Radiative energy loss Marco van Leeuwen, Utrecht University.
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Transcript of Radiative energy loss Marco 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-
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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
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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
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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
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
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)