Thomas D. Gutierrez UC Davis 1 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Bose-Einstein...

Thomas D. GutierrezUC Davis

1

Wednesday April 30, 2003

UCD Nuclear Physics Seminar

Bose-Einstein Correlations from pp Collisions at RHICThomas D. Gutierrez

University of California, Davis

• Introduction• Analysis• Results• Outlook



2



What are Bose-Einstein Correlations?

Bose-Einstein correlations (BEC) are a joint measurement of more than one boson in some variable of interest.

P2

P1

L >> (d & R)

d

R

rA1

rB1

rA2

rB2

In its simplest form, BEC often predictsan enhancement of boson coincident counts (relative

to the experiment performed with non-bosons). This is usually associated

with Bose-Einstein statistics.But things are rarely this simple.

For example, if the variable of interest is momentum then information about the geometry of boson emission source

can be obtained (more on this later)

BEC often goes under the name HBT or GGLP. I’ll use HBT.


3



What is HBT?

The technique was originally developed by two English astronomers Robert Hanbury-Brown and Richard Twiss (circa 1952)

It’s a form of “Intensity Interferometry”-- as opposed to “regular” amplitude-level(Young or Michelson) interferometry --

and was used to measure the angular sizes of stars

A quantum treatment of HBT generated much controversy and led to a revolution in quantum optics

Later it was used by high energy physicists to measure source sizes of elementary particle or heavy ion collisions (the GGLP effect)

But how does HBT work? And why use it instead of “regular” interferometry?


4



Two slit interference (between coherent sources at A and B)

P1

L >> d

Monochromatic Source

Plane wave

d

A

B

rA1

rB1

sin11 drr AB

)])(cos[1(2|| 112

111

ABrkirki

P rrkeeI BA

“source geometry”(d) is related to interference pattern

11 PP II (brackets indicate time average -- which is what is usually measured)

2

k


5



Two monochromatic but incoherent sources

(i.e.with random, time dependent phase)produce no interference pattern

at the screen -- assuming we time-average

our measurement over manyfluctuations

)])()(cos[1(2|| 112)()(

111

ABABtirkitirki

P rrkeeI BBAA L >> d

A

B

rA1

rB1

P1

21 PI (brackets again indicate time average)

“Two slit interference” (between incoherent sources at A and B)

d


6



2)()(1 || 11 tirkitirkiP

BBAA eeI

2)()(2 || 22 tirkitirkiP

BBAA eeI

21 PI 22 PI

As before...

HBT Example (incoherent sources)

)](cos[24 2121 rrkII PP

But if we take the product before time averaging...

)( 221121 BABA rrrrrr

where

A

B

P2

P1

L >> (d & R)

d

R

rA1

rB1

rA2

rB2

Important: The random phase terms completely dropped out.We can extract information about the source geometry!


7



21

21

II

IIC

])cos[(2

11 RkC

]cos[2

11 QdC

Increasing angular size

Increasing source size d

Particle physics

Astronomy

Notice that the “widths” of these correlation functions are inversely related to the source geometry

For fixed k

A source can also be a continuous distributionrather than just points

Width wsource

Width ~1/wCorrelation function

The width of the correlation function will have a similar inverse relation to

the source size

I’ll drop

21

21

II

IIC


8



More About HBT

As we’ve seen, when treated with classical waves, HBT is basically just a kind of beat phenomenon

When treated quantum mechanically (i.e. actually counting particles)the situation is more complex

3

233

13

32

31

6

2211

1212

21

212

// dpNddpNd

dpdpNd

aaTraaTr

aaaaTr

II

IIC

pppp

pppp

Lets define the two particle correlation function as:

The density matrix in the second expression tells us two very important things:

C2 is sensitive not only to the quantum statistics (determined by the commutation relations of the a and a’)

but also the quantum field configuration;

C2 is sensitive to the source distribution, the dynamics of the problem,as well as any space-momentum correlations


9



Sill more about HBT

C2

Q=|p1-p2|

1/R

Thermal Bosons

1

2

Partly coherent bosons+thermal+contamination

0Non-interacting fermions

Two quantum field configurations of interest:coherent state (like a “laser”) and thermal state (following a Bose-Einstein distribution)

Momentum difference

1

0

1

1

Totally coherent

)2()1(

)2|1(2

PP

PC

Joint probability of measuring a particle at both detectors 1 and 2

Probability of measurement at 1 timesprobability of a measurement at 2

Measuring the correlationfunction is really just a

counting game

Note: if the two measurements are statistically independent then C2=1

22RQλe1C(Q)

1)0( QCChaoticity parameter

C2 is often measured as a function of the momentumdifference and can often be parameterized like a Gaussian:


10



Practicalities of HBT Interferomertry using particles in HEP

• Compare relative 4-momenta (Qinv) of identical particles (e.g. pions) to determine information about space-time geometry of source.

• Experimentally, 1D C2 correlation functions are created by comparing relative 4-momenta of pairs from a “real” event signal to pairs from “mixed” events.

• The mixed background presumably has no HBT signal!

STAR PreliminarySTAR Preliminary

2212

2121 ppEEppQinv


11



More HBT practicalities in HEP

•The correlation function, C2, is created by dividing the “real” pairs by “mixed” pairs. The histogram is then normalized to the baseline. •The data are fit to a Gaussian or an exponential to extract fit parameters Rinv

and λ.

~1/R

~λe

The Coulomb repulsion experienced

by identical charged pairs tends to depletethe correlation function at low Q

-- this can be corrected

Both fits are to the Coulomb corrected

data (dark blue)

STAR Preliminary

=0.397 +/- 0.013;

Rg=1.16 fm +/- 0.032;

=0.749 +/- 0.030;

Re=1.94 fm +/- 0.071

g

e

C2g = 1 + λexp(-Qinv2Rinv

2)

C2e = 1 + λexp(-QinvRinv)


12



Why study HBT in pp Collisions?

• There is a long history of doing Bose-Einstein pion correlations in elementary particle collisions

• In the context of RHIC, it provides a baseline for the heavy ion results

•Dowell., Proc. Of the VII Topical Workshop on Proton-AntiProton Collider Physics, p115, Word Scientific 1989.

•Lindsey. “Results from E735 at the Tevetron Proton-AntiProton Collider with root s= 1.8TeV”, Presented at the Quarkmatter 1991, Gatlinberg, Tennessee, Nov 11-15, 1991.

•OPAL Collaboration. Physics Letters B. Vol 267 #1, 5 September, 1991.

•NA22 Collaboration “Estimation of Hydrodynamical model parameters from the invariant spectrum and the Bose-Einstein Corrilations…”, Nijmegen preprint, HEN-405, Dec. 97.

NA22

AMY

OPAL

UA1

E735π+/p

e+/e-p/pbar

Just a sampling

fm


13



What is HBT Actually Measuring?

Quark scattering and creation

P T

z

t

N K

Hadronization “freeze out”surface (mean)

For non-static sources, HBT becomes sensitive toregions of homogeneity; this gives

rise to a phase space dependence of the radii

HBT radii will often be muchsmaller than actual

hadronizationsurface

y1 y2

In this 1D inside-out fragmentation picture,rapidity and z are correlated. Particles

near each other in rapidity, will alsobe near each other in space.

Particles close in space and momentum contributemost strongly to the HBT signal

Regions of Homogeneity


14



HBT Study of the pp System

• HBT studies in pp interactions provide a peek into the fascinating soft-physics regime of hadronic collisions

• Some HBT-related questions:

• What do the regions of homogeneity look like?

• What is the pair source distribution function?

• How do the HBT parameters depend on event multiplicity?

• Do the HBT parameters depend on the polarization of the initial state (a fun idea but won’t have time to talk about it today)?

This analysis is a first step in answering some of these questions


15



The STAR Experiment

STAR main detector: Time Projection Chamber (a large-acceptance cylindrical detector)

E field and B field along the beam direction.

12 million reversed full field and full field,minimum bias pp events at 200GeV from RHIC using the STAR detector; some datapresented include only the 7 million RFF

Particle identification done by measureingdE/dx (specific energy loss)


16



Track and Event Selection (I)

•For negative and positive pions at two mid-rapidity ranges (-0.5<y<0.5; -

1<y<1), four kt ranges were analyzed (0.15<kt<0.25,

0.25<kt<0.35, 0.35<kt<0.45, 0.45<kt<0.65 GeV/c)

•Particle identification was done by taking a one sigma cut around the pion bethe-

bloch curve while excluding other particles at the two

sigma level.

dEdx vs. P (GeV/c)

e

K

P

similar

STAR Preliminary

Kt is the average PAIR transverse moment

Y is the TRACK rapidity


17



Track and Event Selection (II)Some additional cuts used for this analysis

• Verices accepted 3m across the STAR TPC

• Analysis done separately for 20cm wide regions (results then added)

• For the non-multiplicity dependent analyses: event Multiplicity < 30

• Analysis performed separately for like-multiplicity events (results then added)

•Only accept events with at least 2 tracks

Track level

-0.5 < y < 0.5 and -1<y<1

•PID cuts as discussed

•Primary tracks only

Pair level

Four kt bins between: 0.15 < kt <0.65 GeV/c

anti-merging and anti-splitting cuts applied

fail

pass

zvertex

The effects of pileup in pp have not yet been studied in

the context of HBT

The first order effect would be to reduce the lambda factor

(a pileup would act like a mixed eventthus “watering down” the signal)

STAR Preliminary


18



Pair Cuts (I): Track Merging

looks similar

The above correlation functions are a measure of track merging (2 tracks mistaken as one) relative to a mixed background which presumably has no track merging

Accept >9cm Accept > 9cm

-0.5<y<0.5 -1<y<1

0.15 < kt <0.65 GeV/c for Qinv<0.2 GeV/c

STAR PreliminarySTAR Preliminary


19



Pair Cuts (II): Track Splitting

Accept -0.5<Quality<0.6

-0.5<y<0.5

0.15 < kt <0.65 GeV/c

hitsofnumberTotal

hitswithPADShitwithPADSQuality

21

Qual~0 no splitting

(really DO have 2 tracks)

Qual=1 totally split

(one track mistaken as 2)

Pads with two hits are circled

The above correlation function is a measure of the quality relative to a mixed background.

The mixed background presumably has no splitting (high quality means more splitting)

Splitting is when one track is mistaken as 2

and +/- 1 y looks similar

STAR Preliminary


20



1D Qinv Correlation Functions (I)

All fits are to the Coulomb corrected data:

All plots here0.15<kt<0.25 GeV

The pi+ pi- combined

over -1<y<1 will serve

as the standard

All STAR Preliminary


21



1d Qinv Correlation Functions (II)

All plots here0.15<kt<0.25 GeV;

-1<y<1;pi+ and pi-

The strength of this high Qinv tail depends on the

kinematic cuts; The effect is currently under study

The traditional Gaussian fit (black)

isn’t very good;The exponential fits do

much better;various parameterizations

are under study



22



1D Qinv Correlation Functions (III)


Baseline curvature depends only very weaklyon particle species and zvertex choices;

depends more strongly on rapidity and kt cuts;Still a rather small effect overall

The current hypothesis is that the effectis due to energy-momentum conservation

Pythia pi- (no afterburner);0.15<pt<1.1;-0.5<y<0.5;1M events;

ignore normalization;

evidence of some sloping;will perform a

more systematic study

Qinv

C2



23



1D Qinv HBT Parameters

1.02+/-0.011 1.81+/-0.023 1.62+/-0.037 1.96+/-0.095

0.426+/-0.007

0.803+/-0.014

0.780+/-0.014

0.684+/-0.022

- - - -0.232+/-0.042

- - 0.032+/-0.005

0.184+/-0.029

R (fm)

)1(22QR

g eC )1( QRe eC )1( 2

1 QB )1( 22 QQB

gC eC 1*BCe 2*BCe

All are from0.15<kt<0.25 GeV;

-1<y<1;pi+ and pi-

Highly parameterization dependent values = bad


24



Source Image

Another interesting way to approach HBT is one can transform the correlation function to obtain the actual source numerically

1)(4)( 0

2

2211

12122

drKrSraaTraaTr

aaaaTrQinvC

pppp

pppp

S is the source distribution and represents the probability of emitting a pair of particleswith relative 4-momentum=Qinv separated by a distance r;

S is the quantity we want to extract

Thermal limit: Koonin-Pratt equation

K0 is the angle averaged integration kernel and is given by

drqK 1),(4

1 2

0 is the pair wavefunction and includes all the appropriate quantum statistics and

relevant interactions between the pair


25



Source Image

Qinv r (fm)

Reconstructed correlation function;

red is the non- Coulomb corrected

input Qinv Correlation function

Pair source emission function S(r);

log scale

Generated using Brown and Danielewicz's HBTprogs v.1.0

0.15<kt<0.25;-0.5<y<0.5;

pi- Qinv

`

The different colors represent different parameters in the HBTprogs program

Is there a double Gaussian structure in the source function?More work needs to be done to really determine this.

log(S)C2 STAR Preliminary

A promising method: still a work in progress


26



3D Correlation Functions

y

x

1Tp

2Tp

21 TTT ppK

21 TTT ppp

y

x

Tp

Toutout KQQ ˆ

Tsideside KQQ ˆ

TK

|ˆ| TTout KpQ

TTside KpQ ˆ

21 zzlong ppQ

By looking at a 3D correlation function wecan extract a more complete picture of the source.


27



3D Correlation Functions

C2 = N[1 + λexp(-qout2Rout

2 -qside2Rside

2 -qlong2Rlong

2)]Fits and correlations projected 80MeV in the “other” directions

kt cut with ~0.15 GeV/c pid pt cutcauses Qout “hole”

out side long

C2


-1<y<1;pi+ and pi-

y cuts cause Qlong“cutoff”



28



3D Correlation Parameters

C2 = N[1 + λexp(-qout2Rout

2 -qside2Rside

2 -qlong2Rlong

2)]

0.411+/-0.008

0.728+/-0.047

0.969+/-0.012

1.13+/-0.020

Rout

Rside

Rlong

0.15<kt<0.25 GeV;-1<y<1;

pi+ and pi-


29



3D Correlation Functions: kt dependence

kt kt

R(fm) RlongRsideRout

What causes kt dependence?

STAR PreliminaryCentral

Midcentral

Peripheral

AuAu 200GeV

22TT kmm

M. Lopez-Noriega QM2002


30



What Causes Kt Dependence?

RsideRout

Kt = pair Pt

Space momentum correlationsSpace momentum correlationsSpace momentum correlations

If the source is not static or collective effects are presentthen space-momentum correlations can develop and cause

the radii to change as you look in different locationsin phase space.

Some examplesInside-out fragmentation/ hadronization

jets (the ultimate space-momentum correlation)fireball-like expansion

collective flowNot all of these will give thesame kt dependence. The

trick is in distinguishing between them. This is currently under study

We are looking at a region of homogeneity caused by:


31



Multiplicity Dependence of HBT parameters

It has been reported by some experiments (e.g. UA1 ppbar at 630 GeV) that lambda tends to drop with

event multiplicity while the radius increases slowly

Other experiments (e.g. NA27 pp at 27 GeV) report that lambda is flat as a function of event multiplicity

This puzzle has numerous explanations from the mundane to the exotic.Some current speculations:

All of the above would have the tendency to reduce lambda

Pion emission becomes more coherent in high multiplicity events involvingparticle-antiparticle collisions but not particle-particle

High multiplicity events from ppbar may involve multistring fragmentation -- pions from different strings will not correlate strongly

Resonance contributions and other contaminates may contributeto different degrees at different multiplicities at different experiments


32



Multiplicity dependence of 1D HBT

UA1 ppbar 630 GeV (Gaussian)

NA27 pp 27 GeV (Gaussian)

STAR Gaussian

STAR Exponential

charged

This preliminary STAR pp result indicates

lambda is flat as a functionof event multiplicity

This is clearly not the caseat UA1

NA27, NA23, and NA22 all reported

similar results

Using full RFF+FF

•NA27 ZPC 54,21 1992

•UA1 PLB 226, 410, 1989

Low multiplicity bins (<4) have large systematic error bars -- still being studied

Very Important: Not corrected for resonances or efficiency

STAR Preliminary


33



Multiplicity Dependence of 1D Radius

•NA27 ZPC 54,21 1992

•UA1 PLB 226, 410, 1989This preliminary STAR

pp result indicatesrinv is flat as a function

of event multiplicity

Low multiplicity bins (<4) have large systematic error bars -- still being studied

Very Important: Not corrected for resonances or efficiency

STAR Exponential

STAR Gaussian

STAR Preliminary


34



Summary

Bose-Einstein correlations provide a means of probingthe space-time geometry of the pion emission source in high energy collisions;

The pion emission source size is ~1 fm

A kt dependence is seen in the 3D HBT parameters of pp collisionsindicating a pion source with space-momentum correlations;

The nature of ths source is still under study

Lambda and rinv are constant as a function of event multiplicity;

This is consistent with other pp experimentsbut differ from ppbar results;The effect is still under study

Thomas D. Gutierrez UC Davis 1 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Bose-Einstein...

Documents

Transcript of Thomas D. Gutierrez UC Davis 1 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Bose-Einstein...