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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. The “Problem”. QED. Hadronic. Weak. SUSY. The Muon Anomalous Magnetic Moment.

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Hadrons

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


Hadrons

The “Problem”

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


Hadrons

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


Hadrons

Experimental Progress: from CERN to BNL

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

 Current world average:aexp=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


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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


Hadrons

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


Hadrons

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


Hadrons

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


Hadrons

Contributions to the Dispersion Integrals

2

3 (+,)

4

> 4 (+KK)

1.8 - 3.7

3.7 - 5 (+J/, )

5 - 12 (+)

12 - 

< 1.8 GeV

ahad,LO

2

2[ahad,LO]

2

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


Hadrons

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


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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


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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)

  • 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


Hadrons

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


Hadrons

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


Hadrons

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


Hadrons

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 vectorspectral 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


Hadrons

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


Hadrons

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


Hadrons

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


Hadrons

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


Hadrons

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

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


Hadrons

And the Complete Result

DEHZ (Tau 2006)

BNL E821 (2004):

aexp = (11 659 208.0  6.3) 1010

Observed Difference with Experiment:

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


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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


Hadrons

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  – 1010–10

  • 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


Hadrons

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


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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 section0 at low c.m. energieswith BABAR

  • Comprehensive program at BABAR

  • Results for +0, preliminary results for 2+2, K+K+, 2K+2Kfrom 89.3 fb–1

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


Hadrons

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 ahad (<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


Hadrons

The e+e–2+2– Cross Section

Good agreement with direct ee measurements

Most precise result above 1.4 GeV

contribution to ahad (<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


Hadrons

BaBar ISR: 33

BABAR

BABAR

contribution to ahad (<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


Hadrons

BABAR ISR: 222

BABAR

BABAR

contribution to ahad (<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


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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


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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


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