Dear Graziano, Guido and Henryk,

I am sending you part of my comments and suggestions on the draft, 
starting from the two-page "Introduction".

As, for these first two pages, Graziano also inspired himself from some 
of the parts I wrote for our common paper on e+e- physics in Frascati, I 
dare suggest here a non-negligible number of modifications and 
improvements. Here they are:

1,L,1,6  (page 1, left, paragraph 1, line 6)

between the measurements --> between the precise measurements

1,L,1,11

and there are strong theoretical arguments hinting at the presence of 
physics beyond the SM.	-->

and there are clear phenomenological facts (dark matter, 
matter-antimatter asymmetry in the universe) as well as strong 
theoretical arguments hinting at the presence of physics beyond the SM.

1,L,2,4

"is the fine-structure constant alpha which depends logarithmically on 
the energy scale. It has been determined at zero momentum transfer with 
an impressive accuracy of 0.37 parts per billion (ppb) [1] from the mea-
surement of the anomalous electron magnetic moment [1], relying on the 
validity of perturbative QED."		-->

"is the fine-structure constant alpha, determined from the anomalous 
magnetic moment of the electron with an impressive relative precision of 
0.37 parts per billion (ppb) [1] relying on the validity of perturbative 
QED [2]."

Then add [2], the reference to Kinoshita, in the bibliography:

  G.~Gabrielse, D.~Hanneke, T.~Kinoshita, M.~Nio and B.C.~Odom,
   %``New Determination of the Fine Structure Constant from the Electron
   %  g Value and QED,''
   Phys.\ Rev.\ Lett.\  {\bf 97}, 030802 (2006);
                        {\bf 99}, 039902 (2007) (E)

1,R,1,3

There are several points here. Also, some definitions are missing. I 
propose to replace the piece starting from "At the M_Z scale the..." and 
ending with "prediction of the Higgs mass." with the PDF file in 
attachment. This would uniform the notation and introduce the missing 
definitions. Also, given the importance of Delta_alpha in the context of 
this report, I added a few introductory lines explaining its relevance 
for the SM phenomenology. I hope you'll like them. Please see the 
attachment change.pdf (also in latex: change.tex).


2,L, Eq.(3)

a_mu^had --> a_mu^HLO

2,L,2,3

uses the result in --> uses the hadronic light-by-light result of

2,L,2,10

a_mu --> a_mu^SM

2,L,2,13

proposed experiments of the measurement of a_mu -->
proposed muon g-2 experiments

2,R,1,2

accuray --> accuracy

2,R,7,2&5

a_mu^had --> a_mu^HLO

2,R, 4 lines from bottom

perspectives --> prospects


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I actually have some more comments on other parts of the draft. I'll 
send them to you by tomorrow night, in case you still want to consider 
them.

Thanks for all your work!

All the best, Massimo