Heavy Ion Collisions with p QCD and Ad

Heavy Ion Collisions with p. QCD and Ad. S/CFT W. A. Horowitz The Ohio State University November 24, 2009 With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov 10/25/2021 UW Particle Theory Seminar 1

QCD: Theory of the Strong Force • Running as – -b-fcn • SU(Nc = 3) PDG ALEPH, PLB 284, (1992) • Nf(E) – Nf(RHIC) ≈ 2. 5 Griffiths Particle Physics 10/25/2021 UW Particle Theory Seminar 2

Bulk QCD and Phase Diagram Long Range Plan, 2008 10/25/2021 UW Particle Theory Seminar 3

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 = √(g. YM 2 Nc) ~ 3. 5 >> 1? • New computational techniques – Ad. S? 10/25/2021 UW Particle Theory Seminar 4

Methods of QCD Calculation I: Lattice Long Range Plan, 2008 • All momenta • Euclidean correlators Kaczmarek and Zantow, PRD 71 (2005) 10/25/2021 Davies et al. (HPQCD), PRL 92 (2004) UW Particle Theory Seminar 5

Methods of QCD Calculation II: p. QCD Jäger et al. , PRD 67 (2003) 10/25/2021 d’Enterria, 0902. 2011 • Any quantity • Small coupling (large momenta only) UW Particle Theory Seminar 6

Methods of QCD Calculation III: Ad. S(? ) Maldacena conjecture: SYM in d IIB in d+1 Gubser, QM 09 • All quantities • Nc → ∞ • SYM, not QCD: b = 0 – Probably not good approx. for p+p; maybe A+A? 10/25/2021 UW Particle Theory Seminar 7

Present and Future QGP Experiments • RHIC • LHC – – – – BRAHMS PHENIX PHOBOS STAR ALICE ATLAS CMS LHCb ATLAS PHENIX 10/25/2021 UW Particle Theory Seminar 8

Evolution of a HI Collision T Hirano, Colliding Nuclei from AMe. V to ATe. V 10/25/2021 UW Particle Theory Seminar STAR 9

Geometry of a HI Collision M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II) T Ludlum and L Mc. Lerran, Phys. Today 56 N 10 (2003) • Hydro propagates IC – Results depend strongly on initial conditions • Viscosity reduces momentum anisotropy 10/25/2021 UW Particle Theory Seminar 10

Low-p. T Measurements (I) LRP 2008 – Partonic DOF at hadronization! 10/25/2021 UW Particle Theory Seminar 11

Low-p. T Measurements (II) • Viscosity: why the fuss? – Naive p. QCD => h/s ~ 1 – Naive Ad. S/CFT => h/s ~ 1/4 p Luzum and Romatschke, PRC 78 (2008) 10/25/2021 UW Particle Theory Seminar U Heinz, Quark Matter 2009 12

Why High-p. T Jets? • Tomography in medicine One can learn a lot from a single probe… and even more with multiple probes PET Scan 10/25/2021 SPECT-CT Scan uses internal g photons and external X-rays http: //www. fas. org/irp/imint/docs/rst/Intro/P art 2_26 d. html UW Particle Theory Seminar 13

Tomography in QGP • Requires wellcontrolled theory of: p. T – production of rare, highp. T probes f , g, e- • g, u, d, s, c, b – in-medium E-loss – hadronization • Requires precision measurements of decay fragments 10/25/2021 Invert attenuation pattern => measure medium properties UW Particle Theory Seminar 14

QGP Energy Loss • Learn about E-loss mechanism – Most direct probe of DOF p. QCD Picture Ad. S/CFT Picture 10/25/2021 UW Particle Theory Seminar 15

Jets in Heavy Ion Collisions • p+p • Au+Au Y-S Lai, RHIC & AGS Users’ Meeting, 2009 10/25/2021 UW Particle Theory Seminar PHENIX 16

High-p. T Observables Naively: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, p. T, and angle with respect to the reaction plane, f , g, e- f Fourier expand RAA: 10/25/2021 p. T UW Particle Theory Seminar 17

p. QCD Rad Picture • Bremsstrahlung Radiation – Weakly-coupled plasma • Medium organizes into Debye-screened centers – T ~ 250 Me. V, g ~ 2 • m ~ g. T ~ 0. 5 Ge. V • lmfp ~ 1/g 2 T ~ 1 fm • RAu ~ 6 fm – LPM dp. T/dt ~ -LT 3 log(p. T/Mq) – 1/m << lmfp << L • mult. coh. em. – Bethe-Heitler dp. T/dt ~ -(T 3/Mq 2) p. T 10/25/2021 UW Particle Theory Seminar 18

p. QCD 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 d. Ng/dy~d. Np/dy 10/25/2021 UW Particle Theory Seminar 19

Trouble for Rad E-Loss Picture • v 2 • e- e- WAH, Acta Phys. Hung. A 27 (2006) 10/25/2021 Djordjevic, Gyulassy, Vogt, and Wicks, PLB 632 (2006) UW Particle Theory Seminar 20

What About Elastic Loss? • Appreciable! • Finite time effects small Mustafa, PRC 72 (2005) 10/25/2021 UW Particle Theory Seminar Adil, Gyulassy, WAH, Wicks, PRC 75 (2007) 21

Quantitative Disagreement Remains p 0 v 2 – v 2 too small – NPE supp. too large WHDG NPE v 2 C. Vale, QM 09 Plenary (analysis by R. Wei) Wicks, WAH, Gyulassy, Djordjevic, NPA 784 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) 10/25/2021 UW Particle Theory Seminar 22

Strongly Coupled Qualitative Successes Ad. S/CFT Blaizot et al. , JHEP 0706 T. Hirano and M. Gyulassy, Nucl. Phys. A 69: 71 -94 (2006) PHENIX, PRL 98, 172301 (2007) 10/25/2021 UW Particle Theory Seminar 23 Betz, Gyulassy, Noronha, Torrieri, PLB 675 (2009)

Jets in Ad. S/CFT • Model heavy quark jet energy loss by embedding string in Ad. S space dp. T/dt = - m p. T m = pl 1/2 T 2/2 Mq – Similar to Bethe-Heitler dp. T/dt ~ -(T 3/Mq 2) p. T J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D 75 (2007) – Very different from LPM dp. T/dt ~ -LT 3 log(p. T/Mq) 10/25/2021 UW Particle Theory Seminar 24

Compared to Data • String drag: reasonable agreement WAH, Ph. D Thesis – Distinguishing measurement? 10/25/2021 UW Particle Theory Seminar 25

p. QCD vs. Ad. S/CFT at LHC • Plethora of Predictions: WAH, M. Gyulassy, PLB 666 (2008) – Taking the ratio cancels most normalization differences – p. QCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) WAH, M. Gyulassy, PLB 666 (2008) – Ad. S/CFT ratio is flat and many times smaller than p. QCD at only moderate p. T 10/25/2021 UW Particle Theory Seminar 26

Not So Fast! – Speed limit estimate for applicability of Ad. S drag • g < gcrit = (1 + 2 Mq/l 1/2 T)2 ~ 4 Mq 2/(l T 2) – Limited by Mcharm ~ 1. 2 Ge. V • Similar to BH LPM – gcrit ~ Mq/(l. T) – No Single T for QGP • smallest gcrit for largest T T = T(t 0, x=y=0): “(” • largest gcrit for smallest T T = Tc: “]” 10/25/2021 UW Particle Theory Seminar D 7 Probe Brane Q Worldsheet boundary Spacelike if g > gcrit x 5 Trailing String “Brachistochrone” “z” D 3 Black Brane 27

LHC Rc. AA(p. T)/Rb. AA(p. T) Prediction (with speed limits) WAH, M. Gyulassy, PLB 666 (2008) – T(t 0): “(”, corrections likely small for smaller momenta – Tc: “]”, corrections likely large for higher momenta 10/25/2021 UW Particle Theory Seminar 28

RHIC Rcb Ratio p. QCD Ad. S/CFT WAH, M. Gyulassy, JPhys. G 35 (2008) • Wider distribution of Ad. S/CFT curves due to large n: increased sensitivity to input parameters • Advantage of RHIC: lower T => higher Ad. S speed limits 10/25/2021 UW Particle Theory Seminar 29

Universality and Applicability • How universal are th. HQ drag results? – Examine different theories – Investigate alternate geometries • Other Ad. S geometries – Bjorken expanding hydro – Shock metric • Warm-up to Bj. hydro • Can represent both hot and cold nuclear matter 10/25/2021 UW Particle Theory Seminar 30

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 10/25/2021 vshock Q z Bjorken-Expanding Medium After x Q z vshock x WAH and Kovchegov, PLB 680 (2009) UW Particle Theory Seminar 31

Asymptotic Shock Results • Three t-ind. solutions (static gauge): m X = (t, x(z), 0, 0, z) – x(z) = x 0, x 0 ± m ½ z 3/3 Q z=0 vshock x 0 + m ½ z 3/3 x 0 - m ½ z 3/3 x 0 x z=¥ 10/25/2021 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z 3/3, z << 1, for const. T BH geom. UW Particle Theory Seminar 32

HQ Momentum Loss x(z) = m ½ z 3/3 => Relate m to nuclear properties – Use Ad. S dictionary • Metric in Fefferman-Graham form: m ~ T--/Nc 2 – Nc 2 gluons per nucleon in shock – L is typical mom. scale; L-1 typical dist. scale • E-M in shock rest frame: T’ 00 ~ Nc 2 L 4 10/25/2021 UW Particle Theory Seminar 33

Frame Dragging • HQ Rest Frame Mq vsh 1/L i • Shock Rest Frame vq = 0 L vq = -vsh i Mq vsh = 0 – Change coords, boost Tmn into HQ rest frame: • T-- ~ Nc 2 L 4 g 2 = Nc 2 L 4 (p’/M)2 • p’ ~ g. M: HQ mom. in rest frame of shock – Boost mom. loss into shock rest frame (“lab” frame) – p 0 t = 0: 10/25/2021 UW Particle Theory Seminar 34

Putting It All Together • This leads to –Recall for BH: –Shock gives exactly the same drag as BH for L = p T • We’ve generalized the BH solution to both cold and hot nuclear matter E-loss 10/25/2021 UW Particle Theory Seminar 35

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 = z. M = l½/2 p. Mq – Same speed limit as for BH metric when L = p. T 10/25/2021 UW Particle Theory Seminar 36

Quantitative, Falsifiable p. QCD • Requires rigorous p. QCD estimates, limits 10/25/2021 UW Particle Theory Seminar 37

Multiple Models WHDG, Nucl. Phys. A 784: 426 -442, 2007 Bass et al. , Phys. Rev. C 79: 024901, 2009 – Inconsistent medium properties – Distinguish between models? 10/25/2021 UW Particle Theory Seminar Bass et al. 38

Quantitative Parameter Extraction • Vary input param. • Find “best” value Need for theoretical uncertainty PHENIX, PRC 77: 064907, 2008 10/25/2021 UW Particle Theory Seminar 39

Mechanics of p. QCD Rad Calculation • Derive single inclusive gluon emission Gyulassy, Levai, and Vitev NPB 594 (2001) – Ambiguity in literature: x from light cone vs. Minkowski coords • d. Ng/dx+dk. T related to d. Ng/dx. Edk. T by Jacobian • Poisson convolution – Approximate multiple gluon emission – Single inclusive used as kernel 10/25/2021 UW Particle Theory Seminar 40

Collinear Approximation • Assume small angle emission – k. T << w = x. EE k. T w • x+ = x. E for k. T = 0 • Affects ALL current p. QCD models • Enforce via kinematic cutoffs 10/25/2021 WAH and B Cole, ar. Xiv: 0910. 1823 UW Particle Theory Seminar 41

Collinearity and Gluon Mass • Larger x, smaller collinear effects • Thermal gluon mass alters coherence m 2 10/25/2021 WAH and B Cole, ar. Xiv: 0910. 1823 UW Particle Theory Seminar 42

Huge Sensitivity WAH and B Cole, ar. Xiv: 0910. 1823 10/25/2021 UW Particle Theory Seminar 43

Conclusions I • QCD is a theory with rich structure – Traditional techniques (Lattice, p. QCD) • Qualitatively successeful – Ad. S/CFT exciting new tool • Also qualitatively successful • Jet observables to disambiguate – Examine mass, momentum dependence • Charm and bottom RAA • Double ratio: Rc. AA/Rb. AA(p. T) 10/25/2021 UW Particle Theory Seminar 44

Conclusions II • Generalize Ad. S/CFT HQ Drag – Hot and cold nuclear matter – Gain confidence in universality • Systematic theoretical uncertainty for p. QCD – 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 10/25/2021 UW Particle Theory Seminar 45