[d2n-analysis-talk] A Fit to the Ratio of Unpolarized Structure Functions F_2

[David Flay]

Hi all,

So I've spent some time coming up with a modest fit to parameterize
R^{np}, which will influence how we estimate R = F_2^n/F_2^{3He}.

Attached is my (initial) result.  I initially wanted to go with a
polynomial fit, but I was able to achieve a \chi^2/ndf ~ 1 using the form
I display in the plot -- a linear combination of a gaussian and an
exponential.  The reasoning for the gaussian was to try to get a nice fit
to the region for x ~ 0.1, where we see R^{np} ~ 1, and from there on out,
I wanted the exponential to take care of the rest (that is, after x ~
0.22, and hence why p_1 = 0.22).  This didn't necessarily work, but
because the \chi^2/ndf came out pretty good, I decided to keep this form. 
The parameters p_0, p_2, and p_3 were arbitrary.

I chose to fit only the data shown in Xiaochao's thesis to start.

Even at the lowest x values, one could argue that the fit is decent, given
the large errors on those data points.  The same could be said of the
highest x points as well.

I've also been trying to get a fit using all the data I have found for
R^{np}, however, I can only get a \chi^2/ndf ~ 4-5 at best,as there is a
decent amount of disagreement at high x for the (newer) data sets with
respect to the data from SLAC (shown in Xiaochao's thesis).  I chose a
different fit for this plot, using f(x) = p_0*exp(-(x - p_1)) - p_2*x. 
Using a similar fit to that seen in the first plot doesn't really change
things too much.  See plot 2.

Overall, I think this parameterization fits the data well for our x range
(0.2 < x < 0.8) in the first plot and should be a decent parameterization
for this first order estimation of R (using the fit from plot 1).

What do you think?

Thanks,

Dave


-------------------------------------------------
David Flay
Physics Department
Temple University
Philadelphia, PA 19122

office: Barton Hall, BA319
phone: (215) 204-1331

e-mail: flay at jlab.org
            flay at temple.edu

website: http://www.jlab.org/~flay
              http://quarks.temple.edu
-------------------------------------------------


-------------- next part --------------
A non-text attachment was scrubbed...
Name: R_np_fit_10_26_10.png
Type: image/png
Size: 289271 bytes
Desc: not available
Url : https://mailman.jlab.org/pipermail/d2n-analysis-talk/attachments/20101026/2f247f7b/attachment-0002.png 
-------------- next part --------------
A non-text attachment was scrubbed...
Name: R_np_fit_all-data_10_26_10.png
Type: image/png
Size: 24100 bytes
Desc: not available
Url : https://mailman.jlab.org/pipermail/d2n-analysis-talk/attachments/20101026/2f247f7b/attachment-0003.png