New Results on the Hadronic Vacuum Polarization Contribution to the - PowerPoint PPT Presentation

New Results on the Hadronic Vacuum Polarization Contribution to the Muon g-2 Michel Davier (LAL – Orsay) • the muon magnetic anomaly • revisited τ spectral functions: Belle + updated corrections • ee spectral functions after KLOE and BaBar • combination of all ee data • discussion and perspectives M.Davier HVP/g-2 1 Phi2Psi Beijing 13-16/10/2009

Most recent data and analyses � τ → π π 0 ν τ data from Belle PRD 78 (2008) 072006 � e + e − → π + π − data - KLOE PLB 670 (2009) 285 - BaBar arXiv:0908.3589v1 � updated τ -based analysis arXiv:0906.5443v2 MD, A. Hoecker, G. Lopez Castro, B. Malaescu, X.H.Mo, G. Toledo Sanchez, P. Wang, C.Z. Yuan, Z. Zhang � updated ee-based analysis arXiv:0908.4300v1 MD, A. Hoecker, B. Malaescu, C.Z. Yuan, Z. Zhang M.Davier HVP/g-2 2 Phi2Psi Beijing 13-16/10/2009

Hadronic Vacuum Polarization and Muon ( g –2) μ Dominant uncertainty from lowest-order HVP piece Cannot be calculated from QCD (low mass scale), but one can use experimental data on e+e −→ hadrons cross section ( ) 2 σ = σ α α (0) Born: ( ) ( ) / ( ) s s s + − σ → γ 0 [ e e hadrons ( ) ] π Π = ≡ 12 Im ( s ) R ( s ) σ γ pt Im[ ] ∝ | hadrons | 2 μ had γ γ ∞ α 2 ( ) ( ) K s γ ∫ = had a d s R s μ π 2 3 s 2 4 m π Dispersion relation M.Davier HVP/g-2 3 Phi2Psi Beijing 13-16/10/2009

The E-821 a μ Measurement at BNL Updated a μ measured from a ratio of frequencies ω a = ω precession − ω cyclotron ω precession = ω L + ω T λ = ω L / ω p = μ μ / μ p from muonium hyperfine splitting value used by E-821 3.18334539(10) new value 3.183345137(85) Mohr et al., RMP 80 (2008) 633 ⇒ change in a μ (+0.92 10 − 10 ) (see next review in RPP2009 (Hoecker-Marciano) exp = (11 659 208.9 ± 5.4 ± 3.3) 10 − 10 updated a μ ( ± 6.3) (0.54 ppm) M.Davier HVP/g-2 4 Phi2Psi Beijing 13-16/10/2009

The Role of τ Data through CVC – SU(2) γ : I =0,1 & V W : I =1 & V , A CVC: I =1 & V ν τ e + γ τ hadrons W e – hadrons Hadronic physics factorizes (spectral Functions) πα 2 4 ⎡ ⎤ ⎡ ⎤ σ = + − → π π + − = υ τ − → π π ν − ( 1) 0 I e e ⎣ ⎦ ⎣ ⎦ τ s ⎡ − − ⎤ τ → π π 0 ν BR 2 1 dN ⎣ ⎦ m τ ⎡ ⎤ υ τ − → π − π ν ∝ 0 0 ππ τ ⎣ ⎦ ( ) ( ) τ ⎡ − − ⎤ 2 τ → ν ν BR N d s − 2 + 2 e 1 / 1 / ⎣ ⎦ s m s m τ 0 ππ e τ τ branching fractions mass spectrum kinematic factor (PS) M.Davier HVP/g-2 5 Phi2Psi Beijing 13-16/10/2009

SU(2) Breaking Corrections for SU(2) breaking applied to τ data for dominant π – π + contrib.: Electroweak radiative corrections: dominant contribution from short distance correction S EW Marciano-Sirlin’ 88 subleading corrections (small) Braaten-Li’ 90 long distance radiative correction G EM ( s ) Cirigliano-Ecker-Neufeld’ 02 Lopez Castro et al.’ 06 Charged/neutral mass splitting: Alemany-Davier-Höcker’ 97, Czy ż -Kühn’ 01 m π – ≠ m π 0 leads to phase space (cross sec.) and width (FF) corrections ρ - ω mixing (EM ω → π – π + decay) corrected using FF model m ρ – ≠ m ρ 0 *** and Γ ρ – ≠ Γ ρ 0 *** Flores-Baez-Lopez Castro’ 08 Davier et al.’09 Electromagnetic decays: ρ → π π γ *** , ρ → π γ , ρ → η γ , ρ → l + l – Quark mass difference m u ≠ m d (negligible) M.Davier HVP/g-2 6 Phi2Psi Beijing 13-16/10/2009

Situation at ICHEP’06 / 08 had [ ee ] = (690.9 ± 4.4) × 10 –10 a μ = (11 659 180.5 ± 4.4 had ± 3.5 LBL ± 0.2 QED+EW ) × 10 –10 a μ [ ee ] Hadronic HO – ( 9.8 ± 0.1) × 10 –10 Hadronic LBL + (12.0 ± 3.5) × 10 –10 τ e + e − BNL Electroweak (15.4 ± 0.2) × 10 –10 QED (11 658 471.9 ± 0.1) × 10 –10 .0 Knecht-Nyffeler (2002), Melnikov-Vainhstein (2003) Davier-Marciano (2004) Kinoshita-Nio (2006) Observed Difference with BNL using e + e − : (27.5 ± 8.4) × 10 –10 a μ [exp] – a μ [SM] = � 3.3 „standard deviations“ But estimate using τ data consistent with E-821 ! M.Davier HVP/g-2 7 Phi2Psi Beijing 13-16/10/2009

Revisited Analysis using τ Data: including Belle Test of the spectral function shapes from different experiments: WA BR used M.Davier HVP/g-2 8 Phi2Psi Beijing 13-16/10/2009

Revisited Analysis τ Data: new IB corrections talk by G. Lopez Castro disagreement with Maltman-Wolfe arXiv:0908.2391 M.Davier HVP/g-2 9 Phi2Psi Beijing 13-16/10/2009

Consistency of τ Data: Dispersion Integrals • using BR from each experiment makes results independent from each other • consistent results • using WA BR checks consistency for the spectral function shapes • WA BR + combined spectral function ⇒ 2 π ,LO =(515.2 ± 2.0 exp ± 0.9 Be ± 2.1 B ππ ± 1.6 IB ) 10 − 10 a μ • 0.7% precision M.Davier HVP/g-2 10 Phi2Psi Beijing 13-16/10/2009

Comparison of ee and τ Data Revisited (1) Relative comparison of IB-corrected τ and ee spectral functions ( τ green band) CMD-2, SND KLOE ⇒ better agreement than before with CMD2-SND ⇒ strong disagreement with KLOE : slope… M.Davier HVP/g-2 11 Phi2Psi Beijing 13-16/10/2009

Comparison of ee and τ Data Revisited (2) Global test of spectral functions: prediction of τ BR using ee data ⇒ apply to ππ 0 channel IB corrections applied to ee data this time • data from CMD2-SND overconsistent ? • fair agreement CMD2-SND with τ • larger disagreement with KLOE M.Davier HVP/g-2 12 Phi2Psi Beijing 13-16/10/2009

Data on e + e − → hadrons (1) Cross section [nb] Cross section [nb] Cross section [nb] Cross section [nb] CMD2-2004 CMD2-2006 1400 1400 1400 1400 1200 1200 1200 1200 CMD-2 (2006) CMD-2 (2004) 1000 1000 1000 1000 800 800 800 800 600 600 600 600 400 400 400 400 200 200 200 200 0 0 0 0 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 Mass [GeV] Mass [GeV] Mass [GeV] Mass [GeV] Cross section [nb] Cross section [nb] Cross section [nb] Cross section [nb] SND KLOE-2008 1400 1400 1400 1400 1200 1200 1200 1200 SND (2006) KLOE (2009) 1000 1000 1000 1000 800 800 800 800 600 600 600 600 400 400 400 400 200 200 200 200 0 0 0 0 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 Mass [GeV] Mass [GeV] Mass [GeV] Mass [GeV] M.Davier HVP/g-2 13 Phi2Psi Beijing 13-16/10/2009

Data on e + e − → hadrons (2) talk by Wenfeng Wang BaBar (2009) M.Davier HVP/g-2 14 Phi2Psi Beijing 13-16/10/2009

BaBar vs.other ee data (0.5-1.0 GeV) direct relative comparison of cross sections with BaBar fit (stat + syst errors included) (green band) BaBar CMD-2 SND KLOE M.Davier HVP/g-2 15 Phi2Psi Beijing 13-16/10/2009

BaBar vs. IB-corrected τ data (0.5-1.0 GeV) relative comparison w.r.t. BaBar of isospin-breaking corrected τ spectral ALEPH functions IB corrections: radiative corr., π masses, ρ - ω interference, ρ masses/widths each τ data normalized to its own BR CLEO Belle M.Davier HVP/g-2 16 Phi2Psi Beijing 13-16/10/2009

Combination of all e + e − Data arXiv: 0908.4300 MD-Hoecker-Malaescu-Yuan-Zhang Improved procedure and software (HVPTools) for combining cross section data with arbitrary point spacing/binning M.Davier HVP/g-2 17 Phi2Psi Beijing 13-16/10/2009

Obtaining the average cross section relative weights • local weighted average performed • full covariance matrices • local χ 2 used for error rescaling • average dominated by BaBar and KLOE, BaBar covering full range error scale factor integrand (dispersion integral) error M.Davier HVP/g-2 18 Phi2Psi Beijing 13-16/10/2009

Consistency of Experiments with Average M.Davier HVP/g-2 19 Phi2Psi Beijing 13-16/10/2009

ππ [2 m π ,1.8 GeV] Computing a μ 503.5 ± 3.5 Pre-BaBar combined ee 514.1 ± 3.8 BaBar 508.4 ± 2.9 Combined ee Combined τ 515.2 ± 3.0 ± 1.6 (3.4) M.Davier HVP/g-2 20 Phi2Psi Beijing 13-16/10/2009

Other hadronic contributions from MD-Eidelman-Hoecker-Zhang NP Proc. Suppl. 169 (2007) 288 τ e + e – Modes Energy [GeV] π + π – 2 π 0 2 m π – 1.8 16.8 ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2 π + 2 π – (+BaBar) 2 m π – 1.8 13.1 ± 0.4 ± 0.0 rad 12.3 ± 1.0 ± 0.4 SU(2) ω (782) 0.3 – 0.81 38.0 ± 1.0 ± 0.3 rad – φ (1020) 1.0 – 1.055 35.7 ± 0.8 ± 0.2 rad – Other excl. (+BaBar) 2 m π – 1.8 24.3 ± 1.3 ± 0.2 rad – J / ψ , ψ (2S) 3.08 – 3.11 7.4 ± 0.4 ± 0.0 rad – R [QCD] 1.8 – 3.7 33.9 ± 0.5 theo – R [data] 3.7 – 5.0 7.2 ± 0.3 ± 0.0 rad – 5.0 – ∞ R [QCD] 9.9 ± 0.2 theo – ⇒ another large long-standing discrepancy in the π + π − 2 π 0 channel ! M.Davier HVP/g-2 21 Phi2Psi Beijing 13-16/10/2009