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Testing String Theory with Jets

Testing String Theory with Jets. William Horowitz The Ohio State University Columbia University Frankfurt Institute for Advanced Studies (FIAS) November 13, 2008. LHC Predictions: Phys. Lett. B666:320, 2008  (arXiv:0706.2336) RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703).

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Testing String Theory with Jets

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  1. Testing String Theory with Jets William Horowitz The Ohio State University Columbia University Frankfurt Institute for Advanced Studies (FIAS) November 13, 2008 LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703) With many thanks to Miklos Gyulassy Nuclear Seminar, The Ohio State University

  2. A Little History: QCD as Theory of Strong Force p m C. M. G. Lattes, H. Muirhead, G. P. S. Occhialini, and C. F. Powell, PROCESSES INVOLVING CHARGED MESONS, Nature 159, 694 (1947). Two and three jet events: R. Brandelik et al. (TASSO), Phys. Lett. B86, 243 (1979) V. E. Barnes et al., OBSERVATION OF A HYPERON WITH STRANGENESS -3, Phys. Rev. Lett. 12, 204 (1964) mW- = 1686 +/- 12 MeV/c2 D. Decamp et al. (ALEPH), Phys. Lett. B284, 151 (1992) • 1935: Yukawa proposes pion as nuclear mediator • 1947: Powell, et al., definitively distinguishes p from m • 1947-: Particle zoo => 1962: Gell-Mann’s Eightfold Way => 1964: W- found at BNL • 1965: Nambu and Hahn propose color to solve Pauli problem • 1969-73: Feynman’s partons—weakly-coupled point-like subnuclear particles • 1973: Coleman and Gross—Asymptotic freedom unique to nonabelian QFTs • 1975: Jets—quarks (’75) and gluons (’79) • 1992: SU(Nc = 3) Nuclear Seminar, The Ohio State University

  3. Lattice QCD pQCD Traditional Toolbox for QCD Previously only two methods: Diagrams! Two 10 Tflops QCDOC Computers: RBRC and DOE Nuclear Seminar, The Ohio State University

  4. Traditional Tools (cont’d) Lattice QCD pQCD • Successful • But limited Davies et al. (HPQCD), PRL 92, 022001 (2004) de Florian, Sassot, Stratmann, Phys.Rev.D75:114010,2007 • Any quantity • Small coupling (large momenta) • All momenta • Euclidean correlators Nuclear Seminar, The Ohio State University

  5. Maldacena Conjecture Bosonic part of IIB low energy effective action TPlasma = THawking Geometry of bosonic part of 10D supergravity, near horizon limit Large Nc limit of d-dimensional conformal field theory dual to string theory on the product of d+1-dimensional Anti-de Sitter space with a compact manifold J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998 Nuclear Seminar, The Ohio State University

  6. Regime of Applicability Q.M. SSYM => C.M. SNG • Large Nc, constant ‘t Hooft coupling ( ) Small quantum corrections • Large ‘t Hooft coupling Small string vibration corrections • Only tractable case is both limits at once Classical supergravity (SUGRA) J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 Nuclear Seminar, The Ohio State University

  7. Strong Coupling Calculation • The supergravity double conjecture: QCD  SYM  IIB • IF super Yang-Mills (SYM) is not too different from QCD, & • IF Maldacena conjecture is true • Then a tool exists to calculate strongly-coupled QCD in SUGRA Nuclear Seminar, The Ohio State University

  8. Testing String Theory Adapted from P Sorensen, WWND ‘08, arXiv:0808.0503 => 1/4p? Kallosh and Linde, JCAP 0704:017,2007: Too small to be detected Huovinen et al., Phys. Lett. B503 (2001) 58 Nuclear Seminar, The Ohio State University

  9. What’s All the Fuss About? …data [from RHIC] appear to be more accurately described using string theory methods than with more traditional approaches. Will Horowitz (OSU) Hold yer horses! Let’s look at the details Brian Greene (TV) Nuclear Seminar, The Ohio State University

  10. QGP Creation • Robust prediction of QCD phase transition Walecka: Hagedorn: S. C. Frautschi, Phys. Rev. D3, 2821 (1971) J. D. Walecka, Theoretical Nuclear and Subnuclear Physics, 2nd ed. Lattice: Karsh et al., Phys. Rev. D62, 034021 (2000), Nucl. Phys. A698, 199 (2002), PoS LAT2005, 193 (2006) M. Cheng et al., Phys. Rev. D77, 014511 (2008) Nuclear Seminar, The Ohio State University

  11. Probing the QGP • Low momentum (low-pT) particles • Collective dynamics of the bulk • Statistical Models: temperature • Hydrodynamics: spectra, elliptic flow • HBT (Hanbury-Brown Twiss): freeze-out surface • High momentum (high-pT) particles • Parton jets, vacuum fragmentation • Learn about medium (jet tomography) • Learn about energy loss mechanism (pQCD, ST) Nuclear Seminar, The Ohio State University

  12. Geometry of a HI Collision M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II) • Hydro propagates IC • Results depend strongly on initial conditions • Viscosity reduces eventual momentum anisotropy T Ludlum and L McLerran, Phys. Today 56N10:48 (2003) Nuclear Seminar, The Ohio State University

  13. Perfect Fluidity:AdS + Hydro’s Most Famous Success D. Teaney, Phys. Rev. C68, 034913 (2003) • Hydro h/s small ~ .1 • QGP fluid near-perfect liquid • Naïve pQCD => h/s ~ 1 • New estimates ~ .1 Z Xu, C Greiner, and H Stoecker, PRL101:082302 (2008) • Lowest order AdS result: h/s = 1/4p • Universality? P Kovtun, D Son, and A Starinets, Phys.Rev.Lett.94:111601 (2005) P Kats and P Petrov, arXiv:0712.0743 M Brigante et al., Phys. Rev. D77:126006 (2008) Nuclear Seminar, The Ohio State University

  14. IC, Viscosity, and Hydro • Sharper IC (CGC) => viscosity • Softer IC (Glauber) => “perfect” • Test IC with fluctuations? • Control over hadronization? T Hirano, et al., Phys. Lett. B636:299-304, 2006 P Sorensen, WWND ‘08, arXiv:0808.0503 Nuclear Seminar, The Ohio State University

  15. Why High-pT Jets? 2D Transverse directions Longitudinal (beam pipe) direction pT pT Figures from http://www.star.bnl.gov/central/focus/highPt/ • IC smaller effect • Vacuum fragmentation well controlled • Compare unmodified p+p collisions to A+A: Nuclear Seminar, The Ohio State University

  16. Jet Physics Terminology pT f Naïvely: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f Convenient to Fourier expand RAA: Nuclear Seminar, The Ohio State University

  17. pQCD Success at RHIC: Y. Akiba for 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 Nuclear Seminar, The Ohio State University

  18. Trouble for wQGP Picture • e- RAA too small • Hydro h/s too small • v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) • wQGP not ruled out, but what if we try strong coupling? Nuclear Seminar, The Ohio State University

  19. Qualitative AdS/CFT Successes: Naïve AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 PHENIX, Phys.Rev.Lett.101:082301,2008 J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • Mach wave-like structures • sstrong=(3/4) sweak, similar to Lattice • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Nuclear Seminar, The Ohio State University

  20. AdS/CFT Energy Loss Models • Langevin model • Collisional energy loss for heavy quarks • Restricted to low pT • pQCD vs. AdS/CFT computation of D, the diffusion coefficient • ASW model • Radiative energy loss model for all parton species • pQCD vs. AdS/CFT computation of • Debate over its predicted magnitude • ST drag calculation • Drag coefficient for a massive quark moving through a strongly coupled SYM plasma at uniform T • not yet used to calculate observables: let’s do it! Moore and Teaney, Phys.Rev.C71:064904,2005 Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007 BDMPS, Nucl.Phys.B484:265-282,1997 Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003 Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007 Gubser, Phys.Rev.D74:126005,2006 Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013,2006 Nuclear Seminar, The Ohio State University

  21. AdS/CFT Drag • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2T2/2Mq J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 Nuclear Seminar, The Ohio State University

  22. Energy Loss Comparison D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 D3 Black Brane (horizon) zh = pT Black Hole z = 0 • AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT • Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) Nuclear Seminar, The Ohio State University

  23. RAA Approximation y=0 RHIC LHC • Above a few GeV, quark production spectrum is approximately power law: • dN/dpT ~ 1/pT(n+1), where n(pT) has some momentum dependence • We can approximate RAA(pT): • RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) Nuclear Seminar, The Ohio State University

  24. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT • Asymptotic pQCD momentum loss: • String theory drag momentum loss: • Independent of pT and strongly dependent on Mq! • T2 dependence in exponent makes for a very sensitive probe • Expect: epQCD 0 vs. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST eST~ 1 - Exp(-m L), m = pl1/2T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 Nuclear Seminar, The Ohio State University

  25. Model Inputs • AdS/CFT Drag: nontrivial mapping of QCD to SYM • “Obvious”: as = aSYM = const., TSYM = TQCD • D 2pT = 3 inspired: as = .05 • pQCD/Hydro inspired: as = .3 (D 2pT ~ 1) • “Alternative”: l = 5.5, TSYM = TQCD/31/4 • Start loss at thermalization time t0; end loss at Tc • WHDG convolved radiative and elastic energy loss • as = .3 • WHDG radiative energy loss (similar to ASW) • = 40, 100 • Use realistic, diffuse medium with Bjorken expansion • PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900) Nuclear Seminar, The Ohio State University

  26. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 • LHC Prediction Zoo: What a Mess! • Let’s go through step by step • Unfortunately, large suppression pQCD similar to AdS/CFT • Large suppression leads to flattening • Use of realistic geometry and Bjorken expansion allows saturation below .2 • Significant rise in RAA(pT) for pQCD Rad+El • Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Nuclear Seminar, The Ohio State University

  27. An Enhanced Signal • 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. of uniform medium gives RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27 • Ratio starts below 1; independent of pT RcbpQCD(pT) ~ 1 - asn(pT) L2 log(Mb/Mc) ( /pT) Nuclear Seminar, The Ohio State University

  28. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • Taking the ratio cancels most normalization differences seen previously • 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 WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] Nuclear Seminar, The Ohio State University

  29. 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 Nuclear Seminar, The Ohio State University

  30. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • T(t0): (, corrections unlikely for smaller momenta • Tc: ], corrections likely for higher momenta Nuclear Seminar, The Ohio State University

  31. Measurement at RHIC y=0 RHIC LHC • Future detector upgrades will allow for identified c and b quark measurements • RHIC production spectrum significantly harder than LHC • NOT slowly varying • No longer expect pQCD dRAA/dpT > 0 • Large n requires corrections to naïve Rcb ~ Mc/Mb Nuclear Seminar, The Ohio State University

  32. RHIC c, b RAA pT Dependence • Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Nuclear Seminar, The Ohio State University

  33. 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 WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Nuclear Seminar, The Ohio State University

  34. Conclusions • Previous AdS qualitative successes inconclusive • AdS/CFT Drag observables calculated • Generic differences (pQCD vs. AdS/CFT Drag) seen in RAA • Masked by extreme pQCD • Enhancement from ratio of c to b RAA • Discovery potential in Year 1 LHC Run • Understanding regions of self-consistency crucial • RHIC measurement possible Nuclear Seminar, The Ohio State University

  35. Backup Slides Nuclear Seminar, The Ohio State University

  36. Another AdS Test: Correlations B Betz, M Gyulassy, J Noronha, and G Torrieri, arXiv:0807.4526 Nuclear Seminar, The Ohio State University

  37. Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007 1D Hubble flow => r(t) ~ 1/t => T(t) ~ 1/t1/3 M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 Nuclear Seminar, The Ohio State University

  38. Langevin Model AdS/CFT here • Langevin equations (assumes gv ~ 1 to neglect radiative effects): • Relate drag coef. to diffusion coef.: • IIB Calculation: • Use of Langevin requires relaxation time be large compared to the inverse temperature: Nuclear Seminar, The Ohio State University

  39. But There’s a Catch (II) • Limited experimental pT reach? • ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II Nuclear Seminar, The Ohio State University

  40. LHC p Predictions • Our predictions show a significant increase in RAA as a function of pT • This rise is robust over the range of predicted dNg/dy for the LHC that we used • This should be compared to the flat in pT curves of AWS-based energy loss (next slide) • We wish to understand the origin of this difference WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, The Ohio State University

  41. Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~a3 Log(E/m2L)/E DEel/E ~a2 Log((E T)1/2/mg)/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, The Ohio State University

  42. K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) Nuclear Seminar, The Ohio State University

  43. Pion RAA • Is it a good measurement for tomography? • Yes: small experimental error • Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool • Maybe not: some models appear “fragile” Nuclear Seminar, The Ohio State University

  44. Fragility: A Poor Descriptor • All energy loss models with a formation time saturate at some RminAA > 0 • The questions asked should be quantitative : • Where is RdataAA compared to RminAA? • How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? • Define sensitivity, s = min. param/max. param that is consistent with data within error Nuclear Seminar, The Ohio State University

  45. Different Models have Different Sensitivities to the Pion RAA • GLV: s < 2 • Higher Twist: s < 2 • DGLV+El+Geom: s < 2 • AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, The Ohio State University

  46. T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, The Ohio State University

  47. A Closer Look at ASW The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a) (b) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) Nuclear Seminar, The Ohio State University

  48. Surface Bias vs. Surface Emission • Surface Emission: one phrase explanation of fragility • All models become surface emitting with infinite E loss • Surface Bias occurs in all energy loss models • Expansion + Realistic geometry => model probes a large portion of medium A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Nuclear Seminar, The Ohio State University

  49. A Closer Look at ASW • Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: • No Bjorken expansion • Glue and light quark contributions not disentangled • Plotted against Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) Nuclear Seminar, The Ohio State University

  50. Additional Discerning Power • Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1 • Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity Nuclear Seminar, The Ohio State University

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