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

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1 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 e+e spectral functions 1

2 The Problem A. Hoecker: Muon g 2: Tau and e+e spectral functions 2

3 The Muon Anomalous Magnetic Moment Diagrams contributing to the magnetic moment QED Hadronic Weak SUSY or some unknown type of new physics? 3

4 Experimental Progress: from CERN to BNL Miller-de Rafael-Roberts, Rept.Prog.Phys.70:795,2007 [ hep-ex/ ] Experiment Beam Measurement Columbia-Nevis ( 57) μ+ g = 2.00(0.10) Columbia-Nevis ( 59) μ (+16)( 12) CERN 1 ( 61) μ+ CERN 1 ( 62) δaμ/aμ Required th. terms g=2 12.4% α/π (22) 1.9% α/π μ (5) 0.43% (α/π)2 CERN 2 ( 68) μ (31) 265 ppm (α/π)3 CERN 3 ( 75) μ (27) 23 ppm (α/π)3 + had CERN 3 ( 79) μ (11) 7.3 ppm (α/π)3 + had BNL E821 ( 00) μ (59) 5 ppm (α/π)3 + had BNL E821 ( 01) μ (16) 1.3 ppm (α/π)4 + had + weak BNL E821 ( 02) μ (8) 0.7 ppm (α/π)4 + had + weak +? BNL E821 ( 04) μ (8)(3) 0.7 ppm (α/π)4 + had + weak +? Î Current world average: aμexp= Dominated by by BNL-E821: [PRD73(06)072003, hep-ex/ ] A. Hoecker: Muon g 2: Tau and e+e spectral functions 4

5 Confronting Experiment with Theory The Standard Model prediction of aμ is decomposed in its main contributions: g 2 aμsm = aμqed + aμhad + aμweak 2 μ of which the hadronic contribution has the largest uncertainty A. Hoecker: Muon g 2: Tau and e+e spectral functions 5

6 The Hadronic Contribution to (g 2) μ Source σ (a μ ) a = a + a + a SM QED had weak μ μ μ μ h a d γ QED Hadrons Z, W exchange ~ ~ (5 4) ~ Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD ( first principles ) but: we can use experiment (!) γ had γ μ a had, LO μ 2 α = 2 3π 4m 2 π ds K( s) s R( s) Dispersion relation, uses unitarity (optical theorem) and analyticity... (see digression) 6

7 digression: Vacuum polarization and the running of α QED 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 (0) 0 = g q q q γ ( q ) Ward identities: only vacuum polarization modifies electron charge α(0) α( s) = with: Δ α( s) = 4παRe γ( s) γ(0) 1 Δ α( s) 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 αs R( s ) ( s) = Re ds 3 π s ( s s ) i ε 0... and equivalently for a μ [had]... and equivalently for a μ [had] 7

8 Panoramic View of Inputs to Dispersion Integral use use data data a had, LO μ 2 α = 2 3π 4m 2 π ( ) ds Ks ( ) s R s QCD Agreement between Data (BES) and pqcd (within correlated systematic errors) use use QCD QCD 8

9 Contributions to the Dispersion Integrals 2π 3π (+ω,φ) 4π > 4π (+KK) (+J/ψ, ψ) 5-12 (+ϒ) 12 - < 1.8 GeV a had,lo μ had,lo μ 5% 2% 1% 0% 12% 5% 3% 2π 92% 72% σσ 2 2 [a had,lo [a μ had,lo ] μ ] 1% 9% 4% 0% 0% 0% 92% 6% 2π 80% 9

10 W e m u s t c o n c e n t r a t e o n 2 - p i o n C h a n n e l 10

11 Overview of e + e π + π (γ) Data Experiment #measurements Energy range (GeV) σ(stat) σ(syst) DM1 ( 78) % 2.2% DEHZ preliminary update ICHEP 06 DEHZ 03 TOF ( 81) OLYA ( 79, 85) CMD ( 85) DM2 ( 89) CMD2 ( 03) KLOE (04) SND ( 06) CMD2 low ( 06) CMD2 rho ( 06) CMD2 high ( 06) % % % % % % % 4.5-7% % % 5% 4% 2% 12% 0.6% % % 0.7% 0.8% % γ ISR Novosibirsk & Orsay experiments: Energy scan method KLOE at DAΦNE: Radiative return method e + hadrons e 11

12 e + e Radiative Corrections Desired measured e + e cross sections: with FSR included but ISR & VP corrected 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 procedure) Initial state radiation (ISR) corrected by experiments Final state radiation (FSR) [need e + e hadrons (γ) in disp. integral] usuy, experiments obtain bare cross section so that FSR has to be added by hand ; done for CMD-2, (supposedly) not done for others 12

13 Comparing e + e π + π (γ) Data Green band corresponds to combined data used in the numerical integration Good agreement in general varying precision Need to see ratio plots to appreciate differences 13

14 Comparison of Recent e + e π + π (γ) Data CMD2 & KLOE measurements compared to fit to SND data CMD2 / SND KLOE / SND Relative systematic error of SND Whereas CMD2 and SND are in good agreement, KLOE shows a significantly different energy dependence. Needs clarification before using KLOE data 14

15 U s i n g a l s o T a u D a t a v i i a t h e c o n s e r v e d v e c t o r c u r r e n t 15

16 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 Experimenty: τ and e + e data are complementary with resp. to normalisation and shape uncertainties 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) 16

17 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% Radiative corrections: S EW ~ 2% (short distance), G EM (s) (long distance) Charged/neutral mass splitting: m π m π 0, ρ -ω mixing, m,γ ρ m,γ ρ 0 Electromagnetic decays: ρ ππγ, ρ πγ, ρ ηγ, ρ l + l Quark mass difference: m u m d negligible Marciano-Sirlin 88 Braaten-Li 90 Cirigliano-Ecker-Neufeld 02 Alemany-Davier-Höcker 97, Czyż-Kühn 01 17

18 Comparing e + e π + π and τ π π 0 ν τ e + e data corrected for vacuum polarisation and initial state radiation Correct τ data for missing ρ -ω mixing (taken from BW fit) and other SU(2)-breaking sources Remarkable agreement But: not good enough

19 The Problem Relative difference between τ and e + e data (form factors) z o o m zoom Clear difference on s dependence in particular for s at GeV 2 19

20 Another Way to Look at the Data Inferτ branching fractions (more robust than spectral functions) from e + e data: 2 m 0 6 π Vud SEW SU(2)-corrected BR CVC ( τ π π ντ ) = ds kin( s) υ ( s) 2 + ee m τ 0 2 τ 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 ) Sigma e + e data for π π + π 0 π 0 not satisfactory 20

21 Results: the Compilation (including newest data) Contributions to a μ had,lo [in ] from the different energy domains: Modes Energy [GeV] e + e τ Low s expansion 2m π rad SU(2) π + π (+SND+CMD-2) rad SU(2) π + π 2π 0 2m π rad SU(2) 2π + 2π (+) 2m π rad SU(2) ω (782) rad φ (1020) rad Other excl. (+) 2m π rad J/ψ, ψ (2S) rad R [QCD] theo R [data] rad R [QCD] theo Sum (w/o KLOE) 2m π rad 0.7 QCD rad 2.8 SU(2) 21

22 And the Complete Result a [ e e ] = ( ) 10 SM + 10 μ had,lo LBL QED+weak DEHZ (Tau 2006) BNL E821 (2004): a μ exp = ( ) Observed Difference with Experiment: a μ exp a μ SM = ( ) standard deviations 22

23 c o m m e n t s a n d p e r s p e c t i i v e s 23

24 c o m m e n t s Will the tau-based result still move? Tau spectral functions unchanged: final results from ALEPH, CLEO, OPAL Waiting for final Belle results, forthcoming Revisiting SU(2)-breaking corrections: Improved long-distance correction G EM (s) [ρωπ vertex, ω πγ not accounted for previously] ρ ππγ decays: large effects from soft/virtual γ s: ΔΓ(ρ 0 ρ ) 1.8 MeV! Re-evaluation of expected effects from pion and rho mass and width differences; improved estimate of ρ ω mixing available [ Suggestion to compare dressed quantities did not enthuse theorists ] Expected improvements should reduce tau-based result by Improvements for e + e : Awaiting s ISR result, and normalised result from KLOE 24

25 a p p e n d i x (A) t h e B A B A R I S R p r o g r a m m e 25

26 Rsdiative Return Cross Section Results from The Radiative Return: benefit from huge luminosities at B and φ Factories to perform continuous cross section measurements γ ISR dσ (, s x) dxd(cos ) ( ) θ σ0 θ = Hsx (,, ) s(1 x) 2 2 α 2 2x+ x x Hsx (,, θ ) =, x 2 = πx sin θ 2 2E γ s H is radiation function High PEP-II luminosity at s = GeV precise measurement of the e + e cross section σ 0 at low c.m. energies with Comprehensive program at Results for π + π π 0, preliminary results for 2π + 2π, K + K π + π, 2K + 2K from 89.3 fb 1 26

27 The e + e π + π π 0 Cross Section Cross section above φ resonance : DM2 missed a resonance! SND compatible compatible with with ω ω (1650) (1650) [m [m GeV, GeV, Γ Γ GeV] GeV] DM2 contribution to a μ had (<1.8 GeV) : before before [10 [10 10 ] ] [10 [10 10 ] ] DM2 DM2 [10 [10 10 ] ]

28 The e + e 2π + 2π Cross Section Good agreement with direct e + e measurements Most precise result above 1.4 GeV contribution to a μ had (<1.8 GeV) before before [10 [10 10 ] ] [10 [10 10 ] ]

29 BaBar ISR: 3π + 3π contribution to a μ had (<1.8 GeV) : before before [10 [10 10 ] ] [10 [10 10 ] ]

30 ISR: 2π + 2π 2π 0 contribution to a μ had (<1.8 GeV) : before before [10 [10 10 ] ] [10 [10 10 ] ]

31 a p p e n d i x (B) P r e l l i i m i i n a r y r e s u l l t s f r o m B e l l l l e 31

32 digression: Preliminary τ π π 0 ν τ Results from Belle Preliminary spectral function presented by Belle at EPS 2005 High statistics: see significant dip at 2.4 GeV 2 for first time in τ data! Discrepancies with ALEPH/CLEO at large mass and with e + e data at low mass 32