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Successes, Failures, and Uncertainties in Jet Physics in Heavy Ion Collisions

This seminar discusses the successes, failures, and uncertainties in jet physics in heavy ion collisions. It covers topics such as QCD theory, methods of QCD calculations, tomography in QGP, high-pT observables, pQCD radiation picture, AdS/CFT picture, strongly coupled qualitative successes, and comparisons to data.

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Successes, Failures, and Uncertainties in Jet Physics in Heavy Ion Collisions

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  1. Successes, Failures, and Uncertainties in Jet Physics in Heavy Ion Collisions W. A. Horowitz The Ohio State University March 12, 2010 With many thanks to Brian Cole, MiklosGyulassy, Ulrich Heinz, and Yuri Kovchegov Wayne State University Seminar

  2. QCD: Theory of the Strong Force • Running as • -b-fcn • SU(Nc = 3) • Nf(E) • Nf(RHIC) ≈ 2.5 PDG ALEPH, PLB284, (1992) Griffiths Particle Physics Wayne State University Seminar

  3. Bulk QCD and Phase Diagram Long Range Plan, 2008 Wayne State University Seminar

  4. Methods of QCD Calculation I: Lattice • All momenta • Euclidean correlators Long Range Plan, 2008 Kaczmarek and Zantow, PRD71 (2005) Davies et al. (HPQCD), PRL92 (2004) Wayne State University Seminar

  5. Methods of QCD Calculation II: pQCD • Any quantity • Small coupling (large momenta only) d’Enterria, 0902.2011 Jäger et al., PRD67 (2003) Wayne State University Seminar

  6. Methods of QCD Calculation III: AdS(?) Maldacena conjecture: SYM in d IIB in d+1 Gubser, QM09 • All quantities • Nc → ∞ • SYM, not QCD: b = 0 • Probably not good approx. for p+p; maybe A+A? Wayne State University Seminar

  7. Why High-pT Jets? and even more with multiple probes SPECT-CT Scan uses internal g photons and external X-rays • Tomography in medicine One can learn a lot from a single probe… PET Scan http://www.fas.org/irp/imint/docs/rst/Intro/Part2_26d.html Wayne State University Seminar

  8. Tomography in QGP pT f • Requires well-controlled theory of: • production of rare, high-pT probes • g, u, d, s, c, b • in-medium E-loss • hadronization • Requires precision measurements of decay fragments , g, e- Invert attenuation pattern => measure medium properties Wayne State University Seminar

  9. QGP Energy Loss • Learn about E-loss mechanism • Most direct probe of DOF pQCD Picture AdS/CFT Picture Wayne State University Seminar

  10. High-pT Observables pT f Naively: if medium has no effect, then RAA = 1 • Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f , g, e- • Fourier expand RAA: Wayne State University Seminar

  11. pQCDRad Picture • Bremsstrahlung Radiation • Weakly-coupled plasma • Medium organizes into Debye-screened centers • T ~ 250 MeV, g ~ 2 • m ~ gT ~ 0.5 GeV • lmfp ~ 1/g2T ~ 1 fm • RAu ~ 6 fm • 1/m << lmfp << L • mult. coh. em. • LPM • dpT/dt ~ -LT3 log(pT/Mq) • Bethe-Heitler • dpT/dt ~ -(T3/Mq2) pT Wayne State University Seminar

  12. pQCD Success at RHIC: Y. Akibafor the PHENIX collaboration, hep-ex/0510008 (circa 2005) • Consistency: RAA(h)~RAA(p) • Null Control: RAA(g)~1 • GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy Wayne State University Seminar

  13. Trouble for Rad E-Loss Picture • v2 • e- e- WAH, Acta Phys.Hung.A27 (2006) Djordjevic, Gyulassy, Vogt, and Wicks, PLB632 (2006) Wayne State University Seminar

  14. What About Elastic Loss? • Appreciable! • Finite time effects small Adil, Gyulassy, WAH, Wicks, PRC75 (2007) Mustafa, PRC72 (2005) Wayne State University Seminar

  15. Quantitative Disagreement Remains v2 too small NPE supp. too large p0 v2 WHDG C. Vale, QM09 Plenary (analysis by R. Wei) NPE v2 Wicks, WAH, Gyulassy, Djordjevic, NPA784 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) Wayne State University Seminar

  16. Strongly Coupled Qualitative Successes AdS/CFT T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Blaizot et al., JHEP0706 PHENIX, PRL98, 172301 (2007) Wayne State University Seminar Betz, Gyulassy, Noronha, Torrieri, PLB675 (2009)

  17. Jets in AdS/CFT • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - mpT m = pl1/2T2/2Mq • Similar to Bethe-Heitler • dpT/dt ~ -(T3/Mq2) pT • Very different from LPM • dpT/dt ~ -LT3 log(pT/Mq) J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007) Wayne State University Seminar

  18. Compared to Data • String drag: qualitative agreement WAH, PhD Thesis Wayne State University Seminar

  19. pQCD vs. AdS/CFT at LHC • Plethora of Predictions: WAH, M. Gyulassy, PLB666 (2008) • Taking the ratio cancels most normalization differences • pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) • AdS/CFT ratio is flat and many times smaller than pQCD at only moderate pT WAH, M. Gyulassy, PLB666 (2008) Wayne State University Seminar

  20. Not So Fast! x5 “z” • Speed limit estimate for applicability of AdS drag • g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) • Limited by Mcharm ~ 1.2 GeV • Similar to BH LPM • gcrit ~ Mq/(lT) • No Single T for QGP • smallest gcrit for largest T T = T(t0, x=y=0): “(” • largest gcrit for smallest T T = Tc: “]” D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane Wayne State University Seminar

  21. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WAH, M. Gyulassy, PLB666 (2008) • T(t0): “(”, corrections likely small for smaller momenta • Tc: “]”, corrections likely large for higher momenta Wayne State University Seminar

  22. 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 pQCD pQCD AdS/CFT AdS/CFT WAH, M. Gyulassy, JPhysG35 (2008) Wayne State University Seminar

  23. Universality and Applicability • How universal are th. HQ drag results? • Examine different theories • Investigate alternate geometries • Other AdS geometries • Bjorken expanding hydro • Shock metric • Warm-up to Bj. hydro • Can represent both hot and cold nuclear matter Wayne State University Seminar

  24. New Geometries vshock Q vshock z Q z x x 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 WAH and Kovchegov, PLB680 (2009) Wayne State University Seminar

  25. Asymptotic Shock Results Q z = 0 vshock x0+ m ½z3/3 x0- m ½z3/3 x0 x z = ¥ • Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) • x(z) = x0, x0 ± m½ z3/3 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z3/3, z << 1, for const. T BH geom. Wayne State University Seminar

  26. Putting It All Together • For L typical momentum scale of the medium • We’ve generalized the BH solution to both cold and hot nuclear matter E-loss • Recall for BH: • Shock gives exactly the same drag as BH for L = p T Wayne State University Seminar

  27. 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 = zM = l½/2pMq • Same speed limit as for BH metric when L = pT Wayne State University Seminar

  28. Back to pQCD: Quant. and Falsifiable • Requires rigorous pQCD estimates, limits: • Different pQCD formalisms, different results Bass et al., Phys.Rev.C79: 024901,2009 Wayne State University Seminar

  29. 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 Wayne State University Seminar

  30. Mechanics of Energy Loss • RAA ~ ∫(1-ϵ)n P(ϵ) dϵ • pf = (1-ϵ)pi • Opacity expansions finds single inclusive gluon emission spectrum • dNg/dxdkTdqT Wayne State University Seminar

  31. Poisson Convolution • Find P(ϵ) by convolving dNg/dx • Approximates probabilistic multiple gluon emission, Sudakov • assume independent emissions • NB: ϵ is a momentum fraction Gyulassy, Levai, and Vitev NPB594 (2001) Wayne State University Seminar

  32. Opacity Expansion Calculation • Want to find dNg/dx • Make approximations to simplify derivation • Small angle emission: kT << xE • Note: ALL current formalisms use collinear approximation • Derived dNg/dxdkT violates collinear approx • Both IR and UV safe • Enforce small angle emission through UV cutoff in kT Wayne State University Seminar

  33. Uncertainty from Collinear Approx • Derived dNg/dxdkT maximally violates collinear approximation • dNg/dx depends sensitively on kT cutoff • Despite UV safety • For effect on extracted prop., must understand x • Discovered through TECHQM Brick Problem WAH and B Cole, arXiv:0910.1823 Wayne State University Seminar

  34. Two Standard x Definitions • ASW-SH: xE • Energy fraction • GLV: x+ • Plus momentum fraction P • NB: gluon always on-shell Wayne State University Seminar

  35. Coordinate Transformations • Same in the limit kT/xE → 0! • UV cutoff given by restricting maximum angle of emission • Previous comparisons with data took qmax=p/2 • Vary qmax to estimate systematic theoretical uncertainty P q Wayne State University Seminar

  36. Jacobians • ϵ is fraction of longitudinal momentum • Need dNg/dxE to find P(ϵ) • A Jacobian is required for x = x+ interpretation Wayne State University Seminar

  37. Rad. Gluon Kin. Sensitivities • UV • What about IR? WAH and B Cole, arXiv:0910.1823 Wayne State University Seminar

  38. Collinearity and Gluon Mass • Massless gluons: • Large IR cutoff sensitivity • Gluons with thermal mass BDMS, JHEP 0109 (2001) ~ Larger x better respects kT << xE Wayne State University Seminar WAH and B Cole, arXiv:0910.1823

  39. Results • Quantitatively compare to PHENIX data • Assumed infinite Elastic precision WAH and B Cole, arXiv:0910.1823 Wayne State University Seminar

  40. Parton Energy Dependence • Dependence on parton energy • Uncertainty on qhat • Assume all formalisms equally affected WAH and B Cole, arXiv:0910.1823 Wayne State University Seminar

  41. Conclusions • pQCD and AdS/CFT enjoy qualitative successes, concerns in high-pT 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 pQCD and AdS • In AdS, control of jet IC, large pT required • In pQCD, wide angle radiation very important, not under theoretical control Wayne State University Seminar

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