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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

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M. Passera parts per million !! a = (60) £ E 821 – PRL 92 (2004) The current world average value:

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M. Passera E821 Homepage

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M. Passera a = ( § 50 stat § 40 sys ) £

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

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M. Passera a QED = (1/2)( / ) Schwinger (27) ( / ) 2 Sommerfield, Petermann, Suura, Wichmann, Elend, MP (43) ( / ) 3 Barbieri, Laporta, Remiddi, …, Czarnecki, Skrzypek, MP (8) ( / ) 4 In progress Kinoshita & Lindquist 81, …, Kinoshita & Nio July (40) ( / ) 5 In progress Kinoshita et al. 90, Yelkhovsky, Milstein, Kataev, Starshenko, Broadhurst, Karshenboim, Laporta, Ellis et al., …, Kinoshita 04 a QED = (0.3) (0.4) x MP 05 with = 1/ (46) [3.3 ppb] PDG04 Adding up I get: The QED Contribution to a

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M. Passera a e th = + (1/2)( / ) (60) ( / ) 2 Schwinger 1948 Sommerfield, Petermann 57, Suura, Wichmann 57, Elend 66, MP (19) ( / ) 3 Barbieri, Laporta, Remiddi, …, Czarnecki, Skrzypek, MP (35) ( / ) 4 In progress Kinoshita & Lindquist 81, …, Kinoshita & Nio July (3.8) ( / ) 5 In progress (12672 mass-indep. diagrams!) Mohr & Taylor 05 (CODATA 2002); Kinoshita & Nio,… in progress (19) x Hadronic Mohr & Taylor 05 (CODATA 2002), Davier & Hoecker 98, Krause 97, Knecht (5) x Electroweak Mohr & Taylor 05 (CODATA 2002) The Electron g-2 and (the best determination of) Alpha Comparing a e th ( ) with a e exp = (42) one gets: CODATA 98 based on Van Dyck Schwinberg and Dehmelt 1987 = (50) [3.6 ppb] Kinoshita & Nio 05, MP 05 versus = (110) [7.7 ppb] Wicht et al = (46) [3.3 ppb] CODATA 02 & PDG 04 Check of QED at 4 loop level !

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

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M. Passera Hadronic contributions - I e + e - Data (CMD2 after ) Bouchiat & Michel 1961 a HLO = 6934 (64) x Hoecker = 6948 (86) x Jegerlehner = 6934 (92) x Ezhela et al = 6924 (64) x Hagivara et al = 6944 (49) x de Troconiz et al 2-04 Are all Radiative Corr. under control (Luminosity, ISR, Vac. Pol. and FSR) ?? New CMD2 data presented at HEP in July agree well with their earlier ones. New SND data released in June: some hint of discrepancy with the CMD2 data (See Logashenko at HEP05). Dec 01 Aug 03 Hagiwara et al., PRD 69 (2004) Ups and downs of the e+ e- data…

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M. Passera Hadronic contributions - II e + e - Data from Radiative Return (KLOE & BABAR) KLOE: The collider operates at fixed energy but s can vary continuously between upper and lower thresholds This is an important independent method! Some discrepancies between KLOEs and CMD2s results, although their integrated contributions to a HLO are similar. SNDs new result (June 05) is significantly higher than KLOEs one above the peak. Comparison in the range (0.37 < s < 0.93) GeV 2 : a = (3786 § 27 stat § 23 sys+th ) £ CMD2 8/03 PLB578 (2004) 285 a = (3756 § 8 stat § 48 sys+th ) £ KLOE ICHEP04 a = (3856 § 52) £ SND hep-ex/ a = (3823 § 19 stat § 31 sys+th § 10 calc ) £ New CMD2 Eidelman, Logashenko (July 2005 Preliminary)

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M. Passera Hadronic contributions - III Tau Data (ALEPH, CLEO, OPAL) Significant discrepancy between 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 tau spectral function data within the accuracy of the measurements (SND, hep-ex/ ). Inconsistencies in the e + e - or tau data? Are all possible isospin-breaking effects properly taken into account?? (Marciano & Sirlin 1988; Cirigliano, Ecker, Neufeld , …) Latest value (Davier,Eidelman, Hoecker, Zhang, August 2003): a HLO = 7110 (58) x

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M. Passera Hadronic contributions - IV Davier, Hoecker, Zhang, hep-ph/

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M. Passera The Hadronic Contribution to (M Z 2 ) 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): had (5) (M z 2 ) = (70) Eidelman, Jegerlehner (36) Burkhardt, Pietrzyk (23) Hagivara et al., (35) Burkhardt, Pietrzyk 6-05 Hagivara et al., PRD69 (2004)

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M. Passera Higher-order Hadronic contributions Vacuum Polarization Light-by-Light a HLO (vp) = -98 (1) x a HLO (lbl) = + 80 (40) x Knecht & Nyffeler 2002 a HLO (lbl) = +136 (25) x Melnikov & Vainshtein 2003 O contribution of diagrams containing hadronic vacuum polarization insertions: The contribution of the O hadronic light-by-light diagram had a troubled life. The latest vales are: Krause96, Alemany et al.98, Hagivara et al.03 Hayakawa, Kinoshita 2001; Bijnens, Pallante, Prades 2001; Knecht, Nyffeler 2001, … This term is likely to become the ultimate limitation of the Standard Model prediction.

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M. Passera Standard Model vs. Experiment Adding up all the above contribution we get the following SM predictions for a and comparisons with the measured value: a HLO (lbl) = 80 (40) x a HLO (lbl) = 136 (25) x [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

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M. Passera Conclusions The future… Discrepancies (Exp-SM) range from 0.7 to 3.2 (!) according to the values chosen for the hadronic contributions. (Exp-SM) » 2-3 using 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!

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M. Passera The End

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M. Passera Backup Slides

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M. Passera R: current status VEPP-2M energy region

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M. Passera CMD2 vs. SND & KLOE: With SND data With KLOE data

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M. Passera M 2 (GeV 2 ) SND or CMD-2 / KLOE - 1 above the mass a significant difference btw SND and KLOE is out of discussion, but not btw CMD-2 and KLOE (at least within errors ) KLOE vs. SND & CMD2: D.

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