S. Manly – U. Rochester Xi’an, China, Nov. 23, 20061 The eccentricities of flow S. Manly University of Rochester International Workshop on Hadron Physics

S. Manly – U. Rochester Xi’an, China, Nov. 23, 2006 1

The eccentricities of flow

S. Manly

University of Rochester

International Workshop on Hadron Physics and Properties of High Baryon Density Matter

Xi’An, China

November 23, 2006

Direct evidence for color strings?


ec·cen·tric·i·ty ( k s n-tr s -t ) n. pl. ec·cen·tric·i·ties

The quality of being eccentric. Deviation from the normal, expected, or established.

An example or instance of eccentric behavior. Physics. The distance between the center of an eccentric and its axis. Mathematics. The ratio of the distance of any point on a conic section

from a focus to its distance from the corresponding directrix. This ratio is constant for any particular conic section.

From American Heritage Dictionary

The eccentricities of flow


Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton,

Russell Betts,

Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo

García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman,

Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming

Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey,

Gerrit van Nieuwenhuizen,

Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland,

Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei

Sukhanov, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin

Verdier,

Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek,

Krzysztof Woźniak, Bolek Wysłouch

ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORYINSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY

NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER

The PHOBOS Collaboration


I offer a humble apology for some repetition to those of you who saw the PHOBOS talks in Shanghai …


Average Flow in PHOBOS

Ring counter

Octagon

Spectrometer arm

Paddle trigger

Vertex detector


Correlate reaction plane determined from azimuthal pattern of hits in one part of detector

Subevent A



with azimuthal pattern of hits in another part of the detector


Subevent B


Or with tracks identified in the spectrometer arms


Tracks


Separation of correlated subevents typically large in



PHOBOS has made differential measurements of the average flow:

CentralitypT

PseudorapidityEnergySpecies

Flow in PHOBOS

I will give you an update of ongoing work on understanding how flow scales from species to species and a new event-by-event measurement

of fluctuations in v2


Elliptic Flow: new results for Cu-Cu at 22.4 GeV

Au+AuAu+AuAu+Au:PHOBOS CollaborationPRL. 94 (2005) 122303

Cu+Cu:PHOBOS CollaborationPRL: nucl-ex/0610037 Cu+CuCu+CuPreliminary


Au+Au:PHOBOS CollaborationPRL 97, 012301 (2006)

Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037

Statistical errors onlyStatistical errors only

Elliptic Flow: new results for Cu-Cu at 22.4 GeV


Preliminary

Preliminary

Au+Au Au+Au

0-20%0-20% 20-40%20-40%

Cu+CuCu+Cu

• Track-based method 0 < < 1.6

Elliptic Flow: Au+Au and Cu+Cu v2 vs pt comparison


Statistical errors onlyStandard Eccentricity

PHOBOS CollaborationPRL: nucl-ex/0610037

Au+Au200 GeV

Cu+Cu200 GeV

Statistical errors only

200 GeV

PRL: nucl-ex/0610037

Au+Au 200 GeV

Cu+Cu200 GeV

PRC C72, 051901R (2005)

Scaling out the geometry


Participant Eccentricity


Au+Au 200 GeVCu+Cu

200 GeV



Cu+Cu200 GeV

Au+Au 200 GeV

Scaling out the geometry


It has been suggested that v2 may scale as instead of

- Bhalerao, Ollitrault – PLB 641, 260 (2006)- Ollitrault – private communications (2006)

• In Collaboration with Ulrich Heinz

2partε partε

PHOBOS MCThe difference

between

is as small as our estimate of the

robustness of the calculation … will

ignore for now.

What is the appropriate form of the eccentricity scaling?


STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments


Au+Au at 200, 130, 62.4 and 19.6 GeV :PHOBOS CollaborationPRL 97, 012301 (2006)

Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037

Cu+Cu at 22.4 GeV PHOBOS Preliminary


Similar area density (1/S)dN/dy Similar area density (1/S)dN/dy


Similar area density (1/S)dN/dy Similar area density (1/S)dN/dy

and and scaled by scaled by partpartStatistical errors only


Au+Au vs. Cu+Cu at Au+Au vs. Cu+Cu at 200 GeV200 GeV Au+Au vs. Cu+Cu at Au+Au vs. Cu+Cu at 62.4 GeV62.4 GeV

Same area density (1/S)dN/dy Same area density (1/S)dN/dy and and Scaled by Scaled by partpart

Statistical errors onlyStatistical errors only

Npart=80Npart=82


Scaled by Scaled by partpart

Same centrality (40%)Same centrality (40%)

Scaled by Scaled by partpart

Same area density (1/S)dN/dySame area density (1/S)dN/dy Statistical errors only Statistical errors only

PHOBOS

PHOBOS


Elliptic flow develops event-by-event with respect to the participant ellipse


Expected fluctuations from the part model

Elliptic flow develops event-by-event with respect to the participant ellipse


A new event-by-event flow analysis from PHOBOS



Determine v2obs



Determine v2obs



Construct kernel



Determine dynamical fluctuations

S. Manly – U. Rochester Xi’an, China, Nov. 23, 2006

Event-by-event mean v2 vs published results

|η|<1<v2>

PRC 72, 051901 (2005)

Number of participants

Very good agreement of the event-by-event measured mean v2 with the hit- and tracked-based, event averaged, published results

<v2>(|η|<1) = 0.5 x (11/12 <v2triangular> + <v2

trapezodial>)


Elliptic flow fluctuations: <v2> and σv2

Au+Au 200 GeV

⟨v2 ⟩


|η|<1 PHOBOS preliminary (90% C.L.)• <v2>

Au+Au 200 GeV

v 2


PHOBOS preliminary (90% C.L.)• σv2

|η|<1

“Scaling” errors cancel in the ratio:relative fluctuations, σv2/<v2>

Mean elliptic flow Dynamical flow fluctuations

Systematic errors: Variation in η-shape Variation of f(v2) MC response Vertex binning Ф0 binning



PHOBOS preliminary (90% C.L.)• σv2/<v2>

|η|<1 Au+Au 200 GeV

2

v

v2

Elliptic flow fluctuations: σv2/ <v2>









2

v

v2

MC with nofluctuations





2

v

v2

MC with nofluctuations

Participanteccentricitymodel prediction

part

part



Things to consider and naïve questionsHow seriously should we take this Glauber-

driven participant eccentricity model?


2

v

v2

Allows us to make sense of both the system size scaling and fluctuations in the data

Really need Cu-Cu fluctuations measurement where the eccentricity fluctuations will be larger … let’s hope the measurements can be made





2

v

v2

PHOBOS fluctuations analysis depends on MC … things not yet in the MC used to determine the kernel (such as short range correlations) can show up as fluctuations

Fortunately, the wonderful and complementary STAR measurement (P. Sorensen – QM2006) provides a consistency check. Data-driven and independent. Agrees well.

Measurement will likely hold up





2

v

v2

Participant eccentricity model calculation has proven to be robust during studies that followed its introduction at QM2005

It seems we should take it seriously

Should we be bothered that we don’t have much room for other sources of fluctuations?


Things to consider and naïve questionsIf we take the participant eccentricity model

seriously, what do we learn?

Whatever the form of the matter in the early stage of the collision, it seems the relevant interactions that drive the flow signal are initially localized transversely in a way similar to the participant nucleons.

Inconsistent with any picture where the initial state is driven by a large number of low-x partons that fill the nuclear transverse area.


Things to consider and naïve questions

It seems we are seeing transversely localized parton production with a granularity not so different from the interacting nucleons! Something

like color strings? Is this telling us something about the reality of some models vs. others? This seems rather fundamental … are there

other measurements that show “stringiness” so directly?

If we take the participant eccentricity model seriously, what do we learn?


Perhaps it seems obvious that this might happen, but it is incredibly cool to see it … and it contradicts the naïve view many

of us might have had (well, me anyway) of a densely packed initial transverse distribution

Documents

S. Manly – U. Rochester Xi’an, China, Nov. 23, 20061 The eccentricities of flow S. Manly University of Rochester International Workshop on Hadron Physics