M pp 2 - INFN Roma

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
The current world average value:
a = 116592080 (60) £
-11
10
E 821 – PRL 92 (2004) 161802
0.5 parts per million !!
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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
i The Dirac theory predicts:
i QED predicts deviations
from the Dirac result:
i Study the photon – lepton vertex:
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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
with
MP ’05
 = 1/137.03599911 (46) [3.3 ppb] PDG’04
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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)
Comparing aeth() with aeexp = 0.0011596521883(42)
one gets:
-1 = 137.035 998 83 (50) [3.6 ppb]
versus
-1 = 137.036 000 10 (110) [7.7 ppb]
-1 = 137.035 999 11 (46) [3.3 ppb]
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’98 based on Van Dyck
Schwinberg and Dehmelt 1987
CODATA
Kinoshita & Nio ’05, MP ’05
Wicht et al. 2002
CODATA ’02 & PDG ’04
Check of QED at 4 loop level !
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Back to a: The Electroweak Contribution
i One-Loop Term:
1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa Lee, Sanda.
i One-Loop plus Higher-Order Terms:
aEW
= 154 (2) (1) x
10-11
Czarnecki, Krause, Marciano ’95; Knecht, Peris, Perrottet,
de Rafael ’02; Czarnecki, Marciano, Vainshtein ’02;
Degrassi, Giudice ’98; Heinemeyer, Stockinger, Weiglein ’04
Hadronic loop uncertainties:
Higgs mass, M_top error,
three-loop nonleading logs
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Hadronic contributions - I
Ups and downs of the e+ e- data…
Bouchiat & Michel 1961
i
e+ e- Data (CMD2 after 8-2003)
aHLO= 6934 (64) x 10-11
= 6948 (86) x 10-11
= 6934 (92) x 10-11
= 6924 (64) x 10-11
= 6944 (49) x 10-11
Hoecker
10-04
Jegerlehner
10-03
Ezhela et al.
1-05
Hagivara et al
12-03
Dec ’01
de Troconiz et al 2-04
• Are all Radiative Corr. under control
(Luminosity, ISR, Vac. Pol. and FSR) ??
Aug ’03
• 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).
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Hagiwara et al., PRD 69 (2004) 093003
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Hadronic contributions - II
i
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 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 r peak.
• Comparison in the range (0.37 < s < 0.93) GeV2:
a = (3786 § 27stat § 23sys+th) £ 10-11 CMD2 8/03 PLB578 (2004) 285
a = (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
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 tau spectral 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):
aHLO= 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 improvement
of the data (mostly CMD-2 and BES):
Dhad(5) (Mz2) =
0.02800 (70)
0.02761 (36)
0.02755 (23)
0.02758 (35)
Eidelman, Jegerlehner’95
Burkhardt, Pietrzyk 2001
Hagivara et al., 2004
Burkhardt, Pietrzyk 6-05
Hagivara et al., PRD69 (2004) 093003
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Higher-order Hadronic contributions
i Vacuum Polarization
O(3) contribution of diagrams containing
hadronic vacuum polarization insertions:
aHLO(vp) = -98 (1) x 10-11
Krause’96, Alemany et al.’98, Hagivara et al.’03
i Light-by-Light
The contribution of the O(3) hadronic light-by-light diagram had a troubled life. The
latest vales are:
aHLO(lbl) = + 80 (40) x 10-11
Knecht & Nyffeler 2002
aHLO(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.
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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:
[1]
[2]
[3]
[4]
[5]
[6]
A. Hoecker, October 2004
F. Jegerlehner, October 2003
Ezhela, Lugovsky, Zenin, January 2005
Hagivara, Martin, Nomura, Teubner, Dec 03
de Troconiz & Yndurain, February 2004
Davier, Eidelman, Hoecker, Zhang, Aug 03
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aHLO(lbl) = 80 (40) x 10-11
aHLO(lbl) = 136 (25) x 10-11
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Conclusions
iDiscrepancies (Exp-SM) range from
0.7 to 3.2 s (!) according to the values
chosen for the hadronic contributions.
(Exp-SM) » 2-3 s using e+e- data
(new SND-CMD2 results not included).
The future…
iThe 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...).
iFuture: 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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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
DF
Plotted is

- 1.
2
F
F (CMD-2 fit)
F (exp)
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 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)
sSND or CMD-2 / sKLOE - 1
KLOE vs. SND & CMD2: D. Leone@HEP’05
M2 (GeV2)
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