1. Dipion Spectrum : e + e - annihilations and τ decays M. Benayoun LPNHE Paris 6/7 1M. Benayoun, e+ e- versus tau

2. The Pion Form factor in e + e - and τ Data Since the advent of τ data, disagreement with e + e - data Large activity in identifying isospin symmetry breaking in both e + e - annihilation and τ decay Disagreement survived accounting for identified isospin breaking corrections! Is there a missing piece, a systematic effect (in e + e - or τ data) or new physics? M. Benayoun, e+ e- versus tau2

3. The Latest Account Inv. Mass dependent missing effect M. Benayoun, e+ e- versus tau3 M. Davier NP Proc. Supp. 169 (2007) 288

4. The Latest Account Inv. Mass dependent missing effect ! Is it isospin breaking? M. Benayoun, e+ e- versus tau4 M. Davier NP Proc. Supp. 169 (2007) 288

5. Possible Missing Effect : (ρ-ω-φ) Mixing M. Benayoun, e+ e- versus tau5 FF’s New Data Isospin 1 part of ω Isospin 1 part of φ

6. Possible Missing Effect : (ρ-ω-φ) Mixing M. Benayoun, e+ e- versus tau6 FF’s New Data Isospin 1 part of ω Isospin 1 part of φ Isospin 0 part of ρ 0 ? Can it be s-dependent?

7. OUTLINE A VMD-like Model : HLS Model (briefly) Breaking of U(3)/SU(3) Symmetries (briefly) The Anomalous Sector (briefly) The Pion Form Factor in e + e - Annihilation and τ Decay (Isospin Breaking) Loop Transition Effects in e + e - : Physical ρ 0, ω, ф Extended Data Sample submitted to fit, Why? Fit results & Plots Conclusions M. Benayoun, e+ e- versus tau7

8. OUTLINE A VMD-like Model : HLS Model (briefly) Breaking of U(3)/SU(3) Symmetries (briefly) The Anomalous Sector (briefly) The Pion Form Factor in e + e - Annihilation and τ Decay (Isospin Brk) Loop Transition Effects in e + e - : Physical ρ 0, ω, ф Extended Data Sample submitted to fit, Why? Fit results & Plots Conclusions M. Benayoun, e+ e- versus tau8

9. The Pion form Factor in e + e - and τ Physics Without Symmetry Breaking : Isospin symmetry breaking: mass splittings + M. Benayoun, e+ e- versus tau9 W. Marciano & A. Sirlin PRL 71 (1993) 3629 V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361

10. The Pion form Factor in e + e - and τ Physics Without Symmetry Breaking : Isospin symmetry breaking : mass splittings + M. Benayoun, e+ e- versus tau10 W. Marciano & A. Sirlin PRL 71 (1993) 3629 V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361 HLS

11. The Pion form Factor in e + e - and τ Physics With Symmetry Breaking : Isospin symmetry breaking : mass splittings + M. Benayoun, e+ e- versus tau11 W. Marciano & A. Sirlin PRL 71 (1993) 3629 V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361 (γ/W)V ? ρππ? δm 2

12. γ/W- ρ Transitions No isospin breaking : Isospin symmetry breaking : ρ ± component M. Benayoun, e+ e- versus tau12 ф I and ω I componentsρ I component

13. Transitions among vector fields at one loop At tree level ideal fields ≡ mass eigenstates At one loop, the HLS Lagrangian piece induces transitions among ideal fields ideal fields ≡ mass eigenstates isospin symmetry breaking : M. Benayoun, e+ e- versus tau13

14. Transitions among vector fields at one loop Define the loops : = K + K -, = K 0 K 0 Then, beside self-masses : = + ~ ε 2 (s) ≠ 0 always = - ≠ 0 by isospin brk = - ~ ε 1 (s) M. Benayoun, e+ e- versus tau VVP Lagrangian K*K loops // Yang-Mills K*K*loops 14 f(s)

15. The Modified Vector Mass Matrix ρI ωIφIρI ωIφI With m 2 = a g 2 f π 2 and μ= z V No SU(3) Brk ::, No SU(2) Brk :: Blue : Loop effectsmagenta : SU(3) breaking red : isospin breaking 15M. Benayoun, e+ e- versus tau

16. Loop Corrections : (ω, ф) Mixing ρI ωIφIρI ωIφI Blue : Loop effectsmagenta : SU(3) breaking red : isospin breaking 16M. Benayoun, e+ e- versus tau

17. Isospin Breaking : (ρ, ω, ф) Mixing ρI ωIφIρI ωIφI Blue : Loop effectsmagenta : SU(3) breaking red : isospin breaking 17M. Benayoun, e+ e- versus tau

18. The Mass Matrix Eigen System Expect : Then solve for the eigensystem perturbatively : and : M. Benayoun, e+ e- versus tau18

19. From Ideal To Physical Fields I : Real analytic matrix function fulfills Unitarity Condition 19M. Benayoun, e+ e- versus tau

20. From Ideal To Physical Fields II Mass term derived from the eigenvalues of M 2 (s) : Leading order propagators become 20M. Benayoun, e+ e- versus tau (Self masses include subtraction polynomials)

21. V π π Couplings *At leading order : ρ term unchanged *s-dependent ω and φ couplings generated 21M. Benayoun, e+ e- versus tau

22. V π π Couplings *At leading order : ρ term unchanged *s-dependent ω and φ couplings generated 22M. Benayoun, e+ e- versus tau Orsay Phase ≈90 ₀ at peak

23. γ – V Couplings In terms of Ideal Fields Becomes With M. Benayoun, e+ e- versus tau23

24. Vector Meson Couplings to γ/W (γ/W) V transitions : constant + (PP,VP…) loops = + loop term : disp. relation (subtractions) tree terms : M. Benayoun, e+ e- versus tau24

25. Vector Meson Coupling to γ/W (γ/W) V transitions : constant + (PP,VP…) loops = + loop term : disp. relation (subtractions) tree terms : M. Benayoun, e+ e- versus tau25 ω I and ф I components of ρ 0

26. Parameter Freedom If only using the pion form factor (e + e -,τ) the parameter freedom is far too large: a (HLS), g, z A, δm 2 (4) Subtraction polynomials in : (~ 8) Too many parameters, too few structures Solution : extend the fitted data sample: more information, less correlations M. Benayoun, e+ e- versus tau26

27. The Extended Data Sample Add anomalous decay modes VPγ, Pγγ : Price : x, z T, z V, z A for 14 modes for free for free + 4 measured data :: Total 18 add. data M. Benayoun, e+ e- versus tau27 M.B.,L.D.,S.E, V.I. & H.OC, PR D 59 (1999) 114027 M.B, H.OC EPJ C22 (2001) 503

28. The Main Guess Main Guess ≈ Proof of Principle 18 Decay Modes + Pion FF in e + e - annihilation Fully reconstruct The Pion FF in τ decay (improvement of parameter fit values) M. Benayoun, e+ e- versus tau28

29. The Χ 2 contributions to fits Data Set (#data points)Full Data FitNo τ dataNo Spacelike Data Decays (18+1)11.1311.5211.48 New Timelike (127+1)128.1122.0125.8 Old Timelike (82+1)59.154.755.2 Spacelike (59+2)65.755.289.8/(59) τ ALEPH (33) 23.942.3/(33)20.8 τ CLEO (25+1) 26.126.2/(25)29.7 Χ 2 /dof Probability 313.8/331 74% 257.7/274 75% 238.8/272 93% M. Benayoun, e+ e- versus tau29

30. The Χ 2 contributions to fits Data Set (#data points)Full Data FitNo τ dataNo Spacelike Data Decays (18+1)11.1311.5211.48 New Timelike (127+1)128.1122.0125.8 Old Timelike (82+1)59.154.755.2 Spacelike (59+2)65.755.289.8/(59) τ ALEPH (33) 23.942.3/(33)20.8 τ CLEO (25+1) 26.126.2/(25)29.7 Χ 2 /dof Probability 313.8/331 74% 257.7/274 75% 238.8/272 93% M. Benayoun, e+ e- versus tau30

31. The Χ 2 contributions to fits Data Set (#data points)Full Data FitNo τ dataNo Spacelike Data Decays (18+1)11.1311.5211.48 New Timelike (127+1)128.1122.0125.8 Old Timelike (82+1)59.154.755.2 Spacelike (59+2)65.755.289.8/(59) τ ALEPH (33) 23.942.3/(33)20.8 τ CLEO (25+1) 26.126.2/(25)29.7 Χ 2 /dof Probability 313.8/331 74% 257.7/274 75% 238.8/272 93% M. Benayoun, e+ e- versus tau31 τ DATA OUTSIDE FIT : Χ 2 distance to prediction

32. The Χ 2 contributions to fits Data Set (#data points)Full Data FitNo τ dataNo Spacelike Data Decays (18+1)11.1311.5211.48 New Timelike (127+1)128.1122.0125.8 Old Timelike (82+1)59.154.755.2 Spacelike (59+2)65.755.289.8/(59) τ ALEPH (33) 23.942.3/(33)20.8 τ CLEO (25+1) 26.126.2/(25)29.7 Χ 2 /dof Probability 313.8/331 74% 257.7/274 75% 238.8/272 93% M. Benayoun, e+ e- versus tau32 Spacelike data OUTSIDE FIT

33. Global Fit to e + e - Data M. Benayoun, e+ e- versus tau33 FF’s New DataCross Sections Old Data

34. Fits to τ Data M. Benayoun, e+ e- versus tau34 ALEPH Data CLEO Data

35. Spacelike Data & ππ Phase Shift M. Benayoun, e+ e- versus tau35 SpaceLike Data I=1 ππ Phase shift NOT A FIT

36. Fit Residuals : No Structure M. Benayoun, e+ e- versus tau36 e + e - Data CLEO ALEPH

37. Isospin Symmetry Breaking : ρ 0 VS ρ ± M. Benayoun, e+ e- versus tau37

38. Isospin Symmetry Breaking : ρ 0 VS ρ ± M. Benayoun, e+ e- versus tau38 Threshold : -6% ρ Peak : + 3% Φ Mass : -2% 0 :: NO IS Brk

39. Conclusions A few radiative decays & the pion form factor in e + e - annihilation predict the observed pion form factor in τ decay Previously unaccounted for effects : I=0 (ω I, ф I ) components inside the ρ 0 meson. The 3.3 σ discrepancy between prediction (using e + e - data) and the BNL measurement for the muon anomalous moment is confirmed M. Benayoun, e+ e- versus tau39

40. Fit Decay Modes Vs PDG M. Benayoun, e+ e- versus tau40 Decay ModeFIT/PDGRemark ρ0 → π0γρ0 → π0γ0.86 ±0.15 ρ± → π±γρ± → π±γ1.12±0.11 ρ 0 → ηγ1.04±0.11 K* ± → K ± γ1.00±0.14 K* 0 → K 0 γ0.98±0.09 ω → π0γω → π0γ0.93±0.03*** ω→ ηγ1.35±0.11*** ф → π0γф → π0γ0.99±0.08 ф → ηγ0.99±0.03 Decay ModeFIT/PDGRemark η‘→ ρ0γη‘→ ρ0γ1.13±0.04 η‘→ ωγ1.04±0.11 ф → η’γф → η’γ0.97±0.12 η→ γγ0.90±0.02!!!!! η'→ γγ0.99±0.07 ω →e+e-ω →e+e- 1.00±0.02 ф →e+e-ф →e+e- ф →π + π - 0.98±0.29 Phase [ф→π + π - ]0.79±0.15

41. The ρ 0 - ρ ± Mass Difference M. Benayoun, e+ e- versus tau41 ALEPH Data δm 2 = 0 Fixed δm 2 Fitted The ρ 0 -ρ ± Mass Difference : 1/ Only visible in ALEPH data 2/ ~1.2 σ from ChPT ρ Peak Region High mass Vector mesons J. Bijnens & P. Gosdzinsky PL B 388 (1996) 203

42. Two New Results Process FIT PDG ρ 0 →e + e - [x10 5 ] 5.56±0.06 4.70±0.08 ω →π + π - (%) 1.13±0.08 1.70±0.27 ρ 0 →π + π - [MeV] 144.5±0.6 149.4±1.0 M. Benayoun, e+ e- versus tau42

43. Two New Results Process FIT PDG ρ 0 →e + e - [x10 5 ] 5.56±0.06 4.70±0.08 ω →π + π - (%) 1.13±0.08 1.70±0.27 ρ 0 →π + π - [MeV] 144.5±0.6 149.4±1.0 M. Benayoun, e+ e- versus tau43 ~ 15 σ apart starting from the same data!

44. Two New Results Process FIT PDG ρ 0 →e + e - [x10 5 ] 5.56±0.06 4.70±0.08 ω →π + π - (%) 1.13±0.08 1.70±0.27 ρ 0 →π + π - [MeV] 144.5±0.6 149.4±1.0 M. Benayoun, e+ e- versus tau44 May change the global fit to ω branching ratios

45. Fit Of The ω Mass Region : Perfect M. Benayoun, e+ e- versus tau45 FF’s New DataCross Sections Old Data

46. Additional Information THE MIXING « ANGLES » The (ρ,ω) and (ρ, ф) mixing «angles» are small (wrt 1) complex numbers The (ω, ф) mixing «angle» is real and small (wrt 1) M. Benayoun, e+ e- versus tau46

47. The (ρ, ω) Mixing «Angle» M. Benayoun, e+ e- versus tau47 Real part Imag. part ~ - 4 %

48. The (ρ, ф) Mixing «Angle» M. Benayoun, e+ e- versus tau48 Real Part Imag. Part

49. The (ω, ф) mixing «angle» M. Benayoun, e+ e- versus tau49 Real Part Imag. Part Start non-zero imaginary part

50. Hadronic Photon Vacuum Polarization M. Benayoun, e+ e- versus tau50 Full Correction Factor (Hadr. & Lept.) Photon Hadronic VP M. Davier et al. H. Burkhardt s (GeV 2 ) ω ф

51. The Pion Form Factor M. Benayoun, e+ e- versus tau51 e+e+ e-e- π+π+ π±π± π-π- π0π0 ντντ τ γ : I=0,1 W : I=1

52. The Hidden Local Symmetry Model Vector Mesons ≡ gauge bosons of a HL symmetry Define Define covariant derivatives Then and The HLS Lagrangian VMD : a=2, Phenomenology a ~ 2.4 M. Benayoun, e+ e- versus tau52 M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 Expanded form: M.Benayoun & H.O’Connell PR D 58 (1998) 074006

53. The Hidden Local Symmetry Model Vector Mesons ≡ gauge bosons of a HL symmetry Define Define covariant derivatives Then and The HLS Lagrangian VMD : a=2, Phenomenology a ~ 2.4 M. Benayoun, e+ e- versus tau53 M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 Expanded form: M.Benayoun & H.O’Connell PR D 58 (1998) 074006 PS field matrix

54. The Covariant Derivatives Covariant derivatives ≠ for left- right-ξ fields : With : M. Benayoun, e+ e- versus tau54 T ± is CKM matrix reduced to V us and V ud terms

55. Breaking of SU(3) Flavor Symmetry M. Benayoun, e+ e- versus tau55 With Breaking matrices z V related to vector meson masses, Bando Kugo Yamawaki op. cit. Benayoun & O’Connell op. cit. Several possible schemes

56. Breaking of SU(3) Flavor Symmetry M. Benayoun, e+ e- versus tau56 With Breaking matrices z V related to vector meson masses, Bando Kugo Yamawaki op. cit. Benayoun & O’Connell op. cit. Several possible schemes

57. Nonet Symmetry Breaking in HLS Model Nonet Symmetry Breaking accounted for by adding determinant terms to HLS Lagrangian Effective way : Radiative decays of light mesons vs glue : no glue but M. Benayoun, e+ e- versus tau57 M. Benayoun L. DelBuono H. O’Connell EPJ C 17 (2000) 593 P.J. O’Donnell RMP 53 (1981) 673 M. Benayoun et al. PR D 59 (1999) 114027

58. Anomalous Sector of the HLS Model HLS Model has an anomalous sector for VPγ and Pγγ couplings ; can be derived from : X T allows for correct account of K* rad. decays [ C = - 3 /(4 π 2 f π ) ] mixing angle related with vanishes when no SU(3) breaking M. Benayoun, e+ e- versus tau58 M. Benayoun et al. PR D 59 (1999) 114027 A. Bramon, A. Grau & G. Pancheri PL B 345 (1995) 263 G. Morpurgo PR D 42 (1990) 1497 MB, LD & HO EPJ C 17 (2000) 593