1. Search for ≥ 7 Pion Decays of the τ-Lepton with BABAR
Richard Kass
The Ohio State University e+
ttag
trec e-
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

2. 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
Multi-pion t decays are important !

3. Provided the decay does not go via resonances
t-  4p- 3p+ (p0) nt
Previous Experiments:
HRS (1987): BR < 2.9 × 10-4
OPAL (1997): BR < 1.8 × 10-5
CLEO (1997): BR < 2.4 × 10-6
PRD 35, 2269
PL B404, 213
PRD 56, 5297
Theory:
amplitude (dynamical factor)
phase space (kinematical factor)
Provided the decay does not go via resonances
S. Nussinov, M. Purohit, Phys.Rev.D (2002)

4. t-  3p- 2p+ 2p0 nt Previous Results:
Theory:
No 7p: BR (t  5p2p0 nt) < 1.1× CLEO PRL, 73, 934 (1994)
But 6p has been measured:
BR (t  5pp0 nt) = (1.7±0.3)×10-4
BR (t  w3pnt) = (1.2±0.2)×10-4
ppp0
CLEO PRL 86,4467 (2001)
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
R. Sobie, Phys. Rev. D (1999)

5. Data Collection at PEPII
The analyses presented here use 232 fb-1 of data*
=206.6x106 τ-pairs
Collected at CM energy ~ GeV
*BaBar has collected a total of ~390 fb-1

6. 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)
No loopers (tracks trapped in B-field)
Well-measured photons
1 (2) reconstructed p0’s on signal side 7pp0 (5p2p0)
Rejected 99.95% of bkg., and 77% of signal
BR(7p/7pp0)=210-5
Lots more bkg. to reject

7. Background Suppression
Against qq
Against t bkg
p-mesons on signal side
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, r, 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
Signal region: 1.3 < M7p < 1.8 GeV/c2
background shifts upwards with pseudo-mass
Shape of pseudo-mass distribution well modeled by MC
BR = 210-5
pseudo-mass

8. t-  4p- 3p+ (p0) nt qq Background Estimate
After preselection (DATA)
After all cuts (DATA)
BABAR
fit
BABAR
m, s
signal region
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

9. t-  4p- 3p+ (p0) nt qq Background Estimate Validation
Validation on:
1) 1-8 data: 1.3 – 1.8 GeV/c2 region (pure qq background)
2) 1-7 data: 1.8 – 2.0 GeV/c2 region
1–8 topology data (after all cuts)
BABAR
validation region
Cuts data data
exp obs exp obs.
Preselection ± ±
7-prong p ID ± ±
7-prong pT ± ±
DOCAXY/pT ± ±
1-prong tag ± ±
1–7 topology data (after all cuts)
BABAR
validation region
Good agreement!

10. t-  4p- 3p+ (p0) nt Systematic Error Estimate
Tracking efficiency %
Particle ID %
1-prong generic t BR %
Limited MC statistics %
Limited t MC statistics %
t  5pp0nt branching ratio %
t  5pnt branching ratio %
Fit parameters (%) %
Num. events fitted (%) %
Fit range (%) %
Signal Efficiency
Total uncertainty of signal efficiency (%) %
t bkgd.
Total uncertainty of t background (%) %
1.3 ± 1.0 events
qq bkgd.
Total uncertainty of qq background (%) %
20.3 ± 0.8 events
Luminosity and t+t- cross-section %

11. Calculated using Bayesian approach
t-  4p- 3p+ (p0) nt Results
t-  4p- 3p+ (p0) nt eff. (9.4 ± 0.6) %
Expected t+t- bkg ± 1.0
Expected qq bkg ± 0.8
Total expected bkg ± 1.3
Observed events
signal region
No evidence for signal !
signal region
Sensitivity (Nexp=Nobs) < 2.5 × 90% CL
Branching ratio < 3.0 × 90% CL
Calculated using Bayesian approach

12. Exclusive t-  4p- 3p+ nt No evidence for signal !
Background estimate method is identical to t -  4p- 3p+ (p0) nt case
Additional cut: no g’s on the 7-prong side.
BABAR
signal region
t-  4p- 3p+ nt eff (5.5 ± 0.3) %
Expected t+t- bkg ± 0.8
Expected qq bkg ± 0.1
Total expected bkg ± 0.8
Observed events
signal region
No evidence for signal !
Sensitivity < 2.2 × @ 90% CL
Branching ratio < 4.3 × @ 90% CL

13. Exclusive t-  4p- 3p+p0 nt No evidence for signal !
Require 1 reconstructed p0 on the 7-prong side:
113 < Mgg < 155 MeV/c2
BABAR
signal region
t-  4p- 3p+ p0 nt eff. (3.6 ± 0.3) %
Expected t+t- bkg ± 0.4
Expected qq bkg ± 0.3
Total expected bkg ± 0.5
Observed events
No evidence for signal !
signal region
Sensitivity < 4.2 × @ 90% CL
Branching ratio < 2.5 × @ 90% CL

14. Search for t-  3p- 2p+ 2p0nt

15. t Background Estimate t- 3p- 2p+ 2p0nt
t  5pp0nt Background MC
After all cuts the t background is dominated by the t  5pp0nt mode.
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 5pp0 pseudo-mass after all cuts.
Scale expected bkg. to 232 fb-1 MC
MC Expected (fit): 3.6 ± 0.6 events
MC Counted : events
Other MC t bkg ± 0.5 events

16. qq Background Estimate t- 3p- 2p+ 2p0ntMC
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
MC PDF
Data PDF
Expected (fit): events
blinded
Validate method by requiring at least three high energy photons on the tag side.
Signal efficiency <0.01%

17. t-  3p- 2p+ 2p0nt Systematic Error Estimate
Tracking efficiency %
Reconstruction of 2p %
Single photon %
Particle ID %
Limited MC statistics %
Tracking, Neutrals, PID, p %
BR (t  5pp0nt) %
Fitting %
Signal Efficiency
Total uncertainty of signal efficiency (%) %
t bkgd.
t  5pp0nt background ± 0.9 events
t  3p2p0nt background ± 0.5 events
Total t background ± 1.0 events
PDF parameters events
Fit function events
qq bkgd.
Total qq background events
Luminosity and t+t- cross-section %

18. Calculated using Cousins-Highland approach incorporating errors
t- 3p- 2p+ 2p0nt Results
BABAR
Signal eff ± 0.05 %
Total expected bkg.
Observed events 10
No evidence for signal !
Sensitivity < 1.8 × @ 90% CL
Branching ratio < 3.4 × @ 90% CL
Calculated using Cousins-Highland approach incorporating errors
R. Barlow, Comput. Phys. Commun. 149, 97 (2002)

19. Search for t-  2ωp-nt Motivation
t  2wpnt should dominate the t  5p 2p0nt decay mode (PRD 60, (1999))
Kinematic constraints of t  2wpnt suppress the bkg. and allows to loosen the cuts.
Sensitivity of O(10-7) can be achieved.
Pre-selection
BABAR
Omega Reconstruction
Loosen photon and p0 selection criteria
Allow hadrons on the tag side
Significantly relax bkg. suppression cuts.
Require 0.76 < Mp+p-p0 < 0.80 GeV/c2
BABAR
w peak
2w efficiency: 8.2%
2w purity: %

20. t- 2ωp-nt Results No evidence for signal !
Kinematics of this decay greatly suppresses the background
Only contribution is from the t w3pnt
BABAR
Signal eff ± 0.13 %
Total exp. bkg.
Observed events 1
τ background
No evidence for signal !
Sensitivity < 4.3 × @ 90% CL
BR (t-  2w p- nt ) < 5.4 × @ 90% CL

21. Summary and Conclusions
Multi-pion mode Previous BABAR
 7p (p0)nt < 2.4 × < 3.0 × 10-7
t  7p nt N/A < 4.3 × PRD72:012003, 2005
t  7p p0 nt N/A < 2.5 × 10-7
t  5p 2p0nt < 1.1 × < 3.4 × 10-6
 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

22. Backup Slides

23. 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

24. The BABAR Detector BABAR features:
1.5 T Solenoid
Electromagnetic Calorimeter (EMC)
Detector of Internally Recflected Cherenkov Light (DIRC)
e+ (3.1 GeV)
e- (9 GeV)
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

25. Pseudo-mass Data-MC Comparison
t-  4p- 3p+ (p0) nt
t-  3p- 2p+ 2p0nt
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

26. Bayesian Approach Bayes’ theorem
- probability of unknown  given observed vector of data x
- likelihood function for the data x given a certain 
- fraction of probability in a given interval [up, low]
- likelihood for Poisson distributed n observed events with expected background b, and a certain signal s
sup – upper limit at confidence level 1-a
Particle Data Group 2004

27. Bayesian Approach
In our case, we want the upper limit on the branching ration:
m = <n> is the mean of the number of observed events (Poisson)
b – number of expected background with error sb (Gaussian)
2Ntte = 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 ) =
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 × 90%CL BR

28. t-  4p- 3p+ (p0) nt Consistency Check
DATA
Cuts t bkg. qq bkg Observed
Topology 128  
Particle ID 28  
Conv. Veto 2.4  
1-prong Tag 1.3  
Agreement between exp. and obs. is consistent throughout cuts
Cuts free fit fixed fit
Topology 574   21
Particle ID 222   10
Conv. Veto 126   5
1-prong Tag 20.2   0.8
Agreement between fixed and free fits is consistent throughout cuts

29. t-  3p- 2p+ p0nt Background Error Estimate
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.

30. 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

31. t- 2ωp-nt Background Estimate
blinded
blinded
blinded
blinded
t bkg.
generic t: events
t  w3pnt: events
qq bkg.
pseudo mass shapes of data and scaled MC agree
no tail expected due to kinematical constraints
expected qq bkg:
extrapolation
Poisson err. 68% CL

32. Measurement of BR(t5p p0nt) as a Cross Check
BABAR Preliminary
Repeat the event selection of t5p 2p0nt (reconst. 1 p0)
Repeat the background estimate method.
Validate qq bkg. estimate with ‘signal-free’ data sample (≥3 high-energy photons on the tag side)
Total bkg.
Signal efficiency (%) 2.16 ± 0.16 %
Expected tau bkg. 67 ± ZZ
Expected qq bkg. 84 ± YY
Observed Data 1742
Observed Signal ± XX ±XX
Branching Ratio (x10-4) 1.79 ± XXX ± XXX
BR(t5pp0nt)
ALEPH, ± 0.7 ± 1.2
OPAL, ± 1.8 ± 0.9
CLEO, ± 0.2 ± 0.2
PDG, ± 0.27
Nice cross-check of the event selection and background estimate methods