1. Vacuum Polarization and the impact of BaBar data
Vacuum Polarization and the impact of BaBar data
Michel Davier
Laboratoire de l’Accélérateur Linéaire, Orsay
QWG Workshop 2007
October , 2007, DESY   
hadrons

2. 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. ”Dispersion relation“
The Muonic (g –2)
Contributions to the Standard Model (SM) Prediction:
Source
(a)
Reference
QED
~ 0.1  10–10
[Schwinger ’48 &others (Kinoshita)]
Hadrons
~ (154  3.5)  10–10
[Eidelman-Jegerlehner ’95 & others]
Z, W exchange
~ 0.2  10–10
[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 integral2
3 (+,) 4
> 4 (+KK)
(+J/, )
(+)
12 - 
< 1.8 GeV
ahad,LO 2
 2[ahad,LO] 2

5. Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585
Improved Determinations of the Hadronic Contribution to (g –2) and  (MZ ) 2
Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585
Energy [GeV]
Input 1995
Input after 1998
2m - 1.8
Data
Data (e+e– & ) (+ QCD)
1.8 – J/
QCD
J/ - 
Data + QCD
 - 40
40 - 
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-Höcker’97, Narison’01, Trocóniz-Ynduráin’01, + later works
Extended use of (dominantly) perturbative QCD
Martin-Zeppenfeld’95, Davier-Höcker’97, Kühn-Steinhauser’98, Erler’98, + others
Improvement in 4 Steps:
Theoretical constraints from QCD sum rules and use of Adler function
Groote-Körner-Schilcher-Nasrallah’98, Davier-Höcker’98, Martin-Outhwaite-Ryskin’00, Cvetič-Lee-Schmidt’01, Jegerlehner et al’00, Dorokhov’04 + others
Better data for the e+e–   + – cross section and multihadron channels
CMD-2’02 (revised 03), KLOE’04, SND’05 (revised 06), CMD-2’06, BaBar’04-06

6. Goals of the BaBar ISR Program
Precise measurements of cross section for all significant processes, e+e hadrons, from threshold to ~4-5GeV
Measure , KK channels with high precision
Summing up exclusive cross sections ==>Improve the precision of R
Study spectroscopy of JPC=1−− states and their decays
M. Davier et al., 2003 Ös

7. 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 Ecm<1.4 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
ISR
H is radiation function

8. BaBar ISR: e+ehadrons
Reactions for which results have been published :
pp PRD 73, (2006)
p+p-p PRD 70, (2004)
2p+2p-, K+K- p+p-, PRD 71, (2005)
K+K- p+p- K+K- p0p0 , 2K+2K PRD 76, (2007)
3p+3p-, 2p+2p-p0p0, K+K-2p+2p PRD 73, (2006)
New results presented last Summer :
K+Kp0, KSKp+, K+Kh, BaBar Preliminary
LL , LS0 , S0S0
submitted to PRD e-Print: arXiv:  [hep-ex]
+pp BaBar Preliminary
2p+2pp0,2p+2ph, KK p+pp0, KKp+ph
accepted by PRD e-Print: arXiv:  [hep-ex]
Work in progress on :
, K+K, p+p3p0
Inclusive R

9. BaBar ISR:  errors include systematics huge discrepancy with DM2
SND
BaBar
DM2
contribution to ahad ( GeV) :
all before BaBar  0.26  0.03
all + BaBar  0.19  0.01
all – DM2 + BaBar  0.09  0.01
x1010

10. BaBar ISR: 22 contribution to ahad (<1.8 GeV) :
all before BaBar  0.87  0.24
all + BaBar  0.44  0.00
x1010

11. BaBar ISR: 33 BaBar contribution to ahad (<1.8 GeV) :
all before BaBar  0.10
all + BaBar  0.016
x1010

12. BaBar ISR: 222 BaBar contribution to ahad (<1.8 GeV) :
all before BaBar  0.30  0.03
all + BaBar  0.093
x1010

13. Only statistical errors plotted
BaBar ISR: +00
Only statistical errors plotted
BaBar
preliminary
ψ ->p0p0J/ψ(->mm)
J/ψ
Previous situation chaotic
Preliminary syst. error: 8% in peak 5%
Good agreement with SND <1.4 GeV
Huge improvement >1.4 GeV
First measurement >2.5 GeV

14. BaBar ISR: +00  --substructure
Intermediate states:
0
+- large and first seen
0 f0(980)
a1(1260)
BaBar
preliminary MC

15. BaBar ISR: ++0 Cross sections of sub-mode: +-  0 
X =  3 + 0 3 : from subtraction /+-

0
3

16. BaBar ISR: +p- BaBar,3 1.35  0.03 0.45  0.14 1.66  0.01
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

17. BaBar ISR: p+-+p- ~4,300 events selected first measurement BaBar
preliminary

18. BaBar ISR: KSK , K+K-p
Dominant states:
K*(980)K and
K2*(1430)K
K+K-p
Isoscalar channel dominates
over isovector
Parameters (1680): PDG
m=172320 MeV, 20
 = 37175 MeV, 50
ee= 58060 eV,
B/BK*K 1/3

19. BaBar ISR: KK , K+K-pp
Substructure in the final state
K*(892) - 1 per event
K+K-0 p0
K+K-0 p0
K1(1270),K1(1400) – 1+
K+K-p+ p-
~ 1500

20. BaBar ISR:KKKK,KKppp,KKpp
jK+K- dominated
J/Y
K+K-+p-p
K+K-+p-
First measurement !

21. BaBar ISR: KKpppp
Cross section
Substructures
K*0(892) j
J/y
first measurement

22. 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, K+K-, KSKL, KSKL, KSK+ -0
remain to be measured

23. 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 analyses
use QCD

24. Update for ICHEP-Tau06 BNL E821 (2004):
ahad [ee ] =
(690.9 ± 4.4)  10 –10
a [ee ]
( ± 4.4had ± 3.5LBL ± 0.2QED+EW)  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 ( ± 0.1)  10 –10
inclu-ding:
Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002)
Melnikov-Vainshtein, hep-ph/
Davier-Marciano, Ann. Rev. Nucl. Part. Sc. (2004)
Kinoshita-Nio (2006)
BNL E821 (2004):
aexp = (  6.3) 10 10
Observed Difference with Experiment (DEHZ)
a [exp ] – a [SM ] =
(27.5 ± 8.4)  10 –10
 3.3 „standard deviations“

25. 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  [e+e – ] 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)