1

hadrons

Revisiting the Tau/ee Discrepancy:

Consequences for the Muon Anomaly Michel Davier

Laboratoire de l’Accélérateur Linéaire, Orsay

with A. Höcker (CERN), X.H. Mo, P. Wang, C.Z. Yuan (IHEP), Z. Zhang (LAL)Muon Magnetic Moment Workshop

October 25- 26, 2007, University of Glasgow

davier@lal.in2p3.fr

2

Improved Determinations 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, + 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 and multihadron channels

CMD-2’02 (revised 03), KLOE’04, SND’05 (revised 06), CMD-2’06, BaBar’04-06

3

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)

4

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

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

5

e+e- Data Comparison: 2006

problems: overall normalization

shape (especially above )

6

Requestioning the Procedure

• spectral functions unchanged

final ALEPH results (Phys. Rep. 2005)

CLEO, OPAL

still waiting for final Belle data; also BaBar coming

• how to relate and ee spectral functions

• revisit corrections for SU(2) violation

7

At What Level to Apply CVC? • ee V0 involves lowest-order -V0 coupling (bare )

+ vacuum polarization (VP) in photon propagator (dressed )

• question: should VP be included or not in the definition of the

V0 hadronic state?

• if V0 is a resonance, does the Breit-Wigner lineshape apply to

the bare or the dressed cross section?

• in our previous analyses we assumed that VP should be left out:

the V spectral function was related to the bare ee V0

cross section

• we now argue that it was incorrect: CVC should relate physical

(dressed) quantities, therefore one should use the dressed ee

8

Magnitude of the VP effect

(0)() 12 (1+FSR)

bare +FSR dressed VP FSR

at s = m2

leptonic VP 2.5%

hadronic VP 1 4%

mass shift from resonant VP:

mRmR(0) 3 Ree / 2

1.4 MeV for

9

Direct Test with J/ and ‘ Masses

• difference between dressed and bare masses: J/ 1.14 MeV

’ 0.50 MeV

• accurate measurements of dressed masses by KEDR: 0.01-0.025 MeV

• also measurements from pbar-p (FNAL/E760) (gluons exchange)

• compare pbar-p and e-e masses under 2 hypotheses for the ee masses

dressed ee masses mJ/ = -0.01 0.03 MeV

m’ = -0.13 0.10

bare ee masses mJ/ = +0.67 0.04

m’ = -0.99 0.10

• clearly favours dressed masses in ee annihilation

10

Testing the Non-resonant VP Effect

• non-resonant VP slowly varying across resonance no mass shift

• only way: compare partial widths (bare or dressed) to total width

• not possible with narrow ccbar/bbar: total width only accessible

through sum of partial widths,except FNAL, but not enough precision

• possible with but precision on leptonic width just at the limit

• best test so far: Z0 at LEP

(dressed) partial widths measured by peak cross sections

total (physical) width measured directly

invisible width consistent with 3 with 0.3% precision

if bare widths used: 3% discrepancy would show up

11

Test with 0 Mass Difference

• resonance wide: mass ill-determined, but mass difference OK

• 0 and ± accessible in ee annihilation and decays: perform

combined fit of spectral functions with free , ± parameters

but same for ’, ’’

m= m0m± = 2.4 ± 0.7 MeV bare ee

1.0 ± 0.7 MeV dressed ee

• also measured by KLOE in decays

0.4 ± 0.9 MeV

• theoretical estimate (mostly EM) Bijnens-Gosdzinsky

0.4 0.7 MeV

• both KLOE and theory favour ee dressed mass in ee/ fit

12

SU(2)-breaking Corrections Revisited (1)

• more precise value of Vud very small change

• better calculation of the long-distance radiative corrections GEM(s)

Lopez Castro et al. vertex, not accounted for in

previous calculation (PT, Cirigliano et al.)

• interference: better ee data, interference better determined

ee fit with 4 parameters: amplitude, phase, m, (last two in

agreement with PDG 3)

• m± m0 effect in cross section and (opposite effects)

• m± m still taken to be 0 ± 1 MeV, consistent with all results

use PT dependence for m3

3 / f2 (stronger effect)

13

SU(2)-breaking Corrections Revisited (2)

• main change: effect of EM decays on ±,

• decay modes

-- previously only calculation (Singer): hard bremsstrahlung

+ guess for divergent piece

-- new calculation just out (Lopez Castro et al.) hard + soft/

virtual finite result, much larger than estimated before

± = 1.83 MeV (0.4 MeV)

• as in all calculations of this type: photon coupling to mesons

point-like

14

SU(2)-breaking Corrections Revisited (3)

± ±

15

e+e- Data Comparison: 2007 (1)

agreement in overall normalization

shape much better

still not perfect (region around 950 MeV, but small impact)

16

e+e- Data Comparison: 2007 (2)

disagreement with KLOE reduced, but still strong

17

Integral #1 : BCVC Test

• integrating over the ee spectral function with the factor

+ correcting for the SU(2)-breaking effects compute BCVC

• compare to measured B() = (25.50 ± 0.10) %

• essentially insensitive to the shape of the spectral function

• BCVC computed using bare (before) or dressed (now) ee SF

bare ee SF (24.95 ± 0.19exp ± 0.12SU(2)) %

2.6 (was 4.5 with previous corrections)

dressed ee SF (25.57 ± 0.19exp ± 0.12SU(2)) %

in agreement with BR within 0.9% (± 0.24%)

18

Integral #2 : ahad,LO[,] (1010)

• update the based calculation of ahad,LO with new VP prescription

and new isospin-breaking corrections

• contribution threshold 1.8 GeV

501.0 ± 3.5exp ± 3.1SU(2) (was 520.1 in DEHZ03)

• VP correction also applied to 4 spectral functions

• also update ee contribution (published CMD-2 since Tau06)

502.5 ± 3.6exp ± 1.0rad good agreement / ee

• at last, justified to combine the 2 approaches

careful! only 77% of hadronic contribution is /ee independent,

remaining 23% comes only from ee (mainly I=0 component)

19

Comparison with BNL-E821

3.1

3.5

3.6

(hadVP)(LBL)(EW)

20

Conclusions (1)

Comparison of and ee spectral functions completely revisited

Previous basis relating bare ee SF to SF found invalid

CVC should apply between dressed (physical) quantities

Several tests performed, which confirm validity of new approach

physical masses of J/ and ’ are dressed, bare are excluded

sum of dressed partial widths is the physical total width (Z)

±/ mass difference favours the dressed mass in ee annihilation

VP correction is the largest change (10.0 units in a)

Isospin breaking corrections reconsidered

better knowledge of interference

long-distance radiative corrections more complete (2.9 units)

contribution to ±/ width difference includes now soft/virtual

part: the next largest change (5.2 units)

21

Conclusions (2)

Results from the new procedure

BCV now in agreement with the direct measurement within 0.9%

contributions to a from and ee (CMD-2+SND) agree within 1.2%

comparison with KLOE still problematic for the SF shape

Combined /ee prediction disagrees with BNL measurement by 3.6

Combined uncertainty for hadVP now at the level of error estimate for LBL

Total theory uncertainty (5.2) significantly smaller than experimental one (6.3)

A new more precise g-2 measurement is desperately needed, as present

precision will overshadow any progress on the theory side