Dilepton production as a measure of QGPthermalization time

Mauricio Martinez1

Work done in collaboration with M. Strickland

1Helmholtz Research School,Frankfurt Institute for Advanced Studies,

Johann Wolfgang Goethe Universitat Frankfurt

Quark Matter 2008Jaipur, India

9th February 2008

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 1 / 16

Pre-equilibrium phase of the QGP

τ0

~ Qs

-1 τ

1

0.1-0.2 fm/c

Expansion rate and isotropization

via interactions balance

<p >T

<p >L

CG

C/G

lasm

a

Bo

ltzm

an

n-

Vla

sov

Tra

nsp

ort

Vis

cou

s H

ydro

System is momentarily isotropicSystem is momentarily isotropicSystem is momentarily isotropic

Expansion rate is much faster

than the interaction time scale

1/τ >> 1/τ int

small plarge p large p

∼ τiso

As a result of the rapid expansion along the beam axis, ananisotropy in the momentum-space is developed.

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 2 / 16

Electromagnetic probes in heavy ion collisions

Electromagnetic signatures giveinformation about initial partondistributions and early timedynamics of the collision.

Photons are more difficult forexperimentalists to measure due tolarge backgrounds.

Dileptons offer a better option fromthe experimental point of view.

Influence of non equilibrium dynamics on dilepton production?

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 3 / 16

Dilepton emission from an anisotropic QGP

Dilepton rate d4R/d4P depends on the direction ofthe anisotropy and the angle of the dilepton pair withrespect to the longitudinal axis.

As an ansatz, we choose an anisotropic phase spacedistribution in momentum-space:

f i (p, x ) = f iiso

(

p2T + (1 + ξ)p2

L

)

ξ measures the strength of the anisotropy and it’s relatedwith the kinematic variables:

ξ =12〈p2

T 〉

〈p2L〉

− 1

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 4 / 16

Model for an anisotropy in momentum-spaceIn a free streaming plasma:

ξFS(τ) =( τ

τ0

)2− 1

limτ≫τ0

E(τ) ⇒ E0

(τ0

τ

)

“T ” = T0

In a hydrodynamical plasma:

ξ(τ) = 0

E(τ) = E0

(τ0

τ

)4/3

T = T0

(τiso

τ

)1/3

Propose a model that interpolates between free streaming andhydrodynamical expansion :

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 5 / 16

Space-time evolution with anisotropies

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 6 / 16

Dilepton production vs. M

⇐ No difference!!!

A K factor of 1.5 was applied to account for NLO corrections.

T0= 845 MeV, τ0= 0.088 fm/c, Tc = 160 MeV.

Cuts: PT > 8 GeV.

M. Martinez and M. Strickland, arXiv:0709.3576 [hep-ph].

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 7 / 16

Dilepton production vs. PT

Large enhancement atintermediate PT fromanisotropy!!!

A K factor of 6 was applied to account for NLO corrections.

T0= 845 MeV, τ0= 0.088 fm/c, Tc = 160 MeV.

Cuts: M > 2 GeV.

M. Martinez and M. Strickland, arXiv:0709.3576 [hep-ph].

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 8 / 16

Conclusions

We construct a model that interpolates between freestreaming and hydrodynamics evolution. The model takesinto account the time dependence of the anisotropy in themomentum-space.

Dilepton production in the kinematic range 3< PT <8 GeVprovides an estimate of the momentum-space anisotropyand a possible measure of the isotropization time, τiso.

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 9 / 16

Backup slides

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 10 / 16

Dilepton rate at leading order

From relativistic kinetic theory, the dilepton rate production forqq → l+l− is:

dNd4xd4p

=dRd4P

=

∫

d3p1

(2π)3

d3p2

(2π)3 fq(p1, T )fq(p2, T )

× υrelσLOqq→l+l−δ4(P − p1 − p2)

The invariant distributions of dileptons as a function of invariantmass and transverse momementum are respectively:

dNdM2dy

= πR2∫

d2PT

∫ τf

τ0

∫

∞

−∞

dRd4P

τdτdη.

dNd2PT dy

= πR2∫

dM2∫ τf

τ0

∫

∞

−∞

dRd4P

τdτdη.

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 11 / 16

Some details about the interpolating model

Smeared stepfunction λγ(τ − τiso)

Time-dependence of E , phard and ξ

E(τ) = EFS(τ) [U(τ)/U(τ0) ]4/3 ,

phard(τ) = T0 [U(τ)/U(τ0) ]1/3 ,

ξ(τ) = a2(1−λ(τ)) − 1 ,

U(τ) =

[

R

(

(τiso

τ

)2− 1)]

3λ(τ)4 (τiso

τ

)λ(τ)

R(ξ(τ)) =

(

11 + ξ(τ)

+arctan(

√

ξ(τ))√

ξ(τ)

)

limτiso≫τ

E(τ) ⇒ E0

(τ0

τ

)

Free streaming limit

limτ≫τiso

E(τ) ⇒ E0

(τiso

τ

)4/3Hydrodynamical limit

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 12 / 16

Dependence on the model parameter γ

A K factor of 6 was applied to account for NLO corrections.

T0= 845 MeV, τ0= 0.088 fm/c, Tc = 160 MeV.

Cuts: M > 2 GeV.

M. Martinez and M. Strickland, arXiv:0709.3576 [hep-ph].

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 13 / 16

Produced fraction of Medium Dileptons in time

T0= 845 MeV, τ0= 0.088 fm/c, Tc = 160 MeV, τiso= 0.5 fm/c.

Cuts: M > 2 GeV.

M. Martinez and M. Strickland, arXiv:0709.3576 [hep-ph]

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 14 / 16

Fixing multiplicities

We could modify the model for the non equilibrium region fixingthe final multiplicities. For doing so, we demand that after agiven τiso, the hard momentum scale is the same.

2 5 10 20 50Τ�Τ0

0.3

0.5

0.7

1

p har

d�

T 0

Τiso =1.6 fm�c

Τiso =0.8 fm�c

Τiso =0.4 fm�c

Τiso =0.1 fm�c

As a consequence, the initial conditions will change and willdepend on τiso.

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 15 / 16

Fixing multiplicities: dilepton spectrum vs. PT

2 4 6 8 10PT @GeVD

-9

-8

-7

-6

-5

-4

-3

log

10H

dN

e+

e

-

�d

yd

pT2@

Ge

V-

2DL

Medium HΤhydro = 2 fm�cL

Medium HΤhydro = 0.088 fm�cL

Jet Conversion

Drell Yan

Dilepton production will be smaller compared with the casewhen the initial conditions are fixed but the effect from ananisotropy remains.A K factor of 6 was applied to account for NLO corrections.

T0= 845 MeV, τ0= 0.088 fm/c, Tc = 160 MeV, τ0 ≤ τiso ≤ 1 fm/c. Cuts: M > 2 GeV.

M. Martinez and M. Strickland, forthcoming

Mauricio Martinez Dilepton production as a measure of QGP thermalization time Quark Matter 2008 16 / 16