Open%20questions%20related%20to%20Bose-Einstein%20correlations%20in%20e e_?%20hadrons

1
Open questions related to Bose-Einstein
correlations in ee_? hadrons
ISMD 2003
G. Alexander
Tel-Aviv University
OUTLINE
1. Introduction
5. 2-D analysis and

2. Emitter size vs. ECM
6. Bose condensates and BEC?
3. Fermi-Dirac correlations
7. Generalized BEC
4. Emitter size vs. mass
8. Summary and conclusions
2
Bose-Einstein Correlation (BEC)
1-Dimension analysis
Correlation function.
GGLP variable
3
Hadron emitter radius in ee_ vs. ECM

• HBT effect in the 50s measured stellar objects
  dimensions.

In heavy ions, an early compilation of r vs. the
projectile A
can be described by
Chacon, P.R. C43 (1991) 2670
AA Collisions


(projectile)
What about the ee_?hadrons BEC dimension vs.
ECM ?
4
r versus No. of jets and multiplicity
ee_ ? Z0 ? hadrons
3-jets
2-jets
5
An approach to the r dependence on ECM
via factorial cumulant moments and hadron sources
1.
2. Cumulant dependence on number of sources
Dealt with by several authors, among them
P. Lipa B. Bushbeck, P.L. B223 (1989) 465
B. Bushbeck, H.C. Eggers P. Lipa, P.L. B481
(2000) 187
G. Alexander E. Sarkisyan, P.L. B487 (2000) 215
6
Dilution factor, Sources and Cumulants
Assumption Pion-pair correlation exist only if
both of the same source
Dilution factor Dq
For identical sources ?
7
Emitter size vs. hadron sources
Consider 2-pion BEC from S sources
?

• Note in AA collisions, S vs. A is hard to
  estimate !

8
r(ee_ ? h) dependence on ECM
Neglect for simplicity four and more jets so that
ee_ ? q q gluon ? hadrons
-
Take
The measured average multiplicity Boutemeur,
Fortschr. Phys. 50 (01)
The gluon energy
is determined from the total averaged charge
multiplicity
? Estimate Dilution Factor
9
ee_ ? hadron Emitter Radius
Words of warning
The experiments use different methods for
Selection of data and cuts
Choice of reference sample
Fitting procedure
Source dilution approach taking ?S ?1
normalized at 40 GeV
10
The extension to Fermi-Dirac correlation
Two Methods
1. Spin-Spin Correlation Functions for e.g.
SS1S2
11
The extension to Fermi-Dirac Correlation (contd)
2. The phase space density approach
Like in the BEC analysis one considers
the density of identical baryon pairs as Q ? 0

Three reference samples
12
r(m) from BEC and FDC analyses
Uncertainty relations
Z0?hadrons
with
QCD potential
13
r(m) derived from the Heisenberg uncertainty
relations
G.Alexander, I.Cohen E.Levin, Phys. Lett. B452
(99) 159
The two bosons are at threshold in their CMS,
i.e. non-relativistic
Here we assume that
essentially independent of the mass and is 10-24
sec
depends on the kinetic energy i.e. potential
energy small
14
A challenge to the Lund string model
A leading model for multi-hadron production
Expects in its rudimental form
1-Dimension string Toy model
15
Baryon production in the Lund Model
16
Energy density of the hadron emitter
Z0 ? hadrons
Dashed lines for
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2-Dimensional BEC analysis
Longitudinal Center of Mass System
2-dimension Correlation Function
Transverse mass
18
rz dependence on mT in ee? Zo?hadrons
Z0 ? hadrons (DELPHI preliminary)
19
Uncertainty relations applied to
1)
2)
3)
G.A., P.L. B506 (2001) 45
20
r(mT) in heavy ion collisions
U. Heinz, Ann.Rev.Nucl.Part.Sci. 49(99)529
1.
2.
21
Bose Condensates Brief reminder
A. Einstein (Sitzber. Kgl. Preuss. Akad. Wiss.
1924/5)
In a Condensate All atoms are in the same
zero energy state
E.A.Cornell, W.Ketterle, C.E.Wieman (Nobel
2001) discovered in 1995 rubidium (Rb), sodium
(Na), lithium (Li) condensates
How ? By cooling down below a TB (500nK
2000nK) dilute bosonic atoms


Any relation between
Condensates and Boson produced in HE reactions ?
Try Inter-Atomic Separation and the dimension
extracted from BEC
22
Inter-Atomic separation in Bose Condensates
G.A. Phys. Lett. B506(01)45
In Bose condensates, when T/TBltlt 1, the atomic
density is
The de Broglie wave length is
Consider two condensates with masses m1 and m2
in the same temperature T0 (ltlt TB1, TB2)

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rBEC(m) formula from Bose condensates
Inter-atomic separation
Replace
to get
However there are obvious differences between
condensates and
hadrons produced in HE reactions, e.g.

1) Condensates in thermal equilibrium, hadrons in
HE reactions ? 2) Condensates in coherent
state, hadrons only partly
Note dBE inter-atomic separation NOT the
condensate dimension !
24
Isospin invariance and generalized BEC (GBEC)
In analogue to the Generalized Pauli exclusion
principle one may consider a Generalized BEC
where I-spin is included demanding an over-all
symmetric state.
This possibility was considered by several
authors among them Bowler (87), Suzuki (87)
and Weiner (2000). Specific GBEC relations
were worked out by Alexander Lipkin (99) in the
case that the multi-hadron final
states emerge from an I0 state.
The cases where hadrons emerge from an I0
state is quit frequent. For example, in hadronic
decays of

Multi-gluon decays of and into odd
numbers of pions
25
Relations between the 2-pion systems in the GBEC
Conclusions (if GBEC is valid)
BEC effect in the
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Summary and Conclusions
In spite of the fact that BEC is studied over
40 years, absent are systematic
studies covering different reactions over a wide
energy range
In addition, a standardization of the analysis
methods and reference samples would allow more
meaningful interpretation of the
experimental results

____________________
r(Ecm) is rather well described by a simple
approach to hadron-jet sources


This approach however seems not to be sufficient
to account for the dr/dnch seen in the
Zo?hadrons
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Summary and Conclusions (contd)
r(m), as determined from BEC and FDC analyses
on the Zo , follows roughly the expectation
derived from the Heisenberg relations as well
as that extracted from a QCD potential.
Needs to be measured also in other reactions !

The dependence dr/dm lt 0 poses a challenge to
hadron production models including the Lund one

Above all, the energy density of about 100
GeV/fm3 affixed to the baryon emitter, awakes
doubt on the r interpretation as an emitter
radius

____________________
Generalized BEC has not so far been
experimentally verified. If confirmed then it
has a considerable effect on the analyses of
resonances and on the choice of reference samples

____________________
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Summary and Conclusions (contd)
The r(mT) extracted from the 2-D BEC analysis
behaves similarly to the r(m) derived from the
1-D analyses and both can be described in
terms of the Heisenberg uncertainty relations

To note is that r(mT) is proportional to
(mT)-1/2 in A-A reactions as is also the case
in ee- collisions even though the latter one
is free of nuclear effects !!

As for Bose condensates,
is the inter-atomic
and NOT the Bose condensate dimension !
Final question

Are the behavior of dr/dm, the energy density and
the meaning of dBE telling us that we
should re-examine what does r measure? ?