The Hadronic Contribution to (g 2) μ

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2006, Cape Cod, USA γ γ hadrons davier@lal.in2p3.

1 γ The Hadronic Contribution to (g 2) μ Michel Davier Laboratoire de l Accélérateur Linéaire, Orsay Lepton Moments Workshop 2006 June 19-22, 2006, Cape Cod, USA γ γ hadrons davier@lal.in2p3.fr Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 1 μ

2 Magnetic Anomaly Q E D γ QED Prediction: Computed up to 4 th order [Kinoshita et al.] (5 th order estimated) ie Γ μ = eγμ + a l σμνq Schwinger 1948 ν 2m α al = = K 2π γ μ QED a μ n α = 10 n= 1 π QED Hadronic Weak SUSY or other new physics? Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 2

3 Why Do We Need to Know it so Precisely? Experimental progress on precision of (g 2) μ BNL (2004) Outperforms theory precision on hadronic contribution Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 3

4 The Muonic (g 2) μ Contributions to the Standard Model (SM) Prediction: a μ g 2 QED had = aμ + aμ + 2 μ a weak μ The Situation 1995 Source σ(a μ ) Reference QED ~ [Schwinger 48 & others] Hadrons ~ (15 4) [Eidelman-Jegerlehner 95 & others] Z, W exchange ~ [Czarnecki et al. 95 & others] Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD ( first principles ) but: we can use experiment (!) a had μ 2 α = 2 3π 4m 2 π ds K( s) s R( s) h a d γ Dispersion relation had μ... γ γ Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 4

5 Hadronic Vacuum Polarization Define: photon vacuum iqx μ ν μν μ ν polarization function Π γ (q 2 ) em ( em ) ( ) i d x e 0 TJ ( x) J ( x) 0 = g q q q γ ( q ) Ward identities: only vacuum polarization modifies electron charge α(0) α( s) = with: Δ α( s) = 4παRe ( s) (0) 1 Δ α( s) γ γ Leptonic Δα lep (s) calculable in QED. However, quark loops are modified by long-distance hadronic physics, cannot (yet) be calculated within QCD (!) Way out: Optical Theorem (unitarity) and the subtracted dispersion relation of Π γ (q 2 ) (analyticity) ( ) 2 (0) Born: σ ( s) = σ( s) α / α( s) (0) + σ [ ee hadrons] 12π Im γ ( s) = R( s) (0) + + σ [ ee μ μ ] Im[ ] hadrons 2 s Im γ ( s ) γ( s) γ(0) = ds π s ( s s ) i ε 0 Δ α had ( ) ( s αs R s ) Re 3 ds = π s ( s s ) i ε 0 Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ... and equivalently for a 5 μ [had]

Contributions to the dispersion integral 2π 3π (+ω,φ) 4π > 4π (+KK) 1.8-3.

6 Contributions to the dispersion integral 2π 3π (+ω,φ) 4π > 4π (+KK) (+J/ψ, ψ) 5-12 (+ϒ) 12 - < 1.8 GeV a had,lo μ 12% 5% 2% 1% 0% 5% 3% 2π 92% 72% σ 2 [a had,lo μ ] 1% 9% 4% 0% 0% 0% 92% 6% 2π 80% Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 6

7 Improved Determination of the Hadronic Contribution to (g 2) μ and α(m Z ) 2 Eidelman-Jegerlehner 95, Z.Phys. C67 (1995) 585 Energy [GeV] Input 1995 Input after 1998 Since then: Improved determination of the dispersion integral: better data extended use of QCD 2m π -1.8 Data Data (e + e & τ) (+ QCD) 1.8 J/ψ Data QCD J/ψ - ϒ Data Data + QCD ϒ -40 Data QCD 40 - Inclusion of precise τ data using SU(2) (CVC) QCD QCD Improvement in 4 Steps: Alemany-Davier-Höcker 97, Narison 01, Trocóniz-Ynduráin 01, + later works Extended use of (dominantly) perturbative QCD Martin-Zeppenfeld 95, Davier-Höcker 97, Kühn-Steinhauser 98, Erler 98, + others Theoretical constraints from QCD sum rules and use of Adler function Groote-Körner-Schilcher-Nasrallah 98, Davier-Höcker 98, Martin-Outhwaite- Ryskin 00, Cvetič-Lee-Schmidt 01, Jegerlehner et al 00, Dorokhov 04 + others Better data for the e + e π + π cross section and multihadron channels CMD-2 02 (revised 03), KLOE 04, SND 05 (revised 06), BaBar Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 7

8 The Role of τ 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 ν τ BR τ 1 dn N ds ππ ( 1 / m ) ( 1 + / m ) e νν 0 e s s τ ππ τ τ m 2 τ branching fractions mass spectrum kinematic factor (PS) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 8

9 SU(2) Breaking Electromagnetism does not respect isospin and hence we have to consider isospin breaking when dealing with an experimental precision of 0.5% 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 to effective 4-fermion coupling (1 + 3α(m τ )/4π)(1+2 Q )log(m Z /m τ ) subleading corrections calculated and small long distance radiative correction G EM (s) calculated [ add FSR to the bare cross section in order to obtain π π + (γ) ] Charged/neutral mass splitting: m π m π0 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 ρ0 and Γ ρ Γ ρ0 [not corrected!] Electromagnetic decays, like: ρ ππγ, ρ πγ, ρ ηγ, ρ l + l Marciano-Sirlin 88 Braaten-Li 90 Cirigliano-Ecker-Neufeld 02 Alemany-Davier-Höcker 97, Czyż-Kühn 01 Quark mass difference m u m d generating second class currents (negligible) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 9

10 e + e Radiative Corrections Multiple radiative corrections are applied on measured e + e cross sections Situation often unclear: whether or not and if - which corrections were applied Vacuum polarization (VP) in the photon propagator: leptonic VP in general corrected for hadronic VP correction not applied, but for CMD-2 (in principle: iterative proc.) Initial state radiation (ISR) corrected by experiments Final state radiation (FSR) [we need e + e hadrons (γ) in dispersion integral] usually, experiments obtain bare cross section so that FSR has to be added by hand ; done for CMD-2, (supposedly) not done for others Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 10

11 Mass Dependence of SU(2) Breaking Multiplicative SU(2) corrections applied to τ π π 0 ν τ spectral function: Only β 3 and EW short-distance corrections applied to 4π spectral functions Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 11

12 analyses of a μ had and new input Motivation for re-analyses New high precision e + e results (0.6% sys. error) around ρ from CMD-2 (Novosibirsk) New τ results from ALEPH using full LEP1 statistics New R results from BES between 2 and 5 GeV New theoretical analysis of SU(2) breaking discrepancy between ee and τ input! CMD-2 PL B527, 161 (2002) ALEPH Phys. Rep BES PRL (2000); PRL 88, (2002) Cirigliano-Ecker-Neufeld JHEP 0208 (2002) 002 Davier-Eidelman-Höcker-Zhang Eur.Phys.J. C27 (2003) 497; C31 (2003) 503 Hagiwara-Martin-Nomura-Teubner, Phys.Rev. D69 (2004) (no τ data) Jegerlehner, hep-ph/ (no τ data) New input: KLOE 2004, SND 2005 (revised 2006), CMD ( GeV) reduction of VP+FSR additional uncertainties BaBar exclusive channels 2ππ 0, 4π, 6π, 4π2π 0 QCD in GeV Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 12

13 e + e data: radiative corrections revised CMD-2 revision % luminosity correction from change in σ Bhabha % change in σ μμ both changes affect event separation ee / μμ / ππ 0.4% systematic error unchanged (0.6% total) Monte Carlo generators not correct for (1) μμ(γ) and (2) ππ(γ) 3% change in σ ππ SND revision % systematic error unchanged (1.3% total) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 13

14 e + e data: comparisons ee results compared to fit of SND data band indicates relative systematic error CMD-2 KLOE Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 14

15 Comparing e + e π + π and τ π π 0 ν τ Correct τ data for missing ρ -ω mixing (taken from BW fit) and all other SU(2)-breaking sources Remarkable agreement But: not good enough Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 15

16 The ee-τ problem Relative difference between τ and e + e data: zoom Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 16

$τ π π 0 ν τ : Comparing ALEPH, CLEO, OPAL Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH).$

17 τ π π 0 ν τ : Comparing ALEPH, CLEO, OPAL Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH). Good agreement observed between ALEPH and CLEO ALEPH more precise at low s CLEO better at high s Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 17

18 e + e - τ data comparisons compare SND lineshape fit to τ spectral functions isospin breaking correction (only β 3 effect) CLEO ALEPH Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 18

19 Today s e + e - τ data comparison Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 19

20 Testing CVC with one number Inferτ branching fractions (more robust than spectral functions) from e + e data: 2 m 0 6 π Vud SEW BR CVC ( τ π πν ) ds kin( s) SU(2)-corrected τ = υ ( s) 2 m τ 0 2 τ Difference: BR[τ ] BR[e + e (CVC)]: Mode Δ(τ e + e ) Sigma τ π π 0 ν τ ± τ π 3π 0 ν τ 0.08 ± τ 2π π + π 0 ν τ ± ee data on π π + π 0 π 0 not satisfactory Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 20

21 τ π π 0 ν τ : preliminary results from BELLE preliminary results from BELLE on τ ππspectral function presented at EPS 2005 high statistics: see dip at 2.4 GeV 2 for first time in τ data discrepancies with ALEPH/CLEO at large mass and ee data at low mass Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 21

22 Partial solution to the lineshape problem Isospin breaking in the ρ ± ρ 0 masses zoom observed ρ ± ρ 0 mass difference: 2.3 ± 0.8 MeV; width 0.2 ± 1.0 MeV Davier, hep-ex/ Jegerlehner, hep-ph/ Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 22

23 Final remarks on main ππ contribution The problem of the π + π contribution : Experimental situation: revised SND results in agreement with CMD-2 τ data without m (ρ ) and Γ(ρ ) corr. in strong disagreement with both data sets ALEPH, CLEO and OPAL τ data in good agreement, preliminary BELLE less so ee spectral functions have now reached the precision of τ data Concerning the remaining line shape discrepancy ( GeV 2 ): SU(2) corrections: basic contributions identified and stable since long; overall correction applied to τ is ( 2.2 ± 0.5) %, dominated by uncontroversial short distance piece; additional long-distance corrections found to be small ρ lineshape corrections can improve the situation, but cannot account for the difference above 0.7 GeV 2 The agreement between SND and CMD-2 invalidates the use of τ data until a better understanding of the discrepancies is achieved (an interesting question as such) Discrepancy between KLOE and CMD-2/SND results: not safe to include KLOE in the calculation and take advantage of decreased error Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 23

24 Other exclusive channels: BaBar ISR systematic program underway using ISR from Υ(4S) energies, taking advantage of high luminosity (B-factory) statistics comparable to CMD-2/SND for E cm <1.4 GeV, much better than DM1/DM2 above full energy range covered at the same time X = 2E γ /E cm γ ISR dσ (, s x) dxd(cos ) ( ) Hsx (,, ) s(1 x) θ σ0 θ = 2 2 α 2 2x+ x x Hsx (,, θ ) =, x 2 = πx sin θ 2 2E γ s H is radiation function Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 24

25 BaBar ISR: π + π π 0 huge discrepancy with DM2 SND BaBar DM2 all before BaBar 2.45 ± 0.26 ± 0.03 contribution to a μ had (>1.05 GeV) : all + BaBar 2.79 ± 0.19 ± 0.01 all DM2 + BaBar 3.25 ± 0.09 ± 0.01 x10 10 Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 25

26 BaBar ISR: 2π + 2π contribution to a μ had : all before BaBar ± 0.87 ± 0.24 all + BaBar ± 0.44 ± 0.00 Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 26

27 BaBar ISR: 3π + 3π BaBar contribution to a μ had : all before BaBar 0.10 ± 0.10 all + BaBar ± Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 27

28 BaBar ISR: 2π + 2π 2π 0 BaBar contribution to a μ had : all before BaBar 1.42 ± 0.30 ± 0.03 all + BaBar ± Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 28

29 Evaluating the Dispersion Integral use data use QCD Agreement between Data (BES) and pqcd (within correlated systematic errors) use QCD Better agreement between exclusive and inclusive (γγ2) data than in analyses Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 29

30 Contributions to a μ had [in ] from the different energy domains Modes Energy [GeV] e + e τ Low s expansion 2m π ± 1.7 ± 1.2 rad 56.0 ± 1.6 ± 0.3 SU(2) π + π (+SND+CMD2) 2m π ± 3.7 ± 0.8 rad ± 3.0 ± 2.3 SU(2) π + π (same +KLOE) 2m π 1.8 [450.4 ± 3.0 ± 0.8 rad ] π + π 2π 0 2m π ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2π + 2π (+BaBar) 2m π ± 0.4 ± 0.0 rad 12.3 ± 1.0 ± 0.4 SU(2) ω (782) ± 1.0 ± 0.3 rad φ (1020) Other excl. (+BaBar) ± 0.8 ± 0.2 rad 2m π ± 1.3 ± 0.2 rad J/ψ, ψ (2S) ± 0.4 ± 0.0 rad R [QCD] ± 0.5 theo R [data] ± 0.3 ± 0.0 rad R [QCD] ± 0.2 theo Sum (w/o KLOE) 2m π ± 5.0 ± 2.6 rad ± 5.0 ± 0.7 rad ±2.8 SU(2) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 30

Update for Lepton Moments (Preliminary) a μ had [ee] = (692.9 ± 5.0 ± 2.6) 10 10 a μ [ee] = (11 659 182.6 ± 5.6 had ± 3.5 LBL ± 0.

31 Update for Lepton Moments (Preliminary) a μ had [ee] = (692.9 ± 5.0 ± 2.6) a μ [ee] = ( ± 5.6 had ± 3.5 LBL ± 0.2 QED+EW ) including: Hadronic contribution from higher order : a μ had [(α/π) 3 ] = (9.8± 0.1) Hadronic contribution from LBL scattering: a μ had [LBL] = + (12.0 ± 3.5) Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) Melnikov-Vainshtein, hep-ph/ Davier-Marciano, Ann. Rev. Nucl. Part. Sc. (2004) BNL E821 (2004): a μ exp = ( ± 5.8) Observed Difference with Experiment: a μ [exp] a μ [SM] = (25.4 ± 8.8) standard deviations Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 31

32 Conclusions Hadronic vacuum polarization is dominant systematics for SM prediction of the muon g 2 Revised ππ data from SND in agreement with CMD-2 KLOE? Discrepancy with τ data (ALEPH & CLEO & OPAL) confirmed Final result from BELLE awaited Until τ /e + e puzzle is solved (interesting by itself), use only e + e data in dispersion integral SM prediction differs by 2.9 σ [e + e ] from experiment (BNL 2004) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 32

33 Perspectives Future experimental input expected from: More π + π CMD-2 data available (larger statistics but worse systematic error) New KLOE analysis with tagged photon in detector (μμγ?) BABAR ISR: in progress π + π spectral function from threshold to 4 5 GeV obtained from ππγ / μμγ K + K π + π 2π 0, KKπ : important channels π + π 3π 0, 2π + 2π π 0, KKππ also an inclusive analysis, but not suited to g-2 (photon resolution) α(m Z2 ) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 33

34 Guesses Expected accuracy over the next years: ππ uncertainty will still dominate for a while (2003) (2006) + BaBar +KLOE? 2.5 (2007) more exclusive analyses from BaBar ISR also should use ratio to μμγ to reduce common syst) guess Δa μ had improvement 7.2 (2003) 5.6 (2006) 3.6 (2007) 2.6 (2009) match to E-869 goal ( ) should provide impetus for theorists to improve LBL contribution (3.5?) Lepton Moments, Cape Cod, June 19-22, 2006 M. Davier Hadronic Contribution to (g 2) μ 34

The Muon g 2 Challenging e+e and Tau Spectral Functions

The Muon g 2 Challenging e+e and Tau Spectral Functions γ The Muon g 2 Chenging e+e and Tau Spectral Functions Andreas Hoecker(*) (CERN) Moriond QCD and High Energy Interactions, La Thuile, Italy, 8 15 March, 2008 γ γ hadrons μ A. Hoecker: Muon g 2: Tau and