Matthias Jamin ICREA & IFAE Universitat Autònoma de Barcelona

Transcription

1 ICREA & IFAE Universitat Autònoma de Barcelona 1

2 Particles With M τ = 1.777GeV, only τ leptons decay into hadrons. Tau lifetime: τ τ = sec Γ τ = h/τ τ = ev. 2

3 Discovered 1975 by Martin Perl and the SLAC group in e + e collisions. Nobel prize in Two important experimental observables: Leptonic branching fractions: B τ l = Br[τ l ν l ν τ ] Total hadronic decay rate: N C = 1 5 = 20% R τ = Γ[τ ν τ + hadrons] Γ[τ e ν e ν τ ] = (1 B τ e B τ µ ) B τ e N C = 3 3

4 (HFAG 2013) Leptonic τ e ν e ν τ (17.82 ± 0.04)% modes: τ µ ν µ ν τ (17.39 ± 0.04)% Non- τ π ν τ (10.81 ± 0.05)% Strange τ π π 0 ν τ (25.50 ± 0.09)% modes: τ π π 0 π 0 ν τ (9.24 ± 0.10)% τ π π + π ν τ (9.00 ± 0.05)% τ π π + π π 0 ν τ (4.62 ± 0.06)% τ K K 0 ν τ (0.16 ± 0.02)% Strange τ K ν τ (0.70 ± 0.01)% modes: τ K 0 π ν τ (0.82 ± 0.02)% τ K π 0 ν τ (0.43 ± 0.01)% Covers > 96% of the total τ decay width. 4

5 have been calculated long ago: Decay τ π ν τ : B τ π = 12π 2 V ud 2 S EW f 2 π M 2 τ 0.61 B τ e = 10.87% (Marciano, Sirlin 1988) ( ) 1 M2 π 2 Mτ 2 B τ e Decay τ K ν τ : B τ K = 12π 2 V us 2 S EW f 2 K M 2 τ 0.04 B τ e = 0.72% ( ) 1 M2 K 2 Mτ 2 B τ e Employing π µ ν µ and K µ ν µ, precise predictions can be made for the branching fractions B τ π and B τ K. 5

6 Decay τ π π 0 ν τ : F V Belle data Our parametrization GS Guerrero-Pich [31] Pich-Portoles [32] Differential decay distribution (Gómez Dumm, Roig 2013) s (GeV 2 ) dγ ππ d s = G2 F V ud 2 Mτ 3 ( 32π 3 1 s ) 2 ( s Mτ s ) Mτ 2 qπ(s) F 3 V π (s) 2 Model for vector form factor FV π (s) required. Starting point: dispersive representation. 6

7 Several hadronic resonances can be included. Low-energy behaviour is implemented to match χpt. Constraints from high-energy can be taken into account. Main fit parameters: Masses and width of resonances; Form factor slopes N Events s [Gev] Decay τ K S π ν τ : (MJ, Pich, Portolés 2006/08) Belle decay distribution. (Boito, Escribano, MJ 2009/10) 7

8 Decay τ π π π + ν τ : )]/N)/(10MeV/c π ([dn/dm(π π + )]/N)/(10MeV/c ([dn/dm(π ) ) M(π π ) (GeV) M(π π + ) (GeV) 1.5 BaBar decay distribution. (Nugent et al. 2013) Work in progress for τ K ππ modes. 8

9 Total hadronic τ decay rate: R exp τ = Γ[τ ν τ + hadrons] Γ[τ e ν e ν τ ] = (94) (HFAG 2013) R τ can be calculated as a spectral integral over basic QCD meson correlation functions: R τ = 12π M τ 2 0 ds M 2 τ ( 1 s ) 2 {( Mτ s ) Mτ 2 ImΠ (T τ ) Π (J) τ (s) corresponds to the combination: Π (J) τ (s) = V ud 2[ Π (V,J) ud (s)+π (A,J) ud ] (s) + V us 2[ Π (s)+imπ (L) τ } (s) (V,J) us (s)+π us (A,J) ] (s) 9

10 Im(s) In QCD, the integral over the physical, Minkowskian region (s > 0) cannot be calculated. 2 mτ Re(s) Way out: (Braaten, Narison, Pich 1992) R τ = 6πi s =M 2 τ ds M 2 τ ( 1 s ) 2 {( Mτ s ) Mτ 2 Π Generally, R τ then assumes the structure: (T +L) τ (s) 2 s R τ = N C S EW {( V ud 2 + V us 2 ) [1 ] + δ (0) [ + D 2 V ud 2 δ (D) ud ] } + V us 2 δ us (D) M 2 τ } Π (L) τ (s) 10

11 Additional experimental information: Inclusive differential decay distributions; Separation into Vector, Axialvector and Strange modes. R τ = M τ 2 0 ds dr τ ds = RV τ + R A τ + R S τ Dominant non-perturbative OPE corrections arise in the strange channel proportional to m 2 s and m s qq. For α s analysis only consider R V τ and R A τ. 11

12 v ALEPH Perturbative QCD (massless) Parton model prediction ππ 0 a ALEPH Perturbative QCD (massless) Parton model prediction π2π 0,3π 2 π3π 0,3ππ 0,6π(MC) 0.8 π4π 0,3π2π 0,5π ωπ,ηππ 0,kk 0 (MC) πkk-bar(mc) 1.5 πkk-bar(mc) s (GeV 2 ) s (GeV 2 ) v(s) OPAL π π 0 3π π 0, π 3π 0 MC corr. perturbative QCD (massless) naïve parton model a(s) OPAL 3π, π 2π 0 3π 2π 0 MC corr. perturbative QCD (massless) naïve parton model s (GeV 2 ) s (GeV 2 ) 12

13 PDG 2012 α s (M τ ) = (58) 13

14 Phenomenologically, R V +A τ can be expressed as follows: ] R V +A τ = 3 V ud 2 S EW [ 1 + δ (0) + δ NP V +A Purely perturbative QCD correction δ (0) know to order α 4 s. Depends on renormalisation-group resummation: Fixed-order perturbation theory (FOPT) Contour-improved perturbation theory (CIPT) δ (0) FO = ± ± = (75) δ (0) CI = ± ± = (58) First error from uncertainty in α s (M τ ). Second error from estimate of O(α 5 s) contribution. Scale resummation induces 2% difference. 14

15 Employing the experimental measurement R exp V +A = (82): δ NP V +A,FO = (80), δ NP V +A,CI = (65) δ NP V +A = δ OPE V +A + δ DV V +A comprises a small ( 1%) correction due to quark masses as well as OPE and duality violations. To disentangle OPE and DV contributions, additional experimental information is required: Moments with different spectral weight functions; Moments with upper integration limit s 0 < M 2 τ. Still, results of this program will depend on the question of renormalisation-group resummation (FOPT versus CIPT). 15

16 Difference between FOPT and CIPT can be understood on the basis of a model for the behaviour of higher orders in α s : Model for Borel transform of Adler function; Incorporates renormalon structure known from RGE; Reproduces the known lowest-order coefficients; Allows resummation of the perturbative series. δ (0) Borel sum FO perturbation theory CI perturbation theory Smallest term Perturbative order n (Beneke, MJ 2008) 16

17 v+a ALEPH K π K ππ K 3π+K - η (MC) K 4π (MC) K 5π (MC) Mass 2 (GeV/c 2 ) 2 17

18 To enhance sensitivity for strange quark effects, consider the flavour-su(3) breaking difference: δr τ = R τ,v +A V ud 2 R ( τ,s V us 2 = 3S EW D 2 (Prades, Pich; ALEPH 1998) δ (D) ud ) δ us (D) Flavour independent uncertainties drop out in the difference. Leading contribution is proportional to m 2 s whose series is not very well behaved. Again RG resummation issue of FOPT versus CIPT. Even more badly behaved scalar/pseudoscalar correlators from phenomenology. (Gámiz, MJ, Pich, Prades, Schwab 2003/05) 18

19 Theoretically, δr τ can be split into three contributions: δr th τ = δr m2 τ + δrτ D 4 + δrτ S+P Last term known from phenomenology: δr S+P τ = (37). Estimates for D 4 contribution small: δr D 4 τ = (28). Largest uncertainty: δr m2 τ = 9.3(3.4) m 2 s = 0.082(31). δr th τ = ± On the other hand from R τ,s = (28) (HFAG 2013): δr exp τ = ± Hence, we face a serious discrepancy. 19

20 Lecture 2: perturbative series for R τ, renormalon based Borel model, resummation dependence. Lecture 3: Multi-moment analysis for α s, duality violation. Lecture 4: Description of exclusive τ decay distributions. 20

21 Lecture 2: perturbative series for R τ, renormalon based Borel model, resummation dependence. Lecture 3: Multi-moment analysis for α s, duality violation. Lecture 4: Description of exclusive τ decay distributions. Thank You! 21