Final State Interactions in
W+W- Production at the
ALEPH Experiment
Matthew Pearson
RAL CMS Tracker
(previously ALEPH WW Group)
Plan
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Overview of the ALEPH detector.
W+W- production and decay (+parton shower).
String/Cluster Hadronization (JETSET, HERWIG,
ARIADNE).
Inter-W QED/QCD Interactions - Final state
interactions.
–
Colour Reconnection
–
Inter/Intra-W Bose-Einstein Correlations
Significance for the W mass.
Search methods and results.
LEP wide search methods and results.
CR and BE at the LHC and LC.
LEP and ALEPH
ALEPH
ALEPH : Apparatus for LEP pHysics
ALEPH in 2001!
HCAL
WW Production
Can produce W+W- with center-of-mass E>161GeV
ADLO each produced ~10,000
W+W- pairs during LEPII
(161GeV to 210GeV,
from 1996 to 2000).
Simulated using KoralW+YFSWW
WW Decay
One W can decay into qq or ln:
BR(W
qq) = 68.5 ± 0.6%
BR(W
ln) = 31.5 ± 0.5%
Therefore:
BR(WW
qqqq) = 46.9 ± 0.8%
BR(WW
qqln) = 43.2 ± 0.8%
BR(WW
lnln) = 9.9 ± 0.3%
W = 3x10-25s
~0.1fm
But, ~1fm
hadronization
scale…
Inter-W QCD
interactions?
Parton Shower
Parton shower – High energy quarks and gluons
Simulated by either PYTHIA, ARIADNE or HERWIG Monte Carlo
•Initial hard gluon emission form additional jets
•Quarks and gluons emit further softer gluons
•Gluon splitting/Angular ordering/Matrix Element matching
-> Many parton jets.
PYTHIA: Initial parton branching are weighted to agree with QCD
matrix elements. Basic angular ordering.
HERWIG: Hardest gluon emission is matched to QCD matrix element.
Angular ordering more naturally introduced.
ARIADNE: Colour dipole model. Subsequent pt of partons must be
smaller than previous branching.
Hadronization
Hadronization starts at about 1GeV scale – Describe QCD fields between
partons as string or cluster.
However, hadronization is a local process – it does not affect the whole
event. The main jet properties: jet rates, angular distribution and
multiplicity are well determined at end of parton shower. (depending on
hadronization model)
STRING
CLUSTER
Inter-W Interactions
QED: the coulomb singularity
Can describe this – It’s QED!
W+
Z/
QCD
Parton level:
q
q
W+
W-
q
q

•2-5% shift in WW x-section.
•5-10MeV shift in W mass.
WCalculable to some extent…
•Potential for very large effects.
However,
•Suppressed by s2/Nc2 – need 2 gluons.
•Approximately 3MeV W mass shift.
•Modelled by AR2 in ARIADNE: Gluons with
energy < 2GeV are forced to interact with
partons from different W systems.
•Can be applied to single hadronization systems (Z, W).
•AR2 is therefore tuned on Z data.
Non-perturbative CR (1)
QCD Hadronization level: This is non-perturbative.
In the string model in JETSET:
Colour reconnection can occur when strings from different
W’s overlap in space-time. The Sjostrand-Khoze models are:
SKI – Strings are long bags of colour field. Radius ~0.5fm. Gaussian fall off of field.
Reconnection probability can be adjusted from 0% to 100%.
Prediction: At 100%, huge W mass shift of ~250MeV.
SKII – Strings have thin core and effectively no colour field beyond this. Reconnection
occurs with unit probability if strings from different W’s overlap.
No tunable parameters. At 170GeV one can expect 37% reconnection.
SKII’ – Same as SKII, except reconnections only occur if string length can be reduced.
Can only be applied to WW systems. Models applied to PYTHIA events without tuning.
All 3 models predict a reduction in WW fully hadronic multiplicity.
Only soft particles affected (ie. <1GeV).
Non-perturbative CR (2)
Also in the JETSET model there is the Rathsman CR model.
This is based on 4-D area overlap of strings.
•Two string configurations can be rearranged if the constituent
partons can form new strings with smaller areas.
•Probability of string to have area A is ~exp(-bA).
•Probability to rearrange strings so that area Aold becomes Anew
is R0[1-exp(-bA)]. Where A = Aold - Anew.
•R0 is a free parameter.
In ALEPH this model was tuned on Z data and R0 was determined
to be 0.004.
Hence, this model has very small effects on W mass and multiplicity.
•Small negative change in multiplicity (same direction as SK models).
Non-perturbative CR (3)
In the cluster model in HERWIG:
Colour reconnection can occur when clusters from
different W’s overlap.
•Each cluster is assigned a size dab.
•If one normally has ab and cd, then these could be rearranged to
form ac and bd if: |dab|2 + |dcd|2 > |dac|2 + |dbd|2.
•New clusters have to be colour singlets.
•Multiple reconnections can occur in one event.
This model is tuned on Z events.
Cluster size is not correlated with multiplicity.
Multiplicity of a cluster is determined by its mass.
One could have an increase in multiplicity due to CR!
Bose-Einstein Correlations
Quantum mechanical ‘force’: affects only identical bosons (KL, , 0)
which are close together in phase space.
No BE
0
0
With BE
0
0
Two types:
1. BE SAME – BE correlations between particles from the same W
2. BE ALL – BE correlations between particles from both the same
W and from different W’s
BE SAME: Confirmed in the Z system at LEPI.
Not in standard LEPII Monte Carlo (single W’s, Z etc.)
BE ALL: Does it exist in W+W- systems?
BE in JETSET
The only Monte Carlo fragmentation program to offer BE simulation
is JETSET.
ALEPH used the BE32 model…
It uses a local re-weighting method:
panew = paold + pab
pbnew = pbold + pbq
This conserves momenta (pab + pbq = 0) but not energy. 
Therefore:
panew = paold + b  a pab +  c  b rac
Event
dependent
parameter.
p shift between any
two identical bosons
a and c.

Prediction: Negative shift of few MeV in W mass (but depends heavily
on reconstruction method). No effect on multiplicity.
BE Evidence
BE correlations are well established from:
•ion-ion collisions at SPS
200GeV/nucleon, 16O with C, Cu, Ag, Au targets
eg. NA35, WA80
~400 charged particles per event
•hadronic Z0 decays at LEPI
~4 million events
~20 tracks per event
Measured for both charged and neutral particle pairs
If in single hadronic Z’s, then surely also in single hadronic
W’s. And since W’s overlap so much in W+W- events then surely
it exsits between W’s too?
FSI Summary
Colour Reconnection:
JETSET: SKI(0-100%), SKII, SKII’, Rathsman.
HERWIG CR
ARIADNE AR2
All predict a change in W mass and multiplicity in
4q channel. Multiplicity can also change in 2q channel.
Bose-Einstein Correlations:
Already seen in Z data (and ion-ion collisions at SPS).
Only in JETSET: BE SAME, BE ALL
Change in W mass in 4q channel.
Why + How to search for FSI?
It depends who you talk to…
Two main reasons:
•It can affect the W mass reconstruction.
All CR and BE models affect W mass (few MeV to ~250MeV)
If we can determine how much CR and BE exists then we can
put an accurate systematic uncertainty on the W mass in 4q channel.
•One better understands non-perturbative QCD
parton shower and hadronization.
String/Cluster?
If string, what shape of string? etc.
How to search for colour reconnection?
Multiplicity, Event Shapes…… Will discuss multiplicity and
factorial moments.
How to search for BE?
Two-particle relative momentum distribution, correlation functions….
Will discuss 2-particle momentum dist. and factorial moments.
ALEPH biased!
W+W- Multiplicity
All CR models change WW multiplicity, but not BE.
Mainly soft particles affected (<1 GeV).
Technique: Measure 4q and 2q WW charged multiplicity.
q
q
q
lepton
~38
q
q
~19
q
neutrino
Compare qqqq and qq multiplicity, eq. 4q-2(2q)
But, in ALEPH we did not correct the data for selection or
momentum cut (200MeV). Data is still biased by selection…
Solution: CR = [4q-2(2q)]data – [4q-2(2q)]MC
Cancel any selection
biases.
W+W- Multiplicity Results
Luminosity weighted average multiplicity:
Data 4q = 35.23  0.13  0.29
2q = 17.46  0.09  0.12
<E>=198GeV 625pb-1
4q-2(2q)=0.310.25
MC 4q = 34.82  0.02 (JETSET without CR)
2q = 17.33  0.01
4q-2(2q)=0.170.03
CR = [4q-2(2q)]data – [4q-2(2q)]MC = 0.140.25  (or )
HERWIG CR = 0.140.25
JETSET+SKI(100%) CR = 0.350.25
HERWIG+CR CR = -0.150.25
ARIADNE+AR2 CR = 0.360.25
OK, so what about low
momentum particles……
•SKI(100%) and AR2 both
predict decrease in soft
particles.
•HERWIG CR predicts
increase in soft particles.
•Data consistent with all
models, with or without
CR 
Multiplicity not sensitive
enough (just!).
OK, but we can study
‘ordinary’ fragmentation
(no CR or BE)……
Fragmentation Results
What do these plots tell us?
•HERWIG best for low momentum particles (<1GeV).
•JETSET best for mid-range particles (1-10GeV), and
HERWIG is quite poor in this region.
•ARIADNE+JETSET not good for low momentum particles.
•Same for 4q and 2q data.
What did we see at LEPI?
•Poor match between data and Monte Carlo for low momentum.
•Big JETSET and HERWIG differences for heavy charged
particles (eg. Protons) for p>9GeV.
Common theme: Cluster fragmentation best for p<1GeV
String fragmentation for p>1GeV
Combine the two? Fragment low energy strings into clusters?!
What about Bose-Einstein?
Q=sqrt((p1-p2)2-(E1-E2)2)
=(N++--sel 4q - N++--mixed 2q)data
-(N++--sel 4q - N++--mixed 2q)MC, noBE
Any deviation from zero near
Q=0 is evidence for BE between
W’s.
Data consistent with no BE
and BE within a single W.
In fact, BE between W’s is
disfavoured.
Still ongoing analysis…….
Using correlation functions
If ordinary variables cannot be used to search for FSI
At LEPII, then lets try something more exotic…
Factorial moments and correlators have been used to
study intermittancy effects in multiparticle production
(from ~1990(?) onwards).
•‘Spiky’ behaviour in particle distributions (couldn’t be explained
by particle production models or statistics).
•Is particle production fractal in nature?
•Able to explain some SPS (UA5, NA22) and LEPI Z data.
(also used in cosmic ray exp. and quantum optics)
Features: Sensitive to dynamical mutliparticle correlations,
and not affected by limited multiplicity.
Factorial Correlator
Factorial moment of order m:
Fm(b) = <xb(xb-1)…(xb-m+1)>
= 1/E e(xb(xb-1)…(xb-m+1)e
e=1..E
Setting m to 1…
F11(b,b’) = <xbxb’> / <xb><xb’>
which is just the correlator.
•Only applies to fully hadronic events (qqqq).
•One has to know which particle comes from which W.
•Make a pt or  distribution for each W.
•Take bin b from one W distribution and bin b’ from the
other W distribution.
F11(b,b’) will measure correlation between multiplicity fluctuations
in bins b and b’ (separated by D).
hep- ph/ 9907536 v1 28 Jul 1999, HZPP-9907, July 28, 1999
Identification of Colour Reconnection using Factorial Correlator
Fu Jinghua Liu Lianshou
Institute of Particle Physics, Huazhong Normal University, Wuhan 430079 China
Factorial Correlator (2)
Study by L3 using
PYTHIA+JETSET
at generator level.
Huge difference
between no
reconnection and the
SK models.
What happens if we
look at the
reconstructed Monte
Carlo?
Factorial Correlator (3)
Factorial Moments
Since factorial correlators are useless for looking at reconstructed
Monte Carlo or real data, what about factorial moments?
•These are sensitive to the fluctuations of a single bin.
•As before, form a multiparticle distribution (but only one, using
particles from both W’s).
•Use horizontal factorial moments (ie. average over bins, then events).
The factorial moment of order m, of bin b in event e, is:
Fm(e,b) = (xb(xb-1)…(xb-m+1))e
Then, average over the bins in the event:
Fm(e) = Bm-1(bFm(e,b))/Nm
Then, average over all the events:
Fm = 1/E eFm(e)
B = #bins in distribution.
E = #events in sample.
N = #charged tracks in event.
Factorial Moments (2)
One is interested in horizontal moments to be sensitive to multiplicity
fluctuations within a single event.
Due to:
•Ordinary fragmentation, or
•Inter-W reconnection effects (both colour reconnection and
Bose-Einstein correlations)
Calculate Fm for a number of distributions and plot as a
function of B (the number of bins).
The scaling of Fm with B is called intermittency
(ie. Fractal jet structure)
But I am only interested in any differences between curves
produced by different fragmentation models.
In the following m=2 (m>2 gives worse results due to low multiplicity
and limited #events).
Factorial Moments (3)
How does ordinary fragmentation affect Fm?
=rapidity wrt the thrust axis
=rapidity wrt the W 4-vector.
Can we combine over the points?
We can, but the correlation
is 70-90% high between points.
No much more information
from considering 20 points
than just one point!
Factorial Moment Results and
Future
So what can we learn?
•Very difficult to explain the changes in Fm using particle distribution.
•Curves are not separated enough to say anything concrete.
Again, it would be useful to have more data!
What about using these at the LHC?
•Fm seems to be quite sensitive to BE correlations.
•Could be useful tool for high multiplicity events, especially at
the ALICE heavy ion experiment (2000-8000 charged particles).
•Certainly useful in highlighting inefficiencies in Monte Carlo
fragmentation models (see LEP1 results).
BE and CR at LHC and LC
Colour Reconnection:
Some LHC events which may be affected by CR:
H->ZZ, tt, WW, ZZ, etc. ->Any pair of hadronically decaying heavy particles.
Also, some LC events:
WW, ZZ, tt, etc.
Bose-Einstein Correlations:
BE will be a large effect at LHC in high multiplicity events (ion-ion,
and decays of tops, Z’s, W’s and H’s).
May affect mass reconstructions, particle distributions, event variables etc.
BE at LC may affect the same sort of events.
-> the LC will finish the job that LEP started in searching for
CR and BE in W+W- events!