Il g-2 del Muone nel Modello Standard

1. Il g-2 del Muone nel Modello Standard Massimo Passera Università and INFN Padova Road-Map INFN: Fisica e+e- a LNF Riunione 1: Milano, 4 Novembre 2005

2. a = 116592080 (60) £ 10-11 E 821 – PRL 92 (2004) 161802 The current world average value: 0.5 parts per million !!

3. E821 Homepage

4. a= (116592080 § 50stat§ 40sys) £ 10-11

5. The Anomalous Magnetic Moment: Theory i The Dirac theory predicts: i QED predicts deviations from the Dirac result: i Study the photon – lepton vertex:

6. The QED Contribution to a aQED = (1/2)(/) Schwinger 1948 + 0.765857410 (27) (/)2 Sommerfield, Petermann, Suura, Wichmann, Elend, MP ’04 + 24.05050964 (43) (/)3 Barbieri, Laporta, Remiddi, … , Czarnecki, Skrzypek, MP ’04 + 130.992 (8) (/)4 In progress Kinoshita & Lindquist ’81, … , Kinoshita & Nio July ’05 + 677 (40) (/)5 In progress Kinoshita et al. ‘90, Yelkhovsky, Milstein, Kataev, Starshenko, Broadhurst, Karshenboim, Laporta, Ellis et al., … , Kinoshita ’04 Adding up I get: aQED = 116584718.7 (0.3) (0.4) x 10-11 MP ’05 with a = 1/137.03599911 (46) [3.3 ppb] PDG’04

7. CODATA ’98 based on Van Dyck Schwinberg and Dehmelt 1987 Comparing aeth() with aeexp = 0.0011596521883(42) one gets: The Electron g-2 and (the best determination of) Alpha aeth = + (1/2)(/) - 0.328 478 444 002 90(60) (/)2 Schwinger 1948 Sommerfield, Petermann ’57, Suura, Wichmann ’57, Elend ’66, MP ’05 + 1.181 234 016 827 (19) (/)3 Barbieri, Laporta, Remiddi, … , Czarnecki, Skrzypek, MP ’05 - 1.7283 (35) (/)4 In progress Kinoshita & Lindquist ’81, … , Kinoshita & Nio July ’05 + 0.0 (3.8) (/)5 In progress (12672 mass-indep. diagrams!) Mohr & Taylor ’05 (CODATA 2002); Kinoshita & Nio,… in progress. + 1.671 (19) x 10-12 Hadronic Mohr & Taylor ’05 (CODATA 2002), Davier & Hoecker ’98, Krause ’97, Knecht ’03 + 0.0297 (5) x 10-12 Electroweak Mohr & Taylor ’05 (CODATA 2002) a-1= 137.035 998 83 (50) [3.6 ppb] Kinoshita & Nio ’05, MP ’05 versus a-1= 137.036 000 10 (110) [7.7 ppb] Wicht et al. 2002 -1= 137.035 999 11 (46) [3.3 ppb] CODATA ’02 & PDG ’04 Check of QED at 4 loop level !

8. i One-Loop plus Higher-Order Terms: Czarnecki, Krause, Marciano ’95; Knecht, Peris, Perrottet, de Rafael ’02; Czarnecki, Marciano, Vainshtein ’02; Degrassi, Giudice ’98; Heinemeyer, Stockinger, Weiglein ’04 aEW = 154 (2) (1) x 10-11 Hadronic loop uncertainties: Higgs mass, M_top error, three-loop nonleading logs Back to a: The Electroweak Contribution i One-Loop Term: 1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa Lee, Sanda.

9. Ups and downs of the e+ e- data… Dec ’01 Aug ’03 Hagiwara et al., PRD 69 (2004) 093003 Hadronic contributions - I Bouchiat & Michel 1961 i e+ e- Data (CMD2 after 8-2003) amHLO= 6934 (64) x 10-11Hoecker 10-04 =6948 (86) x 10-11Jegerlehner 10-03 = 6934 (92) x 10-11 Ezhela et al. 1-05 =6924 (64) x 10-11Hagivara et al 12-03 = 6944 (49) x 10-11de Troconiz et al 2-04 • Are all Radiative Corr. undercontrol • (Luminosity, ISR, Vac. Pol. and FSR) ?? • New CMD2p+p- data presented at HEP • in July agree well with their earlier ones. • New SNDp+p- data released in June: • some “hint of discrepancy” with the • CMD2p+p-data (See Logashenko atHEP’05).

10. Hadronic contributions - II i e+ e- Data from Radiative Return (KLOE & BABAR) • KLOE: The collider operates at fixed energy but sp can vary • continuously between upper and lower thresholds. This is • animportant independent method! • Some discrepancies between KLOE’s and CMD2’s results, • although their integrated contributions to amHLO are similar. • SND’snew result (June ’05) is significantly higher than • KLOE’sone above the r peak. • Comparison in the range (0.37 < sp< 0.93) GeV2: app= (3786 § 27stat§ 23sys+th) £ 10-11CMD2 8/03 PLB578 (2004) 285 app= (3756 § 8stat§ 48sys+th) £ 10-11KLOE Venanzoni@ ICHEP’04 app= (3856 § 52) £ 10-11 SND hep-ex/0506076 app= (3823 § 19stat§ 31sys+th § 10calc) £ 10-11NewCMD2 Eidelman, Logashenko (July 2005 Preliminary)

11. Hadronic contributions - III i Tau Data (ALEPH, CLEO, OPAL) • Significant discrepancy between t and CMD2 (8-2003) e+e- • data above»0.85 GeV. KLOE confirms this deviation. • ”The new SND result agrees with the cross-section • calculated from the tauspectral function data within the • accuracy of the measurements”(SND, hep-ex/0506076). • Inconsistencies in the e+e- or tau data? Are all possible • isospin-breaking effects properly taken into account?? • (Marciano & Sirlin 1988; Cirigliano, Ecker, Neufeld 2001-02, …) • Latest value(Davier,Eidelman, Hoecker, Zhang, August 2003): amHLO= 7110 (58) x 10-11

12. Hadronic contributions - IV Davier, Hoecker, Zhang, hep-ph/0507078

13. The Hadronic Contribution to a(MZ2) • The effective fine-structure constant at the scale s is given by: • The light quarks part is determined by: • Progress due to significant improvement • of the data (mostly CMD-2 and BES): Dahad(5) (Mz2)= 0.02800 (70) Eidelman, Jegerlehner’95 0.02761 (36) Burkhardt, Pietrzyk 2001 0.02755(23)Hagivara et al., 2004 0.02758 (35) Burkhardt, Pietrzyk 6-05 Hagivara et al., PRD69 (2004) 093003

14. i Vacuum Polarization i Light-by-Light Higher-order Hadronic contributions O(a3) contribution of diagrams containing hadronic vacuum polarization insertions: amHLO(vp)= -98 (1) x 10-11 Krause’96, Alemany et al.’98, Hagivara et al.’03 The contribution of the O(a3) hadronic light-by-light diagram had a troubled life. The latest vales are: amHLO(lbl)= + 80 (40) x 10-11Knecht & Nyffeler 2002 amHLO(lbl) = +136 (25) x 10-11 Melnikov & Vainshtein 2003 Hayakawa, Kinoshita 2001; Bijnens, Pallante, Prades 2001; Knecht, Nyffeler 2001, … This term is likely to become the ultimate limitation of the Standard Model prediction.

15. Standard Model vs. Experiment Adding up all the above contribution we get the following SM predictions for am and comparisons with the measured value: amHLO(lbl)= 80 (40) x 10-11 amHLO(lbl) = 136 (25) x 10-11 [1] A. Hoecker, October 2004 [2] F. Jegerlehner, October 2003 [3] Ezhela, Lugovsky, Zenin, January 2005 [4] Hagivara, Martin, Nomura, Teubner, Dec 03 [5] de Troconiz & Yndurain, February 2004 [6] Davier, Eidelman, Hoecker, Zhang, Aug 03

16. Conclusions i Discrepancies (Exp-SM) range from 0.7 to 3.2s (!) according to the values chosen for the hadronic contributions. (Exp-SM) » 2-3 susing e+e- data (new SND-CMD2 results not included). The e+e- vs tau puzzle is still unsolved. Unaccounted isospin viol. corrections? Also disagreements between e+e- data sets (CMD2, KLOE, SND). More work and data needed (BABAR, BELLE...). Future: QED and EW sectors ready for the E969 challenge. The Hadronic sector needs more work and future exp. results: VEPP-2000, LNF? A factor of 2 improvement is challenging but possible! The effort is certainly worth the opportunity to unveil (or constrain) “New Physics” effects! i i The future…

17. The End

18. Backup Slides

19. R: current status (Logashenko@HEP’05) VEPP-2M energy region

20. CMD2 vs. SND & KLOE: Logashenko@HEP’05 With SND data With KLOE data

21. sSND or CMD-2 / sKLOE - 1 Mpp2 (GeV2) KLOE vs. SND & CMD2: D. Leone@HEP’05 • above the r mass a significant difference btw SND and KLOE is out of discussion, but not btw CMD-2 and KLOE (at least within errors)