William Horowitz Department of Physics, Columbia University

1. LHC Predictions1 from an extended theory2 with Elastic, Inelastic, and Path Length Fluctuating Jet Energy Loss William Horowitz Department of Physics, Columbia University 538 W 120th St., New York, NY 10027, USA Frankfurt Institute for Advanced Studies (FIAS) 60438 Frankfurt am Main, Germany November 15, 2006 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 With thanks to Azfar Adil and Carsten Greiner

2. Outline • Energy dependence of jet quenching at the LHC as a test of loss mechanisms • Highly distinct LHC RAA(pT) predictions • Naturalness of the difference • Intro to Physics of Nothing • P0 = Exp(-Nc), the probability of no jet interactions. Nc ~ selrL is the average number of elastic collisions

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, Pg0!) • Nc is the number of elastic collisions suffered while propagating out

4. Probability of Overquench: DE > E • For highly suppressed jets, P(e > 1) has a large support for overabsorption. One of two choices is generally made: • Renormalize (reweight) uniformly • Include an explicit d(1-e) term • We always use the latter

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. 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. Path Length FluctuationsCan Not be Neglected • P(L) is a wide distribution • Flavor independent • Flavor dependent best fixed length approximation LQ’s not a priori obvious S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

8. RHIC p Results • Inclusion of both fluctuating elastic loss and paths is essential to reproduce data • Fully perturbative • dNg/dy = 1000 consistent with entropy data for conservative as = .3 • Results are sensitive to changes in dNg/dy and as • Model is not “fragile” • Running of as will be an important effect WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

9. Suppression of AWS • AWS pQCD-based controlling parameter must be nonperturbatively large to fit RHIC data -pQCD gives = c e3/4, where c ~ 2; c ~ 8-20 required for RHIC data -Needed because radiative only energy loss (and > 1? R = (1/2) L3) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)

10. 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

11. Comparison of LHC p Predictions Curves of AWS-based energy loss are flat in pT (a) (b) 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)

12. Why AWS is Flat • Flat in pT curves result from extreme suppression at the LHC • When probability leakage P(e > 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 RAA(pT) as we do • Vitev used only radiative loss, Prad(e), but assumed fixed path • WHDG similar because elastic and path fluctuations compensate

13. The Rise of GLV Rad+El+Geom • Use of both PradAND Pel implies neither has much weight for DE > E at RHIC • For the dNg/dy values used, high-pT jets at the LHC have asymptotic energy loss: • LHC RAA(pT) dependence caused by deceasing energy loss not altered by the flat production spectra 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

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 • Prad(e) also contains a P(Ng = 0) d(e) due to the probability of no glue emission • For fixed as = .3, including P0 physics accounts for 50% of RAA • Allowing as(T) to run as as(q2=2pT(z)) reduces P0 by a factor of 2 • Integration over momentum transfers with as(q2) given by vacuum running formally gives P0=0

15. Conclusions • LHC RAA(pT) data will distinguish between energy loss models • GLV Rad+El+Geom predicts significant rise in pT • AWS type models predict flat pT dependence • Moderate opacity (GLV, WW) RAA predictions sensitive to noninteracting free jets RAA ~ P0 + (1-P0) RAA(Nc>0), P0 = exp(-selrL)