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Invited Talk aµ (had; VP) update Fred Jegerlehner, DESY Zeuthen/Humboldt University Berlin ' $ Workshop on hadronic vacuum polarization contributions to muon g-2, KEK, Tsukuba, Japan, February 12-14, 2018 & % New updated and expanded edition Jegerlehner F., The Anomalous Magnetic Moment of the Muon. Springer Tracts in Modern Physics, Vol 274 (2017). Springer, Cham (693 pages on one number to 8 digits) F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 Outline of Talk: vHadronic Vacuum Polarization (HVP) – Data & Status vEffective Field Theory: Resonance Lagrangian Approach vSimplified: VMD + sQED and ρ0;! γ Mixing vHVP from lattice QCD − vTheory vs experiment: do we see New Physics? vProspects My focus will be more on less standard issues F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 1 Hadronic Vacuum Polarization (HVP) – Data & Status had Leading non-perturbative hadronic contributions aµ can be obtained in terms of 2 R (s) σ(0)(e+e γ hadrons)=4πα data via Dispersion Relation (DR): γ ≡ − ! ∗ ! 3s 2 ­ Ecut Z data Z1 pQCD αmµ2 Rγ (s) Kˆ (s) Rγ (s) Kˆ (s) ahad = ds + ds µ 3π s2 s2 ¡ 4m2 E2 ¡ ­ π ­ cut l Experimental error implies theoretical uncertainty! l Low energy contributions enhanced: 75% come from region 4m2 < m2 < M2 ∼ π ππ Φ Data: NSK, KLOE, BaBar, BES3, CLEOc had(1) 10 aµ = (686:99 4:21)[687:19 3:48] 10− + ± ± e e−–data based [incl. τ] 2 ∆aµ (δ∆aµ) ρ, ω ρ, ω 1.0 GeV 0.0 GeV, 0.0 GeV, Υ ∞ ∞ ψ 9.5 GeV 3.1 GeV 3.1 GeV 2.0 GeV φ, . 2.0 GeV φ, . 1.0 GeV contribution error2 F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 2 γ hard e+ γ + φ π π−, ρ0 hadrons e− 2 s = M ; s′ = s (1 k), k = E /E φ − γ beam a) b) a) Initial state radiation (ISR), b) Standard energy scan. Experimental input for HVP: BaBar, BESIII, VEPP-2000 Talks Michel Davier, Christoph Redmer, Ivan Logashenko, Sergey Serednyakov Recent BES-III vs BaBar and KLOE F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 3 Recent results: + l π π− from BES-III, CMD-3 and CLEOc + 0 l π π−π from Belle + l K K− from CMD-3 and SND l ωπ0 π0π0γ from SND !0 + 0 0 0 l KS K±π π∓, KS K±π∓η, π π−π π , KS KLπ , 0 0 KS KLη, KS KLπ π from BaBar Energy range ahad[%](error) 1010 rel. err. abs. err. µ × ρ, ! (E < 1 GeV) 540.98 [78.6](2.80) 0.5 % 50.7 % 1 GeV < E < 2 GeV 96.49 [14.0](2.54) 2.6 % 41.5 % 2 GeV < E < incl pQCD 51.09 [ 7.4](1.10) 2.2 % 7.8 % 1 total 688.65 [100.0](3.94) 0.6 % 100.0 % + Additional data besides e e− ones providing improvements: F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 4 Ê τ–decay spectra: good idea, use isospin symmetry to include existing high quality τ–data (after isospin corrections) Alemany et al 1996 + ¯ + e γ γ u,¯ d bare π π− spectrum after photon VP, + π π−, [I = 1] ··· ISR and FSR subtraction e− u,d isospin⇑ rotation CVC isospin rotation symmetry ⇓ $ u¯ 0 τ − W W 0 bare π π− spectrum after EW radia- π π−, ··· ν¯τ d tive and phase space correction + Standard IB corrected data: large discrepancy [ 10%] persists! τ vs. e e− problem! [manifest since 2002 Davier et al, solved∼ 2011] + l pioneered by Alemany, Davier, Hocker¨ 1996 (when e e− ππ data were much less precise that the τ ν ππ data!) ! ! τ Why is it still a good idea to include τ CC spectra? F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 5 + τ data in many respects are much simpler than e e− ones, because the charged ρ± does not mix with other states in the dominant low energy range below about 1.05 GeV (up to above the φ, below ρ0)! In contrast understanding NC data requires modeling: CHPT + spin 1 resonances (VMD) Resonance Lagrangian Approach e.g. HLS (massive Yang-Mills) dynamical) widths, dynamical mixing of γ; ρ0; !; φ ) Commonly forgotten: mixing of ρ0; !; φ with the photon [ρ0 γ mixing] i.e. effect concerning relation − ⊗ ⊗ ↔ A(x) A(0) j(x) j(0) h i h i photon propagator current correlator + + included in NC e e− π π− data, absent in CC τ ντππ data! Also to be accounted! for in lattice QCD calculations!! F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 6 Effective Field Theory: Resonance Lagrangian Approach r Global Fit strategy based on Hidden Local Symmetry (HLS) Benayoun et al Data below E0 = 1:05 GeV (just including the φ) constrain effective Lagrangian couplings, using 45[47] different data sets (6[8] annihilation channels and 10 partial width decays). see Talk Maurice Benayoun r Effective theory predicts cross sections: + 0 0 + + 0 0 π π−; π γ; ηγ; η0γ; π π π−; K K−; K K¯ (83.4%), l Missing part: 4π, 5π, 6π, ηππ, ωπ and regime E > E0 evaluated using data directly and pQCD for perturbative region and tail l Including self-energy effects is mandatory (γρ-mixing, ρω-mixing ..., decays with proper phase space, energy dependent width etc) l Method works in reducing uncertainties by using indirect constraints l Able to reveal inconsistencies in data, e.g. KLOE vs BaBar Remark: HLS supplied by symmetry breakings (isospin, SU(3)) is rather complicated, like EW SM with spin-1 vector bosons as gauge bosons, but with ρ, !, φ (in place of one Z boson) and parity odd sector WZW type Lagranian terms. F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 7 + o Fit of τ +IB from PDG vs π π−–data + Comparing the τ+PDG prediction (red curve) of the pion form factor in e e− annihilation in the ρ ! interference region. Benayoun et al. − F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 8 Simplified: VMD + sQED and ρ0;! γ Mixing − r Usually using Gounaris-Sakurai ansatz GS s GS GS BWρ(770)(s) 1 + δ 2 BW!(s) + β BWρ(1450)(s) + γ BWρ(1700)(s) · M! Fπ(s) = ; 1 + β + γ r Fit e+e -data for F (s) 2 « δ (complex) and set δ = 0 to obtain FI=1(s) 2 − j π j ρω j π j 2 CMD-2 data for Fπ in ρ ! region together with Gounaris-Sakurai fit. Left: beforej j subtraction.− Right: after subtraction of the !. F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 9 r ρ0 γ mixing applied to Breit-Wigner shape and to τ data from ALEPH 2005. − Effective Lagrangian = + e.m. gauge invariant L Lγρ Lπ + +µ 2 + = D π D π− m π π− ; D = @ i e A i g ρ Lπ µ − π µ µ− µ − ρππ µ 2 1 µν 1 µν Mρ µ e µν γρ = Fµν F ρµν ρ + ρµ ρ + ρµν F L −4 − 4 2 2 gρ Note this is a model most people are using (Gounaris-Sakurai, FSR etc) but neglecting 1–loop γ ρ0 mixing contribution! − F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 10 r ρ0 γ mixing applied to Breit-Wigner shape and to τ data from ALEPH 2005. − Effective Lagrangian as used in GS = + not e.m. gauge invariant L Lγρ Lπ + +µ 2 + = D π D π− m π π− ; D = @ i e A i g ρ Lπ µ − π µ µ− µ − ρππ µ 2 2 1 µν 1 µν Mρ µ e Mρ µ γρ = Fµν F ρµν ρ + ρµ ρ ρµA L −4 − 4 2 − gρ Note this is a model most people are using (Gounaris-Sakurai, FSR etc) but neglecting 1–loop γ ρ0 mixing contribution! − F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 11 Photon is mixing with ρ0: propagators are obtained by inverting the symmetric 2 2 self–energy matrix × 2 2 2 ! 1 q + Πγγ(q ) Πγρ(q ) Dˆ − = Π (q2) q2 M2 + Π (q2) γρ − ρ ρρ : Effect well known from LEP Z resonance physics: Z γ mixing affects Z lineshape. − F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 12 Self-energies: pion loops to photon-ρ vacuum polarization i Πµν (π)(q)= + − γγ . i Πµν (π)(q)= + − γρ . i Πµν (π)(q)= + − ρρ . Irreducible self-energy contribution at one-loop bare γ ρ transverse self-energy functions − 2 g2 e 2 egρππ 2 ρππ 2 Πγγ = f (q ) ; Πγρ = f (q ) and Πρρ = f (q ) ; 48π2 48π2 48π2 F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 13 Self-energies: pion loops to photon-ρ vacuum polarization i Πµν (π)(q)= + − γγ . i Πµν (π)(q)= − γρ . i Πµν (π)(q)= + − ρρ . Previous calculations, consider mixing term to be constant bare γ ρ transverse self-energy functions − 2 g2 e 2 egρππ 2 ρππ 2 Πγγ = f (q ) ; Πγρ = f (q ) and Πρρ = f (q ) ; 48π2 48π2 48π2 F. Jegerlehner muonHVPws@KEK, Tsukuba, Japan, February 12-14, 2018 14 where µ2 2 2 2 2 = = + y y 2 y + ; f (q ) q h(q ); h(q ) 2 3 2 (1 ) 2 (1 ) G( ) ln 2 ≡ − − − mπ a scalar self-energy function with y = 2= and y = 1 1+βπ π , for 2 > 2. Note that 4mπ s G( ) 2βπ (ln 1 βπ i ) q 4 mπ − − all components of the (γ, ρ) 2 2 matrix propagator are proportional to the same function f (q2).
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