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M. Incagli - INFN Pisa 13 Nov 2003

t vs e + e - in evaluation of a had m results from the SIGHAD03 workshop held in Pisa (8-10 Oct 2003). M. Incagli - INFN Pisa 13 Nov 2003. Current situation. (exp and theo errors added in quadrature). [DH’98]. [DEHZ’03].

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M. Incagli - INFN Pisa 13 Nov 2003

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  1. t vs e+e- in evaluation of ahadmresults from the SIGHAD03 workshop held in Pisa (8-10 Oct 2003) M. Incagli - INFN Pisa 13 Nov 2003

  2. Current situation (exp and theo errors added in quadrature) [DH’98] [DEHZ’03] Hadronic contribution from higher order : ahad [(s/)3] = – (10.0 ± 0.6) 10–10 Hadronic contribution from LBL scattering : ahad [LBL] = + ( 8.6 ± 3.5) 10–10 inclu-ding: Observed Difference with Experiment:

  3. The conserved vector current - SU(2) W: I=1 &V,A CVC: I=1 &V : I=0,1 &V  e+   p+ W p– p0 e– p– fundamental ingredient relating long distance (resonances) to short distance description (QCD) Hadronic physics factorizes in Spectral Functions: Isospin symmetry (CVC) connects I=1 e+e– cross section to vectorspectral functions:

  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+2Q)log(MZ /m) • subleading corrections calculated and small • long distance radiative correction GEM(s) calculated (add FSRto the bare cross section in order to obtain  – + () ) • Charged/neutral mass splitting: • m–  m0leads to phase space (cross sec.) and width corrections • Assume m– = m0 and correct for  - mixing (EM    –+ decay) corrected • Electromagnetic decays, like:     ,    ,    ,   l+l – ?

  5. Corrections to SU(2) breaking Multiplicative SU(2) corrections applied to –   – 0 spectral function:

  6. Comparison e+e- vs ALEPH, OPAL, CLEO +10% e+e- data -10%

  7. r mass fit after corrections • Fittingt data and ee data, after corrections, a mass difference between r- and r0 is observed • Standard assumption: • KLOE published result: DM(r) = 0.4 ± 0.9 MeV • If the mass difference is confirmed, t data move towards ee data ee data t data M(r-) = 776.0 ± 0.7 MeV M(r0) = 772.5 ± 0.6 MeV

  8. Conclusions • Two sets of reasonably consistent data: t-data (ALEPH, CLEO ; but OPAL?), vs e+e--data (CMD2, KLOE) • Relative difference of ~2% • A possible explanation of the this difference relies on the r mass difference • However this is not supported by current data on r! • An independent determination of the mass difference (if any) is necessary • The DM(r) correction would push the t data towards the e+e- data, confirming the 2s discrepancy of “theory” with respect to the BNL experimental measurement of g-2

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