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 prop- erties of many- body strong force • Test & understand theory of many- body non-Abelian fields Long Range Plan, 2008 2012/08/23 Quark Matter 2012 2
Compare to Easiest QED • “Simple” Hydrogen Phase Diagram Calculated, Burkhard Militzer, Diploma Thesis, Berlin, 2000 2012/08/23 Quark Matter 2012 3
Why Energy Loss? Most direct probe of DOF of QGP pQCD Picture 2012/08/23 Quark Matter 2012 4
Why Energy Loss? Most direct probe of DOF of QGP AdS/CFT Picture 2012/08/23 Quark Matter 2012 5
Heavy Quarks in Context QGP 2012/08/23 Quark Matter 2012 6
Heavy Quarks in Context High p T Light Hadrons QGP 2012/08/23 Quark Matter 2012 7
Heavy Quarks in Context High p T Light Hadrons QGP Quarkonia 2012/08/23 Quark Matter 2012 8
Heavy Quarks in Context High p T Light Hadrons QGP Quarkonia Open Heavy Flavor 2012/08/23 Quark Matter 2012 9
Heavy Quarks in Context High p T Light Hadrons EM Probes QGP Quarkonia Open Heavy Flavor 2012/08/23 Quark Matter 2012 10
Heavy Quarks in Context High p T Light Hadrons EM Probes Your least favorite QGP measurement Quarkonia Open Heavy Flavor 2012/08/23 Quark Matter 2012 11
Heavy Quarks in Context High p T Light Hadrons EM Probes Low-p T particles Your least favorite QGP measurement Quarkonia Open Heavy Flavor 2012/08/23 Quark Matter 2012 12
Heavy Quarks in Context High p T Light Hadrons EM Probes Low-p T particles Your least favorite QGP measurement Quarkonia Open Heavy Flavor Searching for this coherent, consistent picture 2012/08/23 Quark Matter 2012 13
Why Heavy Quarks? • E-loss picture assumes QGP properties => P( Δ p T | p T , L, T, M Q , R) • Want to test P( Δ p T ) – A+B, √ s, centrality, M h , … 2012/08/23 Quark Matter 2012 14
Qualitative Expectations for HF • Energy loss decreases with M Q ⇒ Δ E b < Δ E c < Δ E u,d < Δ E g • For experts: not always true for pQCD ( τ form decreases with M Q ) • DOES NOT IMPLY R AA ORDERING – For approx. power law production and energy loss probability P ( ε ), ε = ( E i - E f )/ E i – Larger n => smaller R AA for same energy loss 2012/08/23 Quark Matter 2012 15
Importance of Production • HQ production spectra softer than lights => Nontrivial ordering of R AA (p T ) √ s = 2.76 TeV LHC 0-20% π 0 WHDG D WHDG B WHDG See also Buzzatti, 5C (NB: High-p T and Jets) 2012/08/23 Quark Matter 2012 16
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)
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-p T particle – Weakly coupled medium coupling weakly to a high-p T particle 2012/08/23 Quark Matter 2012 18
Let’s Assume Strong Coupling • Not crazy – T ~ 250 MeV, g(2 π T) ~ 2, λ = g 2 N c ~ 12 � 1 • Always small T scale – T � T c , lattice deviates from Stefan-Boltzmann – η /s ~ 1/4 π readily explained by AdS/CFT Luzum and Romatschke, PC78 (2008) 2012/08/23 Quark Matter 2012 19 Wuppertal, arXiv:1204.6710
Heavy Quark E-Loss in AdS/CFT • Model heavy quark jet energy loss by embedding string in AdS space dp T /dt = - µ p T µ = πλ 1/2 T 2 /2M q Herzog et al., JHEP 0607 (2006) Gubser, PRD74 (2006) – Similar to Bethe-Heitler dp T /dt ~ -(T 3 /M q 2 ) p T J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007) – Very different from usual pQCD and LPM dp T /dt ~ -LT 3 log(p T /M q ) 2012/08/23 Quark Matter 2012 20
AdS/CFT and HQ • String drag: qualitative agreement at RHIC WAH, PhD Thesis, arXiv:1011.4316 Akamatsu, Hatsuda, and Hirano, PRC79, 2009 2012/08/23 Quark Matter 2012 21
AdS/CFT and HQ at LHC • D Predictions • B Predictions ALICE 0-20% D CMS B → J/ ψ ' ( ( ] ( ( ( WAH, PANIC11 (arXiv:1108.5876) ALICE, arXiv:1203.2160 CMS, JHEP 1205 (2012) 063 • AdS HQ Drag appears to oversuppress D # – Long. fluctuations likely important, not included • Roughly correct description of B → J/ ψ 2012/08/23 Quark Matter 2012 22
Light Quark E-Loss in AdS Chesler et al., PRD79 (2009) • Complications: – string endpoints fall => painful numerics – relation to HI meas. • less obvious than HQ • In principle, compute T µ ν from graviton emission – Extremely hard 2012/08/23 Quark Matter 2012 23
AdS/CFT Light q E-Loss • Static thermal medium => 0.2 TeV very short therm. time – τ th ~ 2.7 fm • AdS likely oversuppresses compared to data • Examine T ~ 1/ τ 1/3 geom – τ th ~ 4.1 fm; Bragg peak disappears R Morad 2.76 TeV WAH, JPhysG38 (2011) Simple Bragg peak model 2012/08/23 Quark Matter 2012 24
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
Strongly Coupled HF into the Future • Measure open HF in p+A – Midrapidity: test production (Tuchin, 2D) – Forward: test CNM HF E-loss Embedded String in Shock Before After v shock Q v shock z Q z x x WAH and Kovchegov, PLB680 (2009) 2012/08/23 Quark Matter 2012 26
Let’s Assume pQCD is the Best Approx • Also not unreasonable – α s (2 π T) = 0.3 • Always large p T scale – 2 � 2 & 2 � 3 pQCD MC suggests η /s ~ few/4 π' El, Muronga, Xu, and Greiner, PRC79 (2009) 2012/08/23 Quark Matter 2012 27
Let’s Assume pQCD is the Way to Go • Thermal Field Theory => – Debye mass µ ~ gT – Mean free path λ mfp ~ 1/g 2 T • Entropy/Hydro => T RHIC(LHC) ~ 350 (450) MeV – µ ~ gT ~ 0.7 (0.8) GeV => 1/ µ ~ 0.3 (0.2) fm gluon – λ mfp ~ 1/g 2 T ~ 0.8 (0.7) fm – R Au,Pb ~ 6 fm • 1/ µ << λ mfp << L – Scattering off separated, well-defined quasiparticles – For HQ, order a few collisions, ~ 4 2012/08/23 Quark Matter 2012 28
pQCD Continued • Two types of E-loss – Collisional (elastic) 2 � 2 • Bjorken, FERMILAB-PUB-82-059-THY • Braaten and Thoma, PRD44:2625–2630, 1991 • Djordjevic, Phys.Rev. C74 (2006) 064907 Djordjevic, PRC74 (2006) • Adil et al., Phys.Rev. C75 (2007) 044906 – Radiative (inelastic) 2 � 3 • Scales => ~few scatterings, mult. coh. em. => LPM • Must include interference with production radiation • Majumder and van Leeuwen, PPNPA66 (2011), and refs therein 2012/08/23 Quark Matter 2012 29
Asymptotic Analytic pQCD • Naively, Δ E el << Δ E rad as E � ∞ • Elastic E-loss: dp T /dt ~ -T 2 log(p T /M Q ) • Radiative E-loss, in expected deep LPM regime: dp T /dt ~ -L T 3 log(p T /M Q ) – Compare to Bethe-Heitler dp T /dt ~ -(T 3 /M 2 )p T 2012/08/23 Quark Matter 2012 30
Results • Naively , Δ E el << Δ E rad as E � ∞ LHC RHIC WAH, PhD Thesis, arXiv:1011.4316 Finite RHIC/LHC kinematics: both radiative and collisional energy loss processes are important for p T ~ 5 GeV/c and higher 2012/08/23 Quark Matter 2012 31
Compare to RHIC & LHC • RHIC R AA : not unreasonable ρ med – dNg/dy = 1400 +200 1400 -375 – α s = 0.3, fixed PHENIX, PRC77 (2008) • For LHC predictions: change only ρ med � dN ch /d η' 2012/08/23 Quark Matter 2012 32
Set Scale for our Expectations • NLO pQCD in pp System ~ factor of 2 PHENIX, PRC84 (2011) CMS, EurPhysJC72 (2012) 2012/08/23 Quark Matter 2012 33
Global Qualitative Agreement • LO pQCD E-loss correct to factor ~2 LHC LHC RHIC CMS h ± 0-5% ALICE D WHDG π 0 WHDG D RHIC LHC LHC CMS h ± 40-50% WHDG π 0 CMS, Eur.Phys.J. C72 (2012) ALICE, arXiv:1203.2160 PHENIX PRL105 (2010) CMS, arXiv:1204.1850 CMS, JHEP 1205 (2012) 063 2012/08/23 Quark Matter 2012 34
Potential Improvements at QM • MC, parton cascade: Uphoff, poster • NLO ansatz, better modeling: Buzzatti, 5C • Additional Channels – In-medium fragmentation: Sharma, 2D – Non-perturbative 2 � 2 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 p T dependence 2012/08/23 Quark Matter 2012 35
Does pQCD or AdS Yield Correct Mass & Momentum Dependecies at LHC? WAH, PANIC11 (arXiv:1108.5876) – T( τ 0 ): “(”, corrections likely small for smaller momenta – T c : “]”, corrections likely large for higher momenta Qualitatively, corrections to AdS/CFT result will drive double ratio to unity See also: 2012/08/23 Quark Matter 2012 36 WAH, M. Gyulassy, PLB666 (2008)
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