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Weak and Strong Coupling Heavy Quark Energy Loss

Weak and Strong Coupling Heavy Quark Energy Loss. W. A. Horowitz University of Cape Town March 18, 2015. R. Morad and WAH, JHEP 1411 (2014) 017 [1409.7545] WAH, arXiv:1501.04693. Motivation: Phenomenological QCD. What are the emergent, many body dynamics of non- Abelian plasma?.

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Weak and Strong Coupling Heavy Quark Energy Loss

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  1. Weak and Strong Coupling Heavy Quark Energy Loss W. A. Horowitz University of Cape Town March 18, 2015 R. Morad and WAH, JHEP 1411 (2014) 017 [1409.7545] WAH, arXiv:1501.04693 ECT*

  2. Motivation: Phenomenological QCD • What are the emergent, many body dynamics of non-Abelianplasma? Long Range Plan, 2008 ECT*

  3. Immodest Goal • Difficult even in E&M • In QCD… ? ? ? ? ? ECT*

  4. This is a Workshop, so… • Bold claim: strong-coupling describes physics at all experimentally relevant scales at RHIC/LHC • (pQCD rad + colldescribes tomo. probes) ECT*

  5. Seek Physics of QGP High-pT Light Hadrons/Jets EM Probes Low-pT particles Your least favorite measurement QGP Quarkonia Open Heavy Flavor Searching for this coherent, consistent picture that describes data ECT*

  6. Why Heavy Quarks? • Nontrivial to test P(DpT | pT, L, T, MQ, R) ALICE 0-20% D pQCD Rad Only fails as fcn of MQ Wicks, WAH, Djordjevic, Gyulassy, NPA784 (2007) ( ( LO AdS/CFT fails as fcn of T WAH, PhD Thesis, arXiv:1011.4316 ECT* WAH, PANIC11 (arXiv:1108.5876)

  7. Gross Oversimplificationof LO QGP Phenomenology • We don’t have a consistent theoretical picture that describes all observables. E.g.: pQCD AdS/CFT low-pT/ collective Rapid thermalization h/s Novel/better weak- coupling physics? Suppression v2 Light & heavy flavors RHIC & LHC high-pT/ energy loss Novel/better strong- coupling physics? ECT*

  8. Review of Weakly-Coupled Picture • Imagine weakly-coupled gas of quarks and gluons • Can trivially compute s, e, etc. • Systematic deviation from Lattice Wuppertal, JHEP 1208 (2012) 053 ECT*

  9. Nearly Inviscid Flow • t0 and h/s from hydro an order of magnitude smaller than pQCD estimate Schenke, Tribedy, Venugopalan, PRL 108:25231 (2012) ECT*

  10. High-pT Observables • Learn about E-loss mechanism • Most direct probe of DoF(scale) pQCD Picture ECT*

  11. pQCD Energy Loss • Use WHDG (nucl-th/0512076) as canonical example (see also Djordjevic & Heinz, 0802.1230) • Weakly-coupled plasma • Medium organizes into Debye-screened centers • T ~ 350 MeV, as = 0.3 (=> g ~ 2) • m ~ gT ~ 0.5 GeV • lmfp ~ 1/g2T ~ 1 fm • RAu ~ 6 fm • Collisional 2 => 2 Processes: HTL from Braaten and Thoma • dpT/dL ~ T2 log(pT/M) • Radiative 2 => 3 Processes: DGLV • LPM => dpT/dL ~ LT3 log(pT/M) • E-loss incorporated self-consistently, no tuning of weights • LO pQCDor FONLL production, KKP or FONLL FFs; reasonable geometry; no shadowing ECT*

  12. Current Lack of Precision • Extracting physics from E-loss requires controlled productionandfragmentation CMS, EurPhysJC72 (2012) WAH, arXiv:1501.04693 ECT*

  13. Nontrivial HF FFs • c,b => D, B; D, B => e- break down at low-pT PHENIX PRC84 (2011) 044905 ECT* WAH, arXiv:1501.04693

  14. Compare to RHIC & LHC • RHIC RAA: not unreasonable rmed • dNg/dy = 1400+200 • as = 0.3, fixed • 1400-375 PHENIX, PRC77 (2008) • For LHC predictions: change only rmed ∝dNch/dh ECT*

  15. pQCD E-loss Describes RHIC/LHC • Constrained by RHIC, LO pQCD predictions strikingly similar to LHC data LHC CMS h± 0-5% WHDG p0 LHC ALICE D WHDG D RHIC RHIC LHC CMS h± 40-50% WHDG p0 LHC CMS, Eur.Phys.J. C72 (2012) CMS, PRL109 (2012) ALICE, JHEP1209 (2012) 112 CMS, JHEP 1205 (2012) 063 PHENIX PRL105 (2010) ECT*

  16. Sins of Our Fathers • Advantages: • Correct quantum treatment of radiation • Disadvantages: • Multigluon emission • Eikonal, collinear approx AndriRasoanaivo Factor 2 uncertainty in medium param from eik, collapprox! ? WAH and B Cole, PRC81 (2010) 024909 ECT* JET, 1312.5003

  17. Hail Mary: Outlook • Is pQCD calculation self-consistent? • Compute NLO, running coupling corrections • What scale(s) do couplings run at? • pT, kT, T? • Derive short-distance corrections • Quantitative p+Asuppression pred. Isobel Kolbé Garry Kemp ECT*

  18. Gross Oversimplificationof LO QGP Phenomenology • We don’t have a consistent theoretical picture that describes all observables. E.g.: pQCD AdS/CFT low-pT/ collective Rapid thermalization h/s Novel/better weak- coupling physics? Suppression v2 Light & heavy flavors RHIC & LHC high-pT/ energy loss Novel/better strong- coupling physics? ECT*

  19. Reminder of AdS Successes I • Rapid thermalization • ttherm ~ 0.35 fm Chesler and Yaffe, PRL106 (2011) ECT*

  20. Reminder of AdS Successes II • Bulk Properties • Energy density, entropy, shear viscosity Luzum and Romatschke, PC78 (2008) Wuppertal, JHEP 1208 (2012) 053 ECT*

  21. High-pT Observables • Learn about E-loss mechanism • Most direct probe of DoF(scale) AdS/CFT Picture ECT*

  22. Why AdS at High-pT? • Perturbatively, 3 couplings for rad E-loss • Not known at which scale(s) couplings run • TQGP ~ LQCD => g(2pT) ~ 2 • Always “small” scale in problem • Perhaps low-Q2 plasma physics dominates over high-Q2 in E-loss physics? • Factorization not proven in AA • Work here assumes all couplings strong • Cf, e.g., Casalderrey-Solana et al. [JHEP 1410 (2014) 19], Iancu et al. [1410.6448] for alternative hybrid models ECT*

  23. LO AdS for Heavy High-pT • Assume all couplings large dpT/dt = - mpT m = pl1/2T2/2Mq Herzog et al., JHEP 0607 (2006) Gubser, PRD74 (2006) J Friess, et al., PRD75 (2007) • Similar to Bethe-Heitler • dpT/dt ~ -(T3/Mq2) pT • Very different from usual pQCD and LPM • dpT/dt ~ -LT3 log(pT/Mq) ECT*

  24. Failure of LO AdS for Heavy High-pT • Constrained by RHIC, oversuppresses LHC RHIC LHC ALICE 0-20% D ( ( ( ( ] ( WAH, PANIC11 (arXiv:1108.5876) ALICE, JHEP 1209 (2012) WAH, PhD Thesis, arXiv:1011.4316 ECT*

  25. Light Flavor String Setup • Use MathematicaNDSolve • Difficult to solve EOM from NG action for full string • Use Polyakov action, worldsheet metric to facilitate numerics • Need to nontrivially invert t(t, s), x(t, s) to find relevant E, p, etc. as fcns of t or x Chesler, Jensen, Karch, Yaffe, PRD79 (2009) 125015 ECT*

  26. Improved AdS Jet Prescription? • All approximations to a full Tmn calc. • Original jet defined by spatial proximity • New suggestion: separation by E scale Jet Medium Jet 500 MeV Medium R Morad and WAH, JHEP 11 (2014) 017 Chesler et al., PRD79 (2009) 0.3/pT ECT*

  27. AdS: No-nucleus Suppression • Original proposed IC => anomalous vacuum suppression! • Suggests oversuppression artifact of string IC VacuumRpp << 1!! R Morad and WAH, JHEP 11 (2014) 017 ECT*

  28. Renormalized Result • Can we capture diff. btwn. naïve AdSpp & AA? • Define renormalized RAdS = “RAA / Rpp”; cf CMS • Use reasonable l = 12 <=> as = 0.3: no fitting • Similar results for renorm. via DErenorm = DEAA - DEpp Very first, fully strongly coupled jet RAA calculation R Morad and WAH, JHEP 11 (2014) 017 ECT*

  29. Limits on Heavy Flavor AdS Setup x5 “z” • For LO AdS: • Space-like quark endpoint • gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(lT2) • Mom. Loss Fluctuations • gcrit = Mq2/(4T2) • Speed limit from fluct parametrically larger, but numerically smaller D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane ECT*

  30. HQ pT Limits RHIC LHC gcrit = Mc2 / 4 T02 ~ 3 – 4 GeV/c ALICE 0-20% D gcrit = Mc2 / 4 T02 ~ 3 – 4 GeV/c ( ( ( ( ] ( WAH, PANIC11 (arXiv:1108.5876) ALICE, JHEP 1209 (2012) WAH, PhD Thesis, arXiv:1011.4316 ECT*

  31. Including Fluctuations in AdS HF • Obeys Einstein’s relations only at v = 0 • Multiplicative Langevin problem! • Results depend on time within timestep kicks are evaluated • Ito, Stratonovich, Hänggi-Klimontovich • Non-Markovian: • Colored (not white) noise • Momentum kicks have a memory Gubser, NPB790 (2008) Teaney and Casalderrey-Solana, JHEP 0912 (2009) 066 ECT*

  32. Discretizing Langevin • Discretizing Riemann Calculus trivial • Sum converges regardless of bin widths and x* in bin as n increases • Ambiguity in Ito Calculus • Results depend on discretization procedure See, e.g., He et al., PRE 88, 032138 (2013) ECT*

  33. Discretization Ambiguity and Einstein • Ex: momentum space distribution of charm • AdS fluctuations very diff from fluc-diss, which lead to relativistic thermal (Jüttner) distribution • Huge diff btwn pre-point and mid-point v = 0.9c in z-direction WAH, 1501.04693 ECT*

  34. Resolving the Ambiguity • Saved by colored noise: • Wong-Zakai Theorem: • As autocorrelation => 0, Langevin => Stratonovich Gubser, NPB790 (2008) ECT*

  35. Model Calculations • Input FONLL c, b production spectra • Discretized Langevin through VISHNU • 2+1D viscous hydro (Shen et al., 1409.8164) • FONLL FFs to B, D, e • Uncertainty in map from QCD to N = 4 SYM • Explore systematics with two reasonable assumptions • as = 0.3 (l = 12), TSYM = TQCD • l = 5.5, TSYM = TQCD/31/4 • NB: no hadronicrescattering, shadowing ECT*

  36. Details of Numerics • Langevin written in C++ • Two speed advantages: • Fast RNG generation • Fast access to hydro background (tables in HDF5) • Power law production spectrum => many runs • One may translate between equivalent Ito, Stratanovich, etc. pictures • Actual evaluation in Ito equivalent to Stratanovich • RNG via Numerical Recipes • NB: write own RNG, seeding function • Fragmentation performed in Mathematica • See arXiv:1501.04693 for details ECT*

  37. Compare to RHIC HF Electrons • Agreement in sweet spot pT ~ 3 – 4 GeV/c • Below 3 GeV production unreliable • Above 4 GeV theory corrections necessary (col. noise,non-const p) • NB: VISHNU medium hotter than from previous calc => larger LO supp. WAH, 1501.04693 ECT*

  38. Compare to LHC ECT* WAH, arXiv:1501.04693

  39. Conclusions and Discussion • LO pQCD E-Loss qualitatively describes multiple observables • Future work: • check self-consistency (coupling) • reduce approximations • compare to additional tomographic observables • Soft physics? • AdS/CFT E-loss also qualitatively describes multiple observables • Future work: • Improve fluc + high-E in HQ, connection to light flavor • Distinguishing Measurements: • Fluctuations destroy double ratio • High-pT B RAA; correlations? Nicole Moodley Robert Moerman ECT*

  40. ECT*

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