Recent Progress on. Tau Lepton Physics. ν τ. A. Pich IFIC, Valencia. Euroflavour 08, IPPP, Durham September 2008

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1 Recent Progress on Tau Lepton Physics ν e, μ W, ν, ν μ, e d θ u A. Pich IFIC, Valencia Euroflavour 08, IPPP, Durham -6 September 8

2 ν 5 GF m Γ( ν lνl ) = f( m / ) 3 l m r 19π EW W e e, μ ν, ν μ 3 4 f ( x) = 1 8x+ 8x x 1x log x r EW = (Marciano-Sirlin) B e Bμ = = ± ± ( ) 10 s ( B B ) e exp μ / = ± 0.39 Physics A. Pich - Euroflavour 08

3 Muon Lifetime ± 0.4 PDG '06 μ ( μs ) = ± 0.4 MuLan ' ± 0.35 FAST ' 08 μ/e separator kicker M U L A N F A S T New World Average: 1 μ 5 GF m μ 3 = (1 + δqed ) 19π δ QED known to 0.3 ppm (van-ritbergen & Stuart) μ = (18) μs G F = (6) x 10-5 GeV - (5 ppm) Physics A. Pich - Euroflavour 08

4 , Br( μ), Br( e) 0.3% precision Future Improvements: BABAR, BELLE, KEDR, BESIII, SuperB, δm ~ 0.03 MeV (1.7 ppm) BESIII 3π ν pseudomass m = ± MeV ± 0.35 MeV ± MeV 0.3 ± (PDG06) (BELLE) (KEDR) + Resonance Depolarization Method ± 0.14 BELLE Physics A. Pich - Euroflavour 08

5 LEPTON UNIVERSALITY g g μ e g g μ Physics A. Pich - Euroflavour 08

6 Physics A. Pich - Euroflavour 08 K K W W e B B B μ π π μ μ μ Γ Γ Γ Γ ± ± ± ± / g g μ ± ± ± ± ± K K K K W W e e e e e B B B B B B B B B B μ π μ π μ πμ π μ / e g g μ W W e B B B μ μ ± ± / e g g

7 LEPTON FLAVOUR VIOLATION 90% CL Upper Limits on Br(l X ) [BABAR / BELLE] Decay U.L. Decay U.L. Decay U.L. μ e γ μ e e + e μ e γγ e γ e e + e e e + μ μ γ e μ + μ μ e + μ e e μ μ μ + μ e π μ π e η μ η e η μ η e Κ * e Κ S μ Κ S μ ρ e K + K e K + π e π + K μ K + K μ K + π μ π + K e π + π μ π + π Λπ e + K K e + K π e + π π μ Κ * e φ μ ω μ + K K μ + K π μ + π π Physics A. Pich - Euroflavour 08

8 MEG: Br(μ eγ) ~ Prism: Pr(μ e) ~ SuperB: Br( μγ) ~ 10-9 Br(μ eγ)/br( μγ) MLFV M.J. Herrero et al V. Cirigliano et al M. Blanke et al LHT Physics A. Pich - Euroflavour 08

9 Arganda-Herrero-Portolés 08 CMSSM Constrained MSSM Seesaw Scenarios NUHM Physics A. Pich - Euroflavour 08

10 HADRONIC TAU DECAY ν Hadrons W d θ d = V d + θ V s ud us u Only lepton massive enough to decay into hadrons R ( ν Hadrons) Γ( ν e νe ) Γ + N C 1 Be Bμ ; R = = ± B e Physics A. Pich - Euroflavour 08

11 e γ γ σ Ιm e + q q e e + + σ ( ee had) + + σ( ee μ μ ) = 1π Im Π ( s) em iqx ( ) Π ( q) i d x e 0 T[ J ( x) J (0)] 0 = g q + q q Π ( q ) μν 4 μ ν μν μ ν em em em em Physics A. Pich - Euroflavour 08

12 e γ γ σ Ιm e + q q e e + + σ ( ee had) + + σ( ee μ μ ) = 1π Im Π ( s) em iqx ( ) Π ( q) i d x e 0 T[ J ( x) J (0)] 0 = g q + q q Π ( q ) μν 4 μ ν μν μ ν em em em em W W Γ ν + had Ιm d,s u ν ν R m s s (1) (0) 1π dx 1 1 Im ( s) Im ( s) 0 Γ( ν +had) = + Π + Π Γ( ν e νe ) m m ( J) ( J) ( J) ( J) ( J) ud ud, V ud, A us us, V us, A Π () s V Π () s +Π () s + V Π () s +Π () s iqx ( ) Π ( ) e 0 [ ( ) (0) ] 0 = + Π ( ) + Π ( ) μν 4 μ ν μν μ ν (1) μ ν (0) ij, J q i d x T Jij x Jij g q q q ij, J q q q ij, J q Physics A. Pich - Euroflavour 08

13 Γ( ν 1 +had) (1) (0) R = 1 π dx (1 x) (1 + x) Im Π ( xm) + Im ( xm) ( ν e ν ) 0 Π Γ e Braaten-Narison-Pich Im(s) m R = + 6 (1 ) ( (0+ 1) ( ) (0) ( πi dx x 1 x) xm x xm ) 1 x = Π Π Re(s) Physics A. Pich - Euroflavour 08

14 Γ( ν 1 +had) (1) (0) R = 1 π dx (1 x) (1 + x) Im Π ( xm) + Im ( xm) ( ν e ν ) 0 Π Γ e Braaten-Narison-Pich Im(s) m R = + 6 (1 ) ( (0+ 1) ( ) (0) ( πi dx x 1 x) xm x xm ) 1 x = Π Π Re(s) ( J ) Π () s = D= n ( J ) D C (, s μ) O ( μ) ( s) D D / OPE Physics A. Pich - Euroflavour 08

15 Γ( ν 1 +had) (1) (0) R = 1 π dx (1 x) (1 + x) Im Π ( xm) + Im ( xm) ( ν e ν ) 0 Π Γ e Braaten-Narison-Pich Im(s) m R = + 6 (1 ) ( (0+ 1) ( ) (0) ( πi dx x 1 x) xm x xm ) 1 x = Π Π Re(s) ( J ) Π () s = D= n ( J ) D C (, s μ) O ( μ) ( s) D D / OPE R ( ) = N S 1 + δp + δ NP = R + R + C EW, V, A, S R SEW = δ NP = 0.59 ± 0.0 Marciano-Sirlin, Braaten-Li, Erler 1.1 (3) ; 04 1 Fitted from data (Davier et al) δ a a a 0 % ; a α m ) / π 3 P = ( s Physics A. Pich - Euroflavour 08

16 Perturbative: (m q =0) d (0+ 1) s Π () s = ds 4π n= 0 Le Diberder- Pich 9 δ P 1 n 0 = 1 = = 3 = αs( s) Kn ; K K 1, K , K π ( n) 3 4 = Kn A ( αs ) = a a + 6 a + 17 a + n= 1 ( n) 1 dx 3 4 αs ( s) n A ( αs ) (1 x x x ) a ; a ( )/ 1 x αs m π πi + = + = x π n K 4 = (Baikov-Chetyrkin-Kühn 08) Physics A. Pich - Euroflavour 08

17 Perturbative: (m q =0) d (0+ 1) s Π () s = ds 4π n= 0 Le Diberder- Pich 9 δ P 1 n 0 = 1 = = 3 = αs( s) Kn ; K K 1, K , K π ( n) 1 dx 3 4 αs ( s) n A ( αs ) (1 x x x ) a ; a ( )/ 1 x αs m π πi + = + = x π n K 4 = (Baikov-Chetyrkin-Kühn 08) ( n) 3 4 = Kn A ( αs ) = a a + 6 a + 17 a + n= 1 Power Corrections: Braaten-Narison-Pich 1 (0+1) n n ΠOPE () s 4 n π ( s) n C O π μν C4 O4 0 αsg Gμν 0 3 δ 1 3 n n NP dx (1 3x + x ) x n = π i = ( xm ) m m n C O C O C O 6 V A Suppressed by m [additional chiral suppression in C6 O + 6 ] Physics A. Pich - Euroflavour 08

18 R, R, R Similar predictions for and the moments, V, A, S kl s0 s s dr R ( s0 ) ds 1 0 s0 m ds k l Different sensitivity to power corrections through k, l The non-perturbative contribution to R can be obtained from the invariant-mass distribution of the final hadrons: δ NP = 0.59 ± 0.14 Davier et al. (ALEPH data) Physics A. Pich - Euroflavour 08

19 R = ± ; R = ± ; R = ± 0.010, V, A, V+ A Davier et al ALEPH α = ± ( ) s m α = ± ( ) s M Z s M Z Zwidth α ( ) = ± 0.7 The most precise test of Asymptotic Freedom α s Z ( MZ) α ( MZ) = s 0.1 ± 0.11 ± 0.7 Z Physics A. Pich - Euroflavour 08

20 Recent α s (m ) Analyses Baikov et al 08: (CIPT + FOPT) / α ( ) = 0.33 ± 0.5 ± 0.01 α ( M ) = 0.10 ± s m s Z Davier et al 08: CIPT α ( ) = ± 0.5 ± 0. α ( M ) = 0.11 ± s m s Z Beneke-Jamin 08: FOPT + Borel sum of ad-hoc renormalon model 0.01 α s ( m ) = α ( ) s M Z = ± Maltman-Yavin 08: CIPT (FOPT). Hadronic spectral moments only α = ± s ( ) = ± 0.46 ± α ( M ) m s Z Physics A. Pich - Euroflavour 08

21 Perturbative Uncertainty on α s (m ) d 1 n Π = K δ = K = r = K + g ( n) n n A ( α ) rn n n n (0+ 1) s () s ( ) n a s P s a ds 4π n= 0 n= 1 n= 0 CIPT FOPT 1 dx n n A ( α ) (1 x+ x x ) a( s) = a + ; a α ( m )/ π ( n) 3 4 s π i 1 x = x s n K n g n r n The dominant corrections come from the contour integration Le Diberder- Pich 199 Physics A. Pich - Euroflavour 08

22 Perturbative Uncertainty on α s (m ) d 1 n Π = K δ = K = r = K + g ( n) n n A ( α ) rn n n n (0+ 1) s () s ( ) n a s P s a ds 4π n= 0 n= 1 n= 0 CIPT FOPT ( n) 1 dx 3 4 n n A ( αs ) (1 x x x ) a( s) a ; a ( )/ 1 x αs m π π i + = + = x n K n g n r n The dominant corrections come from the contour integration Le Diberder- Pich 199 ( s) a a β = = φ ( ) 1 a a i a β1 β1 1 a log s/ m 1 i a n φ n ; φ [ 0,π ] FOPT expansion only convergent if a < 0.13 (0.11) [at 1 (3) loops] Physics A. Pich - Euroflavour 08

23 Experimentally a 0.11 FOPT should not be used (divergent series) The difference between FOPT and CIPT grows at higher orders CIPT gives rise to a well-behaved perturbative series: 1 dx n n A ( ) (1 x+ x x ) a( s) = a + ( n) 3 4 αs π i 1 x = x Uncertainty only related to the unknown K n (n 5) coefficients Physics A. Pich - Euroflavour 08

24 Modelling a better behaved FOPT o Tune large K n corrections to cancel the g n ones (Beneke Jamin) o D = 4 corrections very suppressed in R n = IR renormalons can do the job (K n -g n ) o No sign of renormalon behaviour in known coefficients n = -1,,3 renormalons + linear polynomial 5 unknown constants fitted to K n ( n 5). Ad-hoc value of K 5 o Borel summation: large renormalon contributions. Smaller α s Nice academic model. But too many different possibilities Physics A. Pich - Euroflavour 08

25 SU(3) Breaking R kl N ( ) kl(0) kl( D) kl( D) C S = EW V ud + V us 1 δ V ud δud V us δ us D kl kl, V A R, S kl( D) kl( D) C EW ud us D R kl + δr N S δ δ V V ud us Physics A. Pich - Euroflavour 08

26 Strange Spectral Function: SU(3) Breaking (k,l) ALEPH OPAL (0,0) 0.39 ± ± 0.1 (1,0) 0.38 ± ± 0.09 (,0) 0.37 ± ± 0.07 (3,0) 0.40 ± ± 0.05 (4,0) 0.40 ± ± 0.04 δ R kl R R m m 4 Δkl( αs) V kl kl, V+ A, S s ( ) m ud Vus m (m ) s determination V us and QCD uncertainties Physics A. Pich - Euroflavour 08

27 δ R kl kl kl, V+ A, S ( 4 s m ud Vus R R m m V ) Δ kl ( αs ) Known to s 3 O(α ) Δ kl (α s ) gets longitudinal (J=0) and transverse (J=0+1) contributions Divergent QCD series for J=0 Longitudinal contribution determined through data: Kaon pole (K μν) Pion pole (π μν) (Kπ) J=0 (S-wave Kπ scattering) (dominant J=0 contribution) Smaller uncertainties δ R,th (37) (15) = 0.16 (16) J=0 m s (m ) = 0.1 (10) Physics A. Pich - Euroflavour 08

28 OPAL data Jamin Large uncertainty from V us Strong sensitivity to V us Physics A. Pich - Euroflavour 08

29 V us = R, V+ A V ud R, S δ R,th data: PDG 06: R R V, S, V+ A ud = = (47) = (11) (7) Gámiz-Jamin-Pich-Prades-Schwab Physics A. Pich - Euroflavour 08

30 V us = R, V+ A V ud R, S δ R,th data: PDG 06: R R V, S, V+ A ud = = (47) = (11) (7) Gámiz-Jamin-Pich-Prades-Schwab δ R,th = 0 V us = 0.15 (3) Physics A. Pich - Euroflavour 08

31 V us = R, V+ A V ud R, S δ R,th data: PDG 06: R R V, S, V+ A ud = = (47) = (11) (7) Gámiz-Jamin-Pich-Prades-Schwab δ R,th = 0 V us = 0.15 (3) m ( m ) = 1± 10 MeV Taking as input (from non sources) : s δ R,th = 0.16 (16) V = 0.1 ± 0.31 ± 0.05 us exp th Physics A. Pich - Euroflavour 08

32 V us = R, V+ A V ud R, S δ R,th data: PDG 06: R R V, S, V+ A ud = = (47) = (11) (7) Gámiz-Jamin-Pich-Prades-Schwab δ R,th = 0 V us = 0.15 (3) m ( m ) = 1± 10 MeV Taking as input (from non sources) : s δ R,th = 0.16 (16) V = 0.1 ± 0.31 ± 0.05 us exp th K l3 : Vus = 0.33 ± 0.4 [ f + (0) = 0.97 ± 0.01] The could give the most precise V us determination Physics A. Pich - Euroflavour 08

33 First Measurements from Babar and Belle S. Banerjee KAON 07 Smaller K branching ratios smaller R,S smaller V us R, S (4 R OLD, S = (4 NEW = 7) 0) V us = 0.1 ± 0.31 ± 0.05 V us = ± 0.6 NEW exp ± 0.05th OLD exp th Much more data coming. Precise measurement expected soon Physics A. Pich - Euroflavour 08

34 Huge number of + events at the B Factories Br( K S π ν ) = (0.404 ± 0. stat ±0.013 syst )% K 0 π - Ongoing data analysis Br( K π 0 ν ) = (0.416 ± 0.3 stat ±0.018 syst )% Jamin-Pich-Portolés K - π 0 Physics A. Pich - Euroflavour 08

35 Jamin-Pich-Portolés 08 RχT Description of BELLE data Shape fit: K S π ν M K* = ± 0. MeV Γ K* = 47.5 ± 0.4 MeV RχT normalization fixed Br( K S π ν ) th = (0.47 ± 0.04) % Br( K S π ν ) Belle = (0.404 ± 0. stat ± syst )% Prediction for K l3 Form Factor Slopes: λ ' '' ''' + = ( 5.0 ± 0.33) 10 ; λ+ = ( 1.85 ± 0.31) 10 ; λ+ = ( 9.56 ± 0.8) 10 EXP: (Flavianet Kaon WG) ' λ '' + = ( 5. ± 0.9) 10 ; λ+ = ( 16 ± 4) Physics A. Pich - Euroflavour 08

36 Electron Anomalous Magnetic Moment μ l g l e m l a l 1 ( gl ) a (QED) = A + A ( m / m ) + A ( m / m ) + A ( m / m, m / m ) e 1 e μ e 3 e μ e () α (4) α 3 4 (6) α (8) α Ai = Ai + Ai + Ai + Ai + π π π π (6) A 1 = A ( m / m μ ) = (9) 10 (6) e (Laporta Remiddi) 6 a e (8) A 1 = (35) (Kinoshita Nio) 1 1 ae (QCD) = (19) 10 ; (Weak) = (01) 10 Physics A. Pich - Euroflavour 08

37 Electron Anomalous Magnetic Moment a e = (8) Hanneke-Fogwell-Gabrielse 08 1 α = (51) 0.37 ppb (33) (39) exp th Physics A. Pich - Euroflavour 08

38 μ Anomalous Magnetic Moment exp μ a = ( ± 6.0 ) BNL-E81 HNNT 06 (e + e - ) 180.4±5.1 Davier x a th μ = ± 0.0 QED Kinoshita-Nio, Passera ± 0. EW Czarnecki-Marciano-Vainshtein ± 9.7 hvp (711.0 ± 5.8), (690.9 ± 4.4) e + e Davier et al 9.8 ± 0.1 hvp NLO Krause, Hagiwara et al ± 3.5 light-by-light Melnikov-Vainshtein, Knech et al, Prades et al = ± 10.3 ( ± 6.8), ( ± 5.6) e + e a μ exp - a μ th = 1.3 σ 0.8 σ 3.4 σ Physics A. Pich - Euroflavour 08

39 M. Davier TAU 06 Today s e + e - data comparison CMD: 0.6% syst. error Belle 08 (final): 5.1 ± 0.01 ± σ discrepancy Physics A. Pich - Euroflavour 08

40 CMD- / SND CMD-, SND / KLOE KLOE e + e - data data versus e + e - : Isospin violation Δa μ = (-9.3 ±.4) [(-1.8 ± 0.5)%] OPE contraints satisfied better by data Physics A. Pich - Euroflavour 08 Maltman

41 Physics A. Pich - Euroflavour 08

42 Physics A. Pich - Euroflavour 08 Portolés

43 Inclusive V+A and V A Spectral Functions Results from ALEPH and OPAL and their comparison Of purely nonperturbative origin ALEPH, Phys. Rep. 41 (5) OPAL, EPJ, C7, 571 (1999) Tau 6, Sep 19-, Physics SNS Pisa M. Davier et al.: ALEPH Tau Spectral Functions and QCD A. Pich revisited - Euroflavour 08

44 Non-Perturbative Physics Low-energy QCD engineering ChPT : Chiral sum rules f, m m 0, FA / r π π ± π π L ( M ) = (4.06 ± 0.40) 10, C ( M ) = (4.89 ± 0.19) 10 GeV r 3 r ρ ρ (M. González-Alonso 08) RChT, 1/N C,... Electromagnetic Penguins (Q 7,8 ): ε /ε Physics A. Pich - Euroflavour 08

45 SUMMARY The is a clean laboratory to test the Standard Model Precision physics QCD tests Open questions: (g-) μ Hints of new physics: ν s Future facilities: cf, SuperB Tool for NP searches: LHC There is an exciting future ahead Physics A. Pich - Euroflavour 08

46 Physics A. Pich - Euroflavour 08 ν

47 BACKUP SLIDES Physics A. Pich - Euroflavour 08

48 The could give the most precise V us determination From present data one gets: V = ± 0.6 ± 0.05 us exp th Accuracy similar already to K l3 : V = 0.33± 0.4 [ f + (0) = 0.97 ± 0.01] us Interesting challenge for the B Factories & BESIII Physics A. Pich - Euroflavour 08

49 K l3 Decays arxiv: [hep-ph] Large O(p 6 ) ChPT correction (Bijnens-Talavera) O(p 4 ) O(p 6 ) f+ (0) V us = ± 0.05 f + (0) = 0.97 ± 0.01 V = 0.33± 0.4 us Physics A. Pich - Euroflavour 08

50 A simultaneous m s & V us fit could be possible However: Perturbative QCD corrections need to be better understood (CIPT) Δ (α s ) L+T = Δ 10 (α s ) L+T = Δ 0 (α s ) L+T = Δ 30 (α s ) L+T = Δ 40 (α s ) L+T = Sizeable theoretical uncertainties Resummations, pinched weights (Maltman & Wolfe), Not enough sensitivity with present data Large correlations. Low statistics. Missing decay modes Physics A. Pich - Euroflavour 08

51 Davier-Höcker-Zhang 05 ALEPH Taking V us = 0.5 (1) : Gámiz et al 03, J=0 excluded Chen et al 01, J=0 included Moment m s (m ) [MeV] (0,0) 19 ± 7 (1,0) 164 ± 31 (,0) 137 ± 0 (3,0) 115 ± 17 (4,0) 1 ± 17 s s + 1 ( 6 ) m ( m ) = 10 MeV + 0 ( 5 ) m ( GeV) = 116 MeV ( ) ms ( m ) = 1 ± 17 MeV ( ) m (GeV) = 117± 17 MeV Physics A. Pich - Euroflavour 08 s

52 Strong k dependence with ALEPH data (m s decreases with increasing k) Spectral function underestimated at large invariant masses Missing events / modes (Kππ, Kπππ, ) Much better behaviour with OPAL data: (0,0) V us = 0.08 (34) Gámiz et al 05, J=0 excluded Moment m s (m ) [MeV] (,0) 89 ± 39 (3,0) 84 ± 7 (4,0) 78 ± ( ) ( ) ms( m ) = 84 ± 3 MeV, ms( GeV) = 81± MeV Kν from K μν + OPAL: V us = 0.0 (33) Physics A. Pich - Euroflavour 08