Hadronic Contributions to

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1 Hadronic Contributions to (g-) µ Yuping Guo INSTITUT FÜR KERNPHYSIK JOHANNES GUTENBERG-UNIVERSITÄT MAINZ New Vistas in Low-Energy Precision Physics Mainz, 4-7 April 016

2 Muon Anomaly: a µ = (g-) µ / Experimental: a exp µ = (6.3) (0.54 ppm) [BNL-E81: PRD ] Standard Model prediction: a SM µ = aqed µ + aweak µ + ahad µ Contribution in units QED(γ+lepton) ± Kinoshita et.al. (01) EW ± 0.10 Gnendiger, Stöckinger, Stöckinger-kim (013) HVP,LO 69.3 ± 4. Davier et. al. (011) HVP,NLO ± 0.07 Hagiwara et al. (009) HLbL 11.6 ± 4.0 Jegerlehner, Nyffler (009) Total ± 5.8

3 Hadronic Contributions Hadronic Vacuum Polariza0on q Optical theorem e + q q - e q Dispersion integral!!!"#!,!" = 1!"!!!!! 4!!!"# (!)!!!!!! Kernel function ~ 1/s σ had = σ( e + e - hadrons ) ~ 1/s à Low energy contribu0ons important! 3

4 Hadronic Contributions Hadronic Light- by- Light Only model calculations so far Data-driven approach been developed [Colangelo et al 14; Pauk, Vanderhaeghen 14] e! Transition form factors Spacelike e! e +! Timelike π0, η, η#$! γ! γ ( )! γ ( )! π 0, η, η#$! e +! γ! e! e +! 4

5 Hadronic Cross Section σ had (e + e - hadrons) 5

6 Hadronic Cross Section Energy Scan: CMD & SND at VEPP-M & VEPP-000 in Novosibirsk BESIII at BEPCII in Beijing Initial State Radiation: KLOE at DAφNE in Frascati e + q BABAR at PEP-II in Stanford BESIII at BEPCII in Beijing s - e s q KLOE BESIII BABAR Needs no systematic variation of beam energy High statistics thanks to high integrated luminosities 6

7 Most Relevant Channel: e + e - π + π - KLOE and BABAR dominate the world average Both with uncertainties smaller than 1% Relatively large systematic differences, especially above ρ peak Knowledge of a had µ dramatically limited due to this difference Note: KLOE05 superseded by KLOE08 7

8 Beijing Electron Positron Collider-II Line Storage Ring BEPCII: τ-charm factory Beam energy: 1-.3 GeV Design luminosity: cm-s-1 Data taking from 009 to present 8 BESIII Detector or t a r ele c c ar A

9 Beijing Electron Positron Collider-II SC Magnet: 1Tesla Magnet yoke TOF: (σt) 80 ps / 110 ps Beam pipe Line or t a r ele c c ar A MDC: σp/p: 0.5% at 1GeV/c CsI calorimeter: ΔE/E:.5% / 5.0% at 1 GeV; σz: 0.6 cm/ E BEPCII: τ-charm factory Beam energy: 1-.3 GeV Design luminosity: cm-s-1 Data taking from 009 to present 9 BESIII de/dx: 6% Detector Storage Ring

10 Data Samples for ISR Study Luminosity (pb -1 ) ψ(3770) ψ(s) J/ψ ψ(4040) ~9. fb -1 XYZ s e + - e s ISR luminosity = L dt x H rad q q Radiator function, well known Scan data samples later ) / 0 MeV -1 L ISR dt (pb BABAR (500 fb ) BESIII s > GeV E cm (GeV) 9

11 e + e - γ ISR π + π - at BESIII Event yield acer preliminary selec0on events / 0 MeV γ π + π MC - µ + µ γ MC data ψ(3770) data only (.9 H - 1 ) Tag ISR photon No dedicated background subtrac0on e + e - γπ + π - : large statistics e + e - γµ + µ - : dominate background Data - MC differences visible m π [GeV] Initial publication MeV [Phys. Le<. B753 (016) 69] 10

12 e + e - γ ISR π + π - at BESIII Event yield acer preliminary selec0on events / 0 MeV γ π + π MC - µ + µ γ MC data Compe00ve limit for Dark Photon search ψ(3770) data only (.9 H - 1 ) Tag ISR photon No dedicated background subtrac0on e + e - γπ + π - : large statistics e + e - γµ + µ - : dominate background Data - MC differences visible Initial publication MeV [Phys. Le<. B753 (016) 69] m π [GeV] 10

13 e + e - γ ISR π + π - at BESIII Event yield acer preliminary selec0on events / 0 MeV γ π + π MC - µ + µ γ MC data Compe00ve limit for Dark Photon search ψ(3770) data only (.9 H - 1 ) Tag ISR photon No dedicated background subtrac0on e + e - γπ + π - : large statistics e + e - γµ + µ - : dominate background Data - MC differences visible Initial publication MeV m π [GeV] World s best measurement of Γ ee of J/ψ 10

14 e + e - γ ISR π + π - : π-µ separation TMVA overtraining check for classifier: CFMlpANN dx (1/N) dn/ Signal (test sample) Signal (training sample) Background (test sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = (0.455) µ π U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA method (Neural Network): Trained using γµµ and γππ MC events Information based on track level Efficiency matrix (p,θ) for data, MC Correct for data - MC differences Cross checked for different TMVA methods CFMlpANN response 11

15 e + e - γ ISR π + π - : π-µ separation TMVA overtraining check for classifier: CFMlpANN dx (1/N) dn/ Signal (test sample) Signal (training sample) Background (test sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = (0.455) CFMlpANN response U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA method (Neural Network): Trained using γµµ and γππ MC events Information based on track level µ π Event yield γππ acer π- µ separa0on Efficiency matrix (p,τ) for data, MC events / 5 MeV Correct for data - MC differences Cross checked for different TMVA methods m π [GeV] 11

16 QED Test: e + e - γµ + µ - Event yield γµµ acer π- µ separa0on and all efficiency correc0ons µ π 10% Background from γππ small PHOKHARA uncertainty < 0.5% Luminosity measurement based on Bhabha events, 0.5% accuracy Δ(MC/QED- data) - 1 = (1.0 ± 0.3 stat ± 0.9 syst ) % Excellent agreement with QED Accuracy on 1% level as needed to be compe00ve! 1

17 e + e - π + π - Cross section normalizaton methods: Normaliza0on to L int (obtained from Bhabha events) Normaliza0on to γµµ events, i.e. R ra0o (γππ/γµµ) L int, H rad, δ vac cancel in ra0o )) [nb] (γ - π + π - e + σ bare (e FSR luminosity / R ratio using the luminosity using the R ratio s' [GeV] Statistical error only Good agreement between two methods Luminosity / R rato - 1 = (0.85 ± 1.68) % limited by low γµµ sta0s0cs 13

18 Compare with Existing Data Pion Form Factor F π BESIII fit BaBar KLOE 08 KLOE 10 KLOE 1 BESIII / BESIII fit - 1 π F BESIII fit BaBar BESIII π F s' [GeV] 0.9 % accuracy (dominated by theory) Normaliza0on to luminosity radiator func0on Gounaris and Sakurai parameteriza0on / BESIII fit - 1 π F s' [GeV] BESIII fit KLOE 08 KLOE 10 KLOE s' [GeV] 14

19 Impact on a µ HVP Deviation on (g-) µ between experimental and SM has been confirmed 15

20 Impact on a µ HVP Deviation on (g-) µ between experimental and SM has been confirmed Study of π + π - π 0 and π + π - π 0 π 0 processes undergoing at BESIII 15

21 Energy Scan from.0 to 4.6 GeV World s best measurement from BES/BESII with 5% ~ 8% total uncertainty (statistical uncertainty: 3% ~ 5%) BESIII: aim at systematic uncertainty: 3.0% 151 energy points >10 5 hadronic events each à statistical error negligible Energy region Energy points Note.400~ Mini-scan 3.800~ Fine-scan heavy charm resonant.000~ R&QCD-scan 3.050~ J/ψ-scan 3.54~ τ-scan 3.650,3.671 ψ(3686)-scan Reducing the uncertainty of α em (M Z ) by a factor of à A new quantity of electroweak precision fits 16

22 Meson Transition Form Factor F(Q ) 17

23 Timelike Transition FFs π 0, η, η#$! γ ( )! γ! e! e +! Vector Meson Dominance Model: single-pole: η F(q) = (1-q /Λ ) -1 Λ - = (1.95 ± 0.15 ± 0.10) GeV - In good agreement with previous measurements! [Phys. Rev. C89 (014) ] 18

24 Spacelike Transition FFs + + e e - e q 1 q - e Untag: Only tag the hadron products, P t -balance Q i ~0 GeV, quasi-real photon + e + e Single tag: * q 1 Tag the hadron products - e q - e Tag only one lepton, missing momentum direction Q 1 ~0 GeV, Q 1 =-q GeV ; highly virtual photon e + * * e + - e - e q 1 q Double tag: Tag the hadron products Tag both leptons Both photons are virtual Input for data-driven approach 19

25 Existing Data on Spacelike TFFs e + e - e + e - π 0 e+ e - e + e - η e + e - e + e - η' Recent results from BABAR and BELLE: Q > 4 GeV CELLO: Z. Phys. C (1991) CLEO: Phys. Rev. D57 33 (1998) BaBar: Phys. Rev. D (009) Belle: Phys. Rev. D (01) CLEO: Q > 1.5 GeV CELLO: Q < 1.5 GeV, very poor accuracy Low Q range not covered/precise 0

26 Relevant Q Region w f1 (Q 1,Q ) w g1 (M V,Q 1,Q ) Form factor dependent Universal weight functions Q [GeV] Q 1 [GeV] Q [GeV] Q 1 [GeV] w g (M,Q 1,Q ) w g (M V,Q 1,Q ) Relevant Q region: <1.5 GeV Q [GeV] Q 1 [GeV] Q [GeV] Q 1 [GeV] [M. Knecht and A. Nyffeler: Phys. Rev. D 65, (00)] 1

27 e + e - e + e - π 0 at BESIII L int : 97 pb -1 Tagged lepton: e - π 0 -Octet Model η -Octet Model ψ(3770) Rad. Return (J/ψ,ψ') rad. Bhabha MC Sum Event Selection: Exactly one lepton candidate At least two, max four photons Helicity angle cos θ H > 0.8 Kinematic cuts to reject ISR background MC only, part of full statistics Cut on angle of missing momentum Count π 0 yield in bins of Q Strategy: dσ/dq Form factor F(Q )

28 Spacelike transition FFs: π 0 L int :.9 fb -1 Single tag Both leptons MC only, red error bars corresponding to BESIII statistics Extract TFF for: 0.3 Q [GeV ] 3.1 Significantly improves and extends data set below Q = 1.5 GeV Input for (g-) µ! [CELLO: Z. Phys. C (1991)] [CLEO: Phys. Rev. D57 33 (1998)] 3

29 Spacelike transition FFs: η / η MC only, red error bars corresponding to BESIII statistics L int :.9 fb -1 Single tag η π + π - π 0 π + π - γ γ η π + π - η π + π - γ γ Results competitive to previous measurement More data and more decay modes order of magnitude improvement 4

30 γ γ* à π + π - at BESIII Belle CELLO MARKII All in two real photon case: γγà π + π - In low mass region, only measurement come from MarkII [MARKII: Phys. Rev. D4, 5, 1990] [CELLO: Z. Phys. C56, 381, 199 ] [Belle: Phys. Rev. D75, (R), 007 ] [N. Asmussen, P. Masjuan, M. Vanderhaeghen] Access to: Q region: 0.~.0 GeV M ππ : threshold~.0 GeV 5

31 Conclusion Important results (to be expected) from BESIII for SM prediction of (g-) µ HVP: precision inclusive and exclusive measurements HLbL: spacelike form factors measurement in relevant region Competing experiments: Frascati, Novosibirsk, Belle-II(?) Reduction of factor of of the uncertainty of a µ had in reach 6

32 Backup slides

33 Energy Scan from.0 to 4.6 GeV Reducing the uncertainty of α em (M Z ) by a factor of à A new quantity of electroweak precision fits Online spectrum of R scan recently finished R = σ had /σ µµ with targeted systematic accuracy: 3.0% 15 scan points with >10 5 hadronic events each à statistical error negligible World's best measurement so far from BES /BESII with % total error (with % statistical error)

34 Dark photon and (g-) µ ε - 10 (g-) e WASA KLOE 013 KLOE 014 BABAR (g-) ± σ µ favored NA48/ HADES PHENIX A1 APEX BABAR 014 BESIII E774 BESIII projection E [GeV/c ] m γ' BESIII (Mass GeV/c ) Spin-off of pion FF analysis ( e + e - γµ + µ - / γe + e - ) A1 / MAMI (Mass MeV/c ) Search in Bethe-Heitler process (ez scattering)

35 γ γ* à π + π - at BESIII Hadron form factor Resonance parameters for 0 ±+, ++ states Pion polarizability, probe the structure of pion Re-scattering effect study at low mass region Belle CELLO MARKII All in two real photon case: γγà π + π - In low mass region, only measurement come from MarkII Access to: Q region: 0.~.0 GeV M ππ : threshold~.0 GeV [N. Asmussen, P. Masjuan, M. Vanderhaeghen] 5