CentralityDetermination for √sNN = 200GeV

d+Au Collisions at RHIC

Richard S Hollis

University of Illinois at Chicago

Collaboration

Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Abigail Bickley,

Richard Bindel, Wit Busza (Spokesperson), Alan Carroll, Zhengwei Chai, Patrick Decowski,

Edmundo Garcia, Tomasz Gburek, Nigel George, Kristjan Gulbrandsen, Stephen Gushue,

Clive Halliwell, Joshua Hamblen, Adam Harrington, Conor Henderson, David Hofman, Richard

Hollis,

Roman Hołyński, Burt Holzman, Aneta Iordanova, Erik Johnson, Jay Kane, Nazim Khan, Piotr

Kulinich, Chia Ming Kuo, Willis Lin, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen,

Rachid Nouicer, Andrzej Olszewski, Robert Pak, Inkyu Park, Heinz Pernegger, Corey Reed,

Michael Ricci,

Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Wojtek Skulski, Chadd Smith,

Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek,

Carla Vale, Siarhei Vaurynovich, Robin Verdier, Gábor Veres, Edward Wenger, Frank Wolfs,

Barbara Wosiek, Krzysztof Woźniak, Alan Wuosmaa, Bolek Wysłouch, Jinlong Zhang

ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORYINSTITUTE OF NUCLEAR PHYSICS, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGYNATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO

UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER

Detector

Analysis Apparatus:

4 Multiplicity Array

Central Octagon Barrel

6 Rings at higher (Pseudo) Rapidity

Trigger Apparatus:Paddles → One Hit on

Each Array is the Minimum-Bias Trigger

d

Au

Centrality: What is it?

These Geometrical

Quantities are not

Directly Measurable

b

Ncoll

Npart

Npart

How can we ‘measure’ these variables in d+Au collisions?

• Choose a pseudorapidity region– here it’s |η|<3.0

• Slice the MC Multiplicity into desired percentile cross-section bins

• Map this to Npart

• Determine the mean and width of the resulting Npart distributions

• Finally, slice DATA Multiplicity into same cross-section bins

– Associate Npart from same MC cross-section bins

• More Npart details tomorrow

– See Aneta Iordanova’s Talk “Npart Determination and Systematic Error”

d + Au at √s = 200GeV

Npart

Npart

30

η Coverage

Octagon

Rings Rings

Primary Trigger(Scintillator) Paddles

ηSchematic Plot

not to scale

The aim of the talk is to demonstrate the

reconstruction of the Min-Bias Multiplicity Distribution

5.4-5.4 -3.2 3.2

Which Region of η is best?Five distinct methods

• Should not matter when reconstructing a Min-Bias result– If calculated efficiencies

are correct!

• Unique PHOBOS coverage– Many regions to pick from

• All used a basic algorithm– Sum of all merged hits– Cut noise and background

ETot

EOct

ERing

EAuHem

EdHem

Schematic Distributions

Which Region of η is best?Why do we need so many?

• Auto-Correlations!– Could this introduce a Centrality

Bias?

• Method (here)– Cut on Npart directly (Black)

• Form <dN/dη>• Calculate the <Npart>

– Cut on all the other variables such that all have the same <Npart>

• Form <dN/dη>

• Each method derives a different <dN/dη> for the same <Npart>

• ERing yields the closest shape

<Npart> ≈ 3.1

<Npart> ≈ 15.5

NpartEOctETot

ERingAuHemdHem

Which Region of η is best?Let’s try one, any one

• For illustration, look at ‘EOct’– |η|<3.0 – we started here in January!

• Hijing reproduces the Data well in this region.

• Inherent Problem:– How do we make cross-

section bins if we are inefficient?

EOct

EOct

MC – HIJINGData

MC – HIJING Same cuts as data

Data

Problem: Data is not 100% Efficient

• Making a measurement from the whole range of centralities was crucial, for all our d+Au papers.

• For Au+Au data, assumed all inefficiency was in the last bin → thrown away.

• Two Options presented themselves:– PHOBOS ‘min bias’

• Divide our data into our cross-section bins– don’t know the true cross-section– how to deduce Npart?

– Hijing ‘zero-bias’• Divide this distribution into cross-section bins,

– can estimate the true cross-section,– have to carefully estimate the error associated

with this

• Au+Au (Trigger) Efficiency = 97%• d+Au (Trigger + Vertex) Efficiency = 82.5%

Data

MC

EOct

EOct

Solution: Use Hijing

• Use the Hijing Cross-section as true

• Apply a small scale factor (along x-axis) to match the distributions

• Use a Glauber calculation to estimate the uncertainty in overall efficiency

EOct

EOct

MC

Data

How do we know we are correct?

• There are some issues to consider with this technique– Is the efficiency correct?– Is Hijing Correct?– Does Hijing reproduce the shape well enough?

• Best way to address them is to try another method!– Different (shape matched) efficiencies

• Different efficiencies per centrality bin– Each of the 5 methods have different shape features

Forming the “minimum bias” result

• Form the normalized distributions in 10 equal (Hijing) cross-section bins.

• Sum these and divide by 10 (bins).

• All five methods reconstruct within a few percent of each other (in Hijing).

• Reconstruct to within 2.5% of Hijing zero bias.

• We can then hypothesize:– We have seen the intermediate

centrality distributions are very different for each centrality method

– As are the efficiencies per bin– The final (reconstructed) zero-biases

are the same– Conclusion: the method seems to work

Why do we need bins for “minimum bias” reconstruction

• If we put all the data into one bin– automatically bias

ourselves away from the low multiplicity events

– ~15% rise over zero-bias

• Folding in the efficiency helps

• Increase number of bins → get closer to ‘truth’

All in 1 BinZero Bias

η

dNch

dη

Conclusions

• We have developed a new analysis to determine bins of cross-section for d+Au collisions.

• We can analyse data even when the data falls in an inefficient bin.

• Biased Hijing reconstructs 2.5% higher than unbiased with our methodology.

• Distinct centrality methods in Hijing Reconstruct and agree to within a few percent of each other.

INAL DATA RESULT

If you want tosee it …

Aneta IordanovaSession CC

Tomorrow Morning

PRELIMINARY

INAL DATA RESULT

PRELIMINARY

INAL DATA RESULT

PRELIMINARY

INAL DATA RESULT

PRELIMINARY

INAL DATA RESULT

-4 -2 0 2 4 η

Npart

How do we ‘measure’ these variables in Au+Au collisions?

• Choose a pseudorapidity region (here it’s |η|<3.0)

• Slice the MC Multiplicity into desired percentile cross-section bins

• Map this to Npart

• Determine the mean and width of the resulting Npart distributions

• Finally, slice DATA Multiplicity into same cross-section bins

– Associate Npart from same MC cross-section bins

Au + Au at √s = 200GeV

Npart

400