Jet energy loss at RHIC and LHC including collisional and radiative and geometric fluctuations Simon Wicks, QM2006 Work done with Miklos Gyulassy, William

Jet energy loss at RHIC and LHCJet energy loss at RHIC and LHC including including collisionalcollisional and and radiativeradiative

and and geometricgeometric fluctuations fluctuations

Simon Wicks, QM2006Work done with Miklos Gyulassy, William Horowitz, Magdalena Djordjevic

Institut für Theoretische Physik

Simon Wicks Sunday 19th November 2006 2

pQCD and energy loss

At RHIC and LHC:Radiative mechanisms are important, but not ‘dominant’

SW, W. Horowitz, M. Djordjevic M. Gyulassy (WHDG) nucl-th/0512076

M. Mustafa, Phys. Rev. C72:014905 (2005)


Integration over production positions

Integrals over the initial geometry just have to be done.


WHDG extended theory

~Ideal Our model

ProductionAll orders

pQCDNLO pQCD (FONLL for LHC spectra)

(large uncertainty in normalization, small uncertainty in the power law)

GeometryPropagate through

evolving hydro simulation

Realistic Woods-Saxon nuclear density Jets produced ~ TAA

Propagate through Bjorken expanding ρpart

αs Running Fixed αs=0.3(large uncertainty as energy loss strongly dependent on αs)

Energy loss mechanism

Collisional and radiative in same

theoretical framework

Incoherent addition of

DGLV radiative and leading log TG / BT collisional

NOTE however: we use physical dNg/dy~1000


The results – RHIC Important consistency check: Compare predictions to both pion and electron data

(WHDG = nucl-th/0512076v3)

Result: inclusion of collisional+geometry ~fits pion data, and improves the heavy quark quenching, but still underpredicts pT~4-8 data with FONLL b/c ratio.

(B/D ratio or direct D measurement very important to reduce uncertainties)

STAR: nucl-ex/0607012, PHENIX (QM2006): nucl-ex/0611018


The results – More RHIC

Integrated RAA v2


The results - LHC See William Horowitz’s poster for more details about LHC and

comparison to other predictions. Here: estimate dNg/dy=2900 via CGC

Note the slope of our pion predictions.

Light jets Heavy jets Pions


Improving the model

1) Toward a better description of collisional fluctuations.

2) Effects of running QCD coupling.


Collisional fluctuations in WHDG (Fokker-Planck-like)

Fokker-Planck:Characterised by 2 numbers / functions:

(drag, diffusion)

Small ε approx (used in WHDG):

Gaussian, centered at average energy loss (given by BT or TG), width (in WHDG) given by fluctuation-dissipation theorem, σ2 = 2T<ε> (Green curve = collisional fluctuations in WHDG)


A model of elastic energy lossUse this model in order to study fluctuations: Jet interacts with a medium modified HTL propagator

with initially static medium particles which recoil. Mass of medium particle tuned to give ΔE~ ΔETG or BT

Gives mean free path of quark jet ~ 2.5fmmeff ~0.3 GeV

E,M


Bottom jets – extreme 10 collisions (L~25fm) Multiple collisions:

Poisson weighted convolution of single collision distribution(ie independent collisions)

Bottom, for 10 collisions: Full distribution (red) is

wider than the Gaussian (black).

Full distribution is still slightly skew even at 10 collisions.

Gaussian gives RAA=0.19 vs 0.20

FP good in this case


Bottom jets – typical 2 collisions (L~5fm) Multiple collisions:

Poisson weighted convolution of single collision distribution(ie independent collisions)

Bottom, for 2 collisions: Full distribution (red) is

wider than the Gaussian (black).

Full distribution is very skewed for 2 collisions.

Gaussian (FP) approx misses the physics, BUT gets RAA close!


Light jets – 2 and 5 collisions

For small numbers of collisions, the Gaussian / FP-like approximation over predicts the quenching by ~0.1

(similar result for charm quarks)


Elastic fluctuations: Summary

After all the elastic+geometric fluctuations, we expect: All RAA predictions move up, charm, light quarks, gluons

(by ~0.1). Bottom quarks stay ~ same place.

At RAA~0.1 level there are other effectsthat need to be taken into account:

1) Large theory uncertainty in electron prediction is bottom/charm ratio.

2) … (next slide)


Effect of running the QCD coupling

(Q2)


Running the QCD coupling IA

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Running the QCD coupling II

Peshier = Running α, infinite energy jet (black dashed)

Running α = finite energy jet

“Fixed α (1)”= α at t=(2πT)2

“Fixed α (2)”= α fixed at 0.3

Model: Bjorken estimate, 1/t2, cutoff at t=μ2

1-loop running α, ΛQCD = 0.2GeV.

Result:1) Running alpha results similar to fixed alpha For T< 1GeV except in unphysical E=Infty limit

Further investigation needed to determine:RAA prediction including full geometry and elastic fluctuations (in progress)


Extended WHDG Theory Status 1) WHDG shows that elastic energy loss cannot be neglected in jet tomography. 2) Full geometry path fluctuations must be included. 3) Our extended theory with collisional + radiative +geom comes close to a

consistent explanation of both pion and electron data at RHIC.4) Large uncertainty from bottom/charm ratio, RAA~0.2-0.3.

5) Fokker-Planck formalism misses the physics of small collision number distributions.

6) For light quarks and gluons, WHDG with FP elastic fluctuations probably overestimates the influence of collisional by RAA~0.1. However: for bottom quarks, the WHDG result for RAA is insensitive to (5)).(=> Bottom quark RAA moves closer to light quark RAA)

7) Running alpha increases the collisional quenching. Resulting RAA predictions: calculation in progress.

Documents

Jet energy loss at RHIC and LHC including collisional and radiative and geometric fluctuations Simon Wicks, QM2006 Work done with Miklos Gyulassy, William