Andrej Ficnar
Columbia University
INT 10

2A
June 25, 2010
High order
DGLV
Monte Carlo
and
q
models of jet quenching
^
DGLV approach
color

screened Yukawa potential (GW model)
inverse formation time
cascade amplitudes
(
)
Gyulassy, Levai, Vitev, Nucl.Phys.B594:371

419,2001
Djordjevic, Gyulassy, Nucl.Phys.A733:265

298,2004
Opacity expansion of radiative energy loss including finite
masses of quarks and gluons ( )
INT 10

2A, June 25, 2010
2/13
Monte Carlo computation
In essence:
input
: , , , , , , , opacity order , number of
sampling points & range of
output
: inclusive gluon distribution and statistical
error for each
For each order, do the importance sampling Monte Carlo of:
according to
uniformly
according to
Flexible: easy implementation of different potentials or different
distributions of scattering centers (e.g. dynamical potential)
computations
Buzzatti, Ficnar, Gyulassy, Wicks, to be published
INT 10

2A, June 25, 2010
3/13
Monte Carlo computation
Having in mind (for RHIC) and Poissonian
distribution, it is enough to go to
Time per per is roughly seconds
Current Fortran code tested up to 1+ ... + 9 order
(S. Wick's thesis C

code)
Motivation: building a Monte Carlo bridge between thin ( )
and thick ( ) plasma approximation
INT 10

2A, June 25, 2010
4/13
BDMPS
Multiple soft scattering approximation ( ): Moliere

like
Gaussian diffusion in transverse momentum space
main approximation:
Start from the path integral formulation:
Baier, Dokshitzer, Mueller, Peigne, Schiff, Nucl.Phys.B483:291,1997
dipole approximation
MSS
Zakharov, JETP Lett. 70 (1999) 176

182
Wiedemann, Nucl.Phys. B588 (2000) 303

344
Zakharov, JETP Lett. 63 (1996) 952

957
INT 10

2A, June 25, 2010
5/13
BDMPS
transport coefficient characterizes medium’s
rescattering properties:
it gives transverse momentum squared per unit path length
transferred to the parton
only
this
parametric function of time
controls both the
and
distributions of radiated glu
e
ASW studied this distribution keeping the finite kinematics
( ) and fitting a large to the data
Armesto, Salgado, Wiedemann, Phys.Rev.D69:114003,2004
INT 10

2A, June 25, 2010
6/13
BDMPS
If kinematics are ignored,
the

integrated induced intensity
spectrum is predicted to scale with
via the variable z
:
where: and
T
he opacity series in this approximation misses
the
leading
term
:
Arnold, Phys.Rev.D79:065025,2009
BDMPS
INT 10

2A, June 25, 2010
7/13
BDMPS
By explicit Monte Carlo calculations up to 9th order in opacity
we investigate
whether the radiated energy loss spectrum scales well with z,
i.e. is alone sufficient to describe radiative processes
relevant to LHC and RHIC conditions
INT 10

2A, June 25, 2010
8/13
DGLV & BDMPS z

scaling 1
x

dependence in upper bound in kt makes difference
z<1 domain is not relevant for LHC (at least for L>1)
scaling broken by up to 100%
INT 10

2A, June 25, 2010
Arnold’s opacity expansion
9/13
DGLV & BDMPS z

scaling 2
energy loss spectrum at intermediate opacity
depends in detail on and
INT 10

2A, June 25, 2010
10/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
slow convergence of opacity
series (small formation time)
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
ASW < 0
11/13
DGLV & ASW 1
INT 10

2A, June 25, 2010
ASW < 0
due to slower convergence
distribution > xE is important
11/13
dead cone effect
finite opacity n=5 interpolates
between thin and thick
thin plasma (n=1)
thick plasma (n=∞)
DGLV & ASW 2
INT 10

2A, June 25, 2010
12/13
Summary and Outlook
Constructed a new transparent Fortran Code DGLV

BFW
Demonstrated a practical bridge between thin and thick
plasma approximations
We can now compute and study triple differential radiative
(jet shape) effects up to (and beyond) 9th order in the opacity
BDMPS z

scaling broken by up to 100%
kinematic limits are important
energy loss spectrum at intermediate opacity depends in detail
on and
Outlook: Nonhomogenous dynamical QCD medium with gluon
number fluctuations (A. Buzzatti’s talk)
INT 10

2A, June 25, 2010
13/13
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