QWG07%20DESY - PowerPoint PPT Presentation

Title: QWG07%20DESY


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?
Revisiting the Tau/ee Discrepancy Consequences
for the Muon Anomaly
Michel Davier Laboratoire de lAccélérateur
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
?
?
?
hadrons
davier_at_lal.in2p3.fr
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Improved Determinations of the Hadronic
Contribution to (g 2)? and ? (MZ )
2
Energy GeV Input 1995 Input after 1998
2m? - 1.8 Data Data (ee ?) ( QCD)
1.8 J/? Data QCD
J/? - ? Data Data QCD
? - 40 Data QCD
40 - ? QCD QCD
Eidelman-Jegerlehner95, Z.Phys. C67 (1995) 585

• Since then Improved determi-nation of the
  dispersion integral
• better data
• extended use of QCD

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

Alemany-Davier-Höcker97, later works

• Extended use of (dominantly) perturbative QCD

Martin-Zeppenfeld95, Davier-Höcker97,
Kühn-Steinhauser98, Erler98, others
Improvement in 4 Steps

• Theoretical constraints from QCD sum rules and
  use of Adler function

Groote-Körner-Schilcher-Nasrallah98,
Davier-Höcker98, Martin-Outhwaite-Ryskin00,
Cvetic-Lee-Schmidt01, Jegerlehner et al00,
Dorokhov04 others

• Better data for the ee ? ? ? cross section
  and multihadron channels

CMD-202 (revised 03), KLOE04, SND05 (revised
06), CMD-206, BaBar04-06
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The Role of ? Data through CVC SU(2)
CVC I 1 V
W I 1 V,A
? I 0,1 V
??
e
?
?
hadrons
W
e
hadrons
Hadronic physics factorizes in Spectral Functions

fundamental ingredient relating long distance
(resonances) to short distance description (QCD)
Isospin symmetry connects I1 ee cross section
to vector? spectral functions
branching fractions mass spectrum
kinematic factor (PS)
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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

• 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?)(12?Q?)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? ? m?0 leads to phase space (cross sec.)
  and width (FF) corrections
• ? -? mixing (EM ? ? ? ? decay) corrected
  using FF model
• m? ? m?0 and ?? ? ??0 not corrected !
• Electromagnetic decays, like ? ? ? ? ?, ? ? ?
  ?, ? ? ? ?, ? ? ll
• Quark mass difference mu ? md generating
  second class currents (negligible)

Marciano-Sirlin 88
Braaten-Li 90
Cirigliano-Ecker-Neufeld 02
Alemany-Davier-Höcker 97, Czyz-Kühn 01
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ee?- ? Data Comparison 2006

• problems overall normalization
• shape (especially above
  ?)

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Requestioning the Procedure

• t spectral functions unchanged
• final ALEPH results (Phys. Rep.
  2005)
• CLEO, OPAL
• still waiting for final Belle data
  also BaBar coming
• how to relate t and ee spectral functions
• revisit corrections for SU(2) violation

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At What Level to Apply CVC?

• e?e? ? 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 e?e? ? 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)??(?) ? ??? ?1???2
(1?FSR) bare FSR dressed VP FSR
at s m?2 leptonic VP 2.5 hadronic VP ?1
? 4
mass shift from resonant VP mR?mR(0) ? 3 ?R?ee /
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 r0-r 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? m?0?m? ?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? ? m?0 effect in cross section and ??
  (opposite effects)
• m? ? m?? still taken to be 0 1 MeV,
  consistent with all results
• use ?PT dependence for ?? ? m?3 ??3 / f?2
  (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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ee?- ? 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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ee?- ? 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 a?had,LO??,? (10?10)

• update the ??based calculation of a?had,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 I0
  component)

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Comparison with BNL-E821
(hadVP)(LBL)(EW)
3.1? 3.5? 3.6?
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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-2SND) 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