Rare Tau Decays
Yifan Jin
Belle collaboration
8th June 2020 [email protected] Outline
• Tau at e+e− colliders
• Tau LFV searches
• Recent results of rare tau decays − − + − τ → π ντ ℓ ℓ (ℓ = e or µ) − − τ → ℓ ν ℓ ντ γ (ℓ = e or µ)
• Summary
1 τ and e+e− colliders
• τ lepton discovered back in 1975 has now entered the era of precision. In SM, it only decays via the charged weak interaction.
τ decays to leptons: very clear signature → precise measurement of SM parameters/ contributions from BSM.
Hadronic τ decays: useful tools to study low energy QCD.
Due to its short lifetime (~90 um), the precision of τ results are still way behind that of e/µ. But thanks to its larger mass, contributions of BSM would be enhanced w.r.t. e/µ.
• e+e− collider is the best environment for precision: Low background, high trigger efficiency, good π0 and γ reconstruction. Initial beam condition → missing energy and missing mass.
CLEO, ARGUS, SLD, L3, OPAL, DELPHI, ALEPH, CMD3, BES3, BaBar, Belle, etc…
https://meetings.triumf.ca/indico/event/48/session/11/contribution/68 2 BaBar Detector BaBar and Belle
� = � = 10.58 GeV Common features in design.
Products of τ+τ− are two back to back narrow jets.
3 Flavor-factories
B-factory, Charm-factory, and Tau-factory. �(bb ): 1.05 nb �(cc ): 1.30 nb �(ττ): 0.92 nb
• 9×108 τ+τ− pair events, collected by Belle, still the largest statistics of τ. • LHC experiments also obtain huge statistics of τ from W and heavy flavor decays. 4 e+ e− →
Numerous processes occur at Υ 4� , but distinguishable. A thorough study has been done for τ pair skim.
KKMC → generation of τ+τ−. TAUOLA → τ lepton decays.
5 Tau physics program @ colliders
SM precise measurements:
− − − − • branching fraction of hadronic decays τ → Ksπ ντ , τ → ϕK ντ …
− − 0 − • spectrum of hadronic currents τ → π π ντ , τ → hhhντ …
nd − − • Search for 2 class current τ → π ηντ
• Measurement of |Vus| Br of decays with strange, spectral moments
τ property measurements: • mass • lifetime • EDM • Michel parameters
τ → 3πντ
BSM searches: • τ LFV • τ CPV 0 − − τ → 3ℓ , τ → ℓγ , τ → ℓhh , τ → ℓV … τ → Ksπ ντ
6 τ Lepton Flavor Violation
7 τ LFV
• In neutrino sector, LFV is already seen. So, what about charged leptons?
• Highly suppressed in SM, ∝ ( ) . Not reachable in current experiments. τ SUPER-RARE
• Extensions of SM predict enhancement up to the sensitivity of current experiments.
• Waiting for surprise from the heaviest lepton τ. τ → ℓℓℓ, τ → ℓγ, τ → ℓhh, τ → ℓV0, τ → ℓS0, τ → ℓP0, τ → ∧ h …
8 τ→µ�, τ→µµµ
Reference τ→µ� τ→µµµ SM + � mixing EPJ C8 (1999) 513 10-45 -
-9 -10 SM + heavy Maj �R PRD 66 (2002) 034008 10 10 Non-universal Z’ PLB 547 (2002) 252 10-9 10-8 SUSY SO(10) PRD 68 (2003) 033012 10-8 10-10 τ mSUGRE + seesaw PRD 66 (2002) 115013 10-7 10-9 SUSY higgs PLB 566 (2003) 217 10-10 10-7
BaBar: B(τ→µγ) < 4.4x10-8 PRL 104, 021802 (2010) Belle: B(τ→µγ) < 4.5x10-8 Phys. Lett. B 666, 16 (2008)
Belle: B(τ→3µ) < 2.1x10-8 Phys. Lett. B 687, 139 (2010) BaBar: B(τ→3µ) < 3.3x10-8 PRD 81, 111101 (R) (2010) LHCb: B(τ→3µ) < 4.6x10-8 JHEP 02, 121 (2015) ATLAS:B(τ→3µ) < 3.8x10-7 Eur. Phys. J. C 76, 232 (2016) CMS: B(τ→3µ) < 8.9x10-8 Recent CMS results of a search for τ->3µ decays by Guenakh Mitselmakher 9 τ LFV • A variety of channels have been searched. • Tremendous contributions from several experiments. • We can be more ambitious with Belle II.
•
∎ ∎ ∎ CMS • ATLAS
HFLAV summary plot for τ LFV decays, overlaid with Belle II extrapolation to 50 ab-1 assuming zero background 10 Search for rare decay − − + − τ → π ντ ℓ ℓ
11 − − + − τ → π ντ ℓ ℓ
P. Roig, PRD 88, 033007(2013) Using Resonance Chiral Theory
The first three are QED contributions of a γ emitted off the τ, π and vertex. The solid square (triangle) represents the vector (axial-vector) current contribution. Central value of Br Error band of Br (Theoretical prediction) (Theoretical prediction)
+ − -5 -5 -5 τ → π ντ e e 1.710 x 10 [1.4x10 , 2.8x10 ] + − -6 -7 -5 τ → π ντ µ µ 1.938 x 10 [3x10 , 1x10 ] Belle tries to access these modes for the first time. 12 Physics Motivations
1, Major BKG to the LFV and LNV searches: τ → ℓℓℓ, ℓππ, πℓℓ, whose upper limits on branching fraction have been reduced to the order of 10-8. (π-µ mis- id ~%, π-e mis-id ~‰)
PRD. 85, 011301 (2012) Br < 1.3x10-5 MiniBooNE PRL. 102, 101802 (2009) PRL. 121, 221801 (2018)
2, Probe the New Physics contribution: Heavy long-lived sterile neutrinos.
± ∓ ∗ 3, ℱ ± ∓ ∗ (the π W γ vertex in d and e). + − + − Same vertex in cross channel π → ℓ νl e e : Br(π → e νe e e ) = (3.2 ± 0.5) x -9 + − 10 , lepton universality can be checked. Br(π → µ νµ e e ) is not observed yet, thus can be inferred. Phys. Lett. B 222 533 (1989)
13 − − + − τ → π ντ e e
• Blind analysis of counting events. • Difficulty: contamination from π0, − − + − calibrated by τ → π e e γ ντ.
− − Signal mode: Main BKG(80%): τ → π π ντ (Belle pion form factor) PRD 78, 072006 (2008) π e Dalitz decay of π �-conversion ντ e Br=1.174±0.035% e e π e e π � τ ντ ντ � � e+ e− π0 0 τ + τ τ π e − + − ν τ e e e τ τ 1-prong decay ν τ ν τ 1-prong decay 1-prong decay 14 2 − − + − 1000 DATA τ → π ντ e e ρ-(→π-e+e-γ)ν ρ-(→π-γγ)ν 800 other-ττ non-ττ 5-lepton Invariant Mass of 3 prongs is used 600 MC signal to define the sideband/signal box. Events/0.025 GeV/c L = 562 fb-1 Observed MC BKG MC signal 400 DATA/MC χ2 / ndf 37.95 / 33 events events events Prob 0.2539 p0 0.9841 ± 0.0138 10243 10083±504 202.5±8.1 200 In the sideband, data agree with the
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 known BKG within 1�. M(πee) [GeV/c2]
2 400 DATA 350 ρ-(→π-e+e-γ)ν ρ-(→π-γγ)ν 300 other-ττ Observed events MC BKG events 250 non-ττ 5-lepton 1365 954 ± 45
Events/0.025 GeV/c Signal Region 200 MC signal
150 There is a clear excess of data (closed circles) over the expected background 100 L = 562 fb-1 (colorful histogram). (7.0 � , first 50 observation) 0 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 M(πee) [GeV/c2] 15 − − + − Br(τ → π ντ e e )
Contents Syst. error MC size 3.7% Meanwhile, it is found that the cut ee → ττ 0.3% on invariant mass of three prongs Trigger 1.2% has strong model dependence. 0 For two extreme cases: π veto 1.9% -5 Br_A = (1.46 ± 0.13 ± 0.21) x 10 Br’s of BKG 4.4% -5 Br_V = (3.01 ± 0.27 ± 0.43) x 10 Luminosity 4.7% And a partial Br (M>1.05 GeV/c2) Tracking 4.7% is determined: -6 PID 11.1% (5.09 ± 0.53 ± 0.85 ± 0.11) x 10 stat. syst. model. Total: 14.4% PRD. 100, 071101(R) (2019)
16 − − + − τ → π ντ µ µ
− − + − • Main background is from τ → π π π ντ, where two π’s are misidentified as µ’s. − − + − • Difficulty: PID (π fake rate), calibrated by τ → π π π ντ.
− − + − Signal mode: Main BKG (82%): τ → π π π ντ π → µ misID µ π π π π π π π ντ µ ντ ντ 0 τ τ τ π e+ e− e+ e− e+ e− τ τ τ ν τ ν τ ν τ 1-prong decay 1-prong decay 1-prong decay
17 250 DATA − − + − π-π+π-ν τ → π ντ µ µ - + - 0 200 π π π π ν other-ττ Events/0.4 cm non-ττ Transverse distance of µ+µ− vertex is 150 5-lepton MC signal used to define the sideband/signal box.
100 -1 Observed MC BKG MC signal events L = 562 fb events events DATA/MC χ2 / ndf 14.04 / 17 50 Prob 0.6644 505 477±23 11.4±0.4 p0 0.9912 ± 0.0662 In the sideband, data agree with the 0 0.2 1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2 10.2 known BKG within 1�. Rxy [cm]
250 DATA Syst. of NBKG Observed MC BKG - + - events events π π π ν MC size 1.7% π-π+π-π0ν 2578 2244 ± 109 200 other-ττ Luminosity 1.4% non-ττ ee → ττ 0.3% Events/0.005 cm 150 5-lepton The excess (signal yield) MC signal Tracking 1.4% is 334 ± 51 ± 109 with a Trigger 0.3% 100 -1 significance of 2.8σ. L = 562 fb PID 3.7% Br < 1.14 x 10-5 @90% C.L. Br’s of BKG 1.0% 50 π-µ mis-id 1.5% PRD. 100, 071101(R) (2019)
0 Total 4.9% 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Rxy [cm] 18 First measurement of Michel parameters � and �� − − using τ → ℓ ν ℓ ντ γ
19 Michel parameters in τ
• In the SM, charged weak interaction is described by the exchange of W± with a pure vector coupling to only left-handed fermions (“V-A” Lorentz structure). • The most general, Lorentz invariant matrix element of τ leptonic decay:
Lorentz structure Chirality
• In differential decay width, M square is observable, thus, bilinear combinations of � are accessible → Michel Parameters �, �, �, ��� �. • Deviations towards SM predictions (“V-A”) indicate physics BSM. Contributions from New Physics in τ decays can be enhanced w.r.t µ.
20 − − MP in τ → ℓ �̅ℓ ντ γ
− − • In the radiative leptonic decay τ → ℓ ν ℓ ντ γ:
Final-state radiative photon correlates to the lepton polarisation; in addition, three more Michel parameters, �, � , and ��, become experimentally accessible.
2 � : suppressed by (mℓ/mτ) . @e ~ 8 x 10-8 @µ ~ 4 x 10-3
21 Analysis method
+ + 0 Tag side: τ → π π ν τ, due to its highest b.r.(25%) and simple kinematics.
D0: spin independent; Dij: spin-spin correlation
SM value: 1
The total differential cross section e+ e− → − + 0 (ℓ ν ℓντγ) (π π ν τ) is expressed. As shown in the left figure, MP can differ the shape of the spectrum. 22 Analysis method
Unbinned maximum likelihood method is applied using the following PDF. The negative logarithmic likelihood function (NLL) is constructed and the best estimators of the Michel parameters, � ��� ��, are obtained by minimizing the NLL.
S(x) = S0(x) + S1(x) � + S2(x) �� Bi(x): BKG PDF �(x): selection eff = �i: fraction R(x): correction on MC Corrections: electroweak higher order corrections to e+ e− → τ+ τ−, finite detection ± − resolution, e beam energy spread, external bremsstrahlung of (ℓ ν ℓντγ) + 0 0 (π π ν τ), further MC corrections (trigger, particle ID, track, π and γ + 0 − 0 reconstruction). − + − + (π π ν τ)(π π ντ) (ℓ ν ℓντγ)(π π π ν τ) + 0 − (π π ν τ)(π ντ) Fitter is validated using MC sample with SM parameters. The obtained best-fit values of MP do agree with SM.
23 Lepton spectra
Black and red lines represent distributions of the original and corrected MC. Blue points represent the experimental data.
24 Results
− • For e mode: 776,831 event. Purity: (28.9 ± 0.8)%. BKG: (e ν eντ)[γbrem] e e � is suppressed due to small me; (��) = −0.4 ± 0.8 (stat) ± 0.9 (syst). − • For µ mode: 71,171 event. Purity: (57.4 ± 1.3)%. BKG: (µ ν µντ)[γISR/beam] �µ = −1.3 ± 1.5 (stat) ± 0.8 (syst); (��)µ = 0.8 ± 0.5 (stat) ± 0.3 (syst).
PTEP 2018 (2018) 2, 023C01 (��) = 0.5 ± 0.4 (stat) ± 0.2 (syst).
SM
= 4.95 ± 0.06 ± 0.20
25 syst. dominated by π0 − − Br(τ → ℓ ν ℓ ντ γ)
• A dedicated analysis was done by Babar to measure Br. • Tag side: one prong (85%) >> choosing one mode PRD. 91, 051103(R) (2015) Br(τ → eν νγ) = (1.847±0.015±0.052)x10-2 Br(τ → µν νγ) = (3.69 ± 0.03 ± 0.10)x10-3 = 5.01 ± 0.20
CLEO
PRL. 84, 830 (2000) 26 Summary o Great effort on τ LFV search from several experiments. Observation of LFV will be a clear signature of physics BSM.
o The Br of τ→ πντee is measured FOR THE FIRST TIME, Br = (1.46 ÷ 3.01) x 10-5. A precise Br measurement is important to understand the π±W∓γ∗ vertex. -5 o An upper limit is set on the Br of τ→ πντµµ at 90% CL. Br < 1.14 x 10 . It is the FIRST upper limit on this decay mode. These measurements can be used to constrain parameters of the sterile neutrino models, such as mass, mixing strength, lifetime. Improvement expected at Belle II. o Michel parameters, η and ξκ, measured FOR THE FIRST TIME using τ→ ℓν νγ. � = −1.3 ± 1.5 ± 0.8; �� = 0.5 ± 0.4 ± 0.2, which can verify the Lorentz structure of the charged weak interaction and deviations signify New Physics. Precise and consistent Br measured from Babar and Belle.
“τ physics results and prospects at Belle II” this evening by Michel Villanueva!
27 Signal
Thank you !
28 Back up Uncertainty of the branching fraction
� = � � �
The systematics uncertainty includes: • Cross section of ττ: 0.919 ± 0.003 nb, by KKMC. • Luminosity: 1.4% using Bhabha events. • Statistic error of MC: Poisson variance ∗ 0 0 • Tracking efficiency: Using partially reconstructed D → D πslow, D − + − + → K π π , K → π π (one daughter here allowed not to be reconstructed). Comparing track finding in MC and EXP, 0.35% per 0 *− + − *− track. Low momentum region is checked by B → D π , π in D serves as probe. ∗+ 0 − + • Particle identification: D →D π →K π π for πID (π serve as tag; K−, π+ as probe), γγ→l+l− and J/ψ→l+l− for lepton ID • Trigger: by Belle simulation study • Br of BKG components: taken from PDG. • π0 veto: statistic error of the reference study. • π -> µ mis-identification: statistic error of the reference study. 30 Michel parameters
31 32 BF results
= 4.95 ± 0.06 ± 0.20 PTEP 2018 (2018) 2, 023C01
% % % %
Be/Bµ 1 5.01 ± 0.20
2 4.9 ± 0.06 1. PRD. 91, 051103(R) (2015)
3 5.007 2. PRL. 84, 830 (2000)
3 4.793 3. JHEP. 07, 153 (2015)
3 4.605 33