Search for ≥ 7 Pion Decays
of the τ-Lepton with BABAR
Richard Kass
The Ohio State University
ttag
trec
Introduction
t-  7-prongs nt
inclusive analysis t-  4p- 3p+ (p0) nt
exclusive: 4p- 3p+ nt & 4p- 3p+ p0 nt
t- 3p- 2p+ 2p0 nt
t- 2wp- nt
Results and Conclusions
Richard Kass
TAU06 Sept 19 2006
1
Motivation for Searches
τ decays with ≥ 7 pions have never been observed
We have a lot more statistics than previous experiments (× (50-200))
Better understanding of strong interactions in hadronic τ decays
resonant substructure
exotic resonances ?
Potentially useful bound on nt mass if the decay is observed
Mt - M2wp =74 MeV
Richard Kass
Multi-pion t decays
are important !
TAU06 Sept 19 2006
2
t-  4p- 3p+ (p0) nt
Previous Experiments:
HRS (1987):
BR < 2.9 × 10-4 PRD 35, 2269
OPAL (1997): BR < 1.8 × 10-5 PL B404, 213
CLEO (1997): BR < 2.4 × 10-6 PRD 56, 5297
Theory:

3
d pn
1
d p1
4 4
d =
| M |2
...
(
2
p
)
 ( p0 - p1 - ... - pn )
3
3
2E 0
(2p ) 2 E1 (2p ) 2 En
3
amplitude
(dynamical factor)
phase space
(kinematical factor)
BR (t  7pt )
= 10 -3  6 10 -6
BR (t  5pt )
S. Nussinov, M. Purohit, Phys.Rev.D.65 034018 (2002)
Richard Kass
TAU06 Sept 19 2006
BR (t  7pt ) = 6 10 -12
Provided the decay does not
go via resonances
3
t-  3p- 2p+ 2p0 nt
Previous Results:
No 7p: BR (t  5p2p0 nt) < 1.1×10-4 CLEO PRL, 73, 934 (1994)
But 6p has been measured:
BR (t  5pp0 nt) = (1.7±0.3)×10-4
CLEO PRL 86,4467 (2001)
BR (t  w3pnt) = (1.2±0.2)×10-4
ppp0
Theory:
No theoretical prediction of the decay rate
The decay will most likely go through w meson
If w meson dominates the 7-pion decays, t  5p2p0 nt will most likely have the largest BR
The decay is likely to go through (2wpnt ) channel
(t  5p 2p 0t ) = 2wp 
1
8
18
3
3
7p   5p  2  3p  3 p  w 2p
35
35
35
10
5
R. Sobie, Phys. Rev. D. 60 017301 (1999)
Richard Kass
TAU06 Sept 19 2006
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Data Collection at PEPII
The analyses presented here use 232 fb-1 of data*
=206.6x106 τ-pairs
Collected at CM energy ~ 10.58 GeV
*BaBar has collected a total of ~390 fb-1
Richard Kass
TAU06 Sept 19 2006
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Event Pre-Selection Criteria
Reject background and reduce size of data samples.
2 < Nch.trk < 11 in event
Event divided to 2 hemispheres perpendicular to thrust
Thrust magnitude > 0.9
8 (6) well-measured tracks in event, with 1 track
recoiling against 7: 1-7 topology (1-5 topology).
Zero net charge
No g conversions (Me+e< 5 MeV, DXY < 2cm)
Rejected 99.95%
xis of bkg.,
a
t
andth
77%
rus of signal
p0
g
BR(7p/7pp0)=210-5
g
No loopers (tracks trapped in B-field)
Well-measured photons
X
e+
e-
1 (2) reconstructed p0’s on signal side 7pp0 (5p2p0)
Lots more bkg. to reject
Richard Kass
TAU06 Sept 19 2006
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Background Suppression
Against qq
p-mesons on signal side

Against t bkg


pT >100 MeV/c on signal side
Residual energy on the signal side < 300 MeV



DOCAXY / pT < 0.7cmc/GeV on signal side
1-prong tags: e, m, , h+0g

1.3 < Pseudo-Mass < 1.8 GeV/c2

invariant mass
Use Pseudo-mass instead of Invariant mass
Assume: n is massless & τ direction is given by 7 tracks
m*t2= 2(Ebeam – E7p)(E7p – P7p)+m7p2
BR = 210-5
Signal region: 1.3 < M7p < 1.8 GeV/c2
pseudo-mass
background shifts upwards with pseudo-mass
Shape of pseudo-mass distribution well modeled by MC
Richard Kass
TAU06 Sept 19 2006
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t-  4p- 3p+ (p0) nt qq Background Estimate
After all cuts (DATA)
After preselection (DATA)
BABAR
fit
m, s
signal
region
BABAR
extrapolate
integrate
 Fit from 1.8 to 2.6 GeV/c2 after
pre-selection with a Gaussian function
 Extrapolate the fit below 1.8 GeV/c2
 Integrate from 1.3 to 1.8 GeV/c2
 Use these fit parameters on the final
pseudo-mass spectrum.
Mean and sigma do not vary
significantly throughout the cuts
Richard Kass
TAU06 Sept 19 2006
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t-  4p- 3p+ (p0) nt
qq Background Estimate Validation
Validation on:
1–8 topology data (after all cuts)
1) 1-8 data: 1.3 – 1.8 GeV/c2 region
(pure qq background)
Cuts
1-8 data
1-7 data
exp.
obs.
exp.
obs.
Preselection
19.0 ±2.7
23
3356 ±79
3238
7-prong p ID
12.2 ±1.6
10
1503 ±40
1415
7-prong pT
6.7 ±0.8
8
1092 ±30
1103
DOCAXY/pT
2.7 ± 0.3
1
656 ±18
642
1-prong tag
0.5 ± 0.1
0
114 ± 4
106
Good agreement!
Richard Kass
TAU06 Sept 19 2006
1–7 topology data (after all cuts)
validation region
2) 1-7 data: 1.8 – 2.0 GeV/c2 region
validation region
BABAR
BABAR
9
t bkgd.
Signal
Efficiency
t-  4p- 3p+ (p0) nt Systematic Error Estimate
Tracking efficiency
Particle ID
1-prong generic t BR
Limited MC statistics
5.2 %
2.7 %
0.5 %
0.7 %
Total uncertainty of signal efficiency (%)
6.0 %
Limited t MC statistics
t  5pp0nt branching ratio
t  5pnt branching ratio
75 %
15 %
7%
Total uncertainty of t background (%)
77%
qq bkgd.
1.3 ± 1.0 events
Fit parameters (%)
Num. events fitted (%)
Fit range (%)
3.4 %
2.0 %
0.1 %
Total uncertainty of qq background (%)
4.0 %
20.3 ± 0.8 events
Luminosity and tt- cross-section
Richard Kass
TAU06 Sept 19 2006
2.3 %
10
t-  4p- 3p+ (p0) nt Results
t-  4p- 3p+ (p0) nt eff. (9.4 ± 0.6) %
Expected tt- bkg.
1.3 ± 1.0
Expected qq bkg.
20.3 ± 0.8
Total expected bkg.
21.6 ± 1.3
Observed events
signal
region
24
No evidence for signal !
Sensitivity (Nexp=Nobs) < 2.5 × 10-7 @ 90% CL
Branching ratio
signal region
< 3.0 × 10-7 @ 90% CL
Calculated using Bayesian approach
Richard Kass
TAU06 Sept 19 2006
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Exclusive t-  4p- 3p+ nt
 Background estimate method is identical to
t -  4p- 3p+ (p0) nt case
 Additional cut: no g’s on the 7-prong side.
t-  4p- 3p+ nt eff.
(5.5 ± 0.3) %
Expected tt- bkg.
0.8 ± 0.8
Expected qq bkg.
3.1 ± 0.1
Total expected bkg.
3.9 ± 0.8
Observed events
BABAR
signal
region
8
signal region
No evidence for signal !
Sensitivity
< 2.2 × 10-7 @ 90% CL
Branching ratio < 4.3 × 10-7 @ 90% CL
Richard Kass
TAU06 Sept 19 2006
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Exclusive t-  4p- 3p+p0 nt
Require 1 reconstructed p0 on the 7-prong side:
BABAR
113 < Mgg < 155 MeV/c2
t-  4p- 3p+ p0 nt eff.
(3.6 ± 0.3) %
Expected tt- bkg.
0.4 ± 0.4
Expected qq bkg.
7.8 ± 0.3
Total expected bkg.
8.2 ± 0.5
Observed events
7
No evidence for signal !
Sensitivity
signal
region
signal region
< 4.2 × 10-7 @ 90% CL
Branching ratio < 2.5 × 10-7 @ 90% CL
Richard Kass
TAU06 Sept 19 2006
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Search for t-  3p- 2p+ 2p0nt
Richard Kass
TAU06 Sept 19 2006
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t Background Estimate t- 3p- 2p+ 2p0nt
t  5pp0nt Background
After all cuts the t background is dominated
by the t  5pp0nt mode.
MC
Generate a large sample (3x data) of MC
events for t 5pp0nt
Fit 5pp0 pseudo-mass with a ‘crystal ball’
PDF allowing hadrons on the tag side gives
more statistics
Use the shape parameters to fit the
pseudo-mass after all cuts.
5pp0
MC
Scale expected bkg. to 232 fb-1
MC Expected (fit): 3.6 ± 0.6 events
Richard Kass
MC Counted :
3.2 events
Other MC t bkg.
0.7 ± 0.5 events
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qq Background Estimate t- 3p- 2p+ 2p0nt
MC
Fit qq with a double Gaussian (uu/dd/ss, cc).
data – tMC = qqDATA
Fit qqDATA above 1.8 GeV/c2 with qqMC PDF,
allowing PDF shape parameters float
Extrapolate the fit below 1.8 GeV/c2
BABAR Data
Expected (fit): 2.2
1.7
-1.0
MC PDF
Data PDF
events
blinded
Validate method by requiring at least
three high energy photons on the tag side.
Signal efficiency <0.01%
Richard Kass
TAU06 Sept 19 2006
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qq bkgd.
t bkgd.
Signal Efficiency
t-  3p- 2p+ 2p0nt Systematic Error Estimate
Richard Kass
Tracking efficiency
Reconstruction of 2p0
Single photon
Particle ID
Limited MC statistics
3.9 %
6.6 %
1.8 %
1.7 %
1.8 %
Total uncertainty of signal efficiency (%)
8.3 %
Tracking, Neutrals, PID, p0
BR (t  5pp0nt)
Fitting
8.4 %
14.9 %
16.7 %
t  5pp0nt background
t  3p2p0nt background
Total t background
3.6 ± 0.9 events
0.7 ± 0.5 events
4.3 ± 1.0 events
 1 .6
-1 .0
 0 .7
- 0 .0
PDF parameters
Fit function
events
events
Total qq background
2.2 -11..07 events
Luminosity and tt- cross-section
2.3 %
TAU06 Sept 19 2006
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t- 3p- 2p+ 2p0nt Results
BABAR
Signal eff.
0.66 ± 0.05 %
 2 .0
Total expected bkg. 6.5 -1.4
Observed events
10
No evidence for signal !
Sensitivity
< 1.8 × 10-6 @ 90% CL
Branching ratio < 3.4 × 10-6 @ 90% CL
Calculated using Cousins-Highland
approach incorporating errors
R. Barlow, Comput. Phys. Commun. 149, 97 (2002)
Richard Kass
TAU06 Sept 19 2006
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Search for t-  2ωp-nt
Motivation
t  2wpnt should dominate the t  5p 2p0nt
Pre-selection
decay mode (PRD 60, 017301 (1999))
Kinematic constraints of t  2wpnt suppress the
bkg. and allows to loosen the cuts.
BABAR
Sensitivity of O(10-7) can be achieved.
Omega Reconstruction
Loosen photon and p0 selection criteria
w peak
Allow hadrons on the tag side
BABAR
Significantly relax bkg. suppression cuts.
Require 0.76 < Mp+p-p0 < 0.80 GeV/c2
2w efficiency: 8.2%
2w purity:
Richard Kass
87%
TAU06 Sept 19 2006
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t- 2ωp-nt Results
Kinematics of this decay greatly suppresses
the background
BABAR
Only contribution is from the t w3pnt
Signal eff.
1.53 ± 0.13 %
Total exp. bkg.
0.4 -10..04
τ background
Observed events 1
No evidence for signal !
Sensitivity
< 4.3 × 10-7 @ 90% CL
BR (t-  2w p- nt ) < 5.4 × 10-7 @ 90% CL
Richard Kass
TAU06 Sept 19 2006
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Summary and Conclusions
Multi-pion mode
t 7p (p0)nt
Previous
BABAR
< 2.4 × 10-6
< 3.0 × 10-7
t  7p nt
N/A
< 4.3 × 10-7 PRD72:012003, 2005
t  7p p0 nt
N/A
< 2.5 × 10-7
t  5p 2p0nt
< 1.1 × 10-4
< 3.4 × 10-6
t 2w pnt
N/A
< 5.4 ×
10-7
PRD74:011103, 2006
More details: “Search for Rare Multi-Pion Decays of the Tau Lepton
Using the BABAR Detector” PhD thesis, Ruben Ter-Antonyan,
Ohio State University, 2006.
Tau decays to 7 or more particles (+ neutrino) have not been observed yet.
Unlikely to be observed with < 1 ab-1 of data
Challenge to theory/theorists to predict these decay rates
Richard Kass
TAU06 Sept 19 2006
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Backup Slides
Richard Kass
TAU06 Sept 19 2006
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PEPII-Asymmetric e+e- Collider
Stanford Linear Accelerator Center,
Stanford, California
SLAC is an asymmetric e+e− collider: 9 GeV (e-)/3.1 GeV (e+)
Center of Mass has bg=0.56
Richard Kass
TAU06 Sept 19 2006
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The BABAR Detector
Electromagnetic
Calorimeter
(EMC)
1.5 T Solenoid
Detector of
Internally
Recflected
Cherenkov
Light (DIRC)
Drift Chamber
(DCH)
Instrumented
Flux Return
(IFR)
Silicon Vertex
Tracker (SVT)
BABAR features:
Charged particle tracking (silicon+drift chambers+1.5T Bfield)
Electromagnetic calorimetry (CsI)  g and electron ID
p/K/p separation up to the kinematic limit (dE/dx+DIRC)
Muon/KL identification
Richard Kass
TAU06 Sept 19 2006
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Pseudo-mass Data-MC Comparison
t-  3p- 2p+ 2p0nt
t-  4p- 3p+ (p0) nt
Pseudo-mass shapes of qq data and MC in agreement
Gaussian function is a good fit
To estimate qq bkg. in signal region, fit data with a PDF extracted
from MC
Richard Kass
TAU06 Sept 19 2006
25
Bayesian Approach
P( | x) =
L( x |  ) P( )
 L( x |  ' ) P( ' )d '
Bayes’ theorem
P( | x) - probability of unknown  given observed vector of data x
L( x |  ) - likelihood function for the data x given a certain 
 up
1- = 
 low
P( | x)d
- fraction of probability in a given interval [up, low]
( s  b) n -( s b ) - likelihood for Poisson distributed n observed events
L( n | s ) =
e
with expected background b, and a certain signal s
n!

1 -  =  P( s | n)ds =

sup
-
sup
-

-
L(n | s) P( s)ds
L(n | s) P( s)ds
sup – upper limit at confidence level 1-
Particle Data Group 2004
Richard Kass
TAU06 Sept 19 2006
26
Bayesian Approach
In our case, we want the upper
limit on the branching ration:
m -b
B=
2 Ntt
m = <n> is the mean of the number of observed events (Poisson)
b – number of expected background with error sb (Gaussian)
2Ntt = f – scale factor with error sf (Gaussian)
Likelihood vs. BR
Maximize the likelihood wrt. f, b to obtain B:
B(t-  4p- 3p+ (p0) nt ) =
0.7 -11..34 10 -7
Integrate over all permitted values of f and b to obtain the
likelihood function in the branching fraction:
B(t-  4p- 3p+ (p0) nt ) < 3.0 × 10-7 @ 90%CL
Richard Kass
TAU06 Sept 19 2006
BR
27
t-  4p- 3p+ (p0) nt Consistency Check
DATA
t bkg.
qq bkg.
Observed
Topology
128  13
574  21
695
Particle ID
28  6
241  10
244
Conv. Veto
2.4  1.3 119  5
104
1-prong Tag
1.3  1.0 20.3  0.8
24
Cuts
Richard Kass
Cuts
free fit
fixed fit
Topology
574  21
574  21
Particle ID
222  19 241  10
Conv. Veto
126  18 119  5
1-prong Tag
20.2  7.7 20.3  0.8
TAU06 Sept 19 2006
Agreement
between exp. and
obs. is consistent
throughout cuts
Agreement
between fixed
and free fits is
consistent
throughout cuts
28
t-  3p- 2p+ p0nt Background Error Estimate
s s
 Generate Toy MC for 2D gaussian of m and s (fit
parameters) and their errors. Correlation between m and
s is taken into account.
 Using accept/reject method, plot the estimated bkg.
for accepted toy MC fit parameters.
 ± 1s from the central value is the error.
Richard Kass
TAU06 Sept 19 2006
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qq Background Validation t- 3p- 2p+ 2p0nt
Require ≥3 high-energy (Eg > 300 MeV) photons on 1-pr. side, not associated with p0
Signal efficiency <0.01%
Suppresses tau events, leaving clean
qq sample in the data, which can be
studied unblinded
t  5p2p0nt
BABAR
Data fit of the qq pseudo-mass
spectrum with a PDF taken from
MC nicely describes the tail of the
spectrum and gives a valid
estimate of expected bkg. events in
the signal region
Observe: 12 events
Predict: 11.8 events
Richard Kass
TAU06 Sept 19 2006
30
t- 2ωp-nt Background Estimate
blinded
blinded
blinded
blinded
t bkg.
qq bkg.
generic t:
0 events
1.0
t  w3pnt: 0.4 - 0.4 events
Poisson err. 68% CL
pseudo mass shapes of data and
scaled MC agree
no tail expected due to
kinematical constraints extrapolation
expected qq bkg: 0 0.1
-0
Richard Kass
TAU06 Sept 19 2006
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Measurement of BR(t5p p0nt) as a Cross Check
BABAR Preliminary
Repeat the event selection of t5p 2p0nt (reconst. 1 p0)
Total bkg.
Repeat the background estimate method.
Validate qq bkg. estimate with ‘signal-free’ data sample (≥3
high-energy photons on the tag side)
Signal efficiency (%)
2.16 ± 0.16 %
Expected tau bkg.
67 ± ZZ
Expected qq bkg.
84 ± YY
ALEPH, 96
1.8 ± 0.7 ± 1.2
Observed Data
1742
OPAL, 99
2.7 ± 1.8 ± 0.9
Observed Signal
1591 ± XX ±XX
CLEO, 01
1.7 ± 0.2 ± 0.2
PDG, 04
1.81 ± 0.27
Branching Ratio
(x10-4)
BR(t5pp0nt)
1.79 ± XXX ± XXX
Nice cross-check of the event selection and background estimate methods
Richard Kass
TAU06 Sept 19 2006
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