Slide 1

A VMD Estimate of the Muon g-2 A HLS based approach M. Benayoun LPNHE Paris 6/7 1M. Benayoun, VMD & g-2 estimates Slide 2 OUTLINE Model & Method Symmetry Breaking : BKY & (,,) mixing Global Fit : vs e + e - Global Fit : e + e - /KKbar / / / contribution to g-2 VMD estimate of HVP and g-2 Conclusions M. Benayoun, VMD & g-2 estimates2 Slide 3 HLS : A VMD Model (I) The Hidden Local Symmetry model is : A unified VMD framework including e + e - /KKbar / / / & & PV couplings & / / & Few basic parameters : e, f ,V ud,V us, a (2), g, Present Limits : Up to the mass region ( 1.05 GeV) No scalars mesons, no , no 3M. Benayoun, VMD & g-2 estimates M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M.Bando et al. Phys. Rep. 164 (1988) 217 Slide 4 NSK2:: Breaking the HLS Model HLS not enough Flexible to really account for data Need breaking schemes to become operating: BKY mechanism vector meson mixing 4M. Benayoun, VMD & g-2 estimates M.Bando et al. Nucl. Phys. B259 (1985) 493 M.Benayoun et al. EPJ C55 (2008) 199 M.Benayoun et al. Phys. Rev. D58 (1998) 074006 Breaking the HLS Model A. Bramon et al. Phys. Lett. B345 (1995) 263 M.Benayoun et al. EPJ C65 (2010) 211 Slide 5 HLS and the BKY Mechanism Define Then Standard HLS Lagrangians BKY breaking : Full HLS Lagrangian : BKY Breaking Matrix : Diag PS field matrix M. Benayoun, VMD & g-2 estimates M. Hashimoto, Phys. Rev. D54 (1996) 5611 M. Benayoun et al, arXiv:1106.1315 Slide 6 Isospin Breaking : Vector Field Mixing I tree level:: ideal vector fields mass eigenstates Vector Mass Term Diagonalization: one loop:: s-dependent transitions among R1 fields 6M. Benayoun, VMD & g-2 estimates C. Wolfe&K. Maltman, Phys. Rev. D80 (2009)114024 F. Jegerlehner & R. Szafron EPJ C71 (2011) 1632 Slide 7 Isospin Breaking : Vector Field Mixing II At one loop, the HLS Lagrangian piece induces s-dependent transitions among R1 fields isospin symmetry breaking : 7M. Benayoun, VMD & g-2 estimates Slide 8 Transitions at one loop Define the loops : = K + K -, = K 0 K 0 Then, beside self-masses : + ~ 2 (s) 0 always - 0 by isospin brk - ~ 1 (s) VVP Lagrangian K*K loops // Yang-Mills K*K*loops 8 f(s) M. Benayoun, VMD & g-2 estimates Slide 9 The Mass Matrix Eigen System At one loop: As : Solve perturbatively 9M. Benayoun, VMD & g-2 estimates Slide 10 From Ideal To Physical Fields 10M. Benayoun, VMD & g-2 estimates R 1 Fields Physical Fields Slide 11 Analysis Method GLOBAL FIT to the largest possible data set Why ? Check VMD constraints well accepted by DATA? (correct lineshapes & yields with Proba. OK) IF YES theoretical correlations fulfilled by DATA improved parameters HLS form factors & fit parameters values & errors & covariance matrix contributions to g-2 Procedure fully blind to g-2 M. Benayoun, VMD & g-2 estimates11 Slide 12 Channels Considered Non-Anomalous annihilations : e + e - / or decays : (plays as constraint only!) Anomalous Processes : e + e - // (Anomalous FKTUY Effective Lagrangian pieces) Radiative decays widths ( VP, /) OVERCONSTRAINED MODEL & Breaking Scheme 12M. Benayoun, VMD & g-2 estimates Slide 13 Channels Considered Non-Anomalous annihilations : e + e - / or decays : (constraint) Anomalous Processes : e + e - // (Anomalous Effective Lagrangian pieces) Radiative decays widths ( VP, /) ISR data : NOT INCLUDED OVERCONSTRAINED MODEL & Breaking Scheme Relying on more than 40 (scan) data sets 13M. Benayoun, VMD & g-2 estimates Slide 14 V Couplings: I=1 part of and *At leading order : term unchanged (I=1 part) *small s-dependent and couplings (I=1 part) * Charged and neutral rhos: same coupling to pions 14 Mixing Angles I=1 terms M. Benayoun, VMD & g-2 estimates Slide 15 couplings to /W (/W) V transitions : = + Full agreement between data 15 M. Benayoun, VMD & g-2 estimates One loop corrections Slide 16 couplings to /W (/W) V transitions : = + Full agreement between data 16 M. Benayoun, VMD & g-2 estimates One loop corrections Slide 17 couplings to /W (/W) V transitions : = + Full agreement between data 17 M. Benayoun, VMD & g-2 estimates One loop corrections Slide 18 M. Benayoun, VMD & g-2 estimates18 couplings to /W Re[F(s)] Im[F(s)] Slide 19 Dipion Spectra M. Benayoun, VMD & g-2 estimates19 Slide 20 e + e - Fit Residuals M. Benayoun, e+ e- versus tau20 e + e - Data Slide 21 M. Benayoun, VMD & g-2 estimates21 Tau Fit Residuals Slide 22 M. Benayoun, VMD & g-2 estimates22 Tau Residuals Slide 23 NSK18:: Dipion Mass Spectrum s-dependent (missing) effect ! 23 M. Davier NP Proc. Supp. 169 (2007) 288 M. Benayoun, VMD & g-2 estimates Slide 24 24 3-pion Data Slide 25 M. Benayoun, VMD & g-2 estimates25 K + K - K L K S e + e - K Kbar Data Slide 26 M. Benayoun, VMD & g-2 estimates26 K + K - K L K S e + e - K Kbar Data Ratio Slide 27 e + e - 0 27M. Benayoun, VMD & g-2 estimates Slide 28 e + e - Data 28M. Benayoun, VMD & g-2 estimates Slide 29 29 Effect of Global Fitting on a () L.O. Contribution of to g-2 Integrated from 0.630 to 0.958 GeV/c (x10 -10 ) Reconstructed value consistent with exp. average Global fits provide improved uncertainties Probabilities provided by the (underlying) global fits FSR Corrected Data Set 10 10 a () 2 /dofProbability Exp. Average 360.65 2.55 All NSK + - 360.00 1.64 177/208 93% ++ 359.80 1.47 263/293 90% ++ ( 0 /) 360.09 1.60 437/549 99% ++ ( + - 0 ) 360.91 1.45 661/727 96% ++ K Kbar 362.79 1.43 858/882 71% Slide 30 M. Benayoun, VMD & g-2 estimates30 Data Set 10 10 a () 2 /dofProbability Exp. Average 360.65 2.55 All NSK + - 360.00 1.64 177/208 93% ++ 359.80 1.47 263/293 90% ++ ( 0 /) 360.09 1.60 437/549 99% ++ ( + - 0 ) 360.91 1.45 661/727 96% ++ K Kbar 362.79 1.43 858/882 71% Effect of Global Fit on a () L.O. Contribution of to g-2 Integrated from 0.630 to 0.958 GeV/c (x10 -10 ) Reconstructed value consistent with exp. average Global fits provide improved uncertainties Probabilities provided by the (underlying) global fits Slide 31 M. Benayoun, VMD & g-2 estimates31 Data Set 10 10 a () 2 /dofProbability Exp. Average 360.65 2.55 All NSK + - 360.00 1.64 177/208 93% ++ 359.80 1.47 263/293 90% ++ ( 0 /) 360.09 1.60 437/549 99% ++ ( + - 0 ) 360.91 1.45 661/727 96% ++ K Kbar 362.79 1.43 858/882 71% Effect of Global Fit on a () L.O. Contribution of to g-2 Integrated from 0.630 to 0.958 GeV/c (x10 -10 ) Reconstructed value consistent with exp. average Global fits provide improved uncertainties Probabilities provided by the (underlying) global fits Slide 32 Contributions to g-2 up to () 32M. Benayoun, VMD & g-2 estimates ChannelSolution BSolution AExp. Average +-+- 498.54 1.97497.98 1.76498.53 3.73 0 0 4.64 0.04 4.28 0.04 3.35 0.11 0.65 0.01 0.67 0.01 0.48 0.01 ' ' 0.01 0.00 --- + - 0 42.03 0.60 40.88 0.52 43.24 1.47 K L K S 12.02 0.09 12.07 0.08 12.31 0.33 K+K-K+K- 16.87 0.20 16.93 0.18 17.88 0.54 Total up to 1.05 GeV 574.76 2.10572.82 1.90575.79 4.06 Excl. ISR Uncertainties uniformly improved by a factor 2 Slide 33 Below 1.05 GeV Most of Hadronic VP estimated from our Model (574.76 2.10/ 572.82 1.90) Missing channels ( , , etc) HVP estimated from data (1.55 0.57) Above 1.05 GeV LO HVP estimated from 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 estimates33 VMD estimate of LO HVP Slide 34 LO HVP + HO HVP + LBL +QED +EW give a = ( 11 659 175.37 5.31) 10 -10 (B) Or a = ( 11 659 173.43 5.25) 10 -10 (A) M. Benayoun, VMD & g-2 estimates34 VMD estimate of g-2 Slide 35 M. Benayoun, VMD & g-2 estimates35 VMD estimate of g-2 Slide 36 Conclusions 1/ HLS with BKY and Vector Meson Mixing provides a good simultaneous fit of e + e - /K + K - / K L K S / // 2/ A simultaneous account of e + e - & 3/ VMD physics correlations improve g-2 (Uncertainty : HVP up to uniformly improved by 2) 36M. Benayoun, VMD & g-2 estimates Slide 37 Backup Slides 37M. Benayoun, VMD & g-2 estimates Slide 38 NSK1:: HLS : A VMD Model (I) The Hidden Local Symmetry model is : A unified VMD framework including e + e - /Kkbar / / / & & PV couplings & / / & Few basic parameters : e, f ,V ud,V us, a (2), g, Present Limits : Up to the mass region ( 1.05 GeV) No scalars mesons, no , no 38M. Benayoun, VMD & g-2 estimates M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M.Bando et al. Phys. Rep. 164 (1988) 217 Slide 39 VMD :: The HLS Framework Hidden Local Symmetry Model (HLS) as a whole L A, L V, L YM, L anomalous (/K form factors, VPPP, PPP, VP & P couplings) BKY-like flavor U(3)/SU(3) breaking mechanisms M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 M. Harada & K. Yamawaki Phys. Rep. 381 (2003) 1 M.Benayoun & H.OConnell PR D 58 (1998) 074006 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 M. Benayoun, L. DelBuono & H. OConnell EPJ C 17 (2000) 593 M. Benayoun et al. EPJ C 55 (2008) 139 M.Bando, T. Kugo & K. Yamawaki Phys. Rep. 164 (1988) 217 39M. Benayoun, VMD & g-2 estimates Slide 40 The Hidden Local Symmetry Model : The Non-Anomalous Sector Define Define covariant derivatives Then and The Full HLS Lagrangian : 40 Expanded form: M.Benayoun & H.OConnell PR D 58 (1998) 074006 Universal Vector Coupling PS field matrix M. Benayoun, VMD & g-2 estimates Slide 41 The Covariant Derivatives Covariant derivatives for left- right- fields : With : 41 T is CKM matrix reduced to V us and V ud terms M. Benayoun, VMD & g-2 estimates Slide 42 Anomalous Annihilations/Decays Non-Anomalous annihilations : e + e - / or decays : Anomalous Processes : e + e - // :: Other Effective Lagrangian pieces 42M. Benayoun, VMD & g-2 estimates Slide 43 SIDE RESULT : Prediction for / ( )=53.111.47 PDG : 605 keV ( )=55.820.83 PDG : 604 eV Lineshapes and yields : tests for g value and 0 lineshape M. Benayoun et al. ArXiv 0907.4047 43M. Benayoun, VMD & g-2 estimates Slide 44 BELLE/ALEPH/CLEO 44M. Benayoun, VMD & g-2 estimates