Isospin Breaking corrections to di-pion tau lepton decays

Transcription

1 IHEP, Beijing October 13-16, 9 Iopin Breaking correction to di-pion tau lepton decay G. López Catro Cinvetav, México Collab: * A. Flore, F. Flore, G. Toledo; * M. Davier, A. Höcker, B. Malaecu, X. Mo, P. Wang, C. Yuan, Z. Zhang 1

2 Motivation: pectral function: 73% of a μ had, LO, 83% of it error Very precie eaureent below 1% level of the pectral function and BR in τ decay. However, atpreent, notreliabletopredictg- μ becaue iopin breaking IB i not well undertood e + e v τ dicrepancy. Miing IB correction?, error in data?, both? Soe not very recent reult on IB correction relevant to g- μ

3 3 3 1 F F F i i i β υ = = d dn N B B V e e e ud I ] [ 8 1 τ τ τ ν τ υ ν τ υ α σ + = = = + + τ Branching ratio a pectru CVC hypothei Iopin liit Replacing e+e- by τ data

4 SOURCES OF ISOSPIN BREAKING At fundaental level 1 qτ q + L, Q Q qγ τ q + L u d 3 u d μ 3 e At hadronic level: correct τ data by reoving IB effect in the iopin liit =1 υ τ ν γ 1 S EW FSR G EM β β 3 F F Radiative correction incluive γ ± a diff. Leading IB: ± a & width diff, ω ixing 4

5 Tet of CVC in production in e + e and τ data OLD analyi DEHZ3 IB effect fro: Aleany, Davier & Hocker 1998; Radcorr fro : Cirigliano, Ecker & Neufeld ee v τ dicrepancy Iportant difference above the a region two non-overlaping prediction for a μ had, LO 5

6 Soe recent progre on IB include: New evaluation of τ ν: G EM LD radcorr in New calculation of the ± width difference: F /F_ PRD 74, 6; NPBPS 169, 7; PRD 76, 7; arxiv; [hep-ph] 6

7 SHORT-DISTANCE CORRECIONS Marciano & Sirlin 78 88; Braaten & Li, 199; J. Erler, Rev. Mex. Fi 4 Reued O[α n ln n Z ] O[αα n ln n Z] ter S EW = 1.35 ±.3 Oαα 7

8 LONG-DISTANCE CORRECTIONS Main difference in radiative τ νγ decay γ Cirigliano, Ecker & Neufeld, JHEP, ; Flore, Flore, GLC, Toledo, PRD, 6 τ dγ d + virtual correction dγ d G EM ω SHORT-DISTANCE CORRECIONS Marciano & Sirlin 78 88; Braaten & Li, 199; J. Erler, Rev. Mex. Fi 4 Reued O[α n ln n Z ] O[αα n ln n Z] ter = p + + p S EW = 1.35 ±.3 Oαα 8

9 diff. ω vertex ω reoved.1 Effect on Δa μ had, LO τ: FFLT 1. x 1 1 CEN Appropriate when τ ν ω γ event are reoved, a done by ot experient arxiv: [hep-ph] 9

10 ISOSPIN BREAKING IN FORM FACTORS F = f 1 + δ ω ω i ω Γ ω Leading IB effect: Δ, ΔΓ, δ ω F = f M. Davier et al, arxiv: IB in ± a KLOE a diff+ e a hift for : ± =1. ±.9 MeV rho-oega ixing fro fit to e + e - data: δ ω =. ± e i11.6 ± 1.8o, for GS 1.87 ± e i13. ± 1.7o, for KS GS=Gounari-Sakurai 1968 ; KS= Kühn-Santaaría 199 1

11 IB IN WIDTH DIFFERENCE ΔΓ = Γ[ ± ± γ] Γ[ + γ].8 MeV γ, ηγ, l + l,.. Flore, GLC, Toledo PRD 76,7 Photon incluive rate calculated with virtual + real photon ΔΓ g [ γ ] [ β δ β δ ] 3 3 = =.76 ± Γ.8 MeV, Coparion with previou reult which only included effect of hard photon but neglect rad. correction [P.Singer, PR 1963 ] ΔΓ [ γ ] =.49 ±.58 MeV Aleany, Davier, Hocker 1998 at = 11

12 Effect of ± a & width difference in the ratio of I=1 coponent of pion for factor 1

13 M. Davier et al, arxiv: [hep-ph] -dependent IB correction IB in the ratio of I=1 for factor 13

14 Coparion of ee v. IB corrected τ data Z. Zhang, EPS 9 Relative noralization and hape in better agreeent than before Davier-Eidelan-Hocker-Zhang 3. Sall deviation reain above large deviation for KLOE data 14

15 IB Correction in Δa μ had, LO τ Davier et al arxiv: [hep-ph] OLD DEHZ3-1.1 ± ± ±. -1.4± ±.4 Adding FSR to DEHZ 3, net change becoe x 1 1 Cloer prediction for a had,lo μ, fro e+e- and τ data 15

16 16.% in ± + = + = Δ + F F FSR G S d V B B EM EW ud e CVC β β σ α ν τ τ τ τ τ BR prediction baed on IB corrected e+e data Dicrepancy reduced fro.9 ±.1% DEHZ 3.6±.1 τ ±.8 ee % arxiv: [hep-ph]

17 Coent, concluion Recent progre in calculation of IB correction : Long-ditance radiative correction to τ ν Width difference of ± eon Reduced dicrepancie better agreeent with CVC between: Weak & e pion for factor, Prediction for g- μ fro e + e and τ M. Davier, next talk Prediction for B τ fro e + e data and direct eaureent Mot iportant change induced by ± width difference. IB in pion FF for > till reain. 17

18 Backup lide 18

19 IB in 4 channel Czyz, Kühn, Wapienik 8 IB correction applied: S EW and phae pace No IB oberved within preent accuracy 19

20 ΔΓ = Γ[ ± ± γ] Γ[ +γ].8 MeV γ, ηγ, l + l,.. Flore, GLC, Toledo PRD 76,7 Γ 3.6 ±.4 MeV, KLOE3 Γ = +.76 ±.7 MeV, Thi calc. Γ For Eγ >5 MeV Γ Γ exp theo + γ + γ =.86 ±.14

21 Coparion of radiative branching ratio: Δ Γ γ/γ S63 = P. Singer, PR Our = F. Flore-Baez, GLC, G. Toledo, PRD76, 7 MeV Δ S63 Δ Our 3. S63 in E γ Δ + Δ Our BR 1 3 Sall difference due to Interference w/ + + ω γ 1

22 IB in ± ae: Phyical ae zero of real part of the pole propagator eaured by KLOE [Phy. Lett. B561, 55 3 ] give: phy + =.4 ±.9 phy MeV IB in eon ae: phy + phy = = δ + δ + δ γ ixing loop + loop + δ = 3Γ γ ixing e + e /α = 1.45 MeV Mae entering pion FF are = + δ loop = ± MeV