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