ISR precision measurements of the 2π cross section below 1 GeV with the KLOE experiment and their impact on (g 2) µ

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1 ISR precision measurements of the 2π cross section below 1 GeV with the KLOE experiment and their impact on (g 2) Stefan E. Müller Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf Institute Seminar - Institute of Nuclear and Particle Physics TU Dresden, January 9, 2014 Mitglied der Helmholtz-Gemeinschaft Stefan E. Müller (Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf)

2 The buzz-word dictionary (g 2) : Deviation of muon s gyromagnetic ratio from 2 (often expressed as the anomaly a = (g 2) /2) ISR: Initial State Radiation, e + or e radiate a hard photon prior to collision, lowering the collision energy KLOE detector: K LOng Experiment, multi-purpose detector at the Frascati φ-factory DAΦNE 2π cross section: Cross section for the process e + e π + π, closely related to the 2 pion electromagnetic form factor F 2π 2 1 / 38 Mitglied der Helmholtz-Gemeinschaft

3 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass 2 / 38 Mitglied der Helmholtz-Gemeinschaft

4 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass Muons (s = 1/2): a = (g 2) /2 = 0 (Dirac) 2 / 38 Mitglied der Helmholtz-Gemeinschaft

5 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass Muons (s = 1/2): a = (g 2) /2 = 0 (Dirac) Kusch & Foley (1948): g e = (10) (hyperfine structure of atoms in constant magnetic field) 2 / 38 Mitglied der Helmholtz-Gemeinschaft

6 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass Muons (s = 1/2): a = (g 2) /2 = 0 (Dirac) Kusch & Foley (1948): g e = (10) Schwinger (1948): a e = α/2π (hyperfine structure of atoms in constant magnetic field) (virtual quantum correction) 2 / 38 Mitglied der Helmholtz-Gemeinschaft

7 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass Muons (s = 1/2): a = (g 2) /2 = 0 (Dirac) Kusch & Foley (1948): g e = (10) (hyperfine structure of atoms in constant magnetic field) Schwinger (1948): γ a e = α/2π e (virtual quantum correction) γ e 2 / 38 Mitglied der Helmholtz-Gemeinschaft

8 (g 2) - Introduction Magn. moment: = g e 2mc s = g B s s = spin m = lepton mass Muons (s = 1/2): a = (g 2) /2 = 0 (Dirac) a QED a weak a had γ e γ Z γ had 2 / 38 Mitglied der Helmholtz-Gemeinschaft

9 (g 2) - Experiment: Principles Longitudinally polarized muons are injected into uniform magnetic field relativistic cyclotron motion with angular frequency { ω C = e B + γ2 E } β γm γ 2 1 c muon spin precesses with angular frequency { ω S = e ( (1 + γa ) B γm + γ a + 1 ) } E β γ + 1 c difference between the two frequencies becomes ω a = ω S ω C = e ( {a B + a 1 ) } E β m γ 2 1 c 3 / 38 Mitglied der Helmholtz-Gemeinschaft

10 (g 2) - Experiment: Principles Longitudinally polarized muons are injected into uniform magnetic field relativistic cyclotron motion with angular frequency { ω C = e B + γ2 E } β γm γ 2 1 c muon spin precesses with angular frequency { ω S = e ( (1 + γa ) B γm + γ a + 1 ) } E β γ + 1 c Magic γ = 29.3 difference between the two frequencies becomes Magic p = 3.09 GeV/c ω a = ω S ω C = {a e ( B + a 1 ) } E β m γ 2 1 c 3 / 38 Mitglied der Helmholtz-Gemeinschaft

11 (g 2) - Experiment: Principles Measurement of B-field and ω a determines a 4 / 38 Mitglied der Helmholtz-Gemeinschaft

12 (g 2) - Experiment: Principles Modulation due to strong correlation between e ± direction and muon spin: N(t) e t/γτ [1 Acos(ω a t + φ)] 4 / 38 Mitglied der Helmholtz-Gemeinschaft

13 (g 2) - Experiment: BNL/Fermilab Muon storage ring at Brookhaven National Labs: 5 / 38 Mitglied der Helmholtz-Gemeinschaft

14 (g 2) - Experiment: Results Modulation plot from BNL experiment [PRD73 (2006) ]: N(t) e t/γτ [1 Acos(ω a t + φ)] 6 / 38 Mitglied der Helmholtz-Gemeinschaft

15 (g 2) - Experiment: Results Blum et al., arxiv: (9.4 ppm) CERN (10 ppm) CERN (13 ppm) E821 (97) + (5 ppm) E821 (98) + (1.3 ppm) E821 (99) + (0.7 ppm) + E821 (00) (0.7 ppm) E821 (01) World Average S M Theory a X World average: a EXP = (63) [0.54 ppm] 7 / 38 Mitglied der Helmholtz-Gemeinschaft

16 (g 2) - Experiment: JPARC Proposed experiment at JPARC (Japan): K. Ishida at PHIPSI13 8 / 38 Mitglied der Helmholtz-Gemeinschaft

17 (g 2) - Theory: a theo = a QED + a weak + a had : Evaluated via perturbative expansion in ( α ). Complete π calculation up to 5 loops ( diagrams!) by Kinoshita et al. [PRL 109 (2012) ]. With α from measured value of h/m Rb : a QED a QED = (0.080) a weak : Calculated up to 2 loops, using Higgs-mass from LHC [PRD 88 (2013) ]: a weak = 153.6(1.0) / 38 Mitglied der Helmholtz-Gemeinschaft

18 (g 2) - Theory: a theo = a QED + a weak + a had : Evaluated via perturbative expansion in ( α ). Complete π calculation up to 5 loops ( diagrams!) by Kinoshita et al. [PRL 109 (2012) ]. With α from measured value of h/m Rb : a QED a QED = (0.080) a weak : Calculated up to 2 loops, using Higgs-mass from LHC [PRD 88 (2013) ]: a weak = 153.6(1.0) / 38 Mitglied der Helmholtz-Gemeinschaft

19 (g 2) - Theory: a theo = a QED + a weak + a had : Evaluated via perturbative expansion in ( α ). Complete π calculation up to 5 loops ( diagrams!) by Kinoshita et al. [PRL 109 (2012) ]. With α from measured value of h/m Rb : a QED a QED = (0.080) a weak : Calculated up to 2 loops, using Higgs-mass from LHC [PRD 88 (2013) ]: a weak = 153.6(1.0) / 38 Mitglied der Helmholtz-Gemeinschaft

20 (g 2) - Theory: a theo = a QED + a weak + a had a had,lo splits into three parts: a had,lo :Dominant term, evaluated via dispersion integral a had,lo = 1 4π 3 dsσ had (s)k(s) a had,nlo :Evaluated via dispersion integral, less impact due to higher order a had,lbl :Different approaches used, relies heavily on (effective) field theories and models γ had γ h e γ had 10 / 38 Mitglied der Helmholtz-Gemeinschaft

21 (g 2) - Theory: a theo = a QED + a weak + a had a had,lo splits into three parts: a had,lo :Dominant term, evaluated via dispersion integral a had,lo = 1 4π 3 dsσ had (s)k(s) a had,nlo :Evaluated via dispersion integral, less impact due to higher order a had,lbl :Different approaches used, relies heavily on (effective) field theories and models γ had γ h e γ had 10 / 38 Mitglied der Helmholtz-Gemeinschaft

22 (g 2) - Theory: a theo = a QED + a weak + a had a had,lo splits into three parts: a had,lo :Dominant term, evaluated via dispersion integral a had,lo = 1 4π 3 dsσ had (s)k(s) a had,nlo :Evaluated via dispersion integral, less impact due to higher order a had,lbl :Different approaches used, relies heavily on (effective) field theories and models γ had γ h e γ had 10 / 38 Mitglied der Helmholtz-Gemeinschaft

23 (g 2) - Theory: a theo = a QED + a weak + a had a had,lo splits into three parts: a had,lo :Dominant term, evaluated via dispersion integral a had,lo = 1 4π 3 dsσ had (s)k(s) a had,nlo :Evaluated via dispersion integral, less impact due to higher order a had,lbl :Different approaches used, relies heavily on (effective) field theories and models γ had γ h e γ had 10 / 38 Mitglied der Helmholtz-Gemeinschaft

24 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: 11 / 38 Mitglied der Helmholtz-Gemeinschaft

25 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: γ γ had γ 11 / 38 Mitglied der Helmholtz-Gemeinschaft

26 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: γ γ had γ Im γ had γ γ had 2 11 / 38 Mitglied der Helmholtz-Gemeinschaft

27 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: γ γ had γ Im γ had γ γ had 2 11 / 38 Mitglied der Helmholtz-Gemeinschaft

28 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: γ γ had γ { a had,lo = 1 scut } 4π 3 ds σ had,exp (s)k(s) + ds σ had,qcd (s)k(s) 4mπ 2 s cut 11 / 38 Mitglied der Helmholtz-Gemeinschaft

29 Dispersion integral for a had,lo : a had,lo can be expressed in terms of σ(e + e hadrons) via a dispersion integral: γ γ had γ { a had,lo = 1 scut } 4π 3 ds σ had,exp (s)k(s) + ds σ had,qcd (s)k(s) 4mπ 2 s cut The kernel function K(s) behaves like 1/s, enhancing low energy contributions. 11 / 38 Mitglied der Helmholtz-Gemeinschaft

30 Dispersion integral for a had,lo : Importance of input data due to kernel function: Contribution to a had,lo Contribution to (error) 2 Pie charts by F. Jegerlehner 12 / 38 Mitglied der Helmholtz-Gemeinschaft

31 Hadronic cross section measurements Three ways to obtain hadronic cross sections: Energy scan: Change beam energy changed to desired value. e.g. at VEPP-2M/VEPP2000 colliders in Novosibirsk (SND/CMD-experiments) 13 / 38 Mitglied der Helmholtz-Gemeinschaft

32 Hadronic cross section measurements Three ways to obtain hadronic cross sections: Energy scan: Change beam energy changed to desired value. e.g. at VEPP-2M/VEPP2000 colliders in Novosibirsk (SND/CMD-experiments) Initial State radiation: Run at fixed energy, use initial state radiation process to access lower lying energies or resonances e.g. at DAΦNE, PEP-II, BEPC and KEKB meson factories (KLOE, BaBar, BES, BELLE -experiments). 13 / 38 Mitglied der Helmholtz-Gemeinschaft

33 Hadronic cross section measurements Three ways to obtain hadronic cross sections: Energy scan: Change beam energy changed to desired value. e.g. at VEPP-2M/VEPP2000 colliders in Novosibirsk (SND/CMD-experiments) Initial State radiation: Run at fixed energy, use initial state radiation process to access lower lying energies or resonances e.g. at DAΦNE, PEP-II, BEPC and KEKB meson factories (KLOE, BaBar, BES, BELLE -experiments). Tau data: Derive cross sections from τ spectral functions using CVC theorem. e.g. at LEP, CESR and KEKB colliders (ALEPH, L3, OPAL, CLEO, BELLE -experiments). 13 / 38 Mitglied der Helmholtz-Gemeinschaft

34 Initial State Radiation Particle factories measure hadronic cross sections as a function of the hadronic c.m. energy using a Radiative Return to energies below the collider energy s. Emission of hard γ in the bremsstrahlung process reduces available energy to produce hadronic system. 14 / 38 Mitglied der Helmholtz-Gemeinschaft

35 Initial State Radiation Relate measured differential cross section d σ had+γ /d Mhad 2 to hadronic cross section σ had using radiator function H(s, Mhad 2 ): d σ(e + e had + γ) d M 2 had = σ(e+ e had, M 2 had ) s H(s, M 2 had ) = }{{} measured cross section }{{} resulting cross section }{{} radiator function 15 / 38 Mitglied der Helmholtz-Gemeinschaft

36 Initial State Radiation: MC tools Precise calculation of radiator function H(s, M 2 had ) required: 16 / 38 Mitglied der Helmholtz-Gemeinschaft

37 Initial State Radiation: MC tools Precise calculation of radiator function H(s, M 2 had ) required: EVA MonteCarlo generator: First MC generator for ππγ analysis, ISR implemented at leading order Binner, Kühn, Melnikov [PLB 459 (1999) 279] 16 / 38 Mitglied der Helmholtz-Gemeinschaft

38 Initial State Radiation: MC tools Precise calculation of radiator function H(s, M 2 had ) required: EVA MonteCarlo generator: First MC generator for ππγ analysis, ISR implemented at leading order Binner, Kühn, Melnikov [PLB 459 (1999) 279] PHOKHARA MonteCarlo generator: More channels added, ISR implemented at full next-to-leading order Czyż, Grzelińska, Kühn, Rodrigo [EPJ C27 (2003) 563] 16 / 38 Mitglied der Helmholtz-Gemeinschaft

39 Initial State Radiation: MC tools Precise calculation of radiator function H(s, M 2 had ) required: EVA MonteCarlo generator: First MC generator for ππγ analysis, ISR implemented at leading order Binner, Kühn, Melnikov [PLB 459 (1999) 279] PHOKHARA MonteCarlo generator: More channels added, ISR implemented at full next-to-leading order Czyż, Grzelińska, Kühn, Rodrigo [EPJ C27 (2003) 563] RADIO MONTE CARlow: Working Group on Radiative Corrections and MC Generators for Low Energies 16 / 38 Mitglied der Helmholtz-Gemeinschaft

40 Initial State Radiation vs Energy Scan Energy scan: energy of colliding beams is changed to the desired value direct measurement of cross sections dedicated accelerator/physics program luminosity and beam energy measurement for every data point 17 / 38 Mitglied der Helmholtz-Gemeinschaft

41 Initial State Radiation vs Energy Scan Energy scan: energy of colliding beams is changed to the desired value direct measurement of cross sections dedicated accelerator/physics program luminosity and beam energy measurement for every data point Radiative return (ISR): at fixed-energy machines (meson factories) use ISR process to access lower lying energies data as by-product of standard physics program requires precise calculation of radiator function luminosity and beam energy enter only once for all data points needs larger integrated luminosity 17 / 38 Mitglied der Helmholtz-Gemeinschaft

42 DAΦNE: A φ factory 18 / 38 Mitglied der Helmholtz-Gemeinschaft

43 DAΦNE: A φ factory e + e collider with s = m φ 1.02 GeV Peak luminosity L peak = cm 2 s 1 Total KLOE int. luminosity: Z Ldt 2.1 fb 1 ( ) 2006: Energy scan with 4 points around m φ 250 pb 1 at s = 1 GeV 19 / 38 Mitglied der Helmholtz-Gemeinschaft

44 KLOE: KLOE Detector Driftchamber: σr φ = 150m, σz = 2mm σp /p = 0.4% Excellent momentum resolution 20 / 38 Mitglied der Helmholtz-Gemeinschaft Stefan E. Mu ller (HZDR) ISR measurements at KLOE and (g 2)

45 KLOE: KLOE Detector Electromagnetic Calorimeter p σt = 54ps/ E (GeV p ) 100ps, σe /E = 5.7%/ E (GeV ), Excellent time resolution 20 / 38 Mitglied der Helmholtz-Gemeinschaft Stefan E. Mu ller (HZDR) ISR measurements at KLOE and (g 2)

46 ISR measurements at KLOE: Two methods to obtain the 2π-cross section with KLOE: Absolute normalization: Normalize cross section from independent luminosity measurement using Bhabha events: dσ ππγ dm 2 ππ = Nsel N bkg M 2 ππ 1 1 ε sel Ldt The total cross section is then obtained from σ ππ (M 2 ππ) = s dσ ππγ dm 2 ππ 1 H(s, M 2 ππ) 21 / 38 Mitglied der Helmholtz-Gemeinschaft

47 ISR measurements at KLOE: Luminosity is measured at KLOE using large angle Bhabha events: 55 o < θ < 125 o From the observed events, the integrated luminosity is evaluated via Ldt = N obs N bkg σ eff MC generator used for σ eff : BABAYAGA@NLO [NPB758 (2006) 22] QED radiative corrections using Parton Shower approach Theoretical uncertainty around 0.1% Allows luminosity measurement at KLOE with 0.3% accuracy 21 / 38 Mitglied der Helmholtz-Gemeinschaft

48 ISR measurements at KLOE: Two methods to obtain the 2π-cross section with KLOE: Normalization with muons: Normalize ππγ sample in each energy bin with γ events: F 2π (s ) 2 = 4(1 + 2m2 /s )β β 3 π (dσ ππγ/dm 2 ππ) (dσ γ /dm 2 ) The cross section is then obtained from the formula σ ππ (s ) = πα2 β 3 π 3s F 2π (s ) 2 Advantage: Cancellation of systematic effects and radiative corrections 21 / 38 Mitglied der Helmholtz-Gemeinschaft

49 Selection cuts for analyses: 2 pion (muon) tracks at large angles 50 o < θ π, < 130 o 22 / 38 Mitglied der Helmholtz-Gemeinschaft

50 Selection cuts for analyses: 2 pion (muon) tracks at large angles 50 o < θ π, < 130 o Small angle cuts: Photons at small angles θ γ < 15 o or θ γ > 165 o high statistics for ISR events low FSR contribution suppression of φ π + π π 0 background photon momentum from kinematics: p γ = p miss = ( p + + p ) threshold region not accessible 22 / 38 Mitglied der Helmholtz-Gemeinschaft

51 Selection cuts for analyses: 2 pion (muon) tracks at large angles 50 o < θ π, < 130 o Large angle cuts: Photons at large angles 50 o < θ γ < 130 o lower signal statistics higher FSR contribution photon detection possible (4-momentum constraints) threshold region accessible more φ π + π π 0 background irreducible background from φ f 0 γ π + π γ 22 / 38 Mitglied der Helmholtz-Gemeinschaft

52 Selection cuts for analyses: 2 pion (muon) tracks at large angles 50 o < θ π, < 130 o Large angle cuts: Photons at large angles 50 o < θ γ < 130 o lower signal statistics higher FSR contribution photon detection possible (4-momentum constraints) threshold region accessible more φ π + π π 0 background irreducible background from φ f 0 γ π + π γ reduced using off-peak data 22 / 38 Mitglied der Helmholtz-Gemeinschaft

53 Threshold region: High energetic ISR photon (= small M 2 ππ) at small angle forces also the pions to small angles, where they escape detection. events with M 2 ππ < 0.35 GeV 2 are suppressed in small angle analysis. 23 / 38 Mitglied der Helmholtz-Gemeinschaft

54 Threshold region: If the high-energy photon is emitted at large angles, also the pions will be at large angles, and can be detected. 4m 2 π threshold reachable 23 / 38 Mitglied der Helmholtz-Gemeinschaft

55 Threshold region: MC simulation (PHOKHARA): 23 / 38 Mitglied der Helmholtz-Gemeinschaft

56 Radiative corrections: Radiator function: Crucial ingredient for ISR analyses, quite complex analytic form. Extract radiator function from PHOKHARA MonteCarlo code: H(s, Mππ) 2 = s 3M2 ππ πα 2 β 3 dσisr ππγ(γ) dm 2 ππ F2π 2 =1 Theoretical precision due to missing terms: 0.5% 24 / 38 Mitglied der Helmholtz-Gemeinschaft

57 Radiative corrections: Vacuum polarization: Cross section in dispersion integral needs to be undressed from vacuum polarization effects: σ 0 (s) = σ obs (s) ( ) α(0) 2 σ obs(s)/δ(s) α(s) 24 / 38 Mitglied der Helmholtz-Gemeinschaft

58 Radiative corrections: Final state radiation: Cross section in dispersion integral should be inclusive with respect to FSR: FSR corrections estimated with PHOKHARA MC generator (pointlike-pion approximation). Definitions: Cross section σ ππ : FSR included, vacuum polarization removed (bare or undressed) Pion form factor F 2π 2 : FSR excluded, vacuum polarization included (dressed) 24 / 38 Mitglied der Helmholtz-Gemeinschaft

59 KLOE results: KLOE05: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 of data taken in 2001 a KLOE08: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 data taken in 2002 b KLOE10: 75 points between 0.1 and 0.85 GeV 2, based on pb 1 data taken in 2006 c with s = 1.00 GeV KLOE12: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 data taken in 2002 d, normalized to muons a Phys. Lett. B606 (2005) 12 b Phys. Lett. B670 (2009) 285 c Phys. Lett. B700 (2011) 102 d Phys. Lett. B720 (2013) / 38 Mitglied der Helmholtz-Gemeinschaft

60 KLOE results: KLOE05: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 of data taken in 2001 a Superseded by KLOE08! KLOE08: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 data taken in 2002 b KLOE10: 75 points between 0.1 and 0.85 GeV 2, based on pb 1 data taken in 2006 c with s = 1.00 GeV KLOE12: 60 points between 0.35 and 0.95 GeV 2, based on pb 1 data taken in 2002 d, normalized to muons a Phys. Lett. B606 (2005) 12 b Phys. Lett. B670 (2009) 285 c Phys. Lett. B700 (2011) 102 d Phys. Lett. B720 (2013) / 38 Mitglied der Helmholtz-Gemeinschaft

61 KLOE results: (e + e ) [nb] KLOE KLOE KLOE KLOE M [GeV] 0 26 / 38 Mitglied der Helmholtz-Gemeinschaft

62 KLOE results: KLOE08, KLOE10 and KLOE12: (e + e ) [nb] KLOE12 KLOE10 KLOE (M 0 ) 2 [GeV 2 ] / 38 Mitglied der Helmholtz-Gemeinschaft

63 KLOE results: Comparison KLOE10 with KLOE08 and KLOE12: 27 / 38 Mitglied der Helmholtz-Gemeinschaft

64 KLOE results: KLOE08, KLOE10 and KLOE12 combined using the BLUE method: (Best Linear Unbiased Estimate) Preliminary! (e + e ) [nb] KLOE12 KLOE10 KLOE08 BLUE (M 0 ) 2 [GeV 2 ] / 38 Mitglied der Helmholtz-Gemeinschaft

65 KLOE results: KLOE08, KLOE10 and KLOE12 combined using the BLUE method: (Best Linear Unbiased Estimate) a ππ 600 Preliminary! (e + e ) [nb] KLOE12 KLOE10 KLOE08 BLUE [ GeV 2 ] = (488.6 ± 5.7) (M 0 ) 2 [GeV 2 ] / 38 Mitglied der Helmholtz-Gemeinschaft

66 KLOE10 vs SND & CMD2: F 2 8 KLOE10 6 CMD SND KLOE10 CMD SND (M 0 ) 2 [GeV 2 ] ( F 2 CMD,SND - F 2 K10 ) / F 2 K10 SND CMD-2 (M ) 0 2 [GeV 2 ] / 38 Mitglied der Helmholtz-Gemeinschaft

67 KLOE10 vs BaBar09: BaBar09 50 KLOE BaBar09 KLOE (e + e ) [nb] M 0 [GeV] ( BaBar - KLOE ) / KLOE M 0 [GeV] / 38 Mitglied der Helmholtz-Gemeinschaft

68 The BaBar vs KLOE puzzle: T. Teubner at RadioMClow 30 / 38 Mitglied der Helmholtz-Gemeinschaft

69 τ data: τ ν τ π π 0 e + e π π τ ν τ e e + W γ d u d d π u u π 0 π u u π + 31 / 38 Mitglied der Helmholtz-Gemeinschaft

70 τ data: τ ν τ π π 0 e + e π π τ ν τ e e + W γ d u d d π u u π 0 π u u π + σ I=1 e + e π + π (s) = 4πα2 v π s π 0(s), s mτ Isospin symmetry breaking effects need to be taken into account 31 / 38 Mitglied der Helmholtz-Gemeinschaft

71 τ data: τ ν τ π π 0 e + e π π τ ν τ e e + W γ d u d d π u u π u 0 π u π + Crucial role of γ ρ mixing (Jegerlehner,Szafron [EPJ C71 (2011) 1632]): 31 / 38 Mitglied der Helmholtz-Gemeinschaft

72 a had,lo : Many channels: 32 / 38 Mitglied der Helmholtz-Gemeinschaft

73 a had,lo : Evaluation of dispersion integral depends on many factors: Combination of data from different experiments Choice of data Threshold energy above which pqcd is used... Year Author a had,lo [10 10 ] 1995 Eidelman, Jegerlehner (e + e ) ± Alemany, Davier, Höcker (τ) ± Jegerlehner, Szafron (e + e ) ± Jegerlehner, Szafron (τ) ± Hagiwara, Martin, Nomura, Teubner (e + e ) ± Davier, Höcker, Malaescu, Zhang (e + e ) ± Zhang (τ) ± Benayoun, David, DelBuono, Jegerlehner (e + e + BHLS) ± / 38 Mitglied der Helmholtz-Gemeinschaft

74 a had,ho & a had,lbl : a had,ho : Similar to procedure for a had,ho : Experimental data + dispersion integral with suitable kernel gives (Jegerlehner, Nyffeler [Phys.Rept. 477 (2009) 1]) a had,ho = 10.0(0.1) a had,lbl : Different approaches lead to different values and errors: Year Author a had,lo [10 10 ] 1996(2002) Bijnens, Prades, Pallante 8.3 ± (2002) Hayakawa, Kinoshita 9.0 ± Melnikov, Vainshtein 13.6 ± Davier, Marciano 12.0 ± Bijnens, Prades 11.0 ± Nyffeler 11.6 ± 4.0 a had,lbl = 11.6(4) / 38 Mitglied der Helmholtz-Gemeinschaft

75 a had = a had,lo + a had,ho + a lbl Adding the three parts: a had,lo = (46.5) a had,ho = ( 1.0) a had,lbl = (40.0) a had = (61.3) / 38 Mitglied der Helmholtz-Gemeinschaft

76 Putting it all together: Current status of a from experiment and Standard Model theory: a EXP = (63.) a QED = (0.080) a weak = (1.0) a had = (61.3) a SM = (61.3) / 38 Mitglied der Helmholtz-Gemeinschaft

77 Putting it all together: Current status of a from experiment and Standard Model theory: a EXP = (63.) a QED = (0.080) a weak = (1.0) a had = (61.3) a SM = (61.3) a = a EXP a SM = ( ± 87.90) σ 35 / 38 Mitglied der Helmholtz-Gemeinschaft

78 Putting it all together: 36 / 38 Mitglied der Helmholtz-Gemeinschaft

79 Putting it all together: Blum et al., arxiv: / 38 Mitglied der Helmholtz-Gemeinschaft

80 Conclusions: More than 10 years after its appearance, the (g 2) -puzzle still persists Measured hadronic cross sections at low energies are needed in the theoretical evaluation of a The KLOE collaboration has pioneered the use of ISR for precision cross section measurements, and has performed and published 4 ISR analyses New experiments to measure a are planned at Fermilab and JPARC More and more precise measurements of hadronic cross sections are needed to improve the theoretical evaluation of a 38 / 38 Mitglied der Helmholtz-Gemeinschaft