Radiative energy lossMarco van Leeuwen,Utrecht University

2

Medium-induced radiation

If < f, multiple scatterings add coherently

2ˆ~ LqE Smed

2

2

Tf k

Zapp, QM09

Lc = f,max

propagating

parton

radiatedgluon

Landau-Pomeranchuk-Migdal effectFormation time important

Radiation sees length ~f at once

Energy loss depends on density: 1

2

ˆq

q

and nature of scattering centers(scattering cross section)

Transport coefficient

3

A simple model

)/()( , jethadrTjetshadrT

EpDEPdEdN

dpdN

`known’ from e+e-knownpQCDxPDF

extract

Parton spectrum Fragmentation (function)Energy loss distribution

This is where the information about the medium isP(E) combines geometry with the intrinsic process

– Unavoidable for many observables

Notes:• This formula is the simplest ansatz – Independent fragmentation

after E-loss assumed• Jet, -jet measurements ‘fix’ E, removing one of the convolutions

We will explore this model during the week; was ‘state of the art’ 3-5 years ago

4

Two extreme scenarios

p+p

Au+Au

pT

1/N

bin

d2 N/d

2 pT

Scenario IP(E) = (E0)

‘Energy loss’

Shifts spectrum to left

Scenario IIP(E) = a (0) + b (E)

‘Absorption’

Downward shift

(or how P(E) says it all)

P(E) encodes the full energy loss process

RAA not sensitive to energy loss distribution, details of mechanism

5

What can we learn from RAA?

This is a cartoon!Hadronic, not partonic energy lossNo quark-gluon differenceEnergy loss not probabilistic P(E)

Ball-park numbers: E/E ≈ 0.2, or E ≈ 2 GeV for central collisions at RHIC

0 spectra Nuclear modification factor

PH

EN

IX, P

RD

76, 051106, arXiv:0801.4020

Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this

6

Four formalisms

• Hard Thermal Loops (AMY)– Dynamical (HTL) medium– Single gluon spectrum: BDMPS-Z like path integral– No vacuum radiation

• Multiple soft scattering (BDMPS-Z, ASW-MS)– Static scattering centers– Gaussian approximation for momentum kicks– Full LPM interference and vacuum radiation

• Opacity expansion ((D)GLV, ASW-SH)– Static scattering centers, Yukawa potential – Expansion in opacity L/

(N=1, interference between two centers default)– Interference with vacuum radiation

• Higher Twist (Guo, Wang, Majumder)– Medium characterised by higher twist matrix elements– Radiation kernel similar to GLV– Vacuum radiation in DGLAP evolution

Multiple gluon emission

Fokker-Planckrate equations

Poisson ansatz(independent emission)

DGLAPevolution

See also: arXiv:1106.1106

7

Kinematic variables

Gluon(s)

L: medium lengthT, q: DensityE: incoming parton energy/momentum

: (total) momentum of radiated gluon (=E)kT: transverse momentum of radiated gluonp: outgoing parton momentum = E-E = E-

8

Large angle radiationEmitted gluon distribution

Opacity expansion

kT < k

Calculated gluon spectrum extends to large k at small kOutside kinematic limits

GLV, ASW, HT cut this off ‘by hand’

Estimate uncertainty by varying cut; sizeable effect

Gluon momentum kGluon perp momentum k

9

Limitations of soft collinear approach

Soft: Collinear:

Need to extend results to full phase space to calculate observables(especially at RHIC)

Soft approximation not problematic:For large E, most radiation is softAlso: > E full absorption

Cannot enforce collinear limit:Small , kT always a part of phase space with large angles

E Tk

Calculations are done in soft collinear approximation:

10

Opacity expansions GLV and ASW-SH

Ex

E

xE

x+ ~ xE in soft collinear limit, but not at large anglesDifferent large angle cut-offs:

kT < = xE EkT < = 2 x+ E

Blue: kTmax = xERed: kTmax = 2x(1-x)E

Single-gluon spectrum

Blue: mg = 0Red: mg = /√2

Ho

row

itz an

d C

ole

, PR

C8

1, 0

24

90

9

Single-gluon spectrum

Different definitions of x:

ASW: GLV:

Factor ~2 uncertainty from large-angle cut-off

Ho

row

itz an

d C

ole

, PR

C8

1, 0

24

90

9

11

Opacity expansion vs multiple soft

Salgado, Wiedemann, PRD68, 014008

Different limits:

SH (N=1 OE): interference betweenneighboring scattering centers

MS: ‘all orders in opacity’, gaussianscattering approximation

Quantitative differences sizable

OE and MS related via path integral formalism

Two differences at the same time

12

AMY, BDMPS, and ASW-MS

Single-gluon kernel from AMY based on scattering rate:

BMPS-Z use harmonic oscillator:

BDMPS-Z:

Salgado, Wiedemann, PRD68, 014008

Finite-L effects:Vacuum-medium interference+ large-angle cut-off

13

AMY and BDMPS

Using based on AMY-HTL scattering potential

L=2 fm Single gluon spectra L=5 fm Single gluon spectra

AMY: no large angle cut-off

)(ˆ Tq

+ sizeable difference at large at L=2 fm

14

L-dependence; regions of validity?Emission rate vs (=L)

Caron-Huot, Gale, arXiv:1006.2379

AMY, small L,no L2, boundary effect

Full = numerical solution of

Zakharov path integral = ‘best we know’

GLV N=1Too much radiation at large L(no interference between scatt centers)

H.O = ASW/BDMPS like (harmonic oscillator)Too little radiation at small L

(ignores ‘hard tail’ of scatt potential)

E = 16 GeVk = 3 GeVT = 200 MeV

15

HT and GLV

Single-gluon kernel GLV and HT similar

HT: kernel diverges for kT 0 < L kT > √(E/L)

GLV:

TExxkT 3)1(2max, HT:

ExxkT )1(2max, TEqT 3max,

42

1)(

Tggqg

Fs

T kFxP

CdkdxdN

L

T

zzpk

d0

2

)1(2cos1

HT:

GLV similar structure, phase factor

However HT assumes kT >> qT,so no explicit integral over qT

GLV

HT gives more radiation than GLV

16

Single gluon spectraSame temperature

@Same temperature: AMY > OE > ASW-MS

L = 2 fm L = 5 fm

Size of difference depends on L, but hierarchy stays

17

Multiple gluon emission

Poisson convolution example

d

ddI

N gluon

gluonNn

gluon eNn

nP

!1

)(

Average number of gluons:

Poisson fluctuations:

Total probability:(assumed)

18

Outgoing quark spectraSame temperature: T = 300 MeV

@Same T: suppression AMY > OE > ASW-MS

Note importance of P0

19

Outgoing quark spectraSame suppression: R7 = 0.25

At R7 = 0.25: P0 small for ASW-MSP0 = 0 for AMY by definition

20

Model inputs: medium density

Multiple soft scattering (ASW-MS):

Quenching weights (AliQuenchingWeights)

Inputs: Lq,ˆ2

21 ˆLqc LR c

N.B: keep track of factors hc = 197.327 MeVfm

);/( RxP cQuenching weights:

Opacity expansion (DGLV, ASW-SH):

L,

Gluon spectra ),;(1 LKL

ddI

+Poisson Ansatz for multiple gluon radiation

21

Medium propertiesSome pocket formulas

32

202.116T

32202.172

ˆ Tq s

gluon gas, Baier scheme:

TgT s 42

29 s

1

HTL:

2

2

2

2

lnBaier37.1ln3ˆDD

Ds mmTmq

See also: arXiv:1106.1106

2

ˆ q

22

Geometry

Density profile

Profile at ~ form known

Density along parton path

Longitudinal expansion dilutes medium Important effect

Space-time evolution is taken into account in modeling

23

Geometry II

effcLqvvqdvI 2

21

1 ˆ)(ˆ

LqvqdvI ˆ)(ˆ0

0

12II

Leff

L-moments of density along path:

24

‘Analytic’ calculations vs MC Event Generators

• Analytic calculations (this lecture)– Easy to include interference– So far: only soft-collinear approx– Energy-momentum conservation ad-hoc

• Monte Carlo event generators (modified parton showers)– Energy-momentum conservation exact– May be able to introduce recoil (dynamic scatt centers)– More difficult to introduce interference– Examples: JEWEL, qPYTHIA, YaJEM

25

AliQuenchingWeightsBased on Salgado, Wiedemann, hep-ph/0302184

AliQuenchingWeights::InitMult()Initialises multiple soft scattering Quenching Weights

AliQuenchingWeights::CalcMult(ipart, R, x, cont, disc)Multiple soft scattering Quenching Weights

input: ipart 0=gluon, 1=quark

x = /c

return:cont: dI/ddisc: P(0)

221 ˆLqc

LR c

26

Extra slides

27

Thoughts about black-white scenario

• At RHIC, we might have effectively a ‘black-white scenario’– Large mean E-loss– Limited kinematic range

• Different at LHC?– Mean E-loss not much larger, kinematic range is?– Or unavoidable: steeply falling spectra

In addition: the more monochromatic the probe, the more differential sensitivity -jet, jet-reco promising!

Or: Hitting the wall with P(E)

28

Opacity expansion

Opacity expansion (DGLV, ASW-SH):

L,

Gluon spectra ),;(1 LKL

ddI

Poisson Ansatz: