 1? • New computational techniques • AdS? HIP Seminar

  7. Methods of QCD Calculation I: Lattice • All momenta • Euclidean correlators Long Range Plan, 2008 Kaczmarek and Zantow, PRD71 (2005) Davies et al. (HPQCD), PRL92 (2004) HIP Seminar

  8. Methods of QCD Calculation II: pQCD • Any quantity • Small coupling (large momenta only) d’Enterria, 0902.2011 Jäger et al., PRD67 (2003) HIP Seminar

  9. Methods of QCD Calculation III: AdS(?) Maldacena conjecture: SYM in d IIB in d+1 Gubser, QM09 • All quantities • Nc → ∞ • SYM, not QCD: b = 0 • Probably not good approx. for p+p; maybe A+A? HIP Seminar

  10. Why High-pT Jets? and even more with multiple probes SPECT-CT Scan uses internal g photons and external X-rays • Tomography in medicine One can learn a lot from a single probe… PET Scan http://www.fas.org/irp/imint/docs/rst/Intro/Part2_26d.html HIP Seminar

  11. Tomography in QGP pT f • Requires well-controlled theory of: • production of rare, high-pT probes • g, u, d, s, c, b • in-medium E-loss • hadronization • Requires precision measurements of decay fragments , g, e- Invert attenuation pattern => measure medium properties HIP Seminar

  12. QGP Energy Loss • Learn about E-loss mechanism • Most direct probe of DOF pQCD Picture AdS/CFT Picture HIP Seminar

  13. Jets in Heavy Ion Collisions • p+p • Au+Au PHENIX Y-S Lai, RHIC & AGS Users’ Meeting, 2009 HIP Seminar

  14. High-pT Observables pT f Naively: if medium has no effect, then RAA = 1 • Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f , g, e- • Fourier expand RAA: HIP Seminar

  15. pQCDRad Picture • Bremsstrahlung Radiation • Weakly-coupled plasma • Medium organizes into Debye-screened centers • T ~ 250 MeV, g ~ 2 • m ~ gT ~ 0.5 GeV • lmfp ~ 1/g2T ~ 1 fm • RAu ~ 6 fm • 1/m << lmfp << L • mult. coh. em. Gyulassy, Levai, and Vitev, NPB571 (200) • LPM • dpT/dt ~ -LT3 log(pT/Mq) • Bethe-Heitler • dpT/dt ~ -(T3/Mq2) pT HIP Seminar

  16. pQCD Success at RHIC: Y. Akibafor 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 HIP Seminar

  17. Trouble for Rad E-Loss Picture • v2 • e- e- WAH, Acta Phys.Hung.A27 (2006) Djordjevic, Gyulassy, Vogt, and Wicks, PLB632 (2006) HIP Seminar

  18. What About Elastic Loss? • Appreciable! • Finite time effects small Adil, Gyulassy, WAH, Wicks, PRC75 (2007) Mustafa, PRC72 (2005) HIP Seminar

  19. Quantitative Disagreement Remains v2 too small NPE supp. too large p0 v2 WHDG C. Vale, QM09 Plenary (analysis by R. Wei) NPE v2 Wicks, WAH, Gyulassy, Djordjevic, NPA784 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) HIP Seminar

  20. Strongly Coupled Qualitative Successes AdS/CFT T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Blaizot et al., JHEP0706 PHENIX, PRL98, 172301 (2007) HIP Seminar Betz, Gyulassy, Noronha, Torrieri, PLB675 (2009)

  21. Jets in AdS/CFT • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - mpT m = pl1/2T2/2Mq • Similar to Bethe-Heitler • dpT/dt ~ -(T3/Mq2) pT • Very different from LPM • dpT/dt ~ -LT3 log(pT/Mq) J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007) HIP Seminar

  22. Compared to Data • String drag: qualitative agreement WAH, PhD Thesis HIP Seminar

  23. Light Quark and Gluon E-Loss PHENIX 0-5% p0 WAH, in preparation Gubser, QM09 DLqtherm ~ E1/3 DLgtherm ~ (2E)1/3 HIP Seminar

  24. Baryon to Meson Ratios STAR STAR AdS/CFT AdS/CFT pQCD pQCD WAH, in preparation HIP Seminar

  25. Quantitative g, q from AdS? • Highly sensitive to IC • Distinguishing measurement? Chesler et al., Phys.Rev.D79:125015,2009 HIP Seminar

  26. Looking for a Qualitative, Distinguishing 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 HIP Seminar

  27. LHC c, b RAA pT Dependence WAH, M. Gyulassy, PLB666 (2008) • Unfortunately, large suppression pQCD similar to AdS/CFT HIP Seminar

  28. 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) HIP Seminar

  29. pQCD vs. AdS/CFT at LHC • Plethora of Predictions: WAH, M. Gyulassy, PLB666 (2008) • Taking the ratio cancels most normalization differences • 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 WAH, M. Gyulassy, PLB666 (2008) HIP Seminar

  30. 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 HIP Seminar

  31. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WAH, M. Gyulassy, PLB666 (2008) • T(t0): “(”, corrections likely small for smaller momenta • Tc: “]”, corrections likely large for higher momenta HIP Seminar

  32. 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 WAH, M. Gyulassy, JPhysG35 (2008) HIP Seminar

  33. Universality and Applicability • How universal are th. HQ drag results? • Examine different theories • Investigate alternate geometries • Other AdS geometries • Bjorken expanding hydro • Shock metric • Warm-up to Bj. hydro • Can represent both hot and cold nuclear matter HIP Seminar

  34. New Geometries vshock Q vshock z Q z x x Constant T Thermal Black Brane P Chesler, Quark Matter 2009 Shock Geometries Nucleus as Shock DIS Embedded String in Shock Albacete, Kovchegov, Taliotis, JHEP 0807, 074 (2008) Before After WAH and Kovchegov, PLB680 (2009) HIP Seminar

  35. Asymptotic Shock Results Q z = 0 vshock x0+ m ½z3/3 x0- m ½z3/3 x0 x z = ¥ • Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) • x(z) = x0, x0 ± m½ z3/3 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z3/3, z << 1, for const. T BH geom. HIP Seminar

  36. HQ Momentum Loss Relate m to nuclear properties • Use AdS dictionary • Metric in Fefferman-Graham form: m ~ T--/Nc2 • T’00 ~ Nc2 L4 • Nc2 gluons per nucleon in shock • L is typical mom. scale; L-1 typical dist. scale x(z) = m½ z3/3 => HIP Seminar

  37. Frame Dragging • HQ Rest Frame • Shock Rest Frame • Change coords, boost Tmn into HQ rest frame: • T-- ~ Nc2 L4 g2 ~ Nc2 L4 (p’/M)2 • p’ ~ gM: HQ mom. in rest frame of shock • Boost mom. loss into shock rest frame Mq L vsh Mq vq = -vsh 1/L vq = 0 i i vsh = 0 • p0t = 0: HIP Seminar

  38. Putting It All Together • For L typical momentum scale of the medium • We’ve generalized the BH solution to both cold and hot nuclear matter E-loss • Recall for BH: • Shock gives exactly the same drag as BH for L = p T HIP Seminar

  39. Shock Metric Speed Limit • Local speed of light (in HQ rest frame) • Demand reality of point-particle action • Solve for v = 0 for finite mass HQ • z = zM = l½/2pMq • Same speed limit as for BH metric when L = pT HIP Seminar

  40. Conclusions • pQCD and AdS/CFT enjoy qualitative successes, concerns in high-pT HIC • RHIC suppression of lights and heavies • Future LHC measurements • Quantitative comparisons with rigorous theoretical uncertainty estimates needed for falsification/verification • Theoretical work needed in both in pQCD and AdS • In AdS, control of jet IC, large pT required • In pQCD, wide angle radiation very important, not under theoretical control HIP Seminar

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