P1252428692BaSGl

1

?
Vacuum Polarization and the impact of BaBar data
Michel Davier Laboratoire de lAccélérateur
Linéaire, Orsay
QWG Workshop 2007 October 17 - 20, 2007, DESY
?
?
?
hadrons
davier_at_lal.in2p3.fr
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Essentials of Hadronic Vacuum Polarization
vacuum polarization modifies the interacting
electron charge
with
photon vacuum polarization function ??(q2)
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 subtracted dispersion relation for ??(q2)
(analyticity)
Im ?
hadrons 2
... and equivalently for a? had
3
The Muonic (g 2)?
Contributions to the Standard Model (SM)
Prediction
Source ?(a?) Reference
QED 0.1 ? 1010 Schwinger 48 others (Kinoshita)
Hadrons (15?4 ? 3.5) ? 1010 Eidelman-Jegerlehner 95 others
Z, W exchange 0.2 ? 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
?
?
...
4
Contributions to the dispersion integral
12 - ?
5 - 12 (?)
3.7 - 5 (J/?, ?)
1.8 - 3.7
4?
3? (?,?)
2?
gt 4? (KK)
lt 1.8 GeV
a?had,LO
2?
? 2a?had,LO
2?
5
Improved Determinations 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
  and multihadron channels

CMD-202 (revised 03), KLOE04, SND05 (revised
06), CMD-206, BaBar04-06
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Goals of the BaBar ISR Program

• Precise measurements of cross section for
  all significant processes, ee? ?hadrons, from
  threshold to 4-5GeV
• Measure ????, K?K? channels with high precision
• Summing up exclusive cross sections gtImprove
  the precision of R
• Study spectroscopy of JPC1-- states and their
  decays

M. Davier et al., 2003
Ös
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Exclusive Channels with BaBar ISR

• systematic program underway using ISR from ?(4S)
  energies, taking
• advantage of high luminosity (B-factory)
• statistics comparable to CMD-2/SND for Ecmlt1.4
  GeV, much better than
• DM1/DM2 above
• full energy range covered at the same time
• channels identified using particle ID and
  kinematic fitting
• systematic uncertainties at 5-10 level
• large acceptance for hadronic system (boosted
  opposite to ISR photon)

X 2E? /Ecm
H is radiation function
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BaBar ISR ee??hadrons

• Reactions for which results have been published
• pp
  PRD 73, 012005 (2006)
• pp-p0
  PRD 70, 072004
  (2004)
• 2p2p-, KK- pp-, PRD
  71, 052001 (2005)
• KK- pp- KK- p0p0 , 2K2K-
  PRD 76, 012008 (2007)
• 3p3p-, 2p2p-p0p0, KK-2p2p-
  PRD 73, 052003 (2006)
• New results presented last Summer
• KK?p0, KSK?p, KK?h,
  BaBar Preliminary
• LL , LS0 , S0S0
• 
  submitted to PRD e-Print arXiv0709.1988 hep-ex
  
• ???p?p??
  BaBar Preliminary
• 2p2p?p0,2p2p?h, KK pp?p0, KKpp?h
• 
  accepted by PRD e-Print arXiv0708.2461 hep-ex
  
• Work in progress on
• ????, KK?, pp?3p0
• Inclusive R

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BaBar ISR ??????
errors include systematics huge discrepancy with
DM2
SND
BaBar
DM2
contribution to a?had (1.05-1.8 GeV)

• all before BaBar 2.45 ? 0.26 ?
  0.03
• all BaBar 2.79 ? 0.19 ?
  0.01
• all DM2 BaBar 3.25 ? 0.09 ? 0.01

x10?10
10
BaBar ISR 2??2??
contribution to a?had (lt1.8 GeV)

• all before BaBar 14.20 ? 0.87 ?
  0.24
• all BaBar 13.09 ? 0.44 ?
  0.00

x10?10
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BaBar ISR 3??3??
BaBar
contribution to a?had (lt1.8 GeV)

• all before BaBar 0.10 ? 0.10
• all BaBar 0.108 ? 0.016

x10?10
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BaBar ISR 2??2??2??
BaBar
contribution to a?had (lt1.8 GeV)

• all before BaBar 1.42 ? 0.30 ?
  0.03
• all BaBar 0.890 ? 0.093

x10?10
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BaBar ISR ????0?0
Only statistical errors plotted
BaBar preliminary
? -gtp0p0J/?(-gtmm)
J/?

• Previous situation chaotic
• Preliminary syst. error 8 in peak 5
• Good agreement with SND lt1.4 GeV
• Huge improvement gt1.4 GeV
• First measurement gt2.5 GeV

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BaBar ISR ????0?0 ?--substructure?

• Intermediate states
• ??0
• ??- large and first seen
• ?0 f0(980)
• a1(1260)?

BaBar preliminary
MC
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BaBar ISR ???????0
Cross sections of sub-mode ???- ? ??0 ??? ?X
?? 3? ?0 3? from subtraction ???/???-
???
??0
?3?
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BaBar ISR ??p-?
BaBar preliminary
BaBar,3?
???
??
BaBar preliminary
?f0(980) 1st measurement
1.35 ? 0.03 0.45 ? 0.14 1.66 ? 0.01 0.22 ? 0.04
BaBar,3?
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BaBar ISR p?-?p-?

• 4,300 events selected
• first measurement

BaBar preliminary
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BaBar ISR KSK??? , KK-p?
KSK-?-
Dominant states K(980)K and K2(1430)K
KK-p?
Isoscalar channel dominates over isovector
Parameters ?(1680) PDG m1723?20 MeV,
1680?20 ? 371?75 MeV, 150?50 ?ee
580?60 eV, B??/BKK? 1/3
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BaBar ISR K?K????? , KK-p?p?
KK-p p-
Substructure in the final state
K(892) - 1 per event
KK-?0 p0
KK-?0 p0
K1(1270),K1(1400) 1
KK-p p-
1500
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BaBar ISRK?K?K?K?,K?K?p?p?p?,K?K?p?p??
KK- KK-
jKK- dominated
J/Y
KK-?p-p?
KK-?p-?
First measurement !
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BaBar ISR K?K?p?p?p?p?
Cross section
Substructures
K0(892)
j
J/y
first measurement
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Present BaBar Measurements
only statistical errors syst. 5-10
to obtain R in the energy range 1-2 GeV the
processes ??-, ??-3?0, ??-4?0, KK-, KSKL,
KSKL??, KSK ?-?0 remain to be measured
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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
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Update for ICHEP-Tau06
a?had ee (690.9 4.4) ? 10 10
a? ee (11 659 180.5 4.4had 3.5LBL 0.2QEDEW) ? 10 10 (11 659 180.5 4.4had 3.5LBL 0.2QEDEW) ? 10 10
Hadronic HO ( 9.8 0.1) ? 10
10 Hadronic LBL (12.0 3.5) ? 10
10 Electroweak (15.4 0.2) ? 10
10 QED (11 658 471.9 0.1) ? 10 10
inclu-ding
Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802
Melnikov-Vainshtein, hep-ph/0312226
Davier-Marciano, Ann. Rev. Nucl. Part. Sc.
(2004)
Kinoshita-Nio (2006)
BNL E821 (2004) a?exp (11 659 208.0 ? 6.3) 10
?10
Observed Difference with Experiment (DEHZ)
a? exp a? SM (27.5 8.4) ? 10 10
? 3.3 standard deviations ? 3.3 standard deviations ? 3.3 standard deviations
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Conclusions and Outlook

• Hadronic vacuum polarization is still the
  dominant systematics for SM prediction of the
  muon g 2
• Significant step in precision from new
  experimental input
• CMD-2 SND for 2?
  BaBar for multipion channels
• Precision of SM prediction (?5.6) now exceeds
  experimental precision (?6.3)
• SM prediction for a? differs by 3.3 ? ee
  from experiment (BNL 2004)
• In the next months many new results expected
• KLOE 2p (different
  analyses)
• BaBar 2p, 2K,
  remaining multihadrons in 1-2 GeV range
• VEPP-2000 in the longer
  run
• vacuum polarization calculations in line for the
  next challenges
• new g-2 measurements
• precision EW
  measurements (Tevatron, LHC, ILC)