Post on 22-Feb-2016
description
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 glue
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
The 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