1 hadrons revisiting the tau/ee discrepancy: consequences for the muon anomaly michel davier...
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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
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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
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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)
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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
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e+e- Data Comparison: 2006
problems: overall normalization
shape (especially above )
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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
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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
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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
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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
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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
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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
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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)
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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
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SU(2)-breaking Corrections Revisited (3)
± ±
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e+e- Data Comparison: 2007 (1)
agreement in overall normalization
shape much better
still not perfect (region around 950 MeV, but small impact)
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e+e- Data Comparison: 2007 (2)
disagreement with KLOE reduced, but still strong
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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%)
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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)
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Comparison with BNL-E821
3.1
3.5
3.6
(hadVP)(LBL)(EW)
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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)
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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