Estimates for (g-2) μ using VMD constraints & Global Fits

1. Estimates for (g-2)μusing VMD constraints & Global Fits M. Benayoun LPNHE Paris 6/7 (collaborators : P. David, L. Delbuono, F. Jegerlehner)

2. OUTLINE • The HLSModel & Breaking: BKY&(ρ,ω,φ) mixing • Global Fit Scope: V P γ/ P γ γ/t vs e+ e- & [e+e- → π π /K+K-/KLKS /πγ /ηγ /π ππ] • HLS Estimates of (g-2)μ • Global fits with only scan (NSK) data : e+e- vs τ • «t + PDG » Predictions of e+e- → π πvs data • Global fit with t, scan and ISR π πdata → g-2 • Conclusions M.Benayoun et al. EPJ C72 (2012) 1848 M.Benayoun et al. arXiv: 1210.7184// EPJC

3. NSK2:: Breaking the HLS Model • The HLS Model &Breaking The HLS Lagrangiannot flexible for data handling • Breakingschemesneeded: • BKY mechanism : • vectormesonmixing : • Latest Model Status : M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M.Bando et al. Nucl. Phys. B259 (1985) 493 M.Benayoun et al. Phys. Rev. D58 (1998) 074006 M.Hashimoto Phys. Rev. D54 (1996) 5611 M.Benayoun et al. EPJ C55 (2008) 199 M.Benayoun et al. EPJ C65 (2010) 211 M.Benayoun et al. EPJ C72 (2012) 1848

4. Isospin Breaking : Vector Field Mixing • At one loop, the HLS Lagrangianpiece(no IB) s-dependenttransitions amongvectorfields idealfieldsno longer mass eigenstates PS mesons :: isospin symmetrybreaking : → VVP Lagrangian : K*K loops // Yang-Mills term : K*K*loops →

5. The Mass Matrix Eigen System At one loop: As : Solveperturbatively : (kaon loop)Sum, Difference

6. From Ideal To Physical Fields Physical Fields R1 Fields Atleadingorder in ε1(s) , ε2(s)

7. BHLS : A Global VMD Model • The (Broken) HiddenLocalSymmetry (BHLS) model: • is a unifiedVMDframeworkencompassing e+e- → π π/KKbar /πγ/ηγ/π ππ& τ→ππντ& PVγ, Pγγdecays&η/η’  γπ π/γγ& …… • BHLS :: (almost) an emptyshell : [αem, GF , fπ, Vud, Vus , mπ’s, mK’s, mη, , mη’] • PresentLimits : • Up to the ≈ φ mass region( 1.05 GeV) • No scalarsmesons, no ρ’, no ρ’’ ……

8. HLS : A Global VMD Model • The (Broken) HiddenLocalSymmetry (BHLS) model: • is a unifiedVMDframeworkencompassing e+e- → π π/KKbar /πγ/ηγ/π ππ& τ→ππντ& PVγ, Pγγdecays&η/η’  γπ π/γγ& …… • BHLS :: (almost) an emptyshell : [αem, GF , fπ, Vud, Vus ,mπ’s, mK’s, mη, , mη’] PresentLimits : • Up to the ≈ φ mass region( 1.05 GeV) • No scalarsmesons, no ρ’, no ρ’’ ……

9. HLS : A Global VMD Model • The (Broken) HiddenLocalSymmetry (BHLS) model: • is a unifiedVMDframeworkencompassing e+e- → π π/KKbar /πγ/ηγ/π ππ& τ→ππντ& PVγ, Pγγdecays&η/η’  γπ π/γγ& …… • BHLS :: (almost) an emptyshell : [αem, GF , fπ, Vud, Vus , mπ’s, mK’s, mη , mη’] PresentLimits : • Up to the ≈ φ mass region( 1.05 GeV) • No scalarsmesons, no ρ’, no ρ’’ ……

10. g-2 & Global Models/Fits • NP Hadronic VP contributions to g-2 (interpolation betweenenergy points) • VMD : Underlyingphysicscorrelations-> HLS cross-sections derivedthrough a global fit (param. values & error covariance matrix) : MeasuredXsection MeasuredXsection ModelXsection (φ)

11. HLS→CorrelatedPhysicsChannels • Non-Anomalous annihilations : e+e- → π+π- / • Decayspectra : τ ± → π±π0ντ(lateralso :η/η’→π+π-γ) • AnomalousProcesses : e+e- → π0 γ/ηγ/ π+π-π0 • Radiative decayswidths ( VPγ, π0/η/η’ → γ γ) • φ→ππ (Br ratio and phase) HLSMODEL & BreakingSchemes: OVERCONSTRAINED & **DETERMINED** by more than 40 data sets

12. HLS→CorrelatedPhysicsChannels • Non-Anomalous annihilations : e+e- → π+π- / • Decayspectra : τ ± → π±π0ντ(lateralso :η/η’→π+π-γ) • AnomalousProcesses : e+e- → π0 γ/ηγ/ π+π-π0 • Radiative decayswidths ( VPγ, π0/η/η’ → γ γ) • φ→ππ (Br ratio and phase) New Paradigm : Any information on anychannel (π0 γ) isequivalent to improving the statistics on anyotherchannel (π+π- )

13. HLS→CorrelatedPhysicsChannels • Non-Anomalous annihilations : e+e- → π+π- / • Decayspectra : τ ± → π±π0ντ(lateralso :η/η’→π+π-γ) • AnomalousProcesses : e+e- → π0 γ/ηγ/ π+π-π0 • Radiative decayswidths ( VPγ, π0/η/η’ → γ γ) • φ→ππ (Br ratio and phase) HOWEVER : NonPerturbative Contributions to HVP above ≈1.05 GeV shouldbeestimated as usual

14. VMD Strategy for g-2 Estimate GLOBAL FIT to the largest possible data set • Check::areVMD constraintswellaccepted by DATA? (correct lineshapes& yields with Prob.’s OK) • IF YES : • 1/ VMD correlations are fulfilledby DATA • 2/ THEN :: HLS formfactors& fit parameters values &errors covariance matrixshouldlead to : • Improvedestimates of HVP contributions to g-2 for π+π-/ / /πγ/ηγ/η’ γ/π ππup to 1.05 GeV

15. Global Fit Quality with NSK only Fits : see backup slides

16. Dipion Spectra (τ & e+e-): A puzzle?

17. e+e- vs τ : CMD2/SND Fit Residuals ΔF ΔF/F Global fit : 96% Prob

18. e+e- vs τ : Tau Fit Residuals ΔF ΔF/F

19. A « e+e- - τ» Puzzle ? • s-dependent (missing) effect ! M. Davier NP Proc. Supp. 169 (2007) 288

20. A « e+e- - τ» Puzzle ? • e+e- and τ dipionresiduals : simultaneouslyflat • |Fπ(e+e-)|2 & |Fπ(τ)|2 yield : simultaneouslyχ2π+π- /Nπ+π- & χ2π±π0 /Nπ ± π0 ≈1 • Global fit Probability> 90% • No signal of any e+e- - τmismatch → nothingpuzzling

21. HVP Resultswith scan & τ data • (Updated) All uncertaintiesimproved by ≈ 2

22. HVP Resultswith scan & τ data • (Updated) All uncertaintiesimproved by ≈ 2 Scan +ISR

23. HVP Resultswith scan & τ data • (Updated) Central value shifted by ≈ 3 10-10 Diff=3.1 units

24. τPredictions for π+π-Spectra • τ dipion spectra :basis (Aleph,Belle&Cleo<1 GeV) • ++ Breaking Info from PDG : Γ(ρ→ e+e- ) & Γ(ω→ππ) & Γ(φ→ππ) (& Orsay ) • → → «τ + PDG predictions» for e+e-→ π+π- • generated by the model usingall data for: • τ→ππντ, e+e-→ /π0 γ/ηγ/π+ π-π0 & VPγ &Pγ γ couplings(from PDG)

25. τPredictions for π+π-Spectra • τ dipion spectra :basis (Aleph,Belle&Cleo< 1 GeV) • ++ Breaking Info from PDG : Γ(ρ→ e+e- ) & Γ(ω→ππ) & Γ(φ→ππ) (& Orsay ) • → → «τ + PDG predictions» for e+e-→ π+π- • generated by the model usingall data for: • τ→ππντ, e+e-→ /π0 γ/ηγ/π+ π-π0 &VPγ &Pγ γ couplings(from PDG)

26. τ + PDG Predictions !! Spacelikeregionwellpredicted & Extrapolatesmuchabove 1 GeV!!! Good agreement data versus predictions

27. τ+ PDG Predictions PION Form Factor 0.85 GeV >mππ> 0.70GeV KLOE’salmostperfect! CMD2&SND ≈ OK BaBar too large belowω

28. Guesses About Global Fits • Discrepanciesbetweenπ+π- data sets (oldnews) • Clearproblemat (ρ,ω) Interference for BaBar HOWEVER PDG IB information : Γ(ρ→ e+e- ) & Γ(ω→ππ) almostequivalent to Experimental IB information : (0.76-0.82) GeVRegion Fromeachdata set (NSK,KLOE’s,BaBar)

29. τ+ {BaBar (ρ―ω)} Predictions Prediction PION Form Factor 0.85 GeV >mππ> 0.70GeV Prediction FIT

30. τ+ {(ρ―ω) RegionfromeachExp} Fits KLOE 08 KLOE10 PION Form Factor 0.85 GeV >mππ> 0.70GeV BaBar NSK Fits in «isolation»

31. Fω= Br(ω→π+π-)*Br(ω→e+e-) ρ-ωregion (0.76→0.82 GeV)/φ(PDG)

32. Checkingππ data sets • Fitsperformed with eachππ data set in isolation (scan/KLOE’s/BaBar) • All otherchannelsalwaysincluded in fits (τ→ππντ,e+e-→ K+K-/ K0 K0b/π γ/ηγ/π π π)

33. KLOE raw & correctedResiduals ΔF

34. Fits in isolation : Comments • Good Residuals & Gl. fit Prob. OK & good χ2 : CMD2 & SND & KLOE10 & KLOE12 • (Very) Good Residuals & poorχ2 (1.62) : KLOE08 (correlations in systematics) • Bad Gl. fit Prob . & at [ρ/ω] peakχ2/N= 1.9 BaBar (hardly consistent with non ππ data) • Consistent ππ data sets for Global Treatment : CMD2 & SND & KLOE10 & KLOE12

35. GLOBAL FIT RESULTS • Fits performed with combinations of ππ data sets (incl./excl. Spacelike) • All otherchannelsalwaysincluded in fits (τ→ππντ,e+e-→ K+K-/ K0 K0b/π γ/ηγ/π π π)

36. GLOBAL FIT RESULTS Provesconsistency of CMD2/SND/KLOE10/KLOE12 KLOE’sFits in «isolation» Global Fit

37. HVP Results up to 1.05 GeV Scan +ISR

38. HVP Results up to 1.05 GeV Scan +ISR Scan +ISR

39. g-2 HLS Estimates& Others

40. g-2 HLS Estimates& Others

41. g-2 HLS Estimates& Others

42. aμ(ππ) over mππ=[0.63,0.958] GeV Model Estimate in Accord with expectations Uncertaintiesimproved by ≈45%

43. aμ(ππ) over mππ=[0.63,0.958] GeV Accord with Exp. expectations ≈ No Bias!

44. aμ(ππ) over mππ=[0.63,0.958] GeV No Mismatch!

45. The Spacelike & thresholdRegions Extrapolation to s<0 perfect Low mass tail OK!

46. Predicted Phase shift (I)

47. Predicted Phase shift (II)

48. ThresholdBehavior

49. Conclusions 1/ broken HLS model → good simultaneous fit of all data 2/ suitable IB → NO signal for (e+e-vsτ) puzzle 3/ « τ +PDG » predictions → benchmark for π πsamples! 4/ Relative inconsistencies of π+ π- data sets substantiated 5/ Consistent π + π-data sets : CMD2, SND, KLOE 10 & 12 6/ The discrepancy with BNL g-2 value is≈4.8 to5.1 σ

50. Backup Slides