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Heavy Quark Production and Energy Loss W. A. Horowitz University of Cape Town August 14, 2012 With many thanks to Razieh Morad, Miklos Gyulassy, and Yuri Kovchegov 2012/08/23 Quark Matter 2012 1 What Are We Interested In? Measure the

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SLIDE 1

Heavy Quark Production and Energy Loss

  • W. A. Horowitz

University of Cape Town August 14, 2012

2012/08/23 1 Quark Matter 2012

With many thanks to Razieh Morad, Miklos Gyulassy, and Yuri Kovchegov

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SLIDE 2

What Are We Interested In?

  • Measure the prop-

erties of many- body strong force

  • Test & understand

theory of many- body non-Abelian fields

2012/08/23 Quark Matter 2012 2 Long Range Plan, 2008

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SLIDE 3

Compare to Easiest QED

2012/08/23 Quark Matter 2012 3

  • “Simple” Hydrogen Phase Diagram

Calculated, Burkhard Militzer, Diploma Thesis, Berlin, 2000

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SLIDE 4

Why Energy Loss?

Most direct probe of DOF of QGP

2012/08/23 Quark Matter 2012 4

pQCD Picture

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SLIDE 5

AdS/CFT Picture

Why Energy Loss?

Most direct probe of DOF of QGP

2012/08/23 Quark Matter 2012 5

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SLIDE 6

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 6

QGP

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SLIDE 7

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 7

High pT Light Hadrons

QGP

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SLIDE 8

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 8

High pT Light Hadrons Quarkonia

QGP

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SLIDE 9

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 9

Open Heavy Flavor High pT Light Hadrons Quarkonia

QGP

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SLIDE 10

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 10

Open Heavy Flavor High pT Light Hadrons EM Probes Quarkonia

QGP

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SLIDE 11

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 11

Open Heavy Flavor High pT Light Hadrons EM Probes Quarkonia Your least favorite measurement

QGP

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SLIDE 12

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 12

Open Heavy Flavor High pT Light Hadrons EM Probes Low-pT particles Quarkonia Your least favorite measurement

QGP

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SLIDE 13

Heavy Quarks in Context

2012/08/23 Quark Matter 2012 13

Open Heavy Flavor High pT Light Hadrons EM Probes Low-pT particles Quarkonia Your least favorite measurement

QGP

Searching for this coherent, consistent picture

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SLIDE 14

Why Heavy Quarks?

  • E-loss picture assumes QGP properties

=> P(ΔpT | pT, L, T, MQ, R)

  • Want to test P(ΔpT)

– A+B, √s, centrality, Mh, …

2012/08/23 Quark Matter 2012 14

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SLIDE 15

Qualitative Expectations for HF

  • Energy loss decreases with MQ

⇒ ΔEb < ΔEc < ΔEu,d < ΔEg

  • For experts: not always true for pQCD

(τform decreases with MQ)

  • DOES NOT IMPLY RAA ORDERING

– For approx. power law production and energy loss probability P(ε), ε = (Ei - Ef)/Ei – Larger n => smaller RAA for same energy loss

2012/08/23 Quark Matter 2012 15

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SLIDE 16

Importance of Production

  • HQ production spectra softer than lights

=> Nontrivial ordering of RAA(pT)

2012/08/23 Quark Matter 2012 16 See also Buzzatti, 5C (NB: High-pT and Jets)

√s = 2.76 TeV LHC

0-20% π0 WHDG D WHDG B WHDG

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SLIDE 17

Lesson from RHIC

  • Extremely difficult to consistently describe

all observables

– HF suppression places stringent constraint on possible E-loss mechanism

2012/08/23 Quark Matter 2012 17 Wicks, WAH, Djordjevic, Gyulassy, NPA784 (2007)

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SLIDE 18

Demonstrating E-loss Value

  • Compare E-loss observables to data with

two very different assumptions of properties of QGP:

– Strongly coupled medium coupling strongly to a high-pT particle – Weakly coupled medium coupling weakly to a high-pT particle

2012/08/23 Quark Matter 2012 18

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SLIDE 19

Let’s Assume Strong Coupling

  • Not crazy

– T ~ 250 MeV, g(2πT) ~ 2, λ = g2Nc ~ 12 1

  • Always small T scale

– T Tc, lattice deviates from Stefan-Boltzmann – η/s ~ 1/4π readily explained by AdS/CFT

2012/08/23 Quark Matter 2012 19 Wuppertal, arXiv:1204.6710 Luzum and Romatschke, PC78 (2008)

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SLIDE 20

Quark Matter 2012 20

Heavy Quark E-Loss in AdS/CFT

  • Model heavy quark jet energy loss by

embedding string in AdS space

dpT/dt = - µ pT µ = πλ1/2 T2/2Mq

J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007) 2012/08/23

– Similar to Bethe-Heitler

dpT/dt ~ -(T3/Mq

2) pT

– Very different from usual pQCD and LPM

dpT/dt ~ -LT3 log(pT/Mq)

Herzog et al., JHEP 0607 (2006) Gubser, PRD74 (2006)

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SLIDE 21

Quark Matter 2012 21

AdS/CFT and HQ

  • String drag: qualitative agreement at

RHIC

WAH, PhD Thesis, arXiv:1011.4316 2012/08/23 Akamatsu, Hatsuda, and Hirano, PRC79, 2009

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SLIDE 22

AdS/CFT and HQ at LHC

  • D Predictions
  • B Predictions

2012/08/23 Quark Matter 2012 22 WAH, PANIC11 (arXiv:1108.5876) ALICE, arXiv:1203.2160 CMS, JHEP 1205 (2012) 063

CMS B→J/ψ'

ALICE 0-20% D

( (

  • AdS HQ Drag appears to oversuppress D#

– Long. fluctuations likely important, not included

  • Roughly correct description of B→J/ψ

(

]

( (

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SLIDE 23

Light Quark E-Loss in AdS

  • Complications:

– string endpoints fall

=> painful numerics

– relation to HI meas.

  • less obvious than HQ
  • In principle, compute Tµν

from graviton emission

– Extremely hard

2012/08/23 Quark Matter 2012 23 Chesler et al., PRD79 (2009)

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SLIDE 24

AdS/CFT Light q E-Loss

  • Static thermal medium =>

very short therm. time

– τth ~ 2.7 fm

  • AdS likely oversuppresses

compared to data

  • Examine T ~ 1/τ1/3 geom

– τth ~ 4.1 fm; Bragg peak disappears

2012/08/23 Quark Matter 2012 24 WAH, JPhysG38 (2011)

0.2 TeV

Simple Bragg peak model

2.76 TeV

R Morad

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SLIDE 25

Strongly Coupled HF @QM

  • More information/differing opinions

– Chesler, “Gravitational collapse and holographic thermalization”, 3D – Rajagopal, “Shining a Gluon Beam through Quark-Gluon Plasma”, 5D – Ficnar, “Can falling strings in deformed AdS geometries account for the surprising transparency of the sQGP at LHC?”, Poster

2012/08/23 Quark Matter 2012 25

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SLIDE 26

Strongly Coupled HF into the Future

  • Measure open HF in p+A

– Midrapidity: test production (Tuchin, 2D) – Forward: test CNM HF E-loss

2012/08/23 Quark Matter 2012 26

Embedded String in Shock

Q vshock x z vshock x z Q

Before After

WAH and Kovchegov, PLB680 (2009)

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SLIDE 27

Let’s Assume pQCD is the Best Approx

  • Also not unreasonable

– αs(2πT) = 0.3

  • Always large pT scale

– 22 & 23 pQCD MC suggests η/s ~ few/4π'

2012/08/23 Quark Matter 2012 27 El, Muronga, Xu, and Greiner, PRC79 (2009)

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SLIDE 28

Let’s Assume pQCD is the Way to Go

  • Thermal Field Theory =>

– Debye mass µ ~ gT – Mean free path λmfp ~ 1/g2T

  • Entropy/Hydro => TRHIC(LHC) ~ 350 (450) MeV

– µ ~ gT ~ 0.7 (0.8) GeV => 1/µ ~ 0.3 (0.2) fm – λmfp ~ 1/g2T ~ 0.8 (0.7) fm – RAu,Pb ~ 6 fm

  • 1/µ << λmfp << L

– Scattering off separated, well-defined quasiparticles – For HQ, order a few collisions, ~ 4

2012/08/23 Quark Matter 2012 28

gluon

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SLIDE 29

pQCD Continued

  • Two types of E-loss

– Collisional (elastic) 22 – Radiative (inelastic) 23

  • Scales => ~few scatterings, mult. coh. em. => LPM
  • Must include interference with production radiation

2012/08/23 Quark Matter 2012 29

  • Bjorken, FERMILAB-PUB-82-059-THY
  • Braaten and Thoma, PRD44:2625–2630, 1991
  • Djordjevic, Phys.Rev. C74 (2006) 064907
  • Adil et al., Phys.Rev. C75 (2007) 044906

Djordjevic, PRC74 (2006)

  • Majumder and van Leeuwen, PPNPA66 (2011), and refs therein
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SLIDE 30

Asymptotic Analytic pQCD

  • Naively, ΔEel << ΔErad as E∞
  • Elastic E-loss:

dpT/dt ~ -T2 log(pT/MQ)

  • Radiative E-loss, in expected deep LPM

regime: dpT/dt ~ -L T3 log(pT/MQ)

– Compare to Bethe-Heitler dpT/dt ~ -(T3/M2)pT

2012/08/23 Quark Matter 2012 30

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SLIDE 31

Results

  • Naively, ΔEel << ΔErad as E∞

2012/08/23 Quark Matter 2012 31

RHIC LHC

WAH, PhD Thesis, arXiv:1011.4316

Finite RHIC/LHC kinematics: both radiative and collisional energy loss processes are important for pT ~ 5 GeV/c and higher

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SLIDE 32

1400-375

  • RHIC RAA: not

unreasonable ρmed

– dNg/dy = 1400+200 – αs = 0.3, fixed

Compare to RHIC & LHC

2012/08/23 Quark Matter 2012 32 PHENIX, PRC77 (2008)

  • For LHC predictions: change only

ρmed dNch/dη'

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SLIDE 33

Set Scale for our Expectations

  • NLO pQCD in pp System ~ factor of 2

2012/08/23 Quark Matter 2012 33 PHENIX, PRC84 (2011) CMS, EurPhysJC72 (2012)

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SLIDE 34

Global Qualitative Agreement

  • LO pQCD E-loss correct to factor ~2

2012/08/23 Quark Matter 2012 34 PHENIX PRL105 (2010)

RHIC LHC

ALICE D WHDG D

LHC

CMS h± 0-5% WHDG π0

LHC LHC

CMS h± 40-50% WHDG π0

RHIC

ALICE, arXiv:1203.2160 CMS, JHEP 1205 (2012) 063 CMS, Eur.Phys.J. C72 (2012) CMS, arXiv:1204.1850

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SLIDE 35

Potential Improvements at QM

  • MC, parton cascade: Uphoff, poster
  • NLO ansatz, better modeling: Buzzatti, 5C
  • Additional Channels

– In-medium fragmentation: Sharma, 2D – Non-perturbative 22 x-scns: He, Poster

  • Be careful with:

– Uncontrolled (& esp. uncontrollable) physics – Radiative only or Elastic only – Lack of finite time effects: wrong L dependence – Approximating pQCD with Langevin: far from central limit theorem, wrong pT dependence

2012/08/23 Quark Matter 2012 35

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SLIDE 36

Quark Matter 2012 36

Does pQCD or AdS Yield Correct Mass & Momentum Dependecies at LHC?

– T(τ0): “(”, corrections likely small for smaller momenta – Tc: “]”, corrections likely large for higher momenta

See also: WAH, M. Gyulassy, PLB666 (2008) 2012/08/23

Qualitatively, corrections to AdS/CFT result will drive double ratio to unity

WAH, PANIC11 (arXiv:1108.5876)

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SLIDE 37

Take-away Messages

  • 1. E-loss depends on pT, L, T, MQ
  • 1. MQ dependence provides unique insight into E-loss,

QGP properties

  • 2. Want to vary others, too: consistent, coherent picture
  • 2. Multiple observables demand simultaneous

description: hard

  • 1. Difficult to describe data with AdS/CFT?
  • 2. LO pQCD gives reasonable qualitative description

1. How do we understand sQGP(hydro) => wQGP(E-loss)

  • 3. p+A is more than control experiment
  • 4. HF E-loss physics exciting with much fascinating

research ahead!

2012/08/23 Quark Matter 2012 37

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SLIDE 38

Rich and Vigorous HF E-loss Theory

  • Talks:

– Cao, “Heavy quark evolution and flow in hot and dense medium,” 6A – Buzzatti, “A Running Coupling Explanation of the Surprisingly Transparency of the QGP at LHC,” 5C – Gossiaux, “Heavy quark quenching from RHIC to LHC and the consequences of gluon damping,” 7E – Rapp, “Comprehensive Analysis of In-Medium Quarkonia from SPS to LHC,” 1D – Sharma, “High transverse momentum quarkonium production and dissociation in heavy ion collisions,” 2D

  • Posters:

– Abir, “Soft gluon emission and energy loss of heavy flavors in relativistic heavy ion collisions” – Akamatsu, “Quantum Description of Impurities - Heavy Quarks and Quarkonia” – Begum, “Suppression of D-mesons production at relativistic heavy ion collisions” – Durham, “A detailed study of open heavy flavor production, enhancement, and suppression at RHIC” – Ficnar, “Can falling strings in deformed AdS geometries account for the surprising transparency of the sQGP at LHC?” – Levai, “Charm production in the early phase and the charm baryon-to-meson ratios at LHC energies” – Nahrgang, “Influence of a realistic medium description including fluctuations on heavy quark

  • bservables”

– Petran, “Charm contribution to final hadron yield at LHC” – Uphoff, “Open heavy flavor and J/psi at RHIC and LHC within a transport model” – van Hees, “Heavy-quark diffusion at the LHC within a UrQMD-hydrodynamical hybrid model” – Vogel, “Influence of the medium evolution on heavy quark observables” – Vogel, “Heavy quark energy loss in p+p collisions at the LHC”

2012/08/23 Quark Matter 2012 38

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SLIDE 39

2012/08/23 Quark Matter 2012 39

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SLIDE 40

2012/08/23 Quark Matter 2012 40

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SLIDE 41

2012/08/23 Quark Matter 2012 41

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SLIDE 42

Armesto et al., NPA774 (2006) 2012/08/23 Quark Matter 2012 42

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SLIDE 43

pQCD Rad Picture

  • Bremsstrahlung Radiation

– Weakly-coupled plasma

  • Medium organizes into Debye-screened centers

– T ~ 350 (450) MeV, g ~ 1.9 (1.8)

  • µ ~ gT ~ 0.7 (0.8) GeV
  • λmfp ~ 1/g2T ~ 0.8 (0.7) fm
  • RAu,Pb ~ 6 fm

– 1/µ << λmfp << L

  • multiple coherent emission

2012/08/23 Quark Matter 2012 43

– Bethe-Heitler

dpT/dt ~ -(T3/Mq

2) pT

– LPM

dpT/dt ~ -LT3 log(pT/Mq)

Gyulassy, Levai, and Vitev, NPB571 (2000)

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SLIDE 44

What About Elastic Loss?

  • Appreciable!
  • Finite time effects small

2012/08/23 Quark Matter 2012 44 Mustafa, PRC72 (2005) Adil, Gyulassy, WAH, Wicks, PRC75 (2007)

– For pQCD comparisons with data, use WHDG Rad+El +Geom model; formalism valid for g/lq & hq

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SLIDE 45

pQCD Not Quantitative at RHIC

  • Lack of simultaneous description of

multiple observables

– even with inclusion of elastic loss

2012/08/23 Quark Matter 2012 45 STAR, PRL106 (2011) PHENIX, PRL 105 (2010)

LHC energies?

See also J Jia from QM09, J Nagle QM09

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SLIDE 46
  • Quant. (Qual?) Conclusions Require...
  • Further experimental results
  • Theoretically, investigation of the effects of

– higher orders in

  • αs

(large)

  • kT/xE

(large)

  • MQ/E

(large?)

  • opacity

(large?)

– geometry

  • uncertainty in IC

(small)

  • coupling to flow

(large?)

  • Eloss geom. approx.

(?)

  • τ < τ0

(large: see Buzzatti and Gyulassy)

  • dyn. vs. static centers

(see Djordjevic)

  • hydro background

(see Renk, Majumder)

– better treatment of

  • Coh. vs. decoh. multigluons

(see Mehtar-Tani)

  • elastic E-loss
  • E-loss in confined matter

2012/08/23 Quark Matter 2012 46

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SLIDE 47

(Data – pQCD)/Data

2012/08/23 Quark Matter 2012 47

CMS 0-5% h± CMS 40-50% h± ALICE 0-20% D

LO Calculation

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SLIDE 48

Quark Matter 2012 48

Strong Coupling Calculation

  • The supergravity double conjecture:

QCD ! SYM ! IIB

– IF super Yang-Mills (SYM) is not too different from QCD, & – IF we believe Maldacena conjecture – Then a tool exists to calculate strongly- coupled QCD in SUGRA

2012/08/23

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SLIDE 49

– NB: RAA requires production, E-loss, FF

  • Does not immediately follow that Rπ

AA << RD AA << RB AA'

And D, B (?) RAA at LHC

2012/08/23 Quark Matter 2012 49 WAH and M Gyulassy, PANIC11 (arXiv:1107.2136) ALICE, 1203.2160 CMS B → J/ψ

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SLIDE 50

Comparing to RHIC, LHC

  • In principle, can compute Tmn from

graviton emission

– Extremely hard

2012/08/23 Quark Matter 2012 50 Gubser, Pufu, Yarom, JHEP 0709 (2007) See also Friess et al., PRD75 (2007)

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SLIDE 51

AdS/CFT Light q E-Loss & Dist.

2012/08/23 Quark Matter 2012 51

  • Suggests wide

angle energy loss

Jo Noronha, M Gyulassy, and G Torrieri, PRL102 (2009) WAH, JPhysG38 (2011)

0.2 TeV

Simple Bragg peak model

2.76 TeV

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SLIDE 52

Energy Loss in QGP

  • Claim: LHC predictions from rigorously

RHIC constrained pQCD E-loss in qualitative/quantitative agreement with current data

– Want to stress test the theory with as many experimental levers as possible

  • Counter-claim: LHC predictions from AdS/

CFT not falsified by current data

– Want an obvious distinguishing measurement

2012/08/23 Quark Matter 2012 52

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SLIDE 53

Qualitative Expectations for LHC

– For approx. power law production and energy loss probability P(ε), ε = (Ei - Ef)/Ei

2012/08/23 Quark Matter 2012 53

– Asymptotically, pQCD => ΔE/E ~ log(E/µ)/E

  • ~ flat RAA(pT) at RHIC
  • Rising RAA(pT) at LHC

– NB: LHC is a glue machine

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SLIDE 54

Qualitatively Perturbative at LHC

2012/08/23 Quark Matter 2012 54 Appelshauser, ALICE, QM11

  • pT rise in data readily understood from generic

perturbative physics!

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SLIDE 55

Rise in RAA a Final State Effect?

– Is rise really due to pQCD? – Or other quench (flat?)

+ initial state CNM

effects a la CGC?

2012/08/23 Quark Matter 2012 55 Albacete and Marquet, PLB687 (2010) PHENIX PRL98, 2007 Y-J Lee, QM11

Require p + A and/or direct γ'

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SLIDE 56

pQCD and Jet Measurements

– CMS sees redistribution of lost energy at large angles

  • Naive pQCD expectation: collinear radiation

2012/08/23 Quark Matter 2012 56 Wyslouch, CMS, QM11

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SLIDE 57

pQCD and Wide Angle Radiation

– Naively, pQCD => xtypical, θtypical ~ µ/E; µ ~ 0.5 GeV – All current Eloss calculations assume small angle emission (kT << xE) – Collinear approximation is (maximally) violated; xtyp ~ µ/E – pQCD is not inconsistent with data

2012/08/23 Quark Matter 2012 57 WAH and B Cole, PRC81, 2010 C Roland, CMS, QM11 B Cole, ATLAS, QM11 z

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SLIDE 58

WHDG Compared to RCP

  • Examine RCP, ratio of central to peripheral

RAA

2012/08/23 Quark Matter 2012 58

– p + p uncertainty cancels – 0-5% RAA to 70-80% RAA – Validity of E-loss in very peripheral collisions?

WAH and M Gyulassy, NPA872 (2011)

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SLIDE 59

Quark Matter 2012 59

  • 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.

  • f uniform medium gives

Rcb

pQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27

– Ratio starts below 1; independent of pT

Comparing AdS and pQCD

Rcb

pQCD(pT) ∼ 1 - αs n(pT) L2 log(Mb/Mc) ( /pT)

2012/08/23

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SLIDE 60

Top Energy Predictions

  • For posterity:

2012/08/23 Quark Matter 2012 60 WAH and M Gyulassy, in preparation

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SLIDE 61

Quark Matter 2012 61

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

WAH, M. Gyulassy, JPhysG35 (2008)

pQCD AdS/CFT pQCD AdS/CFT

2012/08/23

slide-62
SLIDE 62

2012/08/23 Quark Matter 2012 62 Chesler et al., PRD79 (2009)

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SLIDE 63

Motivating High Momentum Probes

2012/08/23 Quark Matter 2012 63

Medium Medium

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SLIDE 64

Light Quark and Gluon E-Loss

2012/08/23 Quark Matter 2012 64

ΔLq

therm ~ E1/3

ΔLq

therm ~ (2E)1/3

See also Marquet and Renk, PLB685 (2010), and Jia, WAH, and Liao, arXiv:1101.0290, for v2 Gubser et al., JHEP0810 (2008) Chesler et al., PRD79 (2009) Arnold and Vaman, JHEP 1104 (2011) SS Gubser, QM08 Chesler et al., PRD79 (2009)

  • Light quarks and

gluons: generic Bragg peak

– Leads to lack of T dependence?

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SLIDE 65

Varying αs has huge effect

  • <ε>rad,pQCD ~ αs

3; <ε>el,pQCD ~ αs 2

– Role of running coupling, irreducible uncertainty from non-pert. physics? – Nontrivial changes from better elastic treatment

2012/08/23 Quark Matter 2012 65 S Wicks, PhD Thesis

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SLIDE 66

Quantification of Collinear Uncertainty

  • Factor ~ 3 uncertainty

in extracted medium density!

  • “qhat” values from

different formalisms consistent w/i unc.

2012/08/23 Quark Matter 2012 66 WAH and B Cole, PRC81, 2010

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SLIDE 67
  • Coll. Approx. and Constrained v2
  • Fix dNg/dy from RAA, calculate v2

– Expect: larger v2 for smaller opening angle

  • τcoh = xE/kT

2 larger for smaller θmax

– more paths in deep LPM (ΔE ~ L2) region

– Not large sensitivity

2012/08/23 Quark Matter 2012 67

  • Rad Only
  • Rad + El

WAH, in preparation

v2 pT 20-30% π0 20-30% π0 v2 pT

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SLIDE 68

Geometry, Early Time Investigation

  • Significant progress made

– Full geometry integration, dynamical scattering centers – RHIC suppression with dNg/ dy = 1000 – Large uncertainty due to unconstrained, non- equilibrium τ < τ0 physics – Future work: higher orders in opacity

2012/08/23 Quark Matter 2012 68 Buzzatti and Gyulassy, 1106.3061

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SLIDE 69

Quark Matter 2012 69

– Speed limit estimate for applicability of AdS drag

  • γ < γcrit = (1 + 2Mq/λ1/2 T)2

~ 4Mq

2/(λ T2)

– Limited by Mcharm ~ 1.2 GeV

  • Similar to BH LPM

– γcrit ~ Mq/(λT)

– No Single T for QGP

  • smallest γcrit for largest T

T = T(τ0, x=y=0): “(”

  • largest γcrit for smallest T

T = Tc: “]”

Not So Fast!

D3 Black Brane D7 Probe Brane Q Worldsheet boundary Spacelike if γ > γcrit Trailing String “Brachistochrone” “z” x5

2012/08/23

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SLIDE 70

pQCD pp Predictions vs. Data

2012/08/23 Quark Matter 2012 70 ALICE, arXiv:1205.5423 CMS, arXiv:1202.2554