1. 11/15/06 William Horowitz 1 LHC Predictions 1 from an extended theory 2 with Elastic, Inelastic, and Path Length Fluctuating Jet Energy Loss William Horowitz Department of Physics, Columbia University 538 W 120 th St., New York, NY 10027, USA Frankfurt Institute for Advanced Studies (FIAS) 60438 Frankfurt am Main, Germany November 15, 2006 With thanks to Azfar Adil and Carsten Greiner 1. W.Horowitz et al to be published 2. S.Wicks, W.Horowitz, M.Djordjevic and M.Gyulassy, nucl-th/0512076 v3, NPA in press

2. 11/15/06 William Horowitz 2 Outline Energy dependence of jet quenching at the LHC as a test of loss mechanisms –Highly distinct LHC R AA (p T ) predictions –Naturalness of the difference Intro to Physics of Nothing –P 0 = Exp(-N c ), the probability of no jet interactions. N c ~  el  L is the average number of elastic collisions

3. 11/15/06 William Horowitz 3 Modeling Energy Loss –Different models include some effects while neglecting others Radiative only loss: (AWS, Majumder, Vitev) Convolved radiative and elastic loss (WHDG) Inclusion of probability of nothing (separate from probability of emitting no radiation, P g 0 !) – N c is the number of elastic collisions suffered while propagating out

4. 11/15/06 William Horowitz 4 Probability of Overquench:  E > E –For highly suppressed jets, P(  > 1) has a large support for overabsorption. One of two choices is generally made: Renormalize (reweight) uniformly Include an explicit  ) term –We always use the latter

5. 11/15/06 William Horowitz 5 Our Extended Theory Convolve Elastic with Inelastic energy loss fluctuations ( ) Include path length fluctuations in diffuse nuclear geometry with 1+1D Bjorken expansion

6. 11/15/06 William Horowitz 6 Simplified Treatment Uses Fixed L –Estimates of a fixed, single, representative length: where and the fitted L is found by varying it until it best reproduces the true geometric average. There is no a priori method to determine how much the first two deviate from the actual answer

7. 11/15/06 William Horowitz 7 Path Length Fluctuations Can Not be Neglected P(L) is a wide distribution –Flavor independent Flavor dependent best fixed length approximation L Q ’s not a priori obvious S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

8. 11/15/06 William Horowitz 8 RHIC  Results Inclusion of both fluctuating elastic loss and paths is essential to reproduce data –Fully perturbative –dN g /dy = 1000 consistent with entropy data for conservative  s =.3 Results are sensitive to changes in dN g /dy and  s –Model is not “fragile” –Running of  s will be an important effect WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

9. 11/15/06 William Horowitz 9 Suppression of AWS AWS pQCD-based controlling parameter must be nonperturbatively large to fit RHIC data -pQCD gives = c  3/4, where c ~ 2; c ~ 8-20 required for RHIC data -Needed because radiative only energy loss (and > 1? R = (1/2) L 3 ) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005)

10. 11/15/06 William Horowitz 10 LHC  Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Our predictions show a significant increase in R AA as a function of p T This rise is robust over the range of predicted dN g /dy for the LHC that we used This should be compared to the flat in p T curves of AWS- based energy loss (next slide) We wish to understand the origin of this difference

11. 11/15/06 William Horowitz 11 Curves of AWS-based energy loss are flat in p T 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) (a)(b) Comparison of LHC  Predictions

12. 11/15/06 William Horowitz 12 Why AWS is Flat Flat in p T curves result from extreme suppression at the LHC –When probability leakage P(  > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss Enormous suppression due to: –Already (nonperturbatively) large suppression at RHIC for AWS –Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT) »Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-45 As seen on the previous slide, Vitev predicted a similar rise in R AA (p T ) as we do –Vitev used only radiative loss, P rad (  ), but assumed fixed path –WHDG similar because elastic and path fluctuations compensate

13. 11/15/06 William Horowitz 13 The Rise of GLV Rad+El+Geom Use of both P rad AND P el implies neither has much weight for  E > E at RHIC For the dN g /dy values used, high-p T jets at the LHC have asymptotic energy loss: LHC R AA (p T ) dependence caused by deceasing energy loss not altered by the flat production spectra  E rad /E   3 Log(E/  2 L)/E  E el /E   2 Log((E T) 1/2 /m g )/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

14. 11/15/06 William Horowitz 14 Probability of No Energy Loss Induced radiative energy loss requires at least one jet interaction in medium with probability After at least one elastic collision, the total energy loss is a convolution of the momentum lost to the radiated glue as well as to the scattering centers –P rad (  ) also contains a P(N g = 0)  (  ) due to the probability of no glue emission –For fixed  s =.3, including P 0 physics accounts for 50% of R AA –Allowing  s (T) to run as  s (q 2 =2  T(z)) reduces P 0 by a factor of 2 –Integration over momentum transfers with  s (q 2 ) given by vacuum running formally gives P 0 =0

15. 11/15/06 William Horowitz 15 Conclusions LHC R AA (p T ) data will distinguish between energy loss models –GLV Rad+El+Geom predicts significant rise in p T –AWS type models predict flat p T dependence Moderate opacity (GLV, WW) R AA predictions sensitive to noninteracting free jets R AA ~ P 0 + (1-P 0 ) R AA (N c >0), P 0 = exp(-  el  L)