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Dipion Spectrum : e + e - annihilations and τ decays

Dipion Spectrum : e + e - annihilations and τ decays. M. Benayoun LPNHE Paris 6/7. The Pion Form factor in e + e - and τ Data. Since the advent of τ data, disagreement with e + e - data

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Dipion Spectrum : e + e - annihilations and τ decays

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

  2. The Pion Form factor in e+e- and τ Data • Since the advent of τ data, disagreementwith e+e- data • Large activity in identifying isospin symmetrybreaking in both e+e- annihilation and τdecay • Disagreementsurvivedaccounting for identified isospin breaking corrections! • Is there a missingpiece, a systematiceffect(in e+e- or τ data) or new physics? M. Benayoun, e+ e- versus tau

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

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

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

  6. Possible MissingEffect : (ρ-ω-φ) Mixing FF’s New Data Isospin 1 part of ω Isospin 1 part of φ Isospin 0 part of ρ0 ? Can it be s-dependent? M. Benayoun, e+ e- versus tau

  7. OUTLINE • A VMD-like Model : HLS Model (briefly) • Breaking of U(3)/SU(3) Symmetries (briefly) • The AnomalousSector (briefly) • The Pion Form Factor in e+e- Annihilation and τDecay (Isospin Breaking) • Loop Transition Effects in e+e- :Physicalρ0, ω, ф • Extended Data Samplesubmitted to fit, Why? • Fit results & Plots • Conclusions M. Benayoun, e+ e- versus tau

  8. OUTLINE • A VMD-like Model : HLS Model (briefly) • Breaking of U(3)/SU(3) Symmetries (briefly) • The AnomalousSector (briefly) • The Pion Form Factor in e+e- Annihilation and τDecay (Isospin Brk) • Loop Transition Effects in e+e- :Physicalρ0, ω, ф • Extended Data Samplesubmitted to fit, Why? • Fit results & Plots • Conclusions M. Benayoun, e+ e- versus tau

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

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

  11. The Pion form Factor in e+e- and τPhysics • With Symmetry Breaking : • Isospin symmetry breaking : mass splittings + (γ/W)V ? ρππ? δm2 W. Marciano & A. Sirlin PRL 71 (1993) 3629 V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361 M. Benayoun, e+ e- versus tau

  12. γ/W- ρ Transitions • No isospin breaking : • Isospin symmetry breaking : ρ± component ρI component фI and ωI components M. Benayoun, e+ e- versus tau

  13. Transitions amongvectorfieldsat one loop • Attreelevelidealfields≡mass eigenstates • At one loop, the HLS Lagrangianpiece inducestransitions amongidealfields idealfields≡mass eigenstates isospin symmetrybreaking : M. Benayoun, e+ e- versus tau

  14. Transitions amongvectorfieldsat one loop • Define the loops : = K+ K- , = K0K0 Then, beside self-masses : = + ~ ε2(s) ≠ 0 always = - ≠ 0 by isospin brk = - ~ ε1(s) VVP Lagrangian K*K loops // Yang-Mills K*K*loops f(s) M. Benayoun, e+ e- versus tau

  15. The Modified Vector Mass Matrix ρIωIφI Withm2 = a g2 fπ2 and μ= zV No SU(3) Brk :: , No SU(2) Brk :: Blue : Loopeffectsmagenta : SU(3) breakingred : isospin breaking M. Benayoun, e+ e- versus tau

  16. Loop Corrections : (ω , ф) Mixing ρIωIφI Blue : Loopeffectsmagenta : SU(3) breakingred : isospin breaking M. Benayoun, e+ e- versus tau

  17. Isospin Breaking : (ρ, ω , ф) Mixing ρIωIφI Blue : Loopeffectsmagenta : SU(3) breakingred : isospin breaking M. Benayoun, e+ e- versus tau

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

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

  20. From Ideal To Physical Fields II Mass term derived from the eigenvalues of M2(s) : (Self masses include subtraction polynomials) Leading order propagators become M. Benayoun, e+ e- versus tau

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

  22. V π π Couplings Orsay Phase ≈90₀ atpeak *At leading order : ρ term unchanged *s-dependent ω and φ couplings generated M. Benayoun, e+ e- versus tau

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

  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 tau

  25. Vector Meson Coupling to γ/W • (γ/W) V transitions : constant + (PP,VP…) loops = + • loop term : disp. relation (subtractions) • tree terms : ωI andфI components of ρ0 M. Benayoun, e+ e- versus tau

  26. Parameter Freedom • If onlyusing the pion form factor (e+e-,τ) the parameterfreedomis far too large: • a (HLS), g , zA , δm2 (4) • Subtractionpolynomials in : (~ 8) Toomanyparameters, too few structures • Solution : extend the fitted data sample: more information, lesscorrelations M. Benayoun, e+ e- versus tau

  27. The Extended Data Sample • Addanomalousdecay modes VPγ, Pγγ : • Price : x, zT, zV, zA for 14 modes for free for free + 4 measured data :: Total 18 add. data M.B.,L.D. ,S.E, V.I. & H.OC, PR D 59 (1999) 114027 M.B, H.OC EPJ C22 (2001) 503 M. Benayoun, e+ e- versus tau

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

  29. The Χ2 contributionstofits M. Benayoun, e+ e- versus tau

  30. The Χ2 contributionstofits M. Benayoun, e+ e- versus tau

  31. The Χ2 contributionstofits τ DATA OUTSIDE FIT :Χ2 distance to prediction M. Benayoun, e+ e- versus tau

  32. The Χ2 contributionstofits Spacelike data OUTSIDE FIT M. Benayoun, e+ e- versus tau

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

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

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

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

  37. Isospin SymmetryBreaking : ρ0 VS ρ± M. Benayoun, e+ e- versus tau

  38. Isospin SymmetryBreaking : ρ0 VS ρ± 0 :: NO IS Brk Threshold : -6% ρ Peak : + 3% Φ Mass : -2% M. Benayoun, e+ e- versus tau

  39. Conclusions • No mismatchbetween e+e- and τ data • Radiative decays & pion form factor in e+e- annihilation predict the observed pion form factor in τdecay • Previouslyunaccounted for effects : I=0 (ωI, фI) components inside the ρ0 meson. • The 3.3 σdiscrepancybetweenprediction (using e+e- data) and the BNL measurement for the muon anomalous moment isconfirmed M. Benayoun, e+ e- versus tau

  40. Fit Decay Modes Vs PDG M. Benayoun, e+ e- versus tau

  41. The ρ0 - ρ± Mass Difference ALEPH Data The ρ0-ρ± Mass Difference : 1/ Only visible in ALEPH data 2/ ~1 .2 σ from ChPT δm2= 0 Fixed J. Bijnens & P. Gosdzinsky PL B 388 (1996) 203 ρPeakRegion δm2 Fitted High mass Vectormesons M. Benayoun, e+ e- versus tau

  42. Two New Results M. Benayoun, e+ e- versus tau

  43. Two New Results ~ 15 σapart starting from the same data! M. Benayoun, e+ e- versus tau

  44. Two New Results May change the global fit to ω branching ratios M. Benayoun, e+ e- versus tau

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

  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 tau

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

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

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

  50. Hadronic Photon Vacuum Polarization ω ф M. Davier et al. H. Burkhardt Photon Hadronic VP s (GeV2) Full Correction Factor (Hadr. & Lept.) s (GeV2) M. Benayoun, e+ e- versus tau

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