[Primex] galley proof for Annual Reviews paper on pi0 decay

[tulio at if.usp.br]

Dear Rory,

Congratulations for the excellent and complete review. I have two  
remarks that might be interesting to point out in case you agree.

1) On page 20:

You introduced the following text: "That the fitted parameters C_NC  
and C_NI differ from unity indicates that the theoretical models used  
for the nuclear-coherent and -incoherent cross sections are limited in  
their ability to predict these processes".
Regarding the MCMC calculations for the NI part, I should mention that  
the factor C_NI is affected by three major issues:

A) The normalization of the MCMC model (nuclear cross section) is done  
by fitting the proton data. These data are from the 70`s and represent  
measurements from different facilities that are not necessarily  
consistent with the PrimEx data. So, one should not expect that the  
fitting factor is equal to unit, but close.

B) The correlations between the parameters (P, NC, NI and phi) are  
sensitive to the angular range of the fitting. Basically, if you go to  
4 degrees you get rid of the NC part and the correlation between NC  
and NI should get much smaller. So, the extracted parameters (NC, NI)  
may differ sizably from unit if you take a much smaller angular range,  
which was probably the case.

C) The NI background in PrimEx depends obviously on the pion  
elasticity. So, in order to compare theory and experiment one should  
use not only the angular distributions but also the double  
differential cross sections. The NI events from theory should pass in  
the same criteria of the data. The PrimEx analysis used the angular  
distributions from the MCMC model assuming an elasticity of 0.92. The  
double differential cross section was not used. Consequently, the  
figures from the MCMC model should represent an upper limit, since the  
cuts applied in the analysis were not applied to the theoretical  
prediction of the angular distributions.

So, I believe that your statement "...theoretical models used for the  
nuclear-coherent and -incoherent cross sections are limited in their  
ability to predict these processes" may lead to the conclusion that  
the MCMC model is not able to fit the data with the NI factor close to  
unit, but this was not fully checked in PrimEx. Consequently, I would  
suggest that you mention that the fitting parameters are reasonably  
close to unit and that the absolute normalization does not change the  
decay width, only the shapes of the cross sections. This is just a  
suggestion.

2) Fig. 12:
You have used the text: "The coupling constants in the Regge amplitude  
are constrained...the only free parameter in the calculation is the  
relative sign between the Primakoff and strong amplitudes."
A quick inspection of Fig. 12 shows that the sum of omega plus rho  
poles and the Primakoff amplitudes does not reproduce the data either  
for constructive or destructive interference. In fact, the data at  
forward angles (not in the Primakoff peak) is a factor of three higher  
than the calculation. I also found a similar result when I fit the  
data without the Regge cuts. Since you are proposing to extract the  
decay width by fitting the proton data, you necessarily have to fit  
the whole angular range, including the interference range. So, I  
consider the above statement misleading since you mention that the  
only free parameter is the relative sign but you present a result that  
misses the data by a factor of three in the interference region. I  
would suggest that either you mention this discrepancy and addresses  
possible corrections or you omit the above statement. Again, this is  
just a suggestion.

With my best regards,
-Tulio Rodrigues.






> Hi all,
>
> Attached is the galley proof of the paper I agreed to write for  
> Annual Reviews
> of Nuclear and Particle Science on the pi0 experiment.    Small changes
> are still possible (text changes, references, ...) , big changes are not
> possible (more sections, new figures, ....)  .  The paper is just about
> as big as the editors will allow.  The figures are in the zip file.
> All suggestions are welcome.
>
> Thanks,
> Rory
>
>
>
>



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