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

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

M. Passera 4-11-05 2

0.5 parts per million !!

a= 116592080 (60) £ 10-

11E 821 – PRL 92 (2004) 161802

The current world average value:


E821 Homepage


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


The Anomalous Magnetic Moment: Theory

QED predicts deviations from the Dirac result:

The Dirac theory predicts:

Study the photon – lepton vertex:


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


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 !


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


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…

M. Passera 4-11-05 10

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)

M. Passera 4-11-05 11

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

M. Passera 4-11-05 12

Hadronic contributions - IV

Davier, Hoecker, Zhang, hep-ph/0507078

M. Passera 4-11-05 13

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) (Mz

2) =

0.02800 (70) Eidelman, Jegerlehner’95

0.02761 (36) Burkhardt, Pietrzyk 2001

0.02755 (23) Hagivara et al., 2004

0.02758 (35) Burkhardt, Pietrzyk 6-05Hagivara et al., PRD69 (2004) 093003

M. Passera 4-11-05 14

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.

M. Passera 4-11-05 15

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

M. Passera 4-11-05 16

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!

M. Passera 4-11-05 17

The End

M. Passera 4-11-05 18

Backup Slides

M. Passera 4-11-05 19

R: current status (Logashenko@HEP’05)

VEPP-2M energy region

M. Passera 4-11-05 20

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

With SND data With KLOE data

2

2

(exp)FPlotted is 1.

F (CMD-2 fit)

F

F

M. Passera 4-11-05 21

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

Documents

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