1 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2) hadrons The Hadronic Contribution to (g – 2) Michel Davier

Tau Workshop, Nara, Sept 14-17, 2004 M. Davier – Hadronic Contribution to (g – 2) 1

hadrons

The Hadronic Contribution to (g – 2)

Michel Davier

Laboratoire de l’Accélérateur Linéaire, Orsay

Tau Workshop 2004

September 14 - 17, 2004, Nara, Japan

[email protected]


Magnetic Anomaly

2

aie

e qm Schwinger 1948 QED Prediction:

Computed up to 4th order [Kinoshita et al.] (5th order estimated)

10

1

11614098.1 41321.810

3014.2 38.2 0.6

nQED

n

a

QED

QED Hadronic Weak SUSY... ... or other new physics ?

0.0011612

a


Why Do We Need to Know it so Precisely?

BNL (2004)

Experimental progress on precision of (g –2)

Outperforms theory pre-cision on hadronic contribution


The Muonic (g –2)

Contributions to the Standard Model (SM) Prediction: ha weakQED d2

2

ga aaa

Source (a) Reference

QED ~ 0.3 10–10 [Schwinger ’48 & others]

Hadrons ~ (15 4) 10–10 [Eidelman-Jegerlehner ’95 & others]

Z, W exchange ~ 0.4 10–10 [Czarnecki et al. ‘95 & others]Th

e S

itu

ati

on

19

95

2

2had

24

( )

( )3

m

a R sK

ss

ds

”Dispersion relation“

had

had

...

Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but: we can use experiment (!)


Hadronic Vacuum Polarization

Define: photon vacuum polarization function (q2) †4 2 2

em em 0 ( ) ( ) 0 ( )iqxi d x e TJ x J x g q q q q

Ward identities: only vacuum polarization modifies electron charge

(0)( )

1 ( )s

s

( ) 4 Re ( ) (0)s s 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) ...

(0)

(0)

[ hadrons]12 Im ( ) ( )

[ ]e e

s R se e

2(0)Born: ( ) ( ) / ( )s s s

Im[ ] | hadrons |2

... and the subtracted dispersion relation of (q2) (analyticity)

0

Im ( )( ) (0)

( )

sss ds

s s s i

had

0

( )( ) Re

3 ( )s R s

s dss s s i

... and equivalently for a [had]


Improved Determination of the Hadronic Contribution to (g –2) and (MZ )22

Energy [GeV] Input 1995 Input after 1998

2m - 1.8 Data Data (e+e– & ) + QCD

1.8 – J/ Data QCD

J/ - Data Data + QCD

- 40 Data QCD

40 - QCD QCD

Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585

Imp

rove

men

t in

4 S

tep

s:

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

Extended use of (dominantly) perturbative QCD

Theoretical constraints from QCD sum rules and use of Adler function

Alemany-Davier-Höcker’97, Narison’01, Trocóniz-Ynduráin’01, + later works

Martin-Zeppenfeld’95, Davier-Höcker’97, Kühn-Steinhauser’98, Erler’98, + others

Groote-Körner-Schilcher-Nasrallah’98, Davier-Höcker’98, Martin-Outhwaite-Ryskin’00, Cvetič-Lee-Schmidt’01, Jegerlehner et al’00, Dorokhov’04 + others

Since then: Improved determi-nation of the dispersion integral:

better data

extended use of QCD

Better data for the e+e– + – cross section

CMD-2’02, KLOE’04


The Role of Data through CVC – SU(2)

hadrons

W hadrons

e+

e –

CVC: I =1 & V W: I =1 & V,A : I =0,1 & V

Hadronic physics factorizes in Spectral Functions :

Isospin symmetry connects I=1 e+e– cross section to vector spectral functions:

2( 1) 04I e e

s

0

0

2

22

0

2

0 BR

1 / 1

1

/

BR e

dN

N d

m

ms me s s

branching fractions mass spectrum kinematic factor (PS)

fundamental ingredient relating long distance (resonances) to short distance description (QCD)


SU(2) Breaking

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)(1+2Q)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 – m0 leads to phase space (cross sec.) and width (FF) corrections

- mixing (EM – + decay) corrected using FF model

intrinsic m – m0 and – 0 [not corrected !]

Electromagnetic decays, like: , , , l+l –

Quark mass difference mu md generating “second class currents” (negligible)

Electromagnetism does not respect isospin and hence we have to consider isospin breaking when dealing with an experimental precision of 0.5%

Cirigliano-Ecker-Neufeld’ 02

Marciano-Sirlin’ 88

Braaten-Li’ 90

Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01


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


e+e – Radiative Corrections

Multiple radiative corrections are applied on measured e+e – 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.)

Final state radiation (FSR) [we need e+e

– 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

Initial state radiation (ISR)

corrected by experiments


2002/2003 Analyses of ahad

Motivation for new work:

New high precision e+e – 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 Cirigliano-Ecker-NeufeldJHEP 0208 (2002) 002

ALEPH CONF 2002-19

CMD-2 PL B527, 161 (2002)

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-ZhangEur.Phys.J. C27 (2003) 497; C31 (2003) 503

BES PRL 84 594 (2000); PRL 88,

101802 (2002)

Hagiwara-Martin-Nomura-Teubner, Phys.Rev. D69 (2004) 093003 (no data)

Jegerlehner, hep-ph/0312372 (no data)


Comparing e+e– +

– and –

0

Remarkable agreement

But: not good enough...

...

Correct data for missing - mixing (taken from BW fit) and all other SU(2)-breaking sources


The Problem

zoom

Relative difference between and e+e – data:


– –

0: Comparing ALEPH, CLEO, OPAL

Good agreement observed between ALEPH and CLEO

ALEPH more precise at low s

CLEO better at high s

Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH).


Testing CVC

Infer branching fractions from e+e– data:

2

20

CVC 20

SU(2)-corrected(6 | |

BR kin( ) )m

ud EWV Sds s

ms

Difference: BR[ ] – BR[e+e – (CVC)]:

Mode ( – e+e –) „Sigma“

– – 0 + 0.94 ± 0.32 2.9

– – 3 0 – 0.08 ±

0.110.7

– 2 – + 0 + 0.91 ± 0.25 3.6

leaving out CMD-2 : B0 = (23.69 0.68) % (7.4 2.9) % relative discrepancy!


New Precise e+e –+

– Data from KLOE Using the „Radiative Return“

...

Overall: agreement with CMD-2

Some discrepancy on peak and above ...


The Problem (revisited)

Relative difference between and e+e – data:

zoom

No correction for ± –

0 mass (~ 2.3 ± 0.8 MeV) and width (~ 3 MeV) splitting applied

Jegerlehner, hep-ph/0312372Davier, hep-ex/0312064


Evaluating the Dispersion Integral

Better agreement between exclusive and inclusive (2) data than in 1997-1998 analyses

Agreement bet-ween Data (BES) and pQCD (within correlated systematic errors)

use QCD

use data

use QCD


Results: the Compilation (including KLOE) Contributions to a

had [in 10 –10] from the different energy domains:

Modes Energy [GeV] e+e –

Low s expansion 2m – 0.5 58.0 ± 1.7 ± 1.2rad 56.0 ± 1.6 ± 0.3SU(2)

[ + – (DEHZ’03) ] 2m – 1.8 [ 450.2 ± 4.9 ± 1.6rad ] 464.0 ± 3.0 ± 2.3SU(2)

+ – (incl. KLOE) 2m – 1.8 448.3 ± 4.1 ± 1.6rad –

+ – 20 2m – 1.8 16.8 ± 1.3 ± 0.2rad 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)

(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)


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


Preliminary Results

ahad [ee ] = (693.4 ± 5.3 ± 3.5) 10

–10

a [ee ] = (11 659 182.8 ± 6.3had ± 3.5LBL ± 0.3QED+EW) 10 –10

Hadronic contribution from higher order : ahad [(/)3] = – (10.0 ± 0.6) 10

–10

Hadronic contribution from LBL scattering: ahad [LBL] = + (12.0 ± 3.5) 10

–

10

inclu-ding:

a [exp ] – a [SM ] = (25.2 ± 9.2) 10 –10

2.7 „standard deviations“

Observed Difference with Experiment:

BNL E821 (2004):a

exp = (11 659 208.0 5.8) 10 10

Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802

Melnikov-Vainshtein, hep-ph/0312226 .0

not yet published

not yet published

preliminary

Davier-Marciano, to appear Ann. Rev. Nucl. Part. Sc.


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 / e+e – puzzle is solved, use only e+e

– data in dispersion integral

We find that the SM prediction differs by 2.7 [e+e – ] 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)

Documents

1 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2) hadrons The Hadronic Contribution to (g – 2) Michel Davier