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pQCD vs. String Theory: LHC Heavy Flavors to Decide

pQCD vs. String Theory: LHC Heavy Flavors to Decide. William Horowitz Columbia University January 31, 2006. With many thanks to Simon Wicks, Azfar Adil, Kurt Hinterbichler, Alex Hamilton, and Miklos Gyulassy. RHIC: Heavy Confusion. What produces the nonphotonic electron suppression??.

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pQCD vs. String Theory: LHC Heavy Flavors to Decide

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  1. pQCD vs. String Theory:LHC Heavy Flavors to Decide William Horowitz Columbia University January 31, 2006 With many thanks to Simon Wicks, Azfar Adil, Kurt Hinterbichler, Alex Hamilton, and Miklos Gyulassy. Yale-Columbia Fest Spring ‘07

  2. RHIC: Heavy Confusion What produces the nonphotonic electron suppression?? In-medium fragmentation pQCD Rad + El Langevin w/ D ~ O(1) We must find observable differences! Yale-Columbia Fest Spring ‘07

  3. PHENIX: Light-Headed Stringy Conclusions? Did PHENIX prematurely announce heavy flavor suppression as evidence of perfect fluidity? Beyond assumptions inherent in QCD  SYM  IIB, WHEN can ST calculations be used, WHEN is ST Langevin applicable, and WHAT does ST give for D? Yale-Columbia Fest Spring ‘07

  4. Regimes of Applicability • String Regime • 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) • RHIC/LHC Regime • Mapping QCD Nc to SYM is easy, but coupling is hard aS runs whereas aSYM does not: aSYM is something of an unknown constant • Taking aSYM = aS = .3 gives l ~ 10 Taking aSYM ~ .05 => l ~ 1.8 (keep in mind for later) Yale-Columbia Fest Spring ‘07

  5. ST here Langevin Scheme • 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: Yale-Columbia Fest Spring ‘07

  6. Plugging in Numbers • Langevin pT reach: • gv(8 GeV e- from c) ~ 11 • D/(2pT) = 4/l1/2 from ST: • aSYM = aS = .3 => D/(2pT) ~ 1 • Oversuppresses RAA • aSYM ~ .05 required for D/(2pT) ~ 3 • Mass constraint, (for T = 350 MeV) • aSYM = .3 this gives ~ .6 GeV • aSYM = .05 this gives ~ .25 GeV • Both charm and bottom satisfy this condition • Not entirely unreasonable Yale-Columbia Fest Spring ‘07

  7. Mechanism Disambiguation: pQCD Rad+El and String Theory • Use large LHC pT reach and identification of c and b to distinguish • RAA ~ (1-e(pT))n(pT), pf = (1-e)pi • Asymptotic pQCD momentum loss: • String theory drag momentum loss: • Independent of pT and strongly dependent on m!! • T2 dependence makes for a very sensitive probe erad~a3 Log(pT/m2L)/pT eel~a2 Log((pT T)1/2/mg)/pT eST~ 1 - Exp(-m L), m = plT2/2m Yale-Columbia Fest Spring ‘07

  8. WHDG LHC Predictions • Results from the full calculation • Fluctuating number of gluons emitted, fluctuating path length Yale-Columbia Fest Spring ‘07

  9. Details of Qualitative ST Study • Allow local temperature variation as T(x,y) ~ rmed(x,y)1/3 • Nf = Nc = 3 • Stop energy loss at Tc ~ 160 MeV • Reasonable agreement with Moore and Teaney D/2pT = 3 results Yale-Columbia Fest Spring ‘07

  10. ST Results for the LHC • RAA’s strikingly more suppressed (due to T2 dependence) than for pQCD • Regardless of normalization, more sophisticated calculation maintains RAA decreasing with pT (as compared to strong increase for pQCD) Yale-Columbia Fest Spring ‘07

  11. Mechanism Disambiguation: pQCD Rad+El and AV • High-pT charm free from possible in-medium fragmentation effects • Distance traveled before fragmentation is boosted formation time (given by uncertainty principle) • For D meson, Dt ~ .1 fm • g ~ 21/2 p/m: g(50 GeV) ~ 40, g(100 GeV) ~ 80 • Clear signal: asymptotic pQCD Rad+El behavior modified by increased suppression at low momenta Yale-Columbia Fest Spring ‘07

  12. Examine the Ratio of c and b RAA • Large qualitative differences • STapprox indep of pT, and similar in magnitude for various t0 and aSYM • Dead cone effect creates growth in pT for pQCD • AV ratio will grow greaterthan1, peak at 50<pT<100, then drop down to 1 again Yale-Columbia Fest Spring ‘07

  13. Conclusions • Three very different theories claim to explain the surprisingly suppressed RHIC non-photonic electron RAA • None are particularly unreasonable • Year 1 of LHC will show qualitative differences between energy loss mechanisms: • dRAA(pT)/dpT > 0 => pQCD and/or AV; dRAA(pT)/dpT < 0 => ST • Ratio of charm to bottom RAA will be a discerning observable • PID and large pT reach allow easy disentanglement of the three effects • Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD; grows larger than 1 for pT > 50 GeV and approaches 1 from above in AV • Ratio of RAA’s benefits from cancellation of large systematic errors due to unknown p+p spectrum, binary scaling, etc. Yale-Columbia Fest Spring ‘07

  14. Backup: LHC Asymptopia Yale-Columbia Fest Spring ‘07

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