SciPost Phys. Proc. 1, 002 (2019)

Latest Belle results on Tau decays
Yifan Jin1? , Denis A. Epifanov2,3 and Hiroaki Aihara1 ,on behalf of the Belle collaboration
1 The University of Tokyo, Tokyo, Japan
2 Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russian Federation
3 Novosibirsk State University, Novosibirsk, Russian Federation? jin@hep.phys.s.u-tokyo.ac.jp
Proceedings for the 15th International Workshop on Tau Lepton Physics,
Amsterdam, The Netherlands, 24-28 September 2018
doi:10.21468/SciPostPhysProc.1

Abstract
We present preliminary results of a latest measurement at Belle, the branching fraction ofrare tau decay, τ− → π− ντ `+ `− (` = e or µ), using a 562 fb−1 data set. The branching fraction of τ− → π− e+ e− ντ is measured to be B (τ− → π− e+ e− ντ ) = (2.11 ± 0.19 ± 0.30) × 10−5 ,where the first uncertainty is statistical and the second is systematic. An upper limit isset on the branching fraction of τ− → π− µ+ µ− ντ , B (τ− → π− µ+ µ− ντ ) < 1.06 × 10−5 , at
90% confidence level.
Copyright Y. Jin et al.
This work is licensed under the Creative Commons
Attribution 4.0 International License.
Published by the SciPost Foundation.

1

Received 03-12-2018
Accepted 15-01-2019
Check forupdatesPublished 18-02-2019
doi:10.21468/SciPostPhysProc.1.002

Introduction

The Belle detector, which was installed at the interaction point of the electron-positron
asymmetric energy collider at the KEK (KEKB), was working not only as a B-factory but also asa Tau-factory. The world’s largest statistics of tau leptons was collected at Belle, which makes it
possible to measure branching fractions for rare decays (B ∼ 10−5 ) of tau. We herein present
the preliminary result of a latest measurement by Belle, the branching fraction of rare decay
τ− → π− ντ e+ e− . 1
A γ∗ W ∗ π vertex is involved in the τ− → π− `+ `− ντ decay, which plays an important rolein calculating the radiative corrections to the τ− → π− ντ decays [1] and in the evaluationof contributions from the hadronic light-by-light scattering to the muon anomalous magnetic
moment [2]. The measured result of branching fraction could be used to validate the calculation [3] from Resonance Chiral Theory, a prevailing phenomenological approach to describe
strong interaction at the energy region below tau mass. Meanwhile, rare decays of τ often
serve as a probe of the physics beyond the Standard Model. A sterile neutrino could enter the
diagrams of the decay mode of concern [4], resulting in observable enhancement on branching fraction. Also, a precise measurement of B (τ− → π− ντ `+ `− ) could facilitate searches for
lepton flavour violating decays.
1

unless otherwise specified, charge-conjugated decays are implied throughout the paper

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SciPost Phys. Proc. 1, 002 (2019)2

Detector and MC simulations

A 562 fb−1 data set collected with the Belle detector at the KEKB asymmetric-energy e+ e−
collider is exploited. The Belle detector is a general purpose large-solid-angle spectrometerconsisting of a silicon vertex detector (SVD), a central drift chamber (CDC), an aerogel threshold Cherenkov counter (ACC), a barrel-like arrangement of time-of-flight scintillation counters(TOF), and an electromagnetic calorimeter (ECL) located inside a superconducting solenoid
coil that provides a 1.5 T magnetic field. Outside the coil, an iron flux return yoke is instrumented to detect K L0 mesons and to identify muons (KLM). A detailed description of Belle
detector can be found elsewhere [5].
To determine the contamination of background processes and the detection efficiency ofsignal events, Monte Carlo (MC) samples are employed. The MC samples for hadronic processes are generated by EVTGEN package [6], KKMC [7] for fermion pairs, AAFH [8] for twophoton production of fermion pairs, and CTOY for cosmic ray muons. The decay of τ lepton
is carried out by TAUOLA [9]. The final-state radiation of charged tracks is taken into accountby using PHOTOS [10]. The response of the detector is simulated by a GEANT3-based program [11]. Embedding the signal mode in TAUOLA, a signal generator is prepared according
to Ref. [3]. The optimisation of selection
p criteria using MC samples is implemented by maximising a figure of merit defined as S/ S + B, where S (B) stands for the number of signal(background) events.

3

Event selection and reconstruction

The selection is composed of two stages, aiming at suppressing background processes while
retaining a high efficiency for the decay mode of concern. The first stage selects e+ e− → τ+ τ−
events and substantially reject the backgrounds from other processes that occur at Υ (4S). The
second stage proceeds to select one τ decays into π− ντ `+ `− , where a vertex fit is performedon the `+ `− pair, and the other τ decays into one prong.

3.1

Selection of τ+ τ− events

Events with four tracks and zero net charge are selected. The distance of the closest approachof each charged track to the interaction point must be within ±5 cm along the beam direction(the z axis) and 1 cm in the transverse plane (the x − y plane). All four charged tracks are
required to have transverse momentum larger than 0.1 GeV/c and the maximum of transverse
momenta must exceed 0.5 GeV/c. The total energy deposited in the ECL must be less than 10
GeV. A vertex fit is performed by using all charged tracks to seek for the position of the primaryvertex of the event, which is required to be near the interaction point within 0.5 cm in the x − yplane and ±2.5 cm along the z axis. Photons, neutral tracks reconstructed from clusters in ECL,
are selected with energy threshold of 50 MeV in the barrel region (32◦ < θγ < 130◦ ) and 100
MeV in the end cap region.
In the centre of mass (CMS) frame, the sum of the magnitudes of charged tracks’ momenta
is required to be less than 10 GeV/c, meanwhile the sum of the magnitudes of charged tracks’
momenta and neutral tracks’
P energies
P must be larger than 3 GeV. A missing momentum isdefined as Pmiss = Pinit P− i Ptrk,i − P i Pγ,i , where Pinit is the initial four momentum of thecolliding e+ e− beams, i Ptrk,i and i Pγ,i are the four momentum of the ith charged andneutral tracks. Only events satisfying 1 GeV/c2 < Mmiss < 7 GeV/c2 and 30◦ < θmiss < 130◦are selected, where Mmiss and θmiss are the mass and polar angle of the missing momentum in
the CMS frame, respectively.

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SciPost Phys. Proc. 1, 002 (2019)

The event must satisfy at least one of the following additional conditions. 1, in the CMS
frame, the sum of the magnitudes of charged tracks’ momenta, neutral tracks’ energies and themissing momentum must be less than 9 GeV. 2, in the CMS frame, the maximum of opening
angles between two charged tracks must be larger than 175◦ . 3, in the laboratory frame, atleast two charged tracks are detected in the barrel region. 4, in the laboratory frame, theenergy deposit of all charged tracks in ECL must be less than 5.3 GeV.

3.2

Selection of τ− → π− e+ e− ντ events

For each track, pion (Lπ ) and kaon (LK ) likelihoods are constructed from the ACC response,
the specific ionization (d E/d x) in the CDC and the flight-time measurement in the TOF. A
likelihood ratio PK/π = LK /(Lπ + LK ) is formed and a cut PK/π < 0.6 is applied to selectpions. To select electrons, a likelihood ratio selection Pe = Le /(Le + L x ) > 0.5 is applied,
where the electron (Le ) and non-electron (L x ) likelihood functions include information on
the specific ionization in the CDC (d E/d x), the ratio of the energy of the cluster in the ECL to
the momentum of the track, the transverse shape of the ECL shower and the signal amplitudein the ACC.
In the case of multiple e+ e− vertex candidates, the one with the best vertex fit quality is
chosen. Pion candidates are required to have a momentum larger than 0.2 GeV/c in both the
CMS and LAB frame and its Pe < 0.2. To recover bremsstrahlung effect, photon candidates
that associate to electron tracks with a cross angle within 0.05 radian and an energy lower thanthat of the electron in CMS frame are added to the electron track. Meanwhile, the invariant
mass of the new e+ e− pair must be less than 0.05 GeV/c2 . The fourth charged track is regarded
as the daughter of the accompanying τ.
To mitigate backgrounds due to external gamma conversion, cuts on the position of thee+ e− vertex are applied. Transverse position of the e+ e− vertex (|R x y |) must be less than 1.2
cm, and longitudinal position of e+ e− vertex (Z) must be in the range of [-1 cm, 1.5 cm].
To reduce hadronic background, thrust magnitude and the cosine of the angle between the
momentum of the τ in signal hemisphereand thesystem in the CMS frame are employed.
P −
Pπ``
→
−
→
−
→
→
The thrust magnitude is defined as i | pi · n T |/ i | pi |, where −pi is the momentum of the ith
particle in the CMS frame, either a charged or neutral track, and must locate in the range of[0.85, 0.99]. The angle is calculated under the assumption that the massless neutrino is notreconstructed:
22Ebeam Eπee − m2τ − Mπeecos θτ−πee ≡,(1)2|Pτ | · |Pπee |where Ebeam is the energy of the beam (5.29 GeV), and Eπee , Pπee and Mπee are the energy,
momentum and invariant mass of the πee system, respectively. The cos θτ−3πee is required tolocate in physical region (| cos θτ−3π`` | ≤ 1). To suppress τ− → π− π0 ντ , γ veto and π0 veto
are employed. In the signal hemisphere, at most one photon is allowed with energy less than
300 MeV. A π0 candidate is reconstructed by two photons (110 < Mγγ < 160 MeV/c2 ) or one
photon and a pair of electron (110 < Me+ e− γ < 165 MeV/c2 ). Events with such π0 candidates
are discarded. Also, to further suppress the backgrounds from the ρ − (π− π0 ) resonance, theinvariant mass of πee system (Mπee ) is required to be larger than 1.05 GeV/c2 and less than
1.8 GeV/c2 .
The detection efficiency of the τ− → π− e+ e− ντ events is found to be (1.88 ± 0.07)%. The
main background comes from τ− → π− π0 ντ → π− e+ e− γντ (55.83%) andτ− → π− π0 ντ → π− γγντ (24.22%).

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SciPost Phys. Proc. 1, 002 (2019)

3.3

Selection of τ− → π− µ+ µ− ντ events

Charged tracks with PK/π < 0.6 and Pe < 0.8 are selected as pion candidates. A likelihood
ratio cut Pµ = Lµ /(Lµ + Lπ + LK ) > 0.7 is applied to select muons. The Lµ and L x (x = π, K)
likelihood functions are calculated from two variables: the difference between the ranges
calculated from the momentum of the particle and measured by KLM, and the χ 2 of the KLM
hits with respect to the track prolongated from CDC to KLM.
In the case of multiple µ− µ+ vertices, the candidate owning the smallest angle between µ−
and µ+ in the CMS frame is chosen. Only events with a µ− µ+ vertex whose transverse radius(R x y ) is less than 0.15 cm and invariant mass less than 0.85 GeV/c2 are selected.
To reduce backgrounds from τ− → π− π+ π− ντ mode, a stringent cut Pµ > 0.97 is imposed
upon muon candidates and their transverse momentum are required to be larger than 720
MeV/c to ensure hitting the KLM detector. Meanwhile muon candidates are required to have
PK/π < 0.8 to suppress τ− → K − π+ π− ντ mode. To mitigate backgrounds from hadronic
processes, the event is required to have a thrust magnitude larger than 0.9 in the CMS frame.
The sum of energies of three final state charged tracks (π, µ, µ) of signal τ must be less thanthe energy of the beam. Also, pseudo mass of πµµ system is required to be less than 1.8
GeV/c2 . The pseudo mass of πµµ system is defined as:Ç2m∗ = 2 · Eπµµ (E beam − Eπµµ ) + Mπµµ
− 2 · |Pπµµ |(E beam − Eπµµ ),(2)where Eπµµ , Pπµµ and Mπµµ are the energy, momentum and invariant mass of the πµµ system, respectively. To mitigate backgrounds involving π0 , γ veto is employed. In the signal
hemisphere, the sum of energies of all photons is required to be less than 300 MeV. Moreover,the number of photons in both hemispheres must be less than 6.
The detection efficiency of the τ− → π− µ+ µ− ντ events is found to be (4.13 ± 0.16)%. The
main background comes from τ− → π− π+ π− ντ (81.88%) and τ− → π− π+ π− π0 ντ (8.26%).

4

Results

4.1

Determination of the branching fraction

The signal yield is assumed to be the difference between the number of observed eventsand the number of background events predicted by the MC samples. The branching fractionof τ− → π− `+ `− ντ is calculated in adhering to the following formula:B (τ− → π− `+ `− ντ ) =Nobs − NBKG,
σττ · L · εsig

(3)

where σττ = (0.919 ± 0.003) nb [12] is the cross section of ττ production at Υ (4S), L theluminosity of exploited experimental data, εsig the detection efficiency of signal events, Nobs
the number of observed events from experimental data and NBKG the number of background
events predicted by the MC.

4.2

Estimation of systematic uncertainty

For the measurement of branching fractions, the following sources of systematics are taken
into account. The uncertainty due to the charged tracks’ finding efficiency is estimated byusing the partially reconstructed D∗− → D0 π− , D0 → π− π+ KS0 events. The uncertainty due
to particle identification (PID) includes the contribution from the PK/π requirement, which isinvestigated by a control sample of D∗+ → D0 π+, D0 → K − π+ , and the contribution fromslow
+ −lepton identification studied by the γγ → ` ` and J/ψ → `+ `− processes. In addition, the
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SciPost Phys. Proc. 1, 002 (2019)

π → µ mis-identification (π fake rate) is determined by a control sample of τ± → π± π− π+ ντ .
The uncertainty associated with luminosity is obtained by using Bhabha events where the final state electrons are required to be detected in the barrel region. The uncertainty associatedwith the trigger efficiency is investigated by a dedicated MC program. The uncertainty due tothe π0 reconstruction is investigated by a control sample of τ− → π− π0 ντ , π0 → e+ e− γ. The
uncertainty arising from the limited size of MC samples for the study of background contamination and efficiency of signal events is estimated via its binomial variation. The uncertaintyof the branching fractions of background modes are also taken into account.

4.3

B (τ− → π− e+ e− ντ )After all selection criteria, 676 events are observed in the signal box of τ− → π− ντ e+ e− witha background expectation of 478 ± 23 events and 689 events are observed in the signal boxof the charge-conjugate mode, τ+ → π+ ν̄τ e+ e− , with a background expectation of 476 ± 22
events, as shown in Fig. 1, where daggers over-number the colourful histogram. A clear excess
of events above the expected background is observed, which gives rise to a branching fraction
B (τ− → π− e+ e− ντ ) = (2.11 ± 0.19 ± 0.30)× 10−5 , where the first uncertainty is statistical andthe second one is systematic. The systematic uncertainties are summarized in Table 1.

(a) Signal box of τ− → π− ντ e+ e− .

(b) Signal box of τ+ → π+ ντ e+ e− .

Figure 1: Distribution of the invariant mass of e+ e− π (M (eeπ)). Daggers stand forthe observed data and histogram for MC. MC sample is normalized with respect tothe luminosity.

4.4 B (τ− → π− µ+ µ− ντ )After all selection criteria, 1315 events are observed in the signal box of τ− → π− ντ µ+ µ−with a background expectation of 1129 ± 55 events and 1263 events are observed in the signal box of the charge-conjugate mode, τ+ → π+ ν̄τ µ+ µ− , with a background expectation of1115 ± 54 events, as shown in Fig 2. The observed events are consistent with the backgroundexpectation within 3σ. The systematic uncertainties of background expectation includes luminosity, tracking, particle identification, MC sizes, trigger, accuracies of branching fractions ofbackground modes and π → µ mis-identification calibration. As a result, an upper limit is set
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SciPost Phys. Proc. 1, 002 (2019)

Table 1: The breakdown of systematic uncertainties.
Luminosity
Tracking
PID
MC sizeττ cross section
Trigger
π0 vetoB ’s of BKG modes
In total

4.66%
4.66%
11.14%
3.74%
0.3%
1.16%
1.86%
4.42%
14.4%

on this decay mode taking into account the systematic uncertainty of background expectationand the statistical uncertainty of observed events, B (τ− → π− µ+ µ− ντ ) < 1.06 × 10−5 at 90%
CL.

(a) Signal box of τ− → π− ντ µ+ µ− .

(b) Signal box of τ+ → π+ ντ µ+ µ− .

Figure 2: Distribution of the transverse distance of µ+ µ− vertex (Rxy ). Daggers standfor the observed data and histogram for MC. MC sample is normalized with respect
to the luminosity.

5

Conclusion

Using a 562 fb−1 data set collected at the Υ (4S) resonance with Belle detector at the KEKB
asymmetric-energy e+ e− collider, the branching fraction of τ− → π− e+ e− ντ is obtained for the
first time, B (τ− → π− e+ e− ντ ) = (2.33 ± 0.19 ± 0.30) × 10−5 , where the first error is statisticaland the second error is systematic, with 5.9σ significance to reject background-only hypothesis.
An upper limit is set on the branching fraction of τ− → π− µ+ µ− ντ ,B (τ− → π− µ+ µ− ντ ) < 1.06×10−5 , at 90% CL. The measured result is consistent with the theoretical prediction from the Standard Model and could facilitate searches for physics beyond
the Standard Model.
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SciPost Phys. Proc. 1, 002 (2019)A

MC samples for τ− → π− π0 ντIt is worth mentioning that the MC samples of τ− → π− π0 ντ , main background in theanalysis of τ− → π− e+ e− ντ , is generated according to the Belle pion form factor [13]. The
pion form factor obtained by Belle is consisted with the previous CLEO result at the peak region
while differ in the high mass region as shown in Fig. 3. In this analysis, the pion form factor
from Belle is adopted due to its higher precision.

Figure 3: Comparison of pion form factor obtained by Belle to that of CLEO.

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