and q models of jet quenching ^

taupeselectionMechanics

Nov 14, 2013 (4 years and 1 month ago)

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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