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 January 19, 2010 With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov 10/27/2021 LBL Nuclear 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 10/27/2021 LBL Nuclear Theory Seminar 2

Bulk QCD and Phase Diagram Long Range Plan, 2008 10/27/2021 LBL Nuclear Theory Seminar 3

Evolution of a HI Collision T Hirano, Colliding Nuclei from AMe. V to ATe. V 10/27/2021 LBL Nuclear Theory Seminar STAR 4

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? 10/27/2021 LBL Nuclear Theory Seminar 5

Methods of QCD Calculation I: Lattice Long Range Plan, 2008 • All momenta • Euclidean correlators Kaczmarek and Zantow, PRD 71 (2005) 10/27/2021 Davies et al. (HPQCD), PRL 92 (2004) LBL Nuclear Theory Seminar 6

Methods of QCD Calculation II: p. QCD Jäger et al. , PRD 67 (2003) 10/27/2021 d’Enterria, 0902. 2011 • Any quantity • Small coupling (large momenta only) LBL Nuclear Theory Seminar 7

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? 10/27/2021 LBL Nuclear Theory Seminar 8

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 10/27/2021 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 LBL Nuclear Theory Seminar 9

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 10/27/2021 Invert attenuation pattern => measure medium properties LBL Nuclear Theory Seminar 10

QGP Energy Loss • Learn about E-loss mechanism – Most direct probe of DOF p. QCD Picture Ad. S/CFT Picture 10/27/2021 LBL Nuclear Theory Seminar 11

Jets in Heavy Ion Collisions • p+p • Au+Au Y-S Lai, RHIC & AGS Users’ Meeting, 2009 10/27/2021 PHENIX LBL Nuclear Theory Seminar 12

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: 10/27/2021 p. T LBL Nuclear Theory Seminar 13

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 10/27/2021 LBL Nuclear Theory Seminar 14

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 10/27/2021 LBL Nuclear Theory Seminar 15

Trouble for Rad E-Loss Picture • v 2 • e- e- WAH, Acta Phys. Hung. A 27 (2006) 10/27/2021 Djordjevic, Gyulassy, Vogt, and Wicks, PLB 632 (2006) LBL Nuclear Theory Seminar 16

What About Elastic Loss? • Appreciable! • Finite time effects small Mustafa, PRC 72 (2005) 10/27/2021 LBL Nuclear Theory Seminar Adil, Gyulassy, WAH, Wicks, PRC 75 (2007) 17

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) 10/27/2021 LBL Nuclear Theory Seminar 18

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) 10/27/2021 LBL Nuclear Theory Seminar 19 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) 10/27/2021 LBL Nuclear Theory Seminar 20

Compared to Data • String drag: qualitative agreement WAH, Ph. D Thesis 10/27/2021 LBL Nuclear Theory Seminar 21

Light Quark and Gluon E-Loss PHENIX 0 -5% p 0 WAH, in preparation dpq/dt ~ E 1/3 dpg/dt ~ (2 E)1/3 10/27/2021 LBL Nuclear Theory Seminar 22

Baryon to Meson Ratios STAR Ad. S/CFT p. QCD WAH, in preparation – Distinguishing measurement? 10/27/2021 LBL Nuclear Theory Seminar 23

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 10/27/2021 LBL Nuclear Theory Seminar 24

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: “]” 10/27/2021 LBL Nuclear Theory Seminar D 7 Probe Brane Q Worldsheet boundary Spacelike if g > gcrit x 5 Trailing String “Brachistochrone” “z” D 3 Black Brane 25

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 10/27/2021 LBL Nuclear Theory Seminar 26

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 10/27/2021 LBL Nuclear Theory Seminar 27

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 10/27/2021 LBL Nuclear Theory Seminar 28

New Geometries 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 vshock Q z x Q z vshock x WAH and Kovchegov, PLB 680 (2009) 10/27/2021 LBL Nuclear Theory Seminar 29

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=¥ 10/27/2021 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z 3/3, z << 1, for const. T BH geom. LBL Nuclear Theory Seminar 30

Putting It All Together • For L typical momentum scale of the medium –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 10/27/2021 LBL Nuclear Theory Seminar 31

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 10/27/2021 LBL Nuclear Theory Seminar 32

Back to p. QCD: Quant. and Falsifiable – Requires rigorous p. QCD estimates, limits: – Different p. QCD formalisms, different results 10/27/2021 Bass et al. , Phys. Rev. C 79: 024901, 2009 LBL Nuclear Theory Seminar 33

Need for Theoretical Uncertainty • Want to rigorously: – falsify theories – quantify medium • Therefore need: – Precise observables – Precise theory • Distinguish between systematic uncertainties: – between formalisms • Due to diff. physics assumptions – within formalisms • Due to simplifying approximations • Focus specifically on opacity expansion – GLV; ASW-SH 10/27/2021 LBL Nuclear Theory Seminar 34

Mechanics of Energy Loss – RAA ~ ∫(1 -ϵ)n P(ϵ) dϵ • Ef = (1 -ϵ)Ei – Opacity expansions finds single inclusive gluon emission spectrum • d. Ng/dxdk. Tdq. T 10/27/2021 LBL Nuclear Theory Seminar 35

Poisson Convolution Gyulassy, Levai, and Vitev NPB 594 (2001) • Find P(ϵ) by convolving d. Ng/dx – Approximates probabilistic multiple gluon emission, Sudakov • assume independent emissions – NB: ϵ is a momentum fraction 10/27/2021 LBL Nuclear Theory Seminar 36

Opacity Expansion Calculation • Want to find d. Ng/dx – Make approximations to simplify derivation • Small angle emission: k. T << x. E – Note: ALL current formalisms use collinear approximation – Derived d. Ng/dxdk. T violates collinear approx • Both IR and UV safe • Enforce small angle emission through UV cutoff in k. T 10/27/2021 LBL Nuclear Theory Seminar 37

Uncertainty from Collinear Approx • Derived d. Ng/dxdk. T maximally violates collinear approximation – d. Ng/dx depends sensitively on k. T cutoff • Despite UV safety – For effect on extracted prop. , must understand x • Discovered through TECHQM Brick Problem WAH and B Cole, ar. Xiv: 0910. 1823 10/27/2021 LBL Nuclear Theory Seminar 38

x Definitions • ASW-SH: x. E – Energy fraction P • GLV: x+ – Plus momentum fraction NB: gluon always on-shell 10/27/2021 LBL Nuclear Theory Seminar 39

Coordinate Transformations – Same in the limit k. T/x. E → 0! • UV cutoff given by restricting maximum angle of emission P q – Previous comparisons with data took qmax=p/2 – Vary qmax to estimate systematic theoretical uncertainty 10/27/2021 LBL Nuclear Theory Seminar 40

Jacobians • ϵ is fraction of longitudinal momentum – Need d. Ng/dx. E to find P(ϵ) – A Jacobian is required for x = x+ interpretation 10/27/2021 LBL Nuclear Theory Seminar 41

Rad. Gluon Kin. Sensitivities • UV WAH and B Cole, ar. Xiv: 0910. 1823 • What about IR? 10/27/2021 LBL Nuclear Theory Seminar 42

Collinearity and Gluon Mass • Massless gluons: – Large IR cutoff sensitivity • Gluons with thermal mass BDMS, JHEP 0109 (2001) ~ Larger x better respects k. T << x. E 10/27/2021 LBL Nuclear Theory Seminar WAH and B Cole, ar. Xiv: 0910. 1823 43

Results • Quantitatively compare to PHENIX data WAH and B Cole, ar. Xiv: 0910. 1823 – Assumed infinite Elastic precision 10/27/2021 LBL Nuclear Theory Seminar 44

Parton Energy Dependence • Dependence on parton energy WAH and B Cole, ar. Xiv: 0910. 1823 10/27/2021 • Uncertainty on qhat – Assume all formalisms equally affected LBL Nuclear Theory Seminar 45

Conclusions – p. QCD and Ad. S/CFT enjoy qualitative successes, concerns in high-p. T 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 p. QCD and Ad. S – In Ad. S, control of jet IC, large p. T required – In p. QCD, wide angle radiation very important, not under theoretical control 10/27/2021 LBL Nuclear Theory Seminar 46