Transcript Radiative energy loss

Radiative energy loss
Marco van Leeuwen,
Utrecht University
Medium-induced radiation
Landau-Pomeranchuk-Migdal effect
Formation time important
Zapp, QM09
tf 
radiated
gluon
2
kT2
propagating
parton
Lc = tf,max
Radiation sees
length ~tf at once
Energy loss depends on density:
l
and nature of scattering centers
(scattering cross section)
Transport coefficient qˆ 
1

If l < tf, multiple scatterings
add coherently
Emed
2
ˆ
~ S qL
q2
l
2
A simple model
Parton spectrum Energy loss distribution Fragmentation (function)
dN
dpT

hadr
dN
dE
 P(E )  D( pT ,hadr / E jet )
jets
known
pQCDxPDF
extract
`known’ from e+e-
This is where the information about the medium is
P(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, g-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
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Two extreme scenarios
Scenario I
P(E) = d(E0)
‘Energy loss’
Shifts spectrum to left
1/Nbin d2N/d2pT
(or how P(E) says it all)
Scenario II
P(E) = a d(0) + b d(E)
‘Absorption’
p+p
Downward shift
Au+Au
pT
P(E) encodes the full energy loss process
RAA not sensitive to energy loss distribution, details of mechanism
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What can we learn from RAA?
p0 spectra
Nuclear modification factor
PHENIX, PRD 76, 051106, arXiv:0801.4020
This is a cartoon!
Hadronic, not partonic energy loss
No quark-gluon difference
Energy loss not probabilistic P(E)
Ball-park numbers: E/E ≈ 0.2, or E ≈ 2 GeV
for central collisions at RHIC
Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this
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Four formalisms
Multiple gluon emission
•
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/l
(N=1, interference between two centers default)
– Interference with vacuum radiation
•
Fokker-Planck
rate equations
Poisson ansatz
(independent emission)
Higher Twist (Guo, Wang, Majumder)
– Medium characterised by higher twist matrix elements
– Radiation kernel similar to GLV
– Vacuum radiation in DGLAP evolution
DGLAP
evolution
See also: arXiv:1106.1106
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Kinematic variables
Gluon(s)
L: medium length
T, q: Density
E: incoming parton energy/momentum
: (total) momentum of radiated gluon (=E)
kT: transverse momentum of radiated gluon
p: outgoing parton momentum = E-E = E-
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Large angle radiation
Emitted gluon distribution
Opacity expansion
kT < k
Calculated gluon spectrum extends to large k at small k
Outside kinematic limits
GLV, ASW, HT cut this off ‘by hand’
Estimate uncertainty by varying cut; sizeable effect
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Limitations of soft collinear approach
Calculations are done in soft collinear approximation:
Soft:
  E
Collinear:
kT  
Need to extend results to full phase space to calculate observables
(especially at RHIC)
Soft approximation not problematic:
For large E, most radiation is soft
Also:  > E  full absorption
Cannot enforce collinear limit:
Small ,   kT always a part
of phase space with large angles
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Opacity expansions
GLV and ASW-SH
Single-gluon spectrum
Horowitz and Cole, PRC81, 024909
Blue: kTmax = xE
Red: kTmax = 2x(1-x)E
Blue: mg = 0
Red: mg = m/√2
Horowitz and Cole, PRC81, 024909
Single-gluon spectrum
Different definitions of x:
ASW: xE 

E
GLV: x 
Different large angle cut-offs:
kT <  = xE E
kT <  = 2 x+ E


E
x+ ~ xE in soft collinear limit,
but not at large angles
Factor ~2 uncertainty
from large-angle cut-off
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Opacity expansion vs multiple soft
OE and MS related via path integral formalism
Salgado, Wiedemann, PRD68, 014008
Different limits:
SH (N=1 OE): interference between
neighboring scattering centers
MS: ‘all orders in opacity’, gaussian
scattering approximation
Two differences at the same time
Quantitative differences sizable
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AMY, BDMPS, and ASW-MS
Single-gluon kernel from AMY
based on scattering rate:
Salgado, Wiedemann, PRD68, 014008
BMPS-Z use harmonic oscillator:
BDMPS-Z:
Finite-L effects:
Vacuum-medium interference
+ large-angle cut-off
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AMY and BDMPS
L=2 fm Single gluon spectra
L=5 fm Single gluon spectra
AMY: no large angle cut-off
+ sizeable difference at large  at L=2 fm
Using
qˆ (T ) based on AMY-HTL scattering potential
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L-dependence; regions of validity?
Emission rate vs t (=L)
Caron-Huot, Gale, arXiv:1006.2379
E = 16 GeV
k = 3 GeV
T = 200 MeV
GLV N=1
Too much radiation
at large L
(no interference
between scatt centers)
Full =
numerical solution of
Zakharov path integral
= ‘best we know’
AMY, small L,
no L2, boundary effect
H.O = ASW/BDMPS like (harmonic oscillator)
Too little radiation at small L
(ignores ‘hard tail’ of scatt potential)
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HT and GLV
Single-gluon kernel GLV and HT similar
 s CF
dN
1

P
(
x
)
F

HT:
qg
gg
2
4
dx dkT
p
kT
GLV



kT2 

   d 1  cos
2
p
z
(
1

z
)


0

L
GLV similar structure, phase factor 
However HT assumes kT >> qT,
so no explicit integral over qT
HT: kernel diverges for kT 0
t < L  kT > √(E/L)
HT:
kT ,max  2 x (1  x) E 3T
GLV:
kT ,max  2 x (1  x) E
qT ,max  3 E T
HT gives more
radiation than GLV
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Single gluon spectra
Same temperature
L = 2 fm
L = 5 fm
@Same temperature: AMY > OE > ASW-MS
Size of difference depends on L, but hierarchy stays
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Multiple gluon emission
Average number of gluons:
dI
N gluon  
d
d
Poisson convolution example
Poisson fluctuations:
n  N gluon
1
P ( n) 
N gluon e
n!
(assumed)
Total probability:
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Outgoing quark spectra
Same temperature: T = 300 MeV
@Same T: suppression AMY > OE > ASW-MS
Note importance of P0
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Outgoing quark spectra
Same suppression: R7 = 0.25
At R7 = 0.25: P0 small for ASW-MS
P0 = 0 for AMY by definition
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Model inputs: medium density
Multiple soft scattering (ASW-MS):
Quenching weights (AliQuenchingWeights)
Inputs:
q,
ˆ L
c  12 qˆL2
R  c L
N.B: keep track of factors hc = 197.327 MeVfm
Quenching weights: P( x   / c ; R)
Opacity expansion (DGLV, ASW-SH):
Gluon spectra
m,
L
l
dI
L
 K1 (; m , L)
d l
+Poisson Ansatz for multiple gluon radiation
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Medium properties
Some pocket formulas
gluon gas, Baier scheme:
m  gT  4ps T
m2
qˆ 
l
l
1


qˆ 
16 1.202
p
2
72 1.202 s2
p

T3
9ps2
m2
T3
 2 
 2 
HTL: qˆ  3 s mDT ln 2   1.37 Baier ln 2 
 mD 
 mD 
See also: arXiv:1106.1106
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Geometry
Density profile
Profile at t ~ tform known
Density along parton path
Longitudinal expansion
dilutes medium
 Important effect
Space-time evolution is taken into account in modeling
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Geometry II
L-moments of density along path:
I1   dv qˆ (v) v 
1
2
qˆL2  ceff
I 0   dv qˆ (v)  qˆL
2 I1
Leff 
I0
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‘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
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AliQuenchingWeights
Based 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
c  12 qˆL2
x = /c
R  c L
return:
cont:  dI/d
disc: P(0)
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Extra slides
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Thoughts about black-white scenario
Or: Hitting the wall with P(E)
• 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 g-jet, jet-reco promising!
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Opacity expansion
Opacity expansion (DGLV, ASW-SH):
Gluon spectra
m,
L
l
dI
L
 K1 (; m , L)
d l
Poisson Ansatz:
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