# Presentation: 070470

## Elliptic Flow Fluctuations and

**Non-flow correlations**

- Brookhaven National Laboratory

- Paul Sorensen

- for the

- collaboration

## introduction

- ambiguity arises in calculations from uncertainty in initial conditions
- perfect fluid conclusion depends on ambiguous comparison to ideal hydro

- motivation to measure v2 fluct.: find observable sensitive to initial conditions

- Talk outline:
-  analysis procedures and changes since QM06
-  non-flow 2 and v2 from the q-distribution
-  comparison to cumulants v{2}, v{4}
-  v2 of events with a “ridge” and/or a “jet”!

*See STAR Poster: Navneet Kumar Pruthi*

## flow vector distribution

- q-vector and v2 related by definition:  v2 = cos(2i) = q2,x/√M
- sum over particles is a random-walk  central-limit-theorem
- width depends on
-  non-flow: 			***broadens****	****n** = ****cos(n(****i- ****j**))**** (2-particle corr. nonflow*)
-  v2 fluctuations:		***broadens***

- J.-Y. Ollitrault nucl-ex/9711003; A.M. Poskanzer and S.A. Voloshin nucl-ex/9805001

## flow vector distribution

- x, y directions are unknown:  integrate over all  and study the length of the flow vector |q2|

- from central limit theorem, q2 distribution is a 2-D Gaussian

- fold v2 distributions *ƒ(v**2**)* with the q2 distribution to account for fluctuations v2

- Ollitrault nucl-ex/9711003;
- Poskanzer & Voloshin nucl-ex/9805001

- dynamic width dominated by non-flow and/or fluctuations  not determined independently

- correction to QM06 analysis:
- those results were an upper limit

## non-flow evident

- width depends on the track sample
- differences are due to more or less non-flow in various samples
- smaller 2 for like-sign (charge ordering)
- larger 2 for small  (strong short range correlations)

- also in 2-D correlations: can be fit with a  independent cos(2) term + non-flow structures

*See STAR Talk: Michael Daugherity*

*STAR Preliminary*

*N.B. relationship of measured ****2** from 2 particle correlations and dynamic width is not trivial: depends on ZYAM and 2-component model (see backup slides)*

## dynamic width from dN/dq fit

-  includes systematic errors from comparisons to cumulants
-  minimum 2 derived from differences between subevents [q*q] - [q+*q-]

- see *Miller, Snellings, nucl-ex/0312008*

## mean and width of ƒ(v2)

- analysis places an upper limit on flow fluctuations

## comparison to models

- upper limit challenges models

- confined quark MC:
- treats confined constituent quarks as the participants
- decreases eccentricity fluctuations
- color glass MC:
- includes effects of saturation
- increases the mean eccentricity

- comparison to hydro (NexSPheRio): *Hama et.al. arXiv:0711.4544*
- eccentricity fluctuations from CGC: *Drescher, Nara. Phys.Rev.C76:041903,2007*
- extraction of Knudsen number: *Vogel, Torrieri, Bleicher. nucl-th/0703031*
- fluctuating initial conditions: *Broniowski, Bozek, Rybczynski. Phys.Rev.C76:054905,2007*
- first disagreement with standard and use of quark MC: *Miller, Snellings. nucl-ex/0312008*

## can we eliminate v2 = 0?

- can we eliminate v2 = 0?

- is there any evidence for v2 changing event-to-event?

- consider events containing two high-pT tracks (pT>2 GeV/c)
-  is the average v2(pT<2 GeV/c) still the same in this sample?
-  or when the high pT tracks are correlated at large ? or small ?
-  or when the tracks are uncorrelated?

- dN/dq for low pT tracks vs  for the high pT leading hadrons
**shape of the q-distribution for underlying event has non-trivial dependence on ******** and ******** of the leading and next-to-leading hadron**

- STAR Preliminary

## event classes?

- characteristics of the events yielding a “ridge pair” appear to be very different from those yielding a “jet pair”

-  inferred v2 for events associated with “ridge” pairs is large
-  inferred v2 for events associated with “jet” pairs is small
-  this conclusion is a direct consequence of the zero-yield at minimum assumption and the 3-component model: *(v**2** modulated background + ridge + jet)*

- “ridge”

- “jet”

- STAR Preliminary

*See STAR Poster: Navneet Kumar Pruthi*

-  the “ridge” is calculated by projecting ||>0.7 correlation to ||<0.7
-  the “jet” is the remaining correlation at ||<0.7 after subtracting the “ridge”

## event classes?

- events yielding a “ridge”-like pair have large v2
- events yielding a “jet”-like pair have small v2

- possible interpretations:
-  interactions of a jet with the medium and medium response to a jet (radial flow coupling to a jet *C.Pruneau, nucl-ex/0711.1991*)
-  do initial state quantum fluctuations lead to:
- instabilities and growth of strong color fields *M. Strickland, hep-ph/0511212*
- large q^ and small /s *Majumder, Muller, Bass. Phys.Rev.Lett.99:042301,2007*
- un-quenched jets can preferentially come from events fluctuating towards small q^ and large /s (small flow)?
- strong fields lead to the ridge **and** large v2?
-  what about jets on the periphery? and tangential jets? momentum conservation effects?

## summary

- we find that the case of zero v2 fluctuations cannot be excluded with dN/dq without knowledge of non-flow, cluster flow, and non-poissonian multiplicity fluctuations
- analysis places stringent constraints on 2, v2, and v2:
-  when one parameter is specified, the others are fixed
- measurement challenges standard Monte-Carlo Glauber models:
-  upper limit is below standard nucleon MC Glauber
-  upper limit coincides with participating nucleon eccentricity fluctuations
-  nucleon MC Glauber: leaves no room for other sources of fluctuations & correlations
- Is there any evidence that v2 fluctuates? Not from untriggered dN/dq but analysis of high pT triggered events seems to indicate non-zero v2.

## the following is back-up material

## the statistical decomposition

- decomposition into events that yielded:
-  uncorrelated high pT pairs
-  correlated and ridge-like high-pT pairs
-  correlated and jet-like high-pT pairs

-  each bin has a different signal to background ratio.
-  analyze the q-distribution of events contributing to each bin
-  algebraically solve for the q-distribution of signal and background separately

## acceptance effects

- acceptance effects could mimic correlations unrelated to the event plane
- easy to quantify using simulations run through a TPC filter
- quantified systematics from CLT approximation

- about 4%

## relationship to 2-particle corr.

## more about 2-particle correlations

- zyam b makes 2 too small

- simple case: v2=0.00
- 2 should be the width of the q-distribution

- vary b until
- 2+2v2 matches q width

## more about 2-particle correlations

- vary b until
- 2+2v2 matches q width

- zyam b makes 2 too small

- add some fluctuations: v2=0.010
- 2 should be smaller

## more about 2-particle correlations

- vary b until
- 2+2v2 matches q width

- zyam b makes 2 too small

- add some fluctuations: v2=0.015
- 2 should be smaller

## more about 2-particle correlations

- vary b until
- 2+2v2 matches q width

- zyam b makes 2 too small

- add some fluctuations: v2=0.020
- 2 should be smaller

## more about 2-particle correlations

- vary b until
- 2+2v2 matches q width

- zyam b makes 2 too small

- add some fluctuations: v2=0.025
- 2 should be smaller

## more about 2-particle correlations

- vary b until
- 2+2v2 matches q width

- zyam b makes 2 too small

- add huge fluctuations: v2=0.045
- 2 should be smaller

- v2{2} = 5.154e-02
- v2{4} = 4.093e-02
- <v2> = 6.083e-02
- v2{2} = sqrt(<v2>^2 + sigv^2 + delta) = 5.202e-02
- sigv/<v2> = 73.98%

## more about 2-particle correlations

- huge v2
- and negative 2

- the subtracted yield

- add huge fluctuations: v2=0.045
- 2 is now negative

## what’s going on

- 2 observed in two-component model depends on jet-flow
- difference between simulated 2 and observed 2 depends on cluster flow
- there are still more variables that can come into play
-  highly probable that multiple solutions could match the STAR data

## compared to autocorrelation 2D fit

- difference between 2-D fit and projection over all autocorrelations
-  introduces dependence on function used to fit the data

- !! words of caution about inter-analysis comparisons !!
**be careful**

## comparison to Estruct

- let’s see what happens if we take those values for 2

## v2 and v2

- v2 and v2

- STAR Preliminary

- caution! not necessarily a consistent picture yet

- with fit to autocorrelations

## comparison to geometric 

- comparison to geometric 

- fluctuations from finite bin widths have not been removed yet
- likely to reduce ratio below the model!

- STAR Preliminary

- systematic uncertainties are still large and under investigation

## confined quark monte carlo

- models of the initial conditions are not trivial

## introduction

- motivation for this study
-  use v2 fluctuations to try to access information about initial geometry: distinguish between models of initial conditions
-  reduce systematic errors on v2
- results from 200 GeV Au+Au collisions
-  analysis procedures and change in QM06 conclusions
-  non-flow 2 and v2 from the q-distribution
-  comparison to cumulants v{2}, v{4}
-  v2 of events with a “ridge” and/or a “jet”!

*See STAR Poster: Navneet Kumar Pruthi*