Open problems in g-2 and related topics.

Size: px

Start display at page:

Download "Open problems in g-2 and related topics."

Dwayne Taylor
5 years ago
Views:

1 Open problems in g-2 and related topics. F. JEGERLEHNER DESY Zeuthen Humboldt-Universität zu Berlin Euridice Coll. Meeting, Feb 8-11, 2005, LNF, Frascati (Italy) supported by EU network EURIDICE

2 Outline of Talk: 1 Hadronic Light-by-Light 2 Isospin breaking: τ vs. e + e 3 CMD-2 vs. KLOE 4 Final state radiation of hadrons 5 4-loop QED 6 Outlook

3 1) The problem: (Experiment (BNL 2004)) a ± µ = (6) (Theory) Note: a ± µ = (7.3) a Exp µ a The µ = 25.3 ± σ δa Exp µ = δa HVP µ = ) The α(m Z ) problem: input for electroweak precision physics δα α δg µ G µ δm Z M Z δα(m Z ) α(m Z ) (present) δα(m Z ) α(m Z ) (ILC requirement)

4 1 Hadronic Light-by-Light scattering contribution Melnikov-Vainshtein improvement of EJLN/HGS approach: Hadronic light by light scattering a lbl µ = ( 80 ± 40) (Knecht & Nyffeler 02) a lbl µ = (136 ± 25) (Melnikov & Vainshtein 03) (Kinoshita et al., Bijnens et al.) shift by (12) (13) (3) π 0, η, η π ±, K ± q = (u, d, s,...) L.D. L.D. Low energy effective theory: e.g. ENJL S.D. MV and KN utilize the same model LMD+V form factor:

5 F πγ γ (q2 1, q2) 2 = 4π2 Fπ 2 q1q 2 2(q q2) 2 h 2 q1q h 5 (q1 2 + q2) 2 + (N c M1 4 M2 4 /4π 2 Fπ) 2, N c (q1 2 + M1 2 )(q1 2 + M2 2 )(q2 2 + M1 2 )(q2 2 + M2 2 ) where M 1 = 769 MeV, M 2 = 1465 MeV, h 5 = 6.93 GeV 4. with two modifications: form factor: undressed soft photon (non-renormalization of ABJ) h 2 = 0 ± 20 GeV 2 (KN) vs. h 2 = 10 GeV 2 (MV) fixed by twist 4 in OPE (1/q 4 ) π 0, η, η [π 0 ] a 1 [f 1, f1 ] π± pqcd/qpm tot HK 83(06) 1.7 [a 1-4.5(8.5) 10(11) 90(15) BPP 85(13) -4(3) [a 1 + f 0 ] -19(5) 21(3) 83(32) KN 83(12) 80(40) MV 114.5[76.5] 22[7] (25)

6 2 Isospin breaking: τ vs. e + e The iso-vector part of σ(e + e hadrons) may be calculated by a iso-spin rotation from τ decay spectra (to the extend that CVC is valid) τ ν τ e e + W d ū π π 0 ū u d ū γ π π + u d τ X ν τ e + e X 0 X and X 0 are hadronic states related by iso-spin rotation. The e + e cross section is then given by σ I=1 e + e X 0 = 4πα2 s v 1,X, in terms of the τ spectral function v 1. s Mτ

7 All kind of isospin breaking effects have to be taken into account!!! (V. Cirigliano, G. Ecker and H. Neufeld) After known isospin corrections: ( F π 2 [ee] F π 2 [τ]) / F π 2 [τ] τ Average preliminary CMD-2 Aug CMD OLYA DM1 ( F π 2 [ee] F π 2 [τ]) / F π 2 [τ] τ Average preliminary KLOE CMD-2 CMD OLYA DM s (GeV 2 ) s (GeV 2 ) Experimental problems?

8 Comparison of τ data: 2.5 ALEPH CLEO OPAL τ data may be not so easy; DELPHI, L3 could not measure τ spectral functions; ALEPH vs. OPAL no good agreement.

9 S. Ghozzi, F. J Fit data by same Gounaris-Sakurai formula: Only parameters differ in first place mass and width of ρ! Two parameter fit (crude) ALEP vs. CMD-2: m ρ = 2.7 ± 0.8 and Γ ρ = 1.3 ± 1.0 (S. Ghozzi, F. J.) [ m ρ = 3.1 ± 0.9 and Γ ρ = 2.3 ± 1.6] (M. Davier (Pisa)) Problem with theory: usual argument m 2 ρ = m2 π from a sum rule yields m ρ m ρ 0 = 1 2 m 2 π m ρ MeV!. Too large by factor 2! width?? A. Höcker at ICHEP Bejing August 2004: An empirical isospin-breaking correction of the ρ resonance lineshape (mass and width) improves but does not restore the agreement between the two data sets. It is a consequence of this confirmation that, until the CVC puzzle is solved, only e + e data should be used for the evaluation of the dispersion integral. Doing so, and including the KLOE data, we find that the Standard Model prediction of a µ differs from the experimental value by 2.7 standard deviations. W. Morse, BNL: Is the source of isospin breaking a charged Higgs exchange? Discusses how a charged Higgs propagator would modify the form factor in τ π π 0 ν τ decays.

10 Isospin breaking in τ decays via charged Higgs exchange Typically in 2HDM: Large one-loop RC (M. Krawzcyk, D. Temes) in leptonic τ decays see talk by M. Krawzcyk τ ν τ ν µ τ ν τ ν µ W H µ µ Large isopin violating H exchange in hadronic τ decays (W. Morse)? τ τ τ ν τ ν W π 0 H π 0 π π s R = Ψ W +Ψ H 2 Ψ W 2 Ψ 0 W Correctly normalized effect by far too small!

11 3 KLOE vs. CMD-2 Hadronic Cross Sections

12 Note on new KLOE result: see talk by S. Müller my old value: (5.15) (6.83) [8.56] subtract cmd2: (2.75) (2.59) [3.78] extended to KLOE range (4.35) (6.32) [7.67] KLOE: (0.52) (5.05) [5.08] KLOE range: MeV add weighted (1.14) (2.39) [2.65] my new value (4.50) (6.76) [8.12] Theory of Pion FF: unitarity, analyticity and χpt (G. Colangelo (Pisa)) P χ 2 /d.o.f. χ 2 CMD2/NA a ρ a 2MK r 2 (fm 2 ) / / ± ± ± / / ± ± ± / / ± ± ± / / ± ± ± / / ± ± ± Numerical results for fits to CMD-2 and (spacelike) NA7 data. The errors given are purely statistical. To be compared with: ± 4.95 (stat) from trapezoidal rule. Gain factor of 2 in precision in stat error!

13 4 Final state radiation of hadrons Remainder: Need 1pi blob in dispersion integrals: VP undressed cross-section F π F π F (0) π (s) 2 = F π (s) 2 (α/α(s)) 2 VP effects in physical quantities must include photonic corrections to the hadronic 1pi blob: had + had γ. + Add theoretical prediction for FS radiation (including full photon phase space): F (γ) π (s) 2 = F (0) π (s) 2 ( 1 + η(s) α π to order O(α), where η(s) is a known correction factor (Schwinger 1989 ). The )

14 corresponding O(α) contribution to the anomalous magnetic moment of the muon is δ γ a had µ = (38.6 ± 1.0) Final state radiation in electron positron annihilation into a pion pair (S. Dubinsky, A. Korchin, N. Merenkov, G. Pancheri, O. Shekhovtsova) talk by O. Shekhovtsova

15 5 4-loop QED Recent: Corrections due to internal e- and τ -loops updated a µ = a uni e + a µ (m µ /m e ) + a µ (m µ /m τ ) + a µ (m µ /m e, m µ /m τ ) ( α ) 2 ( α ) 3 a µ (m µ /m e ) = (98) (23) π π ( α ) (72) ( π a µ (m µ /m τ ) = (25) 10 5 α ) ( (21) 10 5 α ) 3 π π ( α ) (41) π ( a µ (m µ /m e, m µ /m τ ) = (17) 10 5 α π ( α ) (83) π ) 3 with α 1 (a.i.) = (10) [7.4 ppb] a QED µ = (0.03) (1.15) (0.85) }{{}}{{}}{{} α 4 α 5 α inp shift by Kinoshita, Nio 04

16 6 Outlook Most problematic region now GeV Contributions: ρ 72% rel. error 2.1 % contribution to final error 1.3% Region GeV: 20% rel. error contribution to final error 1%!

17 In progress : R from ISR: KLOE collect and analyze more data for ππ BABAR in progress R from scan: R from CLEO will resolve Mark I vs. CB discrepancy check soon, run at 7.0, 7.4, 8.4, and 10.3 GeV future plans: BEPCII/BESIII: run at 2.2, 2.6, 3.0 GeV at precision 5.5, 3.4, 3.4 % ([7.6, 7.0, 5.6] % now) VEPP-2000: GeV [ ] factor of 10 in Lumi, CMD-2,SND factor of 2 in precision GeV in progress For precision physics at an ILC, at least a τ charm factory is required 1% hadronic cross section measurements up to 3 GeV mandatory!

18 Previously unaccounted contributions?: e + e σγ, f 0 γ to a had µ (data very poor) δa S µ = 1.0(0.6)[13.0(11.0)] 10 10, i.e., +0.1[1]σ (Narison 03, Dubnikova et al) TH based[pdg based] δa µ ( GeV) < form ππγ, πηγ which include decay products from π 0 γ, σγ, fγ, a 1 γ (Eidelman 03) (A. Dubniĉková et al.) a µ (π 0 γ) = a µ (ηγ) = a µ (η γ) = a µ (σγ) = a µ (a 0 γ) = Controversial!

19 Theory: Radiative corrections for 1) Radiative return calculations: continuing progress Talks by J. Kühn and H. Czyz 2) Bhabha (small/wide) angle progress towards full two-loop: Dixon et al., Penin, Czakon et al. two-loop virtual + soft complete including collinear mass logs (Penin) two additional hard real photons exist (Jadach et al.) missing: one-loop + additional hard real photon I think in 1 year from now complete O(α 2 ) result available. However: at O(α) still 0.5% disagreement between existing calculations! Talk by F. Nguyen 3) µ + µ for normalization/cross check/event separation 4) Hadronic light-by-light?, FSR in hadro production? 4 loop QED? Check: in all calculations presently aimed precision requires e.g. check in your program proper treatment of vacuum polarization (VP) subtraction: now need time like α(s) in s channels: Bhabha: t channel α(t), s channel α(s)

20 Challenge for the future: new experiment under discussion, up to factor 10 improvement α(m Z ) for ILC factor 5 improvement required! The show will go on!

The role of σ hadronic. for future precision physics

The role of σ hadronic. for future precision physics The role of σ hadronic for future precision physics F. JEGERLEHNER DESY Zeuthen Humboldt-Universität zu Berlin Seminar, December 7, 2005, LNF, Fracsati (Italy) supported by EU projects TARI and EURIDICE