BoseEinstein correlations in e e collisions at LEP

1
Bose-Einstein correlations
in ee- collisions at LEP
G. Giacomelli, for the OPAL Coll. University of
Bologna and INFN 9th Workshop on Non-Perturbative
QCD Paris, 4-8 june 2007
1. Introduction 2. Static sources BECs in one
dimension Multiplicity dependence of R, ??
3. Static sources BECs in 2 and 3 dimensions 4.
Expanding sources Bertsch-Prat and
Yano-Koonin parametrizations BECs depend on
the pair momenta 5. Conclusions
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1. Introduction

• Bose-Einstein correlations are a quantum
  mechanical phenomenon which manifests as an
  enhanced probability for identical bosons emitted
  with small relative momenta compared with non
  identical bosons in similar conditions
• The effect arises from the ambiguity of path
  between sources and detectors

a--gtA a--gtB b--gtB
b--gtA
Astronomy LltR Particles LgtR From
the magnitude of the effect it is possible to
determine the space-time dimension of the source

L
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2. BECs in one dimension

• Measured Bose-Einstein Correlations (BECs) are
  defined as
• C(Q)??(Q)/??(Q)
• Q2-(P1-P2)2
• ?(Q)(1/N)dN/dQ measured Q-distribution
  of???, ?-?-, ?0?0
• ??o(Q) reference distribution without BECs ?
• ??????????? ??- for ??, ?-?-
• ???o(Q) event mixing from different events
• MonteCarlo reference sample
  without BECs , .
• C(Q) parametrized as Fourier transform of static
  sphere of emitters with gaussian density
• 
  (1)
• 
  

• NNormalization factor ??chaoticity
  parameter 0.6
• Rradius of source 1 fm
• To take into account of background at large, Q2
  Eq. 1 is multiplied by
• (
  Goldhaber parametrization )
• Coulomb correction

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LEP data ee-gthadrons at s1/291.2 GeV

• ee-gtch hadrons several million events/exp ,
  nch21.4
• Charged pions ee--gtppX
• no particle identification np,p-17 (lt90 of
  ch particles)
• Typical Q-distribution with some residual
  correlations due to hadron resonances, ?(770)
  ,, tail at large Q
• Fit outside resonance regions yields R0.9-1
  fm , ??0.6
• Charged kaons need particle identification ,
  nkch2.23
• pizero-pizero need photon detector and refined
  analysis, smaller phase space available,
  npo9.4
• Kzero V0 detection in central detector ,
  nK02.05
• For pch statistical errors small
• systematic errors dominant

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BECs in 1 or 2 dimensions
DELPHI
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?0 mass resolution

• BECs for p0p0
• Rp0Rpch

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Dependence of R on hadron mass

• BECs for pp, KK
• Difference r?-rK
• may not be so clear
• Fermi-Dirac
• correlations for barions p ,??

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Charged pions

• Dependence of R, ? on multiplicity
• Correlation with number of jets
• R4jets gt R3jets gt R2jets
• BECs for 3pch they are found after
  removing 2p correlations and
• applying the Coulomb correction.
• OPAL obtained
• R3p0.580-0.004-0.029
• Proposed relation
• R3p R2p/v2

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3. BECs in two and three dimensions

• Multidimensional static analyses in 3 dimensions
  using the Longitudinal C. of M. System (LCMS)
  the sum of the impulses of the emitted
• q qbar pair lies in the plane perpendicular
  to the event axis defined by the q qbar
  direction
• The components of the 3-dimensional distribution
  in the longitudinal, out, side projections
  indicate that the two last ones are larger thus
  the longitudinal radius is 20 larger than the
  transverse radius the source is elissoidical,
  elongated in the q qbar direction

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Comparison of BECs in ee and NN

• ee- at LEP
• Pb Pb at SPS
• RPb6.7 fm

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4. Expanding sources

• Expansion may be due to string fragmentation
• Average pair 4-momentum K(p1p2)/v2
• Pair rapidity Y1/2 ln(E1E2)(pl1pl2)/(
  )-( )
  Pair transverse momentum kt1/2pt1pt2
• Bertsch-Prat parametrization
• C(Qt,out,Q t,side, Ql)
• N1lexp -(Q2t,out R2t,out Q2t,side R2t,side
  Q2l R2l -2Ql Qt,outR2 l,tout )
  F(Ql,Qtside,Qtout)
• Yano-Koonin parametrization
• C(qt,ql,q0)N1?exp-(q2tR2t?2(ql-vq0)2R2l?2(q0
  -vql)2 F(qt,ql,q0) F(Ql,Qtside,Qtout) and
  F(qt,ql,q0) are introduced to take into account
  residual long range 2-particle correlations due
  to energy and charge conservation. vlongitudinal
  velocity of source element in C.M.
• BEC Radii depend on the pair momenta -gt
  position-momentum correlations

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Differential distribution in Y and kt for data
and MC
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Correlations CCDATA/CMC. Bertsch-Prat approach

• (Clike/Cunlike)MC

0.8ltYlt1.6 , 0.3ltktlt0.4GeV, Qtoutlt0.2GeV(Qt or
Qllt0.2 GeV)
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Yano-Koonin approach
0.8ltYlt1.6 , 0.3ltktlt0.4 GeV, qt or q0lt0.2 GeV
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Y-K rapidity YYK1/2ln(1v)/(1-v) vs pair
rapidity Y
YYK measures the rapidity of the source element
with respect to CM
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Comparisons of YK,BP fits (StatSyst errors)
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5. Conclusions

• Static sources
• The radius changes with the mass of the emitted
  particles Rp0.8 fm, RK0.5 fm (Rp,L0.15 fm)
• For pions the radius increases with nch (by 10)
  
• -gt Rp for 2 jet events lt Rp for multi jet events
• Genuine multipion BECs are present up to 5
  R3R2/v2
• Ellipsoidical emitting region Rtransverse0.8
  Rlongitudinal
• Expanding sources
• Yano-Koonin, Bertsch-Pratt
• Rt and Rl decrease for increasing kt
• YYK scales with the pair rapidity(boost
  invariant expansion)
• Results similar to more complex systems
• The duration of the particle emission, R0c, not
  available

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Reserve slide
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Yano-Koonin fits
Reserve slide