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A VMD Estimate of the Muon g-2 A HLS based approach

A VMD Estimate of the Muon g-2 A HLS based approach. M. Benayoun LPNHE Paris 6/7. OUTLINE. Model & Method Symmetry Breaking : BKY & ( ρ , ω , φ ) mixing Global Fit : t vs e + e - Global Fit : e + e - → π π / KKbar / π γ / η γ / π π π ππ contribution to g-2

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A VMD Estimate of the Muon g-2 A HLS based approach

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  1. A VMD Estimate of the Muon g-2 A HLS basedapproach M. Benayoun LPNHE Paris 6/7 M. Benayoun, VMD & g-2 estimates

  2. OUTLINE • Model & Method • Symmetry Breaking : BKY & (ρ,ω,φ) mixing • Global Fit : t vs e+ e- • Global Fit : e+e- → π π/KKbar /πγ/ηγ/π ππ • ππ contribution to g-2 • VMD estimate of HVP and g-2 • Conclusions M. Benayoun, VMD & g-2 estimates

  3. HLS : A VMD Model (I) • The HiddenLocalSymmetry model is: • A unifiedVMDframeworkincluding e+e- → π π/KKbar /πγ/ηγ/π ππ& τ→ππντ& PVγcouplings&η/η’  γπ π/γγ& …… • Few basic parameters : e, fπ,Vud,Vus, a (≈2), g ,… • PresentLimits : • Up to the ≈ φ mass region( 1.05 GeV) • No scalarsmesons, no ρ’, no ρ’’ …… M.Bando et al. Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M. Benayoun, VMD & g-2 estimates

  4. NSK2:: Breaking the HLS Model Breaking the HLS Model HLS not enoughFlexible to reallyaccount for data • Needbreakingschemes to become operating: • BKY mechanism • vectormesonmixing M.Bando et al. Nucl. Phys. B259 (1985) 493 A. Bramon et al. Phys. Lett. B345 (1995) 263 M.Benayoun et al. Phys. Rev. D58 (1998) 074006 M.Benayoun et al. EPJ C55 (2008) 199 M.Benayoun et al. EPJ C65 (2010) 211 M. Benayoun, VMD & g-2 estimates

  5. HLS and the BKY Mechanism • Define • Then • Standard HLS Lagrangians • BKY breaking : • Full HLS Lagrangian : • BKY Breaking Matrix : Diag PS fieldmatrix M. Hashimoto, Phys. Rev. D54 (1996) 5611 M. Benayoun et al, arXiv:1106.1315 M. Benayoun, VMD & g-2 estimates

  6. Isospin Breaking : Vector Field Mixing I • treelevel:: idealvectorfields≡mass eigenstates • Vector Mass TermDiagonalization: • one loop:: s-dependenttransitions among R1 fields F. Jegerlehner & R. Szafron EPJ C71 (2011) 1632 C. Wolfe&K. Maltman, Phys. Rev. D80 (2009)114024 M. Benayoun, VMD & g-2 estimates

  7. Isospin Breaking : Vector Field Mixing II • At one loop, the HLS Lagrangian piece induces s-dependenttransitions among R1 fields isospin symmetry breaking : M. Benayoun, VMD & g-2 estimates

  8. Transitions at 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, VMD & g-2 estimates

  9. The Mass Matrix Eigen System At one loop: As : Solveperturbatively M. Benayoun, VMD & g-2 estimates

  10. From Ideal To Physical Fields Physical Fields R1 Fields M. Benayoun, VMD & g-2 estimates

  11. Analysis Method GLOBAL FIT to the largest possible data set • Why ? • Check VMD constraintswellaccepted by DATA? (correct lineshapes & yields with Proba. OK) • IF YES ↔ theoreticalcorrelationsfulfilled by DATA →→ improvedparameters • HLS formfactors& fit parameters values &errors& covariance matrix→ contributions to g-2 • Procedurefullyblind to g-2 M. Benayoun, VMD & g-2 estimates

  12. Channels Considered • Non-Anomalous annihilations : e+e- → π π/ or decays : τ→ππντ(plays as constraintonly!) • AnomalousProcesses : e+e- → π γ/ηγ/π ππ(Anomalous FKTUY Effective Lagrangianpieces) • Radiative decayswidths (VPγ, η/η’→ππγ) OVERCONSTRAINED MODEL & BreakingScheme M. Benayoun, VMD & g-2 estimates

  13. Channels Considered • Non-Anomalous annihilations : e+e- → π π/ or decays : τ→ππντ(constraint) • AnomalousProcesses : e+e- → π γ/ηγ/π ππ(Anomalous Effective Lagrangianpieces) • Radiative decayswidths (VPγ, η/η’→ππγ) • ISR data : NOT INCLUDEDOVERCONSTRAINED MODEL & BreakingScheme Relying on more than 40 (scan) data sets M. Benayoun, VMD & g-2 estimates

  14. V π π Couplings: I=1 part of ω and φ Mixing Angles I=1 terms *Atleadingorder : ρtermunchanged(I=1 part) *smalls-dependentω and φcouplings (I=1 part) * Charged and neutralrho’s: samecoupling to pions M. Benayoun, VMD & g-2 estimates

  15. ρ couplings to γ/W • (γ/W) V transitions : = + Full agreement between data One loop corrections M. Benayoun, VMD & g-2 estimates

  16. ρ couplings to γ/W • (γ/W) V transitions : = + Full agreement between data One loop corrections M. Benayoun, VMD & g-2 estimates

  17. ρ couplings to γ/W • (γ/W) V transitions : = + Full agreement between data One loop corrections M. Benayoun, VMD & g-2 estimates

  18. ρ couplings to γ/W Re[F(s)] Im[F(s)] M. Benayoun, VMD & g-2 estimates

  19. Dipion Spectra M. Benayoun, VMD & g-2 estimates

  20. e+e-Fit Residuals e+e- Data M. Benayoun, e+ e- versus tau

  21. Tau Fit Residuals M. Benayoun, VMD & g-2 estimates

  22. Tau Residuals M. Benayoun, VMD & g-2 estimates

  23. NSK18:: Dipion Mass Spectrum • s-dependent (missing) effect ! M. Davier NP Proc. Supp. 169 (2007) 288 M. Benayoun, VMD & g-2 estimates

  24. 3-pion Data M. Benayoun, VMD & g-2 estimates

  25. e+e- → K Kbar Data K+ K- KL KS M. Benayoun, VMD & g-2 estimates

  26. e+e- → K Kbar Data Ratio K+ K- KL KS M. Benayoun, VMD & g-2 estimates

  27. e+e- → π0 γ M. Benayoun, VMD & g-2 estimates

  28. e+e- → ηγ Data M. Benayoun, VMD & g-2 estimates

  29. Effect of Global Fitting on aµ(ππ) L.O. Contribution of ππ to g-2 Integratedfrom 0.630 to 0.958 GeV/c (x10-10) FSR Corrected • Reconstructed value consistent with exp. average • Global fits provideimproveduncertainties •  Probabilitiesprovided by the (underlying) global fits M. Benayoun, VMD & g-2 estimates

  30. Effect of Global Fit on aµ(ππ) L.O. Contribution of ππ to g-2 Integratedfrom 0.630 to 0.958 GeV/c (x10-10) • Reconstructed value consistent with exp. average • Global fits provideimproveduncertainties •  Probabilitiesprovided by the (underlying) global fits M. Benayoun, VMD & g-2 estimates

  31. Effect of Global Fit on aµ(ππ) L.O. Contribution of ππ to g-2 Integratedfrom 0.630 to 0.958 GeV/c (x10-10) • Reconstructed value consistent with exp. average • Global fits provideimproveduncertainties •  Probabilitiesprovided by the (underlying) global fits M. Benayoun, VMD & g-2 estimates

  32. Contributions to g-2 up to F () Excl. ISR Uncertaintiesuniformlyimproved by a factor 2 M. Benayoun, VMD & g-2 estimates

  33. VMD estimate of LO HVP Below 1.05 GeV • Most of Hadronic VP estimatedfromour Model (574.76 ± 2.10/ 572.82 ± 1.90) • Missingchannels(ηπ π, π π π π, etc…) HVP estimatedfrom data (1.55 ± 0.57) Above 1.05 GeV • LO HVP estimatedfrom data and pQCD (111.41 ± 4.10) • Total LO HVP : B → 687.72 ± 4.63 //A → 685.78 ± 4.55 M. Benayoun, VMD & g-2 estimates

  34. VMD estimate of g-2 • LO HVP + HO HVP + LBL +QED +EW give aµ= (11 659 175.37 ± 5.31) 10-10 (B) Or aµ= (11 659 173.43 ± 5.25) 10-10 (A) M. Benayoun, VMD & g-2 estimates

  35. VMD estimate of g-2 M. Benayoun, VMD & g-2 estimates

  36. Conclusions 1/ HLS with BKY and Vector Meson Mixing provides a good simultaneous fit of e+e- → → π π/K+K-/ KLKS/ π γ/ηγ/π ππ 2/ A simultaneous account of e+e- → → π π& τ→ππντ 3/ VMD physics correlations improveg-2 (Uncertainty : HVP up to f uniformly improved by 2) M. Benayoun, VMD & g-2 estimates

  37. Backup Slides M. Benayoun, VMD & g-2 estimates

  38. NSK1:: HLS : A VMD Model (I) • The HiddenLocalSymmetry model is: • A unifiedVMDframeworkincluding e+e- → π π/Kkbar /πγ/ηγ/π ππ& τ→ππντ& PVγcouplings&η/η’  γπ π/γγ& …… • Few basic parameters : e, fπ,Vud,Vus, a (≈2), g ,… • PresentLimits : • Up to the ≈ φ mass region( 1.05 GeV) • No scalarsmesons, no ρ’, no ρ’’ …… M.Bando et al. Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M. Benayoun, VMD & g-2 estimates

  39. VMD :: The HLS Framework • HiddenLocal Symmetry Model (HLS) as a whole LA, LV, LYM , Lanomalous (π/K formfactors, VPPP, γPPP, VPγ & Pγγcouplings) • BKY-like flavor U(3)/SU(3) breakingmechanisms M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M.Benayoun & H.O’Connell PR D 58 (1998) 074006 M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 A. Bramon, A. Grau & G. Pancheri PL B 345 (1995) 263 M. Benayounet al. PR D 59 (1999) 114027 G. Morpurgo PR D 42 (1990) 1497 M. Benayoun, L. DelBuono & H. O’Connell EPJ C 17 (2000) 593 M. Benayoun et al. EPJ C 55 (2008) 139 M. Benayoun, VMD & g-2 estimates

  40. The HiddenLocal Symmetry Model :The Non-AnomalousSector • Define • Define covariant derivatives • Then and • The Full HLS Lagrangian : PS fieldmatrix Expandedform: M.Benayoun & H.O’Connell PR D 58 (1998) 074006 UniversalVectorCoupling M. Benayoun, VMD & g-2 estimates

  41. The Covariant Derivatives • Covariant derivatives ≠ for left- right-ξ fields : • With : T± is CKM matrix reduced to Vus and Vud terms M. Benayoun, VMD & g-2 estimates

  42. Anomalous Annihilations/Decays • Non-Anomalous annihilations : e+e- → π π/ or decays : τ→ππντ • AnomalousProcesses : e+e- → π γ/ηγ/π ππ :: Other Effective Lagrangianpieces M. Benayoun, VMD & g-2 estimates

  43. SIDE RESULT : Prediction for η/η’→ ππγ M. Benayoun et al. ArXiv 0907.4047 Г(η’→ ππγ)=53.11±1.47 PDG : 60±5 keV Г(η→ ππγ)=55.82±0.83 PDG : 60±4 eV Lineshapes and yields : tests for g valueand ρ0 lineshape M. Benayoun, VMD & g-2 estimates

  44. BELLE/ALEPH/CLEO M. Benayoun, VMD & g-2 estimates

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