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, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov 11/13/2018 HIP Seminar

QCD: Theory of the Strong Force ALEPH, PLB284, (1992) PDG Running as -b-fcn SU(Nc = 3) Nf(E) Nf(RHIC) ≈ 2.5 Griffiths Particle Physics 11/13/2018 HIP Seminar

Bulk QCD and Phase Diagram Long Range Plan, 2008 11/13/2018 HIP Seminar

Present and Future QGP Experiments RHIC BRAHMS PHENIX PHOBOS STAR LHC ALICE ATLAS CMS LHCb ATLAS PHENIX 11/13/2018 HIP Seminar

Evolution of a HI Collision T Hirano, Colliding Nuclei from AMeV to ATeV STAR 11/13/2018 HIP Seminar

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 = √(gYM2 Nc) ~ 3.5 >> 1? New computational techniques AdS? Theoretical techniques up next! 11/13/2018 HIP Seminar

Methods of QCD Calculation I: Lattice Long Range Plan, 2008 Kaczmarek and Zantow, PRD71 (2005) Davies et al. (HPQCD), PRL92 (2004) All momenta Euclidean correlators 11/13/2018 HIP Seminar

Methods of QCD Calculation II: pQCD Jäger et al., PRD67 (2003) d’Enterria, 0902.2011 Any quantity Small coupling (large momenta only) 11/13/2018 HIP Seminar

Methods of QCD Calculation III: AdS(?) Maldacena conjecture: SYM in d  IIB in d+1 Gubser, QM09 Next up, experiments! All quantities Nc → ∞ SYM, not QCD: b = 0 Probably not good approx. for p+p; maybe A+A? 11/13/2018 HIP Seminar

Why High-pT Jets? Tomography in medicine One can learn a lot from a single probe… and even more with multiple probes SPECT-CT Scan uses internal g photons and external X-rays PET Scan http://www.fas.org/irp/imint/docs/rst/Intro/Part2_26d.html 11/13/2018 HIP Seminar

Tomography in QGP 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 pT f , g, e- Invert attenuation pattern => measure medium properties 11/13/2018 HIP Seminar

QGP Energy Loss Learn about E-loss mechanism Most direct probe of DOF AdS/CFT Picture pQCD Picture 11/13/2018 HIP Seminar

Jets in Heavy Ion Collisions p+p Au+Au PHENIX Y-S Lai, RHIC & AGS Users’ Meeting, 2009 11/13/2018 HIP Seminar

High-pT Observables 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 pT f , g, e- Fourier expand RAA: 11/13/2018 HIP Seminar

pQCD Rad 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 11/13/2018 HIP Seminar

pQCD Success at RHIC: (circa 2005) Null Control: RAA(g)~1 Y. Akiba for the PHENIX collaboration, hep-ex/0510008 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 11/13/2018 HIP Seminar

Trouble for Rad E-Loss Picture v2 e- WAH, Acta Phys.Hung.A27 (2006) Anticorrelated; have e- come in later e- Djordjevic, Gyulassy, Vogt, and Wicks, PLB632 (2006) 11/13/2018 HIP Seminar

What About Elastic Loss? Appreciable! Finite time effects small Adil, Gyulassy, WAH, Wicks, PRC75 (2007) Mustafa, PRC72 (2005) 11/13/2018 HIP Seminar

Quantitative Disagreement Remains v2 too small NPE supp. too large p0 v2 C. Vale, QM09 Plenary (analysis by R. Wei) WHDG Wicks, WAH, Gyulassy, Djordjevic, NPA784 (2007) NPE v2 Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) 11/13/2018 HIP Seminar

Strongly Coupled Qualitative Successes T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Blaizot et al., JHEP0706 AdS/CFT PHENIX, PRL98, 172301 (2007) Betz, Gyulassy, Noronha, Torrieri, PLB675 (2009) 11/13/2018 HIP Seminar

Jets in AdS/CFT Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2 T2/2Mq J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007) Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) 11/13/2018 HIP Seminar

Compared to Data String drag: qualitative agreement WAH, PhD Thesis 11/13/2018 HIP Seminar

Light Quark and Gluon E-Loss WAH, in preparation PHENIX 0-5% p0 Gubser, QM09 DLqtherm ~ E1/3 DLgtherm ~ (2E)1/3 11/13/2018 HIP Seminar

Baryon to Meson Ratios STAR STAR AdS/CFT AdS/CFT pQCD pQCD WAH, in preparation 11/13/2018 HIP Seminar

Quantitative g, q from AdS? Highly sensitive to IC Distinguishing measurement? Chesler et al., Phys.Rev.D79:125015,2009 11/13/2018 HIP Seminar

Looking for a Qualitative, Distinguishing Signal 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. eAdS indep of pT!! dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST erad ~ as L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 11/13/2018 HIP Seminar

LHC c, b RAA pT Dependence WAH, M. Gyulassy, PLB666 (2008) Unfortunately, large suppression pQCD similar to AdS/CFT 11/13/2018 HIP Seminar

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 - as n(pT) L2 log(Mb/Mc) ( /pT) 11/13/2018 HIP Seminar

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) 11/13/2018 HIP Seminar

Worldsheet boundary Spacelike if g > gcrit Not So Fast! 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: “]” D3 Black Brane D7 Probe Brane Q Worldsheet boundary Spacelike if g > gcrit Trailing String “Brachistochrone” “z” x5 11/13/2018 HIP Seminar

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 11/13/2018 HIP Seminar

RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WAH, M. Gyulassy, JPhysG35 (2008) Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits 11/13/2018 HIP Seminar

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 11/13/2018 HIP Seminar

New Geometries Constant T Thermal Black Brane Shock Geometries P Chesler, Quark Matter 2009 Nucleus as Shock DIS Embedded String in Shock Albacete, Kovchegov, Taliotis, JHEP 0807, 074 (2008) Before After Q vshock x z vshock x z Q WAH and Kovchegov, PLB680 (2009) 11/13/2018 HIP Seminar

Asymptotic Shock Results Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) x(z) = x0, x0 ± m ½ z3/3 Constant solution unstable Time-reversed negative x solution unphysical Sim. to x ~ z3/3, z << 1, for const. T BH geom. x0 - m ½ z3/3 x0 + m ½ z3/3 x0 vshock Q z = 0 z = ¥ x 11/13/2018 HIP Seminar

HQ Momentum Loss x(z) = m ½ z3/3 => 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 11/13/2018 HIP Seminar

Frame Dragging HQ Rest Frame Shock Rest Frame Mq L vsh vq = -vsh Mq 1/L vq = 0 i i vsh = 0 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 p0t = 0: 11/13/2018 HIP Seminar

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 11/13/2018 HIP Seminar

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 11/13/2018 HIP Seminar

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 11/13/2018 HIP Seminar