The Hadronic Contribution to a μ

Transcription

1 The Hadronic Contribution to a μ (observations of an amateur) Lee Roberts Department of Physics Boston University B. Lee Roberts, INT Seattle 27 October p. 1/44

2 The Hadronic Contribution to a μ (observations of an amateur) La Gazza Ladra of talks Lee Roberts Department of Physics Boston University B. Lee Roberts, INT Seattle 27 October p. 2/44

3 Gioachino Rossini B. Lee Roberts, INT Seattle 27 October p. 3/44

4 Outline Introduction to a μ (Had) Paths to the lowest order hadronic contribution Status of the measurements (Post Tau-2008) Status of hadronic light-by-light scattering Summary and lack of conclusions. Many thanks to Michel Davier, Ivan Logashenko and Graziano Venanzoni for answering many questions about the R measurements. Also thanks to Eduardo de Rafael, Arkady Vainshtein and Bill Marciano. B. Lee Roberts, INT Seattle 27 October p. 4/44

5 The SM Value for electron and muon anomalies e*, e, e, e, e, e, e, e, e vrs. μ e, : relative contribution e, of heavier e, things B. Lee Roberts, INT Seattle 27 October p. 5/44

6 The SM Value for electron and muon anomalies e vrs. μ : relative contribution of heavier things B. Lee Roberts, INT Seattle 27 October p. 6/44

7 a(had) and e + e - Hadrons spectral representation, (using analiticity and the optical theorem) Bouchiat-Michel 61, Brodsky-de Rafael 68 (see Miller, de Rafael, BLR, Rep Prog. Phy. 70(2007) 795 analyticity and the optical theorem hadronic spectral function so the hadronic contribution can be obtained from data B. Lee Roberts, INT Seattle 27 October p. 7/44

8 R(s) measurements at low s Babar/Belle (ISR) KLOE (ISR) VEPP-2000 VEPP-2M At low s the cross-section is measured independently for each final state from Davier/Höcker B. Lee Roberts, INT Seattle 27 October p. 8/44

9 Data from CMD2, SND and KLOE. The vector meson ρ provides the dominant feature of the cross section. BaBar has a large data set that was presented at Tau2008. CMD-2 SND KLOE hep-ex ,98 97 ρ ω meson interference from I. Logashenko - φ to ψ 2006 B. Lee Roberts, INT Seattle 27 October p. 9/44

10 An Intermezzo: tau for two (π)? Can we use hadronic τ decay to get a μ (Had)? B. Lee Roberts, INT Seattle 27 October p. 10/44

11 a(had) from the vector current in hadronic τ decay? Assume: CVC, no 2 nd -class currents then an even number of pions in the final state implies that the decay goes through the vector current isospin breaking corrections. e + e - goes through neutral ρ while τ-decay goes through charged ρ n.b. τ decay has no isoscalar piece, e + e - does no ρ ω interference B. Lee Roberts, INT Seattle 27 October p. 11/44

12 Using also Tau Data through CVC SU(2) W: I =1 & V,A CVC: I =1 & V γ: I =0,1 & V ν τ τ W hadrons e + e γ hadrons Hadronic physics factorizes in Spectral Functions : Isospin symmetry connects I =1 e + e cross section to vectorτ spectral functions: σ 4πα π π = υ τ π π ν τ s 2 ( I = 1) ee fundamental ingredient relating long distance (resonances) to short distance description (QCD) υ τ 0 π π ν τ 0 BR τ π π ντ BR τ νν 1 N dn ππ ds ( 1 / m ) ( 1+ / m ) e 0 e s s τ ππ τ τ m 2 τ branching fractions mass spectrum kinematic factor (PS) from Andreas Höcker A. Höcker The Muon g 2 Challenge 12

13 Testing CVC with one number (circa 2004) Infer τ branching fractions (more robust than spectral functions) from e + e data: Difference: BR[τ ] BR[e + e (CVC)]: Mode τ π π 0 ν τ τ π 3π 0 ν τ τ 2π π + π 0 ν τ Δ(τ e + e ) ± ± ± 0.25 `Sigma ee data on π π + π 0 π 0 not satisfactory from Michel Davier B. Lee Roberts, INT Seattle 27 October p. 13/44

14 τ -decay data from ALEPH, CLEO and OPAL the vector spectral function note the absence of the ρ ω interference Davier-Eidleman-Höcker-Zhang, EPJ: C27-497(03), C31, 503 (03) B. Lee Roberts, INT Seattle 27 October p. 14/44

15 Result (2): Mass spectrum Belle data Unfolded Results Νumber Number of entries of /0.05 /0.05(GeV/c 2 ) 2 ) ρ ρ Data (M ππ 0) 2 (GeV/c 2 ) 2 (Mπ π) Belle G&S Fit (ρ (770) + ρ (1450) + ρ (1700) ) ± 0 2 ρ ( GeV / c ) dn 0 6π V S ππ W Βe s 2s = 1 1+ v N ds m m ππ 0 Mass spectra v = Phase space ππ 0 (s) ud E mτ Βπ τ τ = Form Factor β 3 (s) 12π from Hisaki Hayashii Tau F π (s) 2 15 ππ 0 (s)

16 Result (3) Pion Form Factor F π 2 From 64M τ + τ pairs, Belle selects 5.5M τ π π 0 ν τ events! Belle 45 Fπ 2 F π ρ Belle ALEPH CLEO G&S Fit G&S Fit (ρ (770) + ρ (1450) + ρ (1700) ) ρ ρ F π Belle ALEPH CLEO G&S Fit 10-2 F π (M ππ 0) 2 (GeV/c 2 ) (M± ππ 0) (GeV/c22 2 ) 2 (Mπ π) ( GeV / c ) (M ππ 0) 2 (GeV/c 2 ) 2 Error bars include both statistical and systematic Interference between ρ and ρ Fit with BW 16

17 New isospin calculations Gabriel López Castro Tau Impact on a μ LO,ππ (τ) [Preliminar] (-3.9) As applied to results of BELLE (arxiv: ) [τ π ων removed ] π 0 γ 17

18 Back to the matter at hand: e + e π + π B. Lee Roberts, INT Seattle 27 October p. 18/44

19 Contributions and errors to the integral: 2π 2π 2006, from I. Logashenko, phi-psi 2006 > 5 GeV 2 5 GeV > 5 GeV 2 5 GeV ω, ϕ < 2 GeV ω, ϕ < 2 GeV thanks to Vanya Logashenko 2008, from S. Eidelman, Tau 2008, pre-babar results B. Lee Roberts, INT Seattle 27 October p. 19/44

20 De Rujula: theorist is farmer, experimentalist truffle pig B. Lee Roberts, INT Seattle 27 October p. 20/44

21 De Rujula: theorist is farmer, experimentalist truffle pig caution and care are needed in including the radiative corrections B. Lee Roberts, INT Seattle 27 October p. 21/44

22 Novosibirsk Radiative corrections CMD-2 uses custom Monte- Carlo generator to calculate RC ee, μμ, ππ final states: 1 γ at large angle, multiple γ s along initial or final particles ( 0.2%) CMD-2 calculation is consistent with independent calculations (BHWIDE, KKMC) SND uses BHWIDE for ee final state and CMD-2 generator for μμ, ππ final states from Ivan Logashenko Tau Vacuum polarization Radiation terms ISR+FSR ISR+FSR+VP 22 I Logashenko Tau 2008

23 Narrow resonances ω (782) ϕ (1020) Mass and width are measured to 0.1 MeV, Γ ee to 2-3% 23 I Logashenko Tau 2008

24 e e Cross-section e+e- 4π π πππ ee 0 0 π πππ + + Systematic error 5-7% Efficiency determination gives main contribution to the systematic error Systematic error: SND = 8% CMD2= 15% (discrepancy 15-25%) problem with efficiency determination! CMD2-reanalysis preliminary = 24 8% I Logashenko Tau 2008

25 ee Cross-section e+e- 3π 0 π ππ + + Systematic error: 6% (>1GeV) 1-2% on omega 2.5% on phi Fit: ω, ρφω,,, ω 25 I Logashenko Tau 2008

26 Overview of the results CMD/SND Systematic error: Total error: ~ % 1.0% 0.6% 1.5% % ~ % 1.5% 1--2% 2.0% % 26 Error of R(s) I Logashenko Tau 2008

27 We want CMD2/SND poor μ π discrimination calculate and subtract μμ from ππ numerator calculate μμ and use it for the denominator CMD-2 e π μ Energy deposition MeV B. Lee Roberts, INT Seattle 27 October p. 27/44

28 KLOE and BaBar use ISR (radiative return) BINP scan e + e - beam energy KLOE sit on φ, γ is soft and goes down the beam pipe in data published thus far, use theory to calculate mm cross section. have μ μ data being analyzed KLOE BaBar use ISR to lower collision energy BaBar runs on the Υ 4s, the γ is hard, and is detected excellent particle ID with μ π separation measures R (s) directly Always the issue of radiative corrections B. Lee Roberts, INT Seattle 27 October p. 28/44

29 (BaBar) The Measurement ISR photon at large angle in EMC 1 (for efficiency) or 2 (for physics) tracks of good quality identification of the charged particles separate ππ/kk/μμ event samples kinematic fit (not using ISR photon energy) including 1 additional photon obtain all efficiencies (trigger, filter, tracking, ID, fit) from same data measure ratio of ππγ(γ) to μμγ(γ) cross sections to cancel ee luminosity additional ISR otherwise 3-4% syst error vacuum polarization ISR photon efficiency still need to correct for FSR 2 contribution in μμγ(γ) and additional FSR, both calculated in QED, but also checked in data (ISR-FSR interference, additional detected photons) 0 σ [ ππγ ( γ)]( s) σ [ ππ ( γ)]( s) R exp( s) = = μμ 0 σ [ μμγ ( γ)]( s) (1+ δ ) σ [ μμ ( γ)]( s) FSR = (1+ δ μμ FSR R( s) ) (1+ δ μμ addfsr ) M. Davier - Tau

30 QED Test with μμγ sample absolute comparison of μμ mass spectra in data and in simulation simulation corrected for data/mc efficiencies J/ψ excluded AfkQed corrected for incorrect NLO using Phokhara results for different running periods consistent: (7.9 ±7.5) 10-3 full statistics ( GeV) ISR γ efficiency 5.2 syst. trig/track/pid 4.0 M. Davier - Tau 2008 BaBar ee luminosity 30

31 Unfolding Mass Spectrum measured mass spectrum distorted by resolution effects and FSR (m ππ vs. s ) unfolding uses mass-transfer matrix from simulation 2 MeV bins in GeV mass range, 10 MeV bins outside most salient effect in ρ-ω interference region (little effect on a μ ππ ) M. Davier - Tau

32 BaBar results M. Davier - Tau

33 BaBar results in ρ region M. Davier - Tau

34 BaBar vs. other experiments at large mass M. Davier - Tau

35 BaBar vs.other ee data ( GeV) CMD-2 direct relative comparison of cross sections in the corresponding 2-MeV BaBar bins (interpolation with 2 bins) deviation from 1 of ratio w.r.t. BaBar stat + syst errors included SND KLOE comparison in Davier s talk has a binning problem, so should be ignored. M. Davier - Tau

36 BaBar vs.other ee data (ρ ω interference region) mass calibration of BaBar checked with ISR-produced J/ψ μμ expect (0.16 ± 0.16) MeV at ρ peak ω mass can be determined through mass distribution fit (in progress) Novosibirsk data precisely calibrated using resonant depolarization comparison BaBar/CMD-2/SND in ρ-ω interference region shows no evidence for a mass shift CMD-2 SND M. Davier - Tau

37 BaBar vs. IB-corrected τ data ( GeV) Δ F π 2 / F π BABAR τ(aleph) B A B A R P R E L I M I N A R Y s(gev/c 2 ) relative comparison w.r.t. BaBar of isospin-breaking corrected τ spectral functions BaBar data averaged in wider τ bins and corrected for ρ-ω interference Δ F π 2 / F π BABAR τ(cleo) B A B A R P R E L I M I N A R Y Δ F π 2 / F π BABAR τ(belle) B A B A R P R E L I M I N A R Y s(gev/c 2 ) s(gev/c 2 ) M. Davier - Tau

38 Computing a μ ππ a μ ππ ( ) ALEPH-CLEO-OPAL (DEHZ 2006) (DEHZ 2003) (2008) FSR correction was missing in Belle, new value ± 3.0 ± 2.5 Direct comparison GeV BaBar ± 0.8 ± 2.2 CMD ± 2.4 ± 2.2 CMD ± 1.7 ± 2.9 SND ± 1.2 ± 4.7 M. Davier - Tau

39 Conclusions BaBar analysis of ππ and μμ ISR processes completed Precision goal has been achieved: 0.6% in ρ region ( GeV) Absolute μμ cross section agrees with NLO QED within 1.2% Preliminary results available for ππ in the range GeV Structures observed in pion form factor at large masses Comparison with results from earlier experiments discrepancy with CMD-2 and SND mostly below ρ large disagreement with KLOE better agreement with τ results, especially Belle Contribution to a μ from BaBar agrees better with τ results Deviation between BNL measurement and theory prediction significantly reduced using BaBar ππ data a μ [exp ] a μ [SM ]=(27.5 ± 8.4) (14.0 ± 8.4) Wait for final results and contributions of multi-hadronic modes M. Davier - Tau

40 The Hadronic Light-by-Light Contribution B. Lee Roberts, INT Seattle 27 October p. 40/44

41 vertex function off-shell photon scattering amplitude induced by hadrons Must be calculated using models models must be a good effective theory of QCD. e.g ENJ-L, but nevertheless these models have limitations. Cannot be easily tied to data since you would need γ*γ* π π data there are some limits that can be used to constrain amplitudes in the model All interesting calculations (11±4)x10-10 B. Lee Roberts, INT Seattle 27 October p. 41/44

42 dominant contribution Additional work is needed, and is in progress. see also: E de Rafael, Heidelberg June 08- for some more details (but with smaller errors than have been to agreed to now for the whitepaper) B. Lee Roberts, INT Seattle 27 October p. 42/44

43 My Summary and Conclusions (driven by Tau 2008) At present, the lowest order hadronic contribution is a study in contradictions. On the other hand, the H-LBL situation has improved. representatives of the 3 principal theory groups agree on values and errors of all of the contributions. The τ situation Belle reported 100 times the τ data sample compared with LEP, however they normalized to the PDG value of the τ π π 0 ν τ branching fraction, rather than their own value which was lower than the PDG (and would reduce the value of a μ (Had) from the Belle τ data). new isospin corrections reduce the difference, but do not resolve the previous e + e - -τ differences. B. Lee Roberts, INT Seattle 27 October p. 43/44

44 Summary ctd. The τ e + e - differences have become more confusing after BaBar. recall that while the intergral from BaBar agrees with the old tau results, the shape does not, but rather agrees with the Belle results. Will Belle use their π π BR for normalization? If we take BaBar at face value, then how do we average them with the other e+e- data? Do we use the PDG prescription of increasing the errors so χ 2 /ν 1? We certainly can t throw out the other data just because BaBar is the newest set What about the KLOE μ μ measurement? we need that check of their new result We will have to wait for the final BaBar paper to draw further conclusions. B. Lee Roberts, INT Seattle 27 October p. 44/44

45 B. Lee Roberts, INT Seattle 27 October p. 45/44 45/68

46 Lowest-order Hadronic Vacuum Polarization Define: photon vacuum polarization function Π γ (q 2 ) Ward identities: only vacuum polarization with: modifies electron charge Leptonic Δα lep (s) calculable in QED. However, quark loops are modified by longdistance hadronic physics, cannot (yet) be calculated within QCD (!) Way out: Optical Theorem (unitarity) and the subtracted dispersion relation of Π γ (q 2 ) (analyticity) Im[ ] hadrons 2 from Michel Davier... and equivalently for a B. Lee Roberts, INT Seattle 27 October p. μ [had] 46/44 46/68

47 m 2 ππ distribution Belle data Number of entries /0.05(GeV/c 2 ) K π 0 h2π qq DATA MC(signal) τ - h - (nπ 0 )ν τ τ - K - π 0 ν τ τ - ω 0 π - ν τ ( ω 0 π 0 γ ) continuum B.G. Tau mass limit (M± ± π π 0) (GeV/c 2 ) 2 (Mπ π) from Hisaki Hayashii Tau ( GeV / c ) The signal level is different more than 4th order of magnitude between ρ(770) and ρ (1700). Background non-τ B.G. feed down B.G. BG is important at threshold and ρ region. qq 2.22±0.05% 0 h 2π ντ 6.0% 0 K πν τ 1.6% τ π ων τ (ω π 0 γ) 0.5% 47