Measurement of Bose-Einstein correlations in the first LHC-CMS data

1

Luca PerrozziINFN Padova

on behalf of the CMS Collaboration

WPCF2010, 14-18 June, Kiev

Measurement of Bose-Einstein correlations

in the first LHC-CMS data

WPCF2010, 14-18 September, Kiev2

P1

L >> d

Monochromatic Source

Plane waved

A

B

rA1

rB1

sin11 drr AB

21 || 11 BA rkirkiP eeI

Particles

Introduction

)2,1()2,1()2,1( BAAB

BA xipB

xipABAAB efef 21)2()1()2,1(

)])(cos[1(2 11 AB rrk

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

Optics

The (symmetric) wave-function of identical bosons produced in High-Energy Collision overlaps: Bose-Einstein statisticschanges their dynamics (a.k.a. Hanbury Brown-Twiss, HBT)

p1 p2

A BFor four-momenta small differences, enhancement of the correlation function should be observed


)cos()(

21222

22

21

12 pxff

ffR

BA

BA

22221

2 4)( mMppQ inv

Introduction

)cos(2)(|)2,1(| 22222212 pxffff BABA

)1)((1)( QQrQR

for incoherent sources the joint mean time probability

The correlation function is defined as the ratio:

joint prob. for identical boson emission

independent prob. for identical boson emission R

Experimentally the proximity in phase space can be quantified by the Lorentz-inv. parametrization

• is the Fourier transform of the spatial distribution of the emission region (static models)

• is the strength of the emission source

• r is the radius of the emission source

• accounts for long range Q correlations

r

gives the following correlation function:


IntroductionThe Bose-Einstein correlation was observed for the fist time by Goldhaber (1960)

in proton-antiproton interactions at √s = 2.1 GeV

Several measurements have been reported by different experiments

The most appropriate (Q) function, the value of the correlation source radius r and

the their dependences (i.e. from √s or from the charged-particle multiplicity) are still

open questions.

For the first time we measured the Bose-Einstein correlation in proton-proton collisions

at √s = 900 GeV and √s = 2.36 TeV (December 2009 LHC-CMS data)

√s Min. Bias sel. events # tracks # sel. tracks # sel. pairs

900 GeV ~ 280 k ~ 5500 k ~ 2900 k ~ 11 M

2.36 TeV ~ 14 k ~ 360 k ~ 190 k ~ 1 M


CMS Inner Tracker


Reference samplesR(Q) is measured by dividing:

dQdN

dQdNQR

reference

signal

/

/)(the distribution of pairs of the same charge

a similar distribution with non interfering track pairs

We considered pairs from 7 reference samples:

1. opposite charge (natural choice but contains resonances)

2. opposite hemisphere same charge ( p → -p for one track)

3. opposite hemisphere opposite charge

4. rotated ( [px , py , pz] → [-px , -py , pz] for one track )

5. mixed events (random)

6. mixed events (similar multiplicity)

7. mixed events (similar invariant mass of all charged particles)


Reference samplesAs an example the ratio R(Q) obtained with:

2. opposite-hemisphere same charge

shows a significant excess at small Q values

(in the default MC the Bose-Einstein correlation is not simulated)

PRL 105, 032001 (2010)R (Q)dN/dQ


Coulomb interactionsCoulomb interactions modify the relative momentum pair distribution following the Gamow factors (not simulated in the Monte Carlo):

same charge: Ws= (e2 -1) / 2

different charge: WD= (1-e2) / 2

different charge before Gamow correction after Gamow correction (WD)

The Gamow factor correction is tested with the different charge distribution

and applied to the same charge and different charge distributions

Q

mem

dQdN

dQdN

MC

data

/

/


Double ratioIn order to reduce the bias due to the construction of the reference samples

a double ratio R is defined:

dQdN

dQdN

dQdN

dQdN

R

R

referenceMC

likesignalMC

reference

signal

MC

/

/

/

/

,

,

R

R (single ratio) R (double ratio)CMS PAS QCD-10-003 CMS PAS QCD-10-003


Check 1: reconstruction bias

Pythia includes the functionality to simulate the Bose-Einstein correlation.

To check against possible biases due to the reconstruction we compared the

fitted parameters in the generated tracks and reconstructed tracks

ReconstructedGenerated

Dedicated Monte Carlo: MSTJ(51)=1 PARJ(92)=0.9 PARJ(93)=0.125


Check 2: particle identification

The signal sample is a pair combination between tracks with same charge.

As a cross check the dE/dx measurements are used to select

• enriched sample

• another sample with and non- candidates

R (using dE/dx) dE/dxPRL 105, 032001 (2010)


ParametrizationDifferent (Q) functions where tested

(Exponential, Gaussian, Levy, Kozlov Gaussian, Kozlov exponential)

Gaussian form (Q) = exp [ -(Qr)2 ]Exponential form (Q) = exp (-Qr)

CMS PAS QCD-10-003 CMS PAS QCD-10-003


R(Q) for all reference sample @ 900 GeV

Exponential form (Q) = exp (-Qr)

How to “combine” them ?


Combined reference sampleThe parameters of the correlation function

were obtained using a “combined “ reference sample

r.m.s. from each individual fit provides the systematic error contribution

)1)((1)( QQrQR

7

1 _i irefcombdQ

dN

dQ

dN

Combined reference sample

Gaussian and exponential fit

900 GeV

2.36 TeV

PRL 105, 032001 (2010)


ResultsSystematics:

± 7% for λ ± 12% for rSeveral reference samples none is perfect

The Coulomb interactions were considered with the Gamow factor corrections. The estimated uncertainty for WS is ±15%

± 2.8% for λ ± 0.8% for r

Measurement @ 900 GeV Measurement @ 2.36 TeV

λ = 0.625 ± 0.021stat ± 0.046sys

r = 1.59 ± 0.05stat ± 0.19sys

λ = 0.662 ± 0.073stat ± 0.048sys

r = 1.99 ± 0.18stat ± 0.24sys


ResultsComparison with previous measurements

Most of the previous experiments

provided r measurement with a

“traditional” Gaussian fit.

The comparison can be done

between first momentum

with a scale factor √ :

rQ

1exp

rQ gauss

1

PS: We performed the analysis also on 7 TeV data• Results are still not public• We would like to understand in deeper detail some results• Hopefully we will have a new document in the next months

Stay tuned!


Dependencies

arXiv:1005.3294v1

Small dependence of λ from NCH

Significant increase of the size of the emission region r as the charged track multiplicity increases

Charged track multiplicity dependence


Conclusions• The signal of the Bose-Einstein correlation has been observed for

the first time in proton-proton collisions at √s of 900 GeV and 2.36 TeV

• the exponential form (Q) = exp (-Qr) fits the data significantly better

with respect to the Gaussian form

• the radius of the emission source measured from the fit is

r = 1.59 ± 0.2 (900 GeV) r = 1.99 ± 0.3 (2.36 TeV)

• an increase of the parameter r with charged-particle multiplicity in the

event is observed

The result have been published on PRL

(DOI: 10.1103/PhysRevLett.105.032001) URL: http://link.aps.org/doi/10.1103/PhysRevLett.105.032001


Backup slides


Event and track selectionEvent selection

Charged particles are selected to increase their purity, ensure good two-track separation and remove pathologies:

• Ndof > 5

• “track high purity” selection

• pt > 200 MeV/c

• fit χ2 < 5

• |ηtrack| < 2.4

• |dxy| BS < 0.15 cm (transverse impact parameter w.r.t. the collision point)

• Rxy < 20 cm (first measured hit w.r.t. the primary vertex)

Track selection

The events were selected by requiring activity in both CMS beam scintillator counters


Previuos experiments: table


Detailed results @ 900 GeV


Detailed results @ 2.36 TeV

Documents

Measurement of Bose-Einstein correlations in the first LHC-CMS data