Heavy Ion Collisions with pQCD and AdS/CFT W. A. Horowitz The Ohio State University November 24, 2009 With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

Bulk QCD and Phase Diagram Long Range Plan, 2008 12/4/2018 UW Particle Theory 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! 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

Methods of QCD Calculation II: pQCD Jäger et al., PRD67 (2003) d’Enterria, 0902.2011 Any quantity Small coupling (large momenta only) 12/4/2018 UW Particle Theory 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? 12/4/2018 UW Particle Theory Seminar

Present and Future QGP Experiments RHIC BRAHMS PHENIX PHOBOS STAR LHC ALICE ATLAS CMS LHCb ATLAS PHENIX 12/4/2018 UW Particle Theory Seminar

Evolution of a HI Collision T Hirano, Colliding Nuclei from AMeV to ATeV STAR 12/4/2018 UW Particle Theory Seminar

Geometry of a HI Collision M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II) T Ludlum and L McLerran, Phys. Today 56N10 (2003) Hydro propagates IC Results depend strongly on initial conditions Viscosity reduces momentum anisotropy 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar Low-pT Measurements Viscosity: why the fuss? Naive pQCD => h/s ~ 1 Naive AdS/CFT => h/s ~ 1/4p Luzum and Romatschke, PRC78 (2008) U Heinz, Quark Matter 2009 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar QGP Energy Loss Learn about E-loss mechanism Most direct probe of DOF AdS/CFT Picture pQCD Picture 12/4/2018 UW Particle Theory Seminar

Jets in Heavy Ion Collisions p+p Au+Au PHENIX Y-S Lai, RHIC & AGS Users’ Meeting, 2009 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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: 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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. LPM dpT/dt ~ -LT3 log(pT/Mq) Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar pQCD Success at RHIC: (circa 2005) 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 12/4/2018 UW Particle Theory 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) 12/4/2018 UW Particle Theory Seminar

What About Elastic Loss? Appreciable! Finite time effects small Adil, Gyulassy, WAH, Wicks, PRC75 (2007) Mustafa, PRC72 (2005) 12/4/2018 UW Particle Theory 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) 12/4/2018 UW Particle Theory 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) 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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) 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar Compared to Data String drag: reasonable agreement Distinguishing measurement? WAH, PhD Thesis 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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) 12/4/2018 UW Particle Theory Seminar

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 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar New Geometries Constant T Thermal Black Brane Shock Geometries P Chesler, Quark Matter 2009 Nucleus as Shock DIS Embedded String in Shock Before After Albacete, Kovchegov, Taliotis, JHEP 0807, 074 (2008) Q vshock x z vshock x z Q Bjorken-Expanding Medium WAH and Kovchegov, PLB680 (2009) 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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 Nc2 gluons per nucleon in shock L is typical mom. scale; L-1 typical dist. scale E-M in shock rest frame: T’00 ~ Nc2 L4 12/4/2018 UW Particle Theory Seminar

UW Particle Theory 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 (“lab” frame) p0t = 0: 12/4/2018 UW Particle Theory Seminar

Putting It All Together This leads to 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 12/4/2018 UW Particle Theory 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 12/4/2018 UW Particle Theory Seminar

Quantitative, Falsifiable pQCD Requires rigorous pQCD estimates, limits 12/4/2018 UW Particle Theory Seminar

Joint TECHQM/CATHIE Meeting Acronyms, Acronyms Four major pQCD formalisms for Rad E-loss Opacity expansion: GLV (DGLV), ASW-SH Multiple soft scattering: BDMPS (ASW-MS) Higher Twist: HT Thermal field theory: AMY 12/4/2018 Joint TECHQM/CATHIE Meeting

Joint TECHQM/CATHIE Meeting Energy Loss RAA ~ ∫(1-ϵ)n P(ϵ) dϵ Ef = (1-ϵ)Ei Opacity expansions finds single inclusive gluon emission spectrum dNg/dxdkTdqT 12/4/2018 Joint TECHQM/CATHIE Meeting

Joint TECHQM/CATHIE Meeting Poisson Convolution Find P(ϵ) by convolving dNg/dx Approximates probabilistic multiple gluon emission assume independent emissions Gyulassy, Levai, and Vitev NPB594 (2001) 12/4/2018 Joint TECHQM/CATHIE Meeting

Opacity Expansion Calculation Want to find dNg/dx Make approximations to simplify derivation Small angle emission: kT << xE Note: ALL current formalisms use collinear approximation Derived dNg/dxdkT violates collinear approx Both IR and UV safe Enforce small angle emission through UV cutoff in kT 12/4/2018 Joint TECHQM/CATHIE Meeting

Uncertainty from Collinear Approx Derived dNg/dxdkT maximally violates collinear approximation WAH and B Cole, arXiv:0910.1823 dNg/dx depends sensitively on kT cutoff Despite UV safety For effect on extracted prop., must understand x Discovered through TECHQM Brick Problem 12/4/2018 Joint TECHQM/CATHIE Meeting

Joint TECHQM/CATHIE Meeting ASW-SH Definition of x ASW-SH: xE Minkowski coords Always on-shell P 12/4/2018 Joint TECHQM/CATHIE Meeting

Joint TECHQM/CATHIE Meeting GLV Definition of x GLV: x+ Light-cone coords Always on-shell P 12/4/2018 Joint TECHQM/CATHIE Meeting

Coordinate Transformations Same in the limit kT/xE → 0! UV cutoff given by restricting maximum angle of emission Previous comparisons with data took qmax=p/2 Vary qmax to estimate systematic theoretical uncertainty P q 12/4/2018 Joint TECHQM/CATHIE Meeting

Joint TECHQM/CATHIE Meeting Jacobians ϵ is fraction of longitudinal momentum Need dNg/dxE to find P(ϵ) A Jacobian is required for x = x+ interpretation 12/4/2018 Joint TECHQM/CATHIE Meeting

Rad. Gluon Kin. Sensitivities UV What about IR? WAH and B Cole, arXiv:0910.1823 12/4/2018 Joint TECHQM/CATHIE Meeting

Collinearity and Gluon Mass Massless gluons: Large IR cutoff sensitivity Gluons with thermal mass BDMS, JHEP 0109 (2001) Larger x better respects kT << xE 12/4/2018 Joint TECHQM/CATHIE Meeting WAH and B Cole, arXiv:0910.1823

Joint TECHQM/CATHIE Meeting Results Quantitatively compare to PHENIX data Assumed infinite Elastic precision WAH and B Cole, arXiv:0910.1823 12/4/2018 Joint TECHQM/CATHIE Meeting

Parton Energy Dependence Dependence on parton energy Uncertainty on qhat Assume all formalisms equally affected WAH and B Cole, arXiv:0910.1823 12/4/2018 Joint TECHQM/CATHIE Meeting

UW Particle Theory Seminar Conclusions I QCD is a theory with rich structure Traditional techniques (Lattice, pQCD) Qualitatively successeful AdS/CFT exciting new tool Also qualitatively successful Jet observables to disambiguate Examine mass, momentum dependence Charm and bottom RAA Double ratio: RcAA/RbAA(pT) 12/4/2018 UW Particle Theory Seminar

UW Particle Theory Seminar Conclusions II Generalize AdS/CFT HQ Drag Hot and cold nuclear matter Gain confidence in universality Systematic theoretical uncertainty for pQCD Collinear approximation badly violated Some effects persist to LHC energies Single particle more interesting than full jet reconstruction? Extracted medium properties likely consistent w/i unc. Effects of running coupling not yet rigorously investigated 12/4/2018 UW Particle Theory Seminar