t vs e+e- in evaluation of ahadm
results from the SIGHAD03 workshop
held in Pisa (8-10 Oct 2003)
M. Incagli - INFN Pisa
13 Nov 2003
Current situation
[DEHZ’03]
amhad [ee]
including:
=
(696.3 ± 7.2) 10–10
(exp and theo errors added in quadrature)
[t  e+e ] = (2.1 ± 1.1)%
had [t
]
=
(711.0 ± 5.8)
am [ee]
=
(11 659 180.9 ± 7.2had ± 3.5LBL ± 0.4QED+EW) 10–10
a m [t ]
=
(11 659 195.6 ± 5.8had ± 3.5LBL ± 0.4QED+EW) 10–10
am
692.4 ± 6.2
10–10
Hadronic contribution from higher order
[DH’98]
: amhad [(s/)3] = – (10.0 ± 0.6) 10 –10
Hadronic contribution from LBL scattering : amhad [LBL]
= + ( 8.6 ± 3.5) 10 –10
Observed Difference with Experiment:
am [exp] – am [SM]
(10–10)
22 ± 11
[e+e –]
7 ± 10
[t ]
=
The conserved vector current - SU(2)
t
W: I =1 & V,A
: I =0,1 & V
CVC: I =1 & V
e+
t
W
0
–
+
–
e–
Hadronic physics factorizes in Spectral Functions:
Isospin symmetry (CVC)
connects I=1 e+e– cross
section to vectort spectral
functions:

fundamental ingredient relating
long distance (resonances) to
short distance description (QCD)
2
4

 (I 1) ee      
 t     0 t 
s
SU(2) breaking
Corrections for SU(2) breaking applied to t data for dominant  – + contrib.:
Electroweak radiative corrections:
dominant contribution from short distance correction SEW to
effective 4-fermion coupling  (1 + 3(mt)/4)(1+2Q)log(MZ /mt)
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 corrections
Assume m – = m0 and correct for  - mixing (EM    – +
decay) corrected
Electromagnetic decays, like:     ,    ,    ,   l+l –
Corrections to SU(2) breaking
Multiplicative SU(2) corrections applied to t –   – 0t spectral function:
Comparison e+e- vs ALEPH, OPAL, CLEO
+10%
e+e- data
-10%
 mass fit after corrections
t data
M(-) = 776.0 ± 0.7 MeV
ee data
M(0) = 772.5 ± 0.6 MeV
• Fitting t data and ee data, after corrections, a mass difference between
- and 0 is observed
• Standard assumption: m2  m2  m   m 0
• KLOE published result: M() = 0.4 ± 0.9 MeV
1 m2

 0.02MeV
2 m 0
• If the mass difference is confirmed, t data move towards ee data
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 
mass difference
 However this is not supported by current data on !
 An independent determination of the mass difference (if
any) is necessary
 The M() correction would push the t data towards the
e+e- data, confirming the 2 discrepancy of “theory” with
respect to the BNL experimental measurement of g-2