Diapositive 1

1

?
The Hadronic Contribution to (g 2)?
Michel Davier Laboratoire de lAccélérateur
Linéaire, Orsay
Tau Workshop 2004 September 14 - 17, 2004, Nara,
Japan
?
?
?
hadrons
davier_at_lal.in2p3.fr
2
Magnetic Anomaly
QED
QED Prediction Computed up to 4th order
Kinoshita et al. (5th
order estimated)
Schwinger 1948
?
?
?
QED
Hadronic
Weak
SUSY...
... or other new physics ?
3
Why Do We Need to Know it so Precisely?
Experimental progress on precision of (g 2)?
Outperforms theory pre-cision on hadronic
contribution
BNL (2004)
4
The Muonic (g 2)?
Contributions to the Standard Model (SM)
Prediction
Source ?(a?) Reference
QED 0.3 ? 1010 Schwinger 48 others
Hadrons (15 ? 4) ? 1010 Eidelman-Jegerlehner 95 others
Z, W exchange 0.4 ? 1010 Czarnecki et al. 95 others
Dominant uncertainty from lowest order hadronic
piece. Cannot be calculated from QCD (first
principles) but we can use experiment (!)
The Situation 1995
had
?
Dispersion relation
?
had
?
?
...
5
Hadronic Vacuum Polarization
Define photon vacuum polarization function ??(q2)
Ward identities only vacuum polarization
modifies electron charge
with
Leptonic ??lep(s) calculable in QED. However,
quark loops are modified by long-distance
hadronic physics, cannot (yet) be calculated
within QCD (!)
Way out Optical Theorem (unitarity) ...
... and the subtracted dispersion relation of
??(q2) (analyticity)
Im ?
hadrons 2
... and equivalently for a? had
6
Improved Determination of the Hadronic
Contribution to (g 2)? and ? (MZ )
2
Energy GeV Input 1995 Input after 1998
2m? - 1.8 Data Data (ee ?) QCD
1.8 J/? Data QCD
J/? - ? Data Data QCD
? - 40 Data QCD
40 - ? QCD QCD
Eidelman-Jegerlehner95, Z.Phys. C67 (1995) 585

• Since then Improved determi-nation of the
  dispersion integral
• better data
• extended use of QCD

• Inclusion of precise ? data using SU(2) (CVC)

Alemany-Davier-Höcker97, Narison01,
Trocóniz-Ynduráin01, later works

• Extended use of (dominantly) perturbative QCD

Martin-Zeppenfeld95, Davier-Höcker97,
Kühn-Steinhauser98, Erler98, others
Improvement in 4 Steps

• Theoretical constraints from QCD sum rules and
  use of Adler function

Groote-Körner-Schilcher-Nasrallah98,
Davier-Höcker98, Martin-Outhwaite-Ryskin00,
Cvetic-Lee-Schmidt01, Jegerlehner et al00,
Dorokhov04 others

• Better data for the ee ? ? ? cross section

CMD-202, KLOE04
7
The Role of ? Data through CVC SU(2)
CVC I 1 V
W I 1 V,A
? I 0,1 V
??
e
?
?
hadrons
W
e
hadrons
Hadronic physics factorizes in Spectral Functions

fundamental ingredient relating long distance
(resonances) to short distance description (QCD)
Isospin symmetry connects I1 ee cross section
to vector? spectral functions
branching fractions mass spectrum
kinematic factor (PS)
8
SU(2) Breaking
Electromagnetism does not respect isospin and
hence we have to consider isospin breaking when
dealing with an experimental precision of 0.5

• Corrections for SU(2) breaking applied to ? data
  for dominant ? ? contrib.
• Electroweak radiative corrections
• dominant contribution from short distance
  correction SEW to effective 4-fermion coupling ?
  (1 3?(m?)/4?)(12?Q?)log(MZ /m?)
• subleading corrections calculated and small
• long distance radiative correction GEM(s)
  calculated add FSR to the bare cross
  section in order to obtain ? ? (?)
• Charged/neutral mass splitting
• m? ? m?0 leads to phase space (cross sec.)
  and width (FF) corrections
• ? -? mixing (EM ? ? ? ? decay) corrected
  using FF model
• intrinsic m? ? m?0 and ?? ? ??0 not
  corrected !
• Electromagnetic decays, like ? ? ? ? ?, ? ? ?
  ?, ? ? ? ?, ? ? ll
• Quark mass difference mu ? md generating
  second class currents (negligible)

Marciano-Sirlin 88
Braaten-Li 90
Cirigliano-Ecker-Neufeld 02
Alemany-Davier-Höcker 97, Czyz-Kühn 01
9
Mass Dependence of SU(2) Breaking
Multiplicative SU(2) corrections applied to ? ?
? ? 0?? spectral function
Only ? 3 and EW short-distance corrections
applied to 4? spectral functions
10
ee Radiative Corrections
Multiple radiative corrections are applied on
measured ee cross sections

• Situation often unclear whether or not and if -
  which corrections were applied
• Vacuum polarization (VP) in the photon
  propagator
• leptonic VP in general corrected for
• hadronic VP correction not applied, but for
  CMD-2 (in principle iterative proc.)

• Initial state radiation (ISR)
• corrected by experiments

• Final state radiation (FSR) we need ee ?
  hadrons (?) in disper-sion integral
• usually, experiments obtain bare cross section
  so that FSR has to be added by hand done for
  CMD-2, (supposedly) not done for others

11
2002/2003 Analyses of a?had

• Motivation for new work
• New high precision ee results (0.6 sys.
  error) around ? from CMD-2 (Novosibirsk)
• New ? results from ALEPH using full LEP1
  statistics
• New R results from BES between 2 and 5 GeV
• New theoretical analysis of SU(2) breaking

CMD-2 PL B527, 161 (2002)
ALEPH CONF 2002-19
BES PRL 84 594 (2000) PRL 88, 101802 (2002)
Cirigliano-Ecker-Neufeld JHEP 0208 (2002) 002

• Outline of the 2002/2003 analyses
• Include all new Novisibirsk (CMD-2, SND) and
  ALEPH data
• Apply (revisited) SU(2)-breaking corrections to
  ? data
• Identify application/non-application of
  radiative corrections
• Recompute all exclusive, inclusive and QCD
  contributions to dispersion integral revisit
  threshold contribution and resonances
• Results, comparisons, discussions...

Davier-Eidelman-Höcker-Zhang Eur.Phys.J. C27
(2003) 497 C31 (2003) 503
Hagiwara-Martin-Nomura-Teubner, Phys.Rev. D69
(2004) 093003 (no ? data)
Jegerlehner, hep-ph/0312372 (no ? data)
12
Comparing ee ? ? ? and ? ? ? ? 0??
Correct ? data for missing ? -? mixing (taken
from BW fit) and all other SU(2)-breaking sources
Remarkable agreement But not good enough...
...
13
The Problem
Relative difference between ? and ee data
zoom
14
? ? ? ? 0?? Comparing ALEPH, CLEO, OPAL
Shape comparison only. SFs normalized to WA
branching fraction (dominated by ALEPH).

• Good agreement observed between ALEPH and CLEO
• ALEPH more precise at low s
• CLEO better at high s

15
Testing CVC
Infer? branching fractions from ee data
Difference BR? BRee (CVC)
Mode ?(? ee ) Sigma
? ? ? ? 0 ?? 0.94 0.32 2.9
? ? ? 3? 0 ?? 0.08 0.11 0.7
? ? 2? ? ? 0 ?? 0.91 0.25 3.6
leaving out CMD-2 B??0 (23.69 ? 0.68)
? (7.4 ? 2.9) relative discrepancy!
16
New Precise ee ??? Data from KLOE
Using the Radiative Return
Overall agreement with CMD-2
Some discrepancy on ? peak and above ...
...
17
The Problem (revisited)
Relative difference between ? and ee data
zoom
No correction for ? ? 0 mass ( 2.3 0.8 MeV)
and width ( 3 MeV) splitting applied
Jegerlehner, hep-ph/0312372
Davier, hep-ex/0312064
18
Evaluating the Dispersion Integral
use data
Agreement bet-ween Data (BES) and pQCD (within
correlated systematic errors)
use QCD
Better agreement between exclusive and inclusive
(??2) data than in 1997-1998 analyses
use QCD
19
Results the Compilation (including KLOE)
Contributions to a?had in 10 10
from the different energy domains
Modes Energy GeV ee ee ?
Low s expansion 2m? 0.5 58.0 1.7 1.2rad 56.0 1.6 0.3SU(2) 56.0 1.6 0.3SU(2)
? ? (DEHZ03) 2m? 1.8 450.2 4.9 1.6rad 464.0 3.0 2.3SU(2) 464.0 3.0 2.3SU(2)
? ? (incl. KLOE) 2m? 1.8 448.3 4.1 1.6rad
? ? 2?0 2m? 1.8 16.8 1.3 0.2rad 21.4 1.3 0.6SU(2) 21.4 1.3 0.6SU(2)
2? 2? 2m? 1.8 14.2 0.9 0.2rad 12.3 1.0 0.4SU(2) 12.3 1.0 0.4SU(2)
? (782) 0.3 0.81 38.0 1.0 0.3rad
? (1020) 1.0 1.055 35.7 0.8 0.2rad
Other exclusive 2m? 1.8 24.0 1.5 0.3rad
J /?, ? (2S) 3.08 3.11 7.4 0.4 0.0rad
R QCD 1.8 3.7 33.9 0.5 0.0rad
R data 3.7 5.0 7.2 0.3 0.0rad
R QCD 5.0 ? 9.9 0.2theo
Sum (incl. KLOE) 2m? ? 693.4 5.3 3.5rad 711.0 5.0 0.8rad 2.8SU(2) 711.0 5.0 0.8rad 2.8SU(2)
20
Discussion

• The problem of the ? ? contribution
• Experimental situation
• new, precise KLOE results in approximate
  agreement with latest CMD-2 data
• ? data without m (? ) and ?(? ) corr. in
  strong disagreement with both data sets
• ALEPH, CLEO and OPAL ? spectral functions in
  good agreement within errors
• Concerning the remaining line shape discrepancy
  (0.7- 0.9 GeV2)
• SU(2) corrections basic contributions
  identified and stable since long overall
  correction applied to ? is ( 2.2 0.5) ,
  dominated by uncontroversial short distance
  piece additional long-distance corrections found
  to be small
• ? lineshape corrections cannot account for the
  difference above 0.7 GeV2

The fair agreement between KLOE and CMD-2
invalidates the use of ? data until a better
understanding of the discrepancies is achieved
21
Preliminary Results
a?had ee (693.4 5.3 3.5) ? 10 10
a? ee (11 659 182.8 6.3had 3.5LBL 0.3QEDEW) ? 10 10 (11 659 182.8 6.3had 3.5LBL 0.3QEDEW) ? 10 10
Hadronic contribution from higher order
a?had (?/?)3 (10.0 0.6) ? 10 10 Hadronic
contribution from LBL scattering a?had LBL
(12.0 3.5) ? 10 10
inclu-ding
Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802
Melnikov-Vainshtein, hep-ph/0312226
.0
Davier-Marciano, to appear Ann. Rev. Nucl. Part.
Sc.
BNL E821 (2004) a?exp (11 659 208.0 ? 5.8) 10
?10
not yet published
Observed Difference with Experiment
not yet published
a? exp a? SM (25.2 9.2) ? 10 10
? 2.7 standard deviations ? 2.7 standard deviations ? 2.7 standard deviations
preliminary
22
Conclusions and Perspectives

• Hadronic vacuum polarization is dominant
  systematics for SM prediction of the muon g 2
• New data from KLOE in fair agreement with CMD-2
  with a (mostly) independent technique
• Discrepancy with ? data (ALEPH CLEO OPAL)
  confirmed
• Until ? / ee puzzle is solved, use only ee
  data in dispersion integral
• We find that the SM prediction differs by 2.7 ?
  ee from experiment (BNL 2004)

• Future experimental input expected from
• New CMD-2 results forthcoming, especially at
  low and large ? ? masses
• BABAR ISR ? ? SF over full mass range,
  multihadron channels
  (2? 2? and ? ? ? 0 already available)