Precise measurement of hadronic tau-decays

Precise measurement of hadronic tau-decays with eta mesons at Belle 2008.9.23 Tau08 Yoko Usuki Nagoya Univ. K. Inami and Belle collaboration Belle 1

Introduction Belle detector has collected the τ-pair data with the highest statistics in the world. 700fb -1 500fb -1 300fb -1 At the present, about 850fb -1 of data have been collected. It corresponds to 7.0x10 8 τ-pairs! 2000 2004 2008 τ hadronic decay from e + e τ + τ process is very clean. τ hadronic decay is good for studying low energy QCD phenomena. Test of the Vector dominance model (VDM) Test of the conserved vector current (CVC) through BR and mass spectra in τ ππ 0 ην decay. 2

Motivation We can test CVC through τ ππ 0 ην decay. CLEO s data (τ ππ 0 ην) data BG MC (phase space) CLEO collaboration has already studied τ ππ 0 ην decay, but experimental statistics was very limited. M ππ0η is not distinguishable from phase space alone. By using a 100 times larger data sample than that t of CLEO, we can test CVC from not only BR(τ ππ 0 ην ) but also M ππ0η. M.Artuso et.al, CLEO collaboration, PRL 69 (1992) 23 3

Contents Event selection η with 1 charged track τ K ην, K π 0 ην, π π 0 ην with η γγ Cross check for τ K η( γγ)ν τ K η( πππ 0 )ν Result η with K S τ π K S ην, K K S ην Result τ K* ην study τ K π 0 ην, π K S ην Discussion Compare with the previous result Compare with the theoretical predictions Check for CVC 4

Event selection Data set:490fb -1 tag side τ + l + νν; 1 charged track Require lepton (to suppress qq events) signal side τ X ην; ; 1 or 3 charged tracks X : K, K π 0, π π 0, π K S, K* (892) systems η π + π π 0 is used for τ K ην decay only π 0 γγ : 105<M γγ<165mev/c 2 other requirements π 0 veto missing momentum (X denotes K, K π 0, π π 0, π K S, K* (892) systems) π 0 γγ K + S π π K* (892) K S π The number of signal events is evaluated from η mass or K* mass distribution. 5

η with 1 charged track 6

Kην N η =1,387±43 τ K ην (η γγ) data Fit result BG shape CLEO s result in τ Kη( γγ)ν mode Kπ 0 ην Kην ππ 0 ην Crystal-Ball function + second-order polynomial function Kηην πηην qq with η Mi Main η-peaking BG components for τ KηνK are τ KπK 0 ην, ππ 0 ην, ee qq. By evaluating the number of η, B( K Br(τ Kην) )is measured. But the signal η peak is contaminated by Kπ 0 ην, ππ 0 7 ην etc.

Peaking BG : Kηην,πηην,qq (η γγ) Kπ 0 ην Kηην Kην πηην ππ 0 ην qq with η We estimate the contamination of Kηη, πηη and qq to the signal from data. τ K ηην, π ηην Kηην (Special selection of K/π ηηcandidates) πηην data Fit result BG shape Crystal-Ball function + second-order polynomial function BR(τ Kηην)<3.0x10-6 @90%C.L. BR(τ πηην)<7.4x10-6 @90%C.L. The contamination to the signal mode can be ignored. qq with η evaluate qq events by comparing data and qqmc with qq enriched selection (M tag >M τ, no M sig <M τ, P e/μ <0.8) qq contamination is evaluated to 2.8%, 10% and 3.6% of the signal candidates, N η, in the τ Kην, τ Kπ 0 ην and τ ππ 0 ην decay, respectively. 8

Kην τ K ην, π π 0 ην, K π 0 ην (η γγ) Kπ 0 ην ππ 0 ην N η =1,387±43 N η =270±33 N η =5,959±105 dt data Fit result BG shape N = 2N N j ττ 0 0 ( i, j = K ην, K π ην, π π ην ) i ε j B i efficiency Branching ratio i Kπ 0 ην Kηνη ππ 0 ην Kηην πηην qq with η estimate η yield fit Crystal Ball function for γγ mass distributions Simultaneously, l their BR are evaluated. We can suppress systematic errors for each modes 9

Cross check for τ K ην (η γγ) data Fit result BG shape Kη( πππ 0 )ν As a cross check for τ Kη( γγ)ν mode, we measure the BR of τ Kη( πππ 0 )ν mode. BR(τ Kην) =(1.60±0.15±0.10)x10-4 @η π + π π 0 =(1.57±0.05±0.09)x10 05±0 09)x10-4 @η γγ Crystal-Ball function + second-order d polynomial l function CLEO s result in τ Kη( πππ 0 )ν mode We find a good agreement between these two results. Our measurements have self consistency! 10

Systematic study Signal modes Kην Kπ 0 ην ππ 0 ην Kην Items η γγ η πππ 0 BG subtraction Kην -- 0.6 1.8x10-3 -- Kπ 0 ην ππ 0 ην 0.3 7.5x10-2 -- 3.3 4.2x10-2 -- 0.4 0.1 ππ 0 π 0 ην qq -- 1.5 -- 6.0 04 0.4 0.5 -- 1.5 Detection efficiency K/π / lepton-id 3.3/2.3 2.2/2.8 1.0/2.6 2.8/2.6 Tracking π 0 / η γγ π 0 veto 1.3 --/2.0 2.8 1.3 2.0/2.0 2.8 1.3 2.0/2.0 2.8 3.3 2.0/-- -- stat. error of signal MC BR(τ πππ 0 ) Luminosity 1.4 σ(e + e τ + τ ) 0.3 total 5.9% 9.1% 5.3% 6.2% By evaluating cross-feed BG simultaneously, we can suppress systematic errors. 0.5 -- 1.7 -- 0.5 -- 1.3 1.6 11

Results (η with 1 charged track) Belle preliminary Modes Our Br or upper limit τ Kην (@η γγ) (1.57±0.05±0.09)x10 0.09) 0-4 τ Kην (combined) (1.58±0.05±0.09)x10-4 combined τ Kην (@η πππ 0 ) (1.60±0.15±0.10)x10-4 consistent τ Kπ 0 ην (4.6±1.1±0.4)x10-5 τ ππ 0 ην (1.35±0.03±0.07)x10-3 τ Kηην <3.0x10-6 @90% C.L. τ πηην <7.4x10-6 @90% C.L. The self consistency shows that our results are reliable. 12

η with K S 13

πk s ην N η =161±18 τ π K s ην data Fit result BG shape KK s ην 3πην (ex.k S ) N η =5.6±3.6 N η =67.9±17.0 ππ 0 K s ην N j 3πην = efficiency i 2 Nττ ε jb ) i i πk s ην ( i, j ± = π K Sην, K K Sην,3π ην Branching ratio Simultaneously, these BR are evaluated. (K s sideband) KK s ην BR(τ ( ππ 0 K ππ 0 s sη ην) ) K s sην qq with η <2.5x10-5 @90%C.L. Crossfeed:1% Crossfeed:13% 14 Crystal-Ball function + second-order polynomial function

Results (η with K S ) Belle preliminary Modes Our Br or upper limit τ πk s ην (4.4±0.7±0.3)x10-5 τ KK s sην <4.5x10-6 @90% C.L.. τ ππ 0 K s ην <2.5x10-5 @90% C.L. The systematic error for τ πk s ην Total : 6.4% Fitting function : 4.1% The uncertainty from the fitting function is dominant one 15

τ Κ ην study 16

τ K* ην Charged K*(892) decays into Kπ 0 or πk S with same rate because isospin relation. BR(τ Kπ 0 ην)=(4.6±1.1±0.4)x10-5 τ Kπ 0 ην BR(τ πk 4±0-5 s ην)= (4.4±0.7±0.3)x10 Convoluted Breit-Wigner function + bg function K* N Κ =122±17 This agreement suggests that K* is dominant in both modes. τ πk S ην K* N Κ =123±14 data Fit result BG shape Main BGs in these modes are evaluated from M γγ side bands, respectively. These fitting results show that K*(892) is almost 100% in the final state in both τ Kπ 0 ην and τ πk S ην decays. 17

Modes Results (τ Κ ην ) Our Br Belle preliminary τ K*ην (combined) (1.34±0.12±0.09)x10-4 0-4 τ K*ην (@Κ Κπ ) (1.13±0.17±0.18)x10 combined τ K*ην (@Κ πκ S ) (1.46±0.16±0.09)x10-4 consistent τ πk S ην mode plays a role as a cross check for τ Kπ 0 ην. The self consistency shows that our results are reliable. The systematic error for τ K*ην (@Κ Κπ 0 ) Total : 16.2% / Fitting function : 15.0% The systematic error for τ K*ην (@Κ πκ S ) Total : 6.4% / Fitting function : 4.1% The uncertainty t from the fitting function is dominant one 18

DISCUSSION 19

Comparison with previous CLEO results We obtain precise results in each τ decay mode including η. Bll Belle preliminary i Modes Our Br(x10-3 ) CLEO s Br(x10-3 ) Error ratio δ(cleo)/δ(belle) τ Kην 0.158±0.005±0.009 0.26±0.05±0.05 7.0 τ Kπ 0 ην 0.046±0.011±0.004 0.177±0.056±0.071 7.5 τ ππ 0 ην 135±003±007 1.35±0.03±0.07 17±0 1.7±0.2±0.2 2±02 38 3.8 τ K S πην 0.044±0.007±0.002 0.100±0.035±0.011 5.3 τ K*ην 0.134±0.012±0.009 0.290±0.080±0.042 6.0 Modes τ K s Kην Our Upper limit <4.5x10-6 @90% C.L. The central values of our BRs in all modes are lower than those of the CLEO s results. τ K s ππ 0 ην <2.5x10-5 @90% C.L. Underestimate BG contributions in CLEO τ Kηην <3.0x10-6 @90% C.L. Cross feed BG contribution τ πηην <7.4x10-6 @90% C.L. qq High statistics enable us to reliably estimate BG contributions for each mode using data. We check the self consistency of BR in several modes. 20

Comparison with theoretical predictions Modes Our Br Theoretical predictions of Br CVC Belle preliminary Chiral perturbation theory τ Kην (1.58±0.05±0.09)x10 05±0 09)x10-4 ---------- 1.2x10-4 [3], 2.2x10 2x10-4 [5], 1.6x10-4 [6] τ Kπ 0 ην (4.6±1.1±0.4)x10-5 ---------- 8.8x10-6 [3], 7.7x10-6 [6] τ ππ 0 ην (1.35±0.03±0.07)x10-3 (1.3±0.2)x10-3 [1], 1.5x10-3 [2] 3x10-3 [3], 1.4x10-3 [4], 1.9x10-3 [5] τ K 4±0 11 10 s πην (4.4±0.7±0.2)x10-5 ---------- 1.1x10-5 [3], 0.9x10-5 [6] τ K*ην (1.34±0.12±0.09)x10-4 ---------- 1.0x10-4 [5] Modes Our Upper limit Theoretical predictions of Br CVC Chiral perturbation theory τ K s Kην <4.5x10-6 @90% C.L. ---------- 1.6x10-7 [3], 1.4x10-7 [6] τ K -5 s ππ 0 ην <2.5x10 @90% C.L. ---------- ---------- τ Kηην <3.0x10-6 @90% C.L. ---------- 1.6x10-9 [3], 7.0x10-9 [6] τ πηην <7.4x10-6 @90% C.L. ---------- 1.1x10-9 [3] [1]S.I.Eidelman, PLB 257 (1991) 437 [2]F.J.Gilman, PRD 35 (1987) 3541 [3]APich [3]A.Pich, PLB 196 (1987) 561 [4]E.Braaten, PRD 36 (1987) 2188 [5]B.A.Li, PRD 55 (1997) 1436 [6]G.J.Aubrecht, PRD 24 (1981) 1318 The CVC prediction of BR(τ ππ 0 ην) agrees well with our result. (our result is more precise) High precision of our experiment will allow to discriminate between different theoretical models.

Check for CVC Belle preliminary τ ππ 0 ην MC generator is designed based on σ(e + e π + π η) measured more than 10 years ago, assuming CVC. M ππ0 data ππ 0 ην MC ττ MC M ππ0η The distributions for the observed data and MC agree well. CLEO s data M ππ0η data BG MC (phase space) CVC e + +e hd hadrons τ hd hadrons + ν TAUOLA MC program : S.Jadach, B.F.L.Ward, Z.Was, Comp.Phys.Commun. 130 (2000) 260 22

Check for CVC Belle preliminary τ ππ 0 ην MC generator is designed based on σ(e + e π + π η) measured more than 10 years ago, assuming CVC. M ππ0 data ππ 0 ην MC ττ MC M ππ0η The distributions for the observed data and MC agree well. CLEO s data M ππ0η data BG MC (phase space) CVC e + +e hd hadrons τ hd hadrons + ν Now we can compare τ hadrons+ν and e + e hadrons Check in high accuracy Now, we can compare τ hadrons+ν and e e hadrons with high accuracy to check CVC. 23 TAUOLA MC program : S.Jadach, B.F.L.Ward, Z.Was, Comp.Phys.Commun. 130 (2000) 260

Summary We perform a high-precision h ii study td of τ X+ηνX based on 4.5x10 8 τ-pairs. i Improve the uncertainty of BR(τ X+ην) by a factor of 3.8~7.5 times BR(τ Kην)=(1.58±0.05±0.09)x10± ± -4 BR(τ Kπ 0 ην)= (4.6±1.1±0.4)x10-5 BR(τ K s Kην) < 4.5x10-6 @90% C.L. BR(τ ππ 0 ην)= (1.35±0.03±0.07)x10-3 BR(τ K s ππ 0 ην) < 2.5x10-5 @90% C.L. BR(τ Kηην) < 3.0x10-6 @90% C.L. BR(τ K s πην)= (4.4±0.7±0.2)x10-5 BR(τ πηην) < 7.4x10-6 @90% C.L. BR(τ K*ην)= (1.34±0.12±0.09)x10-4 Our results are reliable e BG estimation All ττ BGs are evaluated ourselves. qq BG are estimated by data. The self consistency in τ Kην and τ K*ην branching ratios Check CVC with high accuracy Belle Belle preliminary The precise measurement of τ ππ 0 ην decay High statistical data The CVC prediction of BR(τ ππ 0 ην) agrees well with our result. M ππ0 and M ππ0η distributions show that CVC model works well at this level.

BACK UP 25

MC generation For these modes, the efficiency is determined assuming V-A VAinteraction ti and dthe phase space decay for the hadronic system. τ Kην τ Kπ 0 ην τ Kηην τ πηην τ K K s πην τ K s Kην τ K K 0 s ππ ην τ K*ην 26

CLEO s results Kην Phys. Rev. Lett. 76, 4119 4123 (1996) Kην πην Integrated luminosity of 3.5 fb 1 was analyzed. Totally, 50 events were observed. They assume branching ratio of Kπ 0 ην, ~ 10 6 from theory B(K Br(Kην) = (2.6±0.5±0.4) 10 05 04) 4 Br(πην) < 1.4 10 4 27

Event selection for Kηην and πηην 1-1 topology, η γγ Signal-side N γ=4 K/π ID for track π 0 veto for γ η P ητ selection in τ rest frame for Kηην η E γ >0.1 (0.3) GeV for Kηην (πηην) Lepton tag e ν τ η η γ γ K /π e + γ γ l + τ + ν ν 28

Event selection for K S πην τ K s ( π π + )π ην 3-1 topology Signal side Nγ=2 0.45<M ππ <0.55 Vertex const. fit h signal side 0.5<r<30 cm for K s vertex Electron veto for hadrons τ Remove Bhabha BG with shower Eγ>0.3 γ for eta daughters Tag side Lepton tag Nγ<3 e τ π + K s π τ + e + tag side γ η γ 29