on the Δ t time scale in bose-einstein and fermi-dirac correlations

On the Δt time scalein Bose-Einstein and Fermi-Dirac correlations

Gideon Alexander and Erez Reinherz-Aronis

Tel-Aviv University

OUTLINE

1. A brief introduction

3. A closer look at Δt

2. R1D from Z0 decays

4. Δt as the particle emission time

5. It’s consequence to heavy ions

arXiv: 0910.0138 [hep-ph]

6. Comments and remarks

WPCF 2009

G. Alexander, E. Reinherz-Aronis

Bose-Einstein Correlation (BEC)-Reminder

1-Dimension analysisof two identical bosons

2 1, 22 1 2

1 1 2 2

( )( , )

( ) ( )

p pC p p

p p

22221

22 4)( BBB mMppQ

Correlation function:

GGLP variable:

2 21 2

22 2( ) 1 DR QC Q e 1

1nnR nR


Taken from WA98 collaboration (2007)arXiv 0709.2477

π± π± BEC from heavy nuclei – dependence on A

Note: only few BEC of K-pairs

R vs. the target A1/3

1 / 31DR ( m ) ( 0.91 0.02 ) A fm


The extension to Fermi-Dirac Correlation for di-fermions

2. The phase space density approach (Pauli Exclusion principle)

Like in the BEC analysis one considers the density of the identical baryon pairs as Q 0

2 2 2 2s 2 R Q a 2 R Q

1,2 1,2| | 1 e and | | 1 e 2 22

1,2R Q| | 1 0.5e

ΛΛ FDC Three referencesamples

Aleph

P.L. B475 (00) 395

No need forCoulomb correction!

1 .ΛΛ Spin-Spin correlation (Alexander & Lipkin P.L. B352 (1995) 162)

Does not need a reference sample nor Coulomb correction


R1D (m) from BEC and FDC analysesof the Z0 hadronic decays at LEP


R(m) derived from the Heisenberg uncertainty relations[G.Alexander, I.Cohen, E.Levin, Phys. Lett. B452 (99) 159, G.Alexander, Phys.Lett. B506 (2001) 45]

The two bosons are near threshold in their CMS, i.e. non-relativistic

2c

p R c vR mvR Rp

2

2 / /p

E t t p m t p m tm

1D

hc/ /Δt c ΔtR (m)= =

m m

It was further assumed that:

1) Δt

2) ΔE

3) RΔR

Represents the interaction strength i.e.~10-24 sec for S.I.

Depends on the kinetic energy i.e. potential energy is small

Note: For m≠0


R1D (m) from BEC and FDC analysesof the Z0 hadronic decays at LEP

Uncertainty relations

1 /DR c t m

For S.I. QCD potential

r

crV S

3

4

fmGeV /7.0

)/87.12ln(9

2

rS

24(1 0.5) 10 st -D = ± ´


Application of the Bjorken-Gottfried relation to R(mT)

There exists a linear relation qµ=λxµ between the 4-momentum and the time-space which implies λ=mT/τ

where τ=(t2-z2)0.5 is the longitudinal proper time

mT [GeV]

Bialas et al. P.R. D62 (00) 114007 ;

Bialas et al. Acta Phys. Polon. B32 (01) 2901

2 20T T

Transverse mass

m m p

0: 0T TJust note m m when P


Question: Is this m dependence of R unique to the Z decays ?WA98 Collaboration (2007); arXiv:0709.2477

Central Pb +Pb collisions at 158 GeV/A

Δt=(1.28±0.04)x10-22 sec

1/ 2

1

(2.75 0.04)( )

( )D

Const fmGeVR m

m m GeV

1st time BEC of di-deuteron


Δt=10 -24 sec

Δt=10 -19 sec

Δt=10 -12 sec

π K p,Λ

Q: Is Δt a measure of the interaction strengthof the two identical outgoing particles?

R1D as a function of m and Δt

Unfortunately so far no systematic

BEC or FDC of WI particles

have been measured !

Aggarwal et al. (WA98) PRL 93 (04) 022301

γγ BEC in Pb + Pb at 158 GeV/A

π

100<KT <200 MeV

200<KT <300 MeV

1

1

5.4 0.8 0.9

5.8 0.8 1.2

ID

IID

R fm

R fm

Aggarwal et al. (WA98) arXiv:0709.2477

R ) long

long T

T

c Δt(m ≈

m

[G. Alexander, P.L. B506 (2001) 45]

Δtlong=(1.61±0.05)x10-22 sec


Thus we assign Δt as a measure of the particle emission time

1D

c tR m

m

0 25 24: 10 10 sec ZFor Z decay to

Z0 Hadronic decay


As a next steplet us relate the R dependence on A

13

1DR m aA

a=0.91 fm

with

1D

c tR m

m


22

32

m at A

c

To get the particle emission time which depends on the

surface area of the nucleus

Question: Does it have an energy dependence?

NA49 Collaboration, P.R. C77 (2008) 064908 found that

3

20, 30, 40, 80, 158 /

( )D

In Pb Pb collisions at and GeV A

the R m values change very little if at all


Particle emission time Δt vs the Atomic number A

Δt(A=1)=Δt(proton)=2.4x10-24 sec for a=1 fm[Data from: WA80, WA98, STAR Collaborations and from Chacon et. al,. (1991)]

22

32

m at A

c

a=1.2 fm

a=0.8 fm

a=1 fm

From measured Rcalculate

2

2

( )m R mt

c

and insert


Comments and remarks

2) One should have more BEC and FDC analyzes like that of WA98

3) In heavy ion collisions Heisenberg derived formulae are applied

1) Δt is attributed to the particles’ emission time

4) A simple merge of the 1D Heisenberg derived formula with R vs A

22/

23 23 2 2; 1 , 10 10 secfor A and

m at A

ca fm t is to

5) Consistent with the data

7) An extension of this work from 1D to 3D should be explored

6) The Δt dependence on A2/3 e.g. Fireball shell model ?


Experimental opportunity may be offered by the SLHC pp Z0Z0 + X data

Comments and remarks (con’t)

8) FDC of directly produced e±e±/µ±µ± are unlikely to be measured

9) An attractive possibility may be the BEC study of Z0Z0 pairs

a) It is a BEC of weak interacting particles (what is its Δt value?)

b) R determination of a very high mass boson

c) No Coulomb correction

Because :

7) BEC and/or FDC for WI particles are of interest to measure


Pythia MC study of ppZ0Z0 at 14 TeV

Monte Carlopp->ZZ->4ℓ (ℓ= e/μ)Pythia 6.403, CTEQ 6L1

Generated events (study sample)~69000Equivalent to 1200 fb-1

Expected generated events (100 1/fb) 5600

Major selection cuts:pT > 20 GeVAt least 1 μ

2 lepton pairs

Invariant mass cut (for both)74 GeV <Mz<110 GeV

Pythia includes the Z’s width

Detection efficiency after detector simulation

~25%

Fraction of the ZZ->4ℓ (ℓ=e or μ) decay ~0.36%Fraction of Z->Jets Z->2ℓ (ℓ= e or μ) decay ~9.32%


Pythia MC study of ppZ0Z0 at 14 TeV

One parameter fit: R1D=0.019 ± 0.006 fm24

110 sec ( ) 0.025D ZFor t one expects R m fm


Last remark

MANY THANKS FOR YOUR ATTENTION

0 /e e Z qq hadrons


Backup slides


Energy density of the hadron emitter

3.exp

2

4

3

h

h

r

m

2/33

2/5

mode )(2

3

tc

mhl

Z0 hadrons

[Dashed lines for sec]10)3.032.1( 24t

[A simple minded approach , G. Alexander. RPP 66 (03) 481]


Baryon production in the Lund Model

See e.g., Delgado, Gustafson, Lönnblad, (LUND group)

Eur. Phys. J.C. 52 (2007) 113

on the Δ t time scale in bose-einstein and fermi-dirac correlations

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