Il g-2 del Muone nel Modello Standard

Massimo PasseraUniversità and INFN Padova

Road-Map INFN: Fisica e+e- a LNF Riunione 1: Milano, 4 Novembre 2005

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0.5 parts per million !!

a= 116592080 (60) £ 10-

11E 821 – PRL 92 (2004) 161802

The current world average value:

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E821 Homepage

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

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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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aQED = (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

aQED = 116584718.7 (0.3) (0.4) x 10-11

MP ’05

with= 1/137.03599911 (46) [3.3 ppb] PDG’04

Adding up I get:

The QED Contribution to a

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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)

The Electron g-2 and (the best determination of) Alpha

Comparing aeth() with ae

exp = 0.0011596521883(42)one gets:

CODATA ’98 based on Van Dyck Schwinberg and Dehmelt 1987

= 137.035 998 83 (50) [3.6 ppb] Kinoshita & Nio ’05, MP ’05 versus= 137.036 000 10 (110) [7.7 ppb] Wicht et al. 2002= 137.035 999 11 (46) [3.3 ppb] CODATA ’02 & PDG ’04

Check of QED at 4 loop level !

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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 10-

11

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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Hadronic contributions - I

e+ e- Data (CMD2 after 8-2003)

Bouchiat & Michel 1961

aHLO= 6934 (64) x 10-11 Hoecker 10-04

= 6948 (86) x 10-11 Jegerlehner 10-03 = 6934 (92) x 10-11 Ezhela et al. 1-05 = 6924 (64) x 10-11 Hagivara et al 12-03 = 6944 (49) x 10-11 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 HEP’05).

Dec ’01

Aug ’03

Hagiwara et al., PRD 69 (2004) 093003

Ups and downs of the e+ e- data…

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Hadronic contributions - II

e+ e- Data from Radiative Return (KLOE & BABAR)• KLOE: The collider operates at fixed energy but scan 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 a

HLO are similar. • SND’s new result (June ’05) is significantly higher than KLOE’s one above the peak.• Comparison in the range (0.37 < s< 0.93) GeV2:

a = (3786 § 27stat § 23sys+th) £ 10-11 CMD2 8/03 PLB578 (2004)

285a = (3756 § 8stat § 48sys+th) £ 10-11 KLOE Venanzoni@ ICHEP’04

a = (3856 § 52) £ 10-11 SND hep-ex/0506076

a = (3823 § 19stat § 31sys+th § 10calc) £ 10-11 New CMD2 Eidelman,

Logashenko (July 2005

Preliminary)

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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 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): aHLO= 7110 (58) x

10-11

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Hadronic contributions - IV

Davier, Hoecker, Zhang, hep-ph/0507078

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The Hadronic Contribution to (MZ2)

The effective fine-structure constant at the scale s is given by:

The light quarks part is determined by:

Progress due to significant improvementof the data (mostly CMD-2 and BES):had

(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

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Higher-order Hadronic contributions

Vacuum Polarization

Light-by-Light

aHLO(vp) = -98 (1) x 10-

11

aHLO(lbl) = + 80 (40) x 10-11 Knecht & Nyffeler

2002

aHLO(lbl) = +136 (25) x 10-11 Melnikov & Vainshtein

2003

O contribution of diagrams containinghadronic vacuum polarization insertions:

The contribution of the O hadronic light-by-light diagram had a troubled life. The latest vales are:

Krause’96, 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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Standard Model vs. Experiment

Adding up all the above contribution we get the following SM predictions for a and comparisons with the measured value:

aHLO(lbl) = 80 (40) x

10-11

aHLO(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

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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- datasets (CMD2, KLOE, SND). More workand 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 factorof 2 improvement is challenging but possible! The effort is certainly worth the opportunity to unveil (or constrain) “New Physics” effects!

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The End

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Backup Slides

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R: current status (Logashenko@HEP’05)

VEPP-2M energy region

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

With SND data With KLOE data

2

2

(exp)FPlotted is 1.F (CMD-2 fit)

FF

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M2 (GeV2)

SN

D o

r C

MD

-2 / K

LO

E -

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. Leone@HEP’05