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hadrons

The Muon g–2 Challenging

e+e– and Tau Spectral Functions

Andreas Hoecker(*) (CERN)

Moriond QCD and High Energy Interactions, La Thuile, Italy, 8 – 15 March, 2008

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

The “Problem”

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

QED

Hadronic

Weak

SUSY...

The Muon Anomalous Magnetic Moment

- Diagrams contributing to the magnetic moment

... or some unknown type of new physics ?

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Experimental Progress: from CERN to BNL

Miller-de Rafael-Roberts, Rept.Prog.Phys.70:795,2007 [ hep-ex/0602035]

Current world average:aexp=11 659 208.0 ± 5.4 ± 3.3 × 10–10

Dominated by by BNL-E821: [PRD73(06)072003, hep-ex/0602035]

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Confronting Experiment with Theory

The Standard Model prediction of a is decomposed in its main contributions:

of which the hadronic contribution has the largest uncertainty

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

had

Dispersion relation, uses unitarity (optical theorem) and analyticity

had

... (see digression)

The Hadronic Contribution to (g–2)

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

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

digression: Vacuum polarization … and the running of QED

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]

... and equivalently for a [had]

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Panoramic View of Inputs to Dispersion Integral

use data

Agreement between Data (BES) and pQCD (within correlated systematic errors)

QCD

use QCD

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Contributions to the Dispersion Integrals

2

3 (+,)

4

> 4 (+KK)

1.8 - 3.7

3.7 - 5 (+J/, )

5 - 12 (+)

12 -

< 1.8 GeV

ahad,LO

2

2[ahad,LO]

2

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

W e m u s t c o n c e n t r a t e o n 2 - p i o n C h a n n e l

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Overview of e+e– +–() Data

DEHZ preliminary update ICHEP 06

DEHZ 03

ISR

Novosibirsk & Orsay experiments:

Energy scan method

KLOE at DAΦNE:

Radiative return method

e+

hadrons

e

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

e+e– Radiative Corrections

Desired measured e+e– cross sections: with FSR included but ISR & VP corrected

- 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 procedure)

- Vacuum polarization (VP) in the photon propagator:

- Initial state radiation (ISR)
- corrected by experiments

- Final state radiation (FSR) [need e+e– hadrons () in disp. 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

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Comparing e+e– +–() Data

Green band corresponds to combined data used in the numerical integration

Good agreement in general – varying precision

Need to see ratio plots to

appreciate differences

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Comparison of Recent e+e– +–() Data

CMD2 & KLOE measurements compared to fit to SND data

CMD2 / SND

KLOE / SND

Relative systematic error of SND

Whereas CMD2 and SND are in good agreement, KLOE shows a significantly different energy dependence.

Needs clarification before using KLOE data

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

U s i n g a l s o T a u D a t a

v i a t h e c o n s e r v e d v e c t o r c u r r e n t

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Using also Tau Data through CVC – SU(2)

W: I=1 &V,A

CVC: I=1 &V

: I=0,1 &V

e+

hadrons

W

e–

hadrons

Hadronic physics factorizes inSpectral Functions :

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

Experimentally: and e+e– data are complementary with resp. to normalisation and shape uncertainties

branching fractionsmass spectrum kinematic factor (PS)

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

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%

- Radiative corrections:SEW ~ 2%(short distance), GEM(s) (long distance)
- Charged/neutral mass splitting: m – m 0, - mixing, m, – m,0
- Electromagnetic decays: , , , l+l –
- Quark mass difference: mu md negligible

Marciano-Sirlin’ 88

Braaten-Li’ 90

Cirigliano-Ecker-Neufeld’ 02

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

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Comparing e+e– +– and ––0

e+e– data corrected for vacuum polarisation and initial state radiation

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

Remarkable agreement

But: not good enough...

...

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

The Problem

Relative difference between and e+e– data (form factors)

z o o m

zoom

Clear difference on s dependence in particular for s at 0.7 – 1.0 GeV2

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Another Way to Look at the Data

Infer branching fractions (more robust than spectral functions) from e+e– data:

Difference: BR[ ] – BR[e+e– (CVC)]:

e+e– data for – + 0 0 not satisfactory

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

Results: the Compilation (including newest data) Contributions to ahad,LO[in 10–10]from the different energy domains:

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

And the Complete Result

DEHZ (Tau 2006)

BNL E821 (2004):

aexp = (11 659 208.0 6.3) 1010

Observed Difference with Experiment:

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

c o m m e n t s

a n d p e r s p e c t i v e s

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

c o m m e n t s

- Will the tau-based result still move ?
- Tau spectral functions unchanged: final results from ALEPH, CLEO, OPAL
- Waiting for final Belle results, BABAR forthcoming
- Revisiting SU(2)-breaking corrections:
- Improved long-distance correction GEM(s) [ vertex, not accounted for previously]
- → decays: large effects from soft/virtual ’s: (0 – ±) 1.8 MeV !
- Re-evaluation of expected effects from pion and rho mass and width differences; improved estimate of – mixing available
- [ Suggestion to compare “dressed” quantities did not enthuse theorists ]
- Expected improvements should reduce tau-based result by – 1010–10

- Improvements for e+e–:
- Awaiting BABAR’s ISR result, and normalised result from KLOE

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

a p p e n d i x (A)

t h e B A B A R I S R p r o g r a m m e

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

ISR

Rsdiative Return Cross Section Results from BABAR

- The Radiative Return: benefit from huge luminosities at B and Factories to perform continuous cross section measurements

H is radiation function

- High PEP-II luminosity at s = 10.58 GeV precise measurement of the e+e– cross section0 at low c.m. energieswith BABAR
- Comprehensive program at BABAR
- Results for +0, preliminary results for 2+2, K+K+, 2K+2Kfrom 89.3 fb–1

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

The e+e–+–0 Cross Section

- Cross section above resonance : DM2 missed a resonance !

compatible with (1650) [m 1.65 GeV, 0.22 GeV]

SND

BABAR

DM2

contribution to ahad (<1.8 GeV) :

- all before BABAR [10–10] 2.45 0.26 0.03
- all + BABAR [10–10] 2.79 0.19 0.01
- all + BABAR – DM2 [10–10] 3.25 0.09 0.01

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

The e+e–2+2– Cross Section

Good agreement with direct ee measurements

Most precise result above 1.4 GeV

contribution to ahad (<1.8 GeV)

- all before BABAR [10–10] 14.20 0.87 0.24
- all + BABAR [10–10] 13.09 0.44 0.00

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

BaBar ISR: 33

BABAR

BABAR

contribution to ahad (<1.8 GeV) :

- all before BABAR [10–10] 0.10 0.10
- all + BABAR [10–10]0.108 0.016

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

BABAR ISR: 222

BABAR

BABAR

contribution to ahad (<1.8 GeV) :

- all before BABAR [10–10] 1.42 0.30 0.03
- all + BABAR [10–10]0.89 0.09

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

a p p e n d i x (B)

P r e l i m i n a r y r e s u l t s f r o m B e l l e

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

digression: Preliminary – –0 Results from Belle

- Preliminary spectral function presented by Belle at EPS 2005
- High statistics: see significant dip at 2.4 GeV2 for first time in data !
- Discrepancies with ALEPH/CLEO at large mass and with e+e– data at low mass

A. Hoecker: Muon g – 2: Tau and e+e– spectral functions