Peter Kolb, November 18, 2003Momentum Anisotropies1 Momentum Anisotropies -- Probing the detailed...

Peter Kolb, November 18, 2003Peter Kolb, November 18, 2003 Momentum AnisotropiesMomentum Anisotropies 11

Momentum Anisotropies --Probing the detailed Dynamics

Department of Physics and AstronomyState University of New YorkStony Brook, NY 11794

with support from theAlexander von Humboldt Foundation

Peter F. Kolb

Brookhaven National LaboratoryFlow and QGP Workshop

November 18, 2003


Non-Central Collisions Feature Broken Symmetry

Characterize azimuthal dependence of the resulting observables by their Fourier expansion

With the given symmetries and the chosen coordinate system:

no sin terms

no odd cos termsfor equal nuclei and z = 0


Elliptic Flow - A Prominent Observable

Z.W. Lin and C.M. Ko, PRC 65 (2002) 034904 * requires strong rescattering * requires strong rescattering PFK et al., PLB 500 (2001) 232

D. Molnar and M. Gyulassy, NPA 698 (2002) 379

* … at very early stages* … at very early stages

PFK, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909

* is sensitive on the * is sensitive on the nuclear equation of state nuclear equation of state

PFK and U. Heinz, nucl-ex/0204061Teaney, Lauret, Shuryak, nucl-th/0110037

on a timescale < 1 fm/con a timescale < 1 fm/c

heavier particles pick up larger heavier particles pick up larger <<ppTT> in the common flow field> in the common flow field

Greco, Levai, Ko, Molnar, Voloshin, Greco, Levai, Ko, Molnar, Voloshin, Fries, Nonaka, Bass, Müller, SorensenFries, Nonaka, Bass, Müller, Sorensen

* shows a quark counting rule* shows a quark counting rule

indicating a soft transition regionindicating a soft transition region

common partonic flowcommon partonic flow

reaching the hydrodynamic limitreaching the hydrodynamic limit

* shows a strong hydrodynamic* shows a strong hydrodynamic mass effect mass effect

Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (2001) 58


Elliptic Flow at Large Pt is HUGE !

PH

EN

IX C

olla

bora

tion

, nuc

l-ex

/030

5013

v2 = 0.25 means that there are 3 times as many particles emitted

into the reaction plane than out of the reaction plane!Furthermore the distribution is not elliptic any longer!

PHENIX Collaboration, nucl-ex/0305013


Higher order term to Counteract ?

develops a minimum in cartesian coordinates at

x=0 for v2 > 0.1

To balance the minimum a v4 > (10v2-1)/34 is

required (this brings the second derivative of

y(x) at x=0 to vanish).

PFK, Phys. Rev. C 68 (2003) 031902(R)


A quadrupole modulation of several percent can be expected !

It is however not sufficient to balance the peanut shape

Differential Expectations on Higher v’s

PFK, and R. Rapp, PRC 67 (2003) 044903From a recent hydrodynamic calculation to describe collisions at 200 GeV

PFK, Phys. Rev. C 68 (2003) 031902(R)


Geometric Anisotropy is Rapidly Converted to Momentum Space

coordinate spacecoordinate space

quantify quantify anisotropiesanisotropies


A short Digression on Fourier Coefficients

Distribution Distribution within the within the reaction planereaction plane

Distribution Distribution out of the out of the reaction planereaction plane

for a delta-function like distributionfor a delta-function like distribution


Geometric Anisotropy is Rapdily Converted to Momentum Space

momentum spacemomentum spacecoordinate spacecoordinate space

quantify quantify anisotropiesanisotropies


Elliptic Flow in the Blast Wave


Blast wave parametrization for non-central collisions

Radial rapidity-field with angular modulation:

Freeze-out on azimuthally symmetric hypersurface of temperature T:

Collapse of the radial integration onto shell:


Reproduces

momentum -

and mass dependence

of elliptic anisotropy

Tdec = 140 MeV = 0.58f2 = 7.7 %

Elliptic Flow in the Blast Wave


Anisotropic Flow in the Blast Wave

Blast wave parametrization for non-central collisions

Radial rapidity-field with angular modulation:

Freeze-out on azimuthally symmetric hypersurface of temperature T:

Collapse of the radial integration onto shell:



Blast Wave - Influence of f4

negative negative ff44 positive positive ff44

1 % distortion1 % distortion



Blast Wave - Influence of f6

negative negative ff66 positive positive ff66




Sensitivity on f2 and f4

A purely elliptic flow anisotropyA purely elliptic flow anisotropyproduces a small quadrupoleproduces a small quadrupolemoment after folding with the moment after folding with the thermal distribution…thermal distribution…

… … an additional small quadropolean additional small quadropoledistortion in the flow field yieldsdistortion in the flow field yieldsa large quadrupole moment ina large quadrupole moment inthe particle distributionthe particle distribution

at some fixed transverse momentum (here pat some fixed transverse momentum (here pTT =2 GeV) =2 GeV)

expandexpand

for small anisotropiesfor small anisotropies


pure surface emission in the high pT limit (i.e. from extreme jet-quenching)

Anisotropies from a Black Lense

Cooper Frye freeze-out from the lense with weights on the emission angle

Parameterize surface in the transverse plane,i.e. for

with normal vector

Carry the idea of Shuryak and Voloshin to higher levels (higher orders):PRC 66 (2002) 027902 NPA 715 (2003) 379

for even n

PFK, Phys. Rev. C 68 (2003) 031902(R)


Limiting Anisotropies versus Centrality

Extremely interesting centrality dependenceThis picture predicts a peanut like distribution as well!

PFK, Phys. Rev. C 68 (2003) 031902(R)


One Thought on Coalescence

assume there are no higher order anisotropies on the quark levelassume there are no higher order anisotropies on the quark level

1/41/4 1/31/3

See talk by Art Poskanzer for experimental results!See talk by Art Poskanzer for experimental results!

2 for mesons2 for mesons3 for baryons3 for baryons

quarksquarks

mesonsmesons baryonsbaryons


Summary: Why Study Higher Harmonics ?

Get a full picture of the transverse momentum spectrum

Ideally, triple differentially for different centrality classes:

with odd coefficients at

Anisotropies areAnisotropies are

generated early in the evolution

very sensitve on details of the flow fields and dynamics

probe the hottest stagesprobe the hottest stages

will allow very quantitative statementswill allow very quantitative statementsfrom all model calculationsfrom all model calculations

Date post:	21-Jan-2016
Category:	Documents
Upload:	john-charles
View:	217 times
Download:	0 times

Peter Kolb, November 18, 2003Momentum Anisotropies1 Momentum Anisotropies -- Probing the detailed...

Documents