[Sane-analysis] Scaling fit to neutral pi photoproduction

Thu Apr 10 15:44:27 EDT 2014

Hi Oscar,

Thank you for your detailed work. 

I wanted to share a link to a note I was working on a while ago, but have since 
focused my energy in a different direction. I will try to get back working on 
it, since I have a few more plots to add.  Here is the link
http://quarks.temple.edu/~whit/SANE/pion_production.pdf

I have inserted comments below.

On Wed, Apr 09, 2014 at 08:36:36PM -0400, O. A. Rondon wrote:
>Since the Alanakian et al. inclusive pi+ photoproduction on C data
>displays good scaling in PT for pion angles from 20 to 60 deg., and the
>pi- 40 deg data agrees with the pi+ within about 25%, I have digitized
>all the data for both pi+ and pi- to combine them to get a scaling fit
>to the neutral pion cross section
>
>To be able to do an apples to apples comparison to pi-
>electroproduction, I have also digitized the pi- electroproduction on C
>at 5 GeV and 13 deg data, of unknown origin, and the epc output included
>in Fig. 1 of O'Connell's Wiser report.
>
>The results are posted on my wiki section on inclusive pion production.
>https://hallcweb.jlab.org/experiments/sane/wiki/index.php/Inclusive_pion_and_nucleon_electroproduction
>
>The following items are relevant
>- plot of all pi+ data, plus 40 deg. pi- data, showing that all data for
>20 to 60 deg. and the 90 deg. data at low PT scale
>https://userweb.jlab.org/~rondon/incl-pi_epc-pt_scaling.pdf

Indeed they do scale. Here is what I get for the 40 degree pi+ using Wiser's 
(Scaling) fit.  
http://quarks.temple.edu/~whit/SANE/analysis_main/results/cross_sections/inclusive/PionProduction_photo_compare_40_40_211.png
and the pi-
http://quarks.temple.edu/~whit/SANE/analysis_main/results/cross_sections/inclusive/PionProduction_photo_compare_40_40_211.png

I should note one thing about the plot above. Upon noticing that the cross 
section for nuclei was not proportional to A, and that it seemed to not really 
matter beyond a factor of two for A>2, I simply  calculate the deuteron cross 
section.  This is just a simple sum of the neturon and proton cross sections 
which should be improved.

Wiser's fit actually has some extra parameters because he even saw that the 
scaling behavior wasn't perfect. From the plots above and your plots of the 
photoproduction scaling behavior I notice a few things:

  - Both Wiser's fit and EPC_v2 (which includes Wiser's fit) get the 
    photoprodution slope wrong.
  - The scaling description works quite nice for a *single beam energy*.

It would be interesting (but a lot of work) to not just do a simple scaling fit 
but to re-fit Wiser's function with his photoproduction data and newer 
photoproduction data along with electroproduction data.

>
>- plots of pi- electroproduction at 5 GeV (O'Connell) and
>photoproduction at 4.5 GeV on C (Yerevan), along with scaling fit and
>epc output.

Here is my version of Wiser's fit to the O'Connell data on the proton.
http://quarks.temple.edu/~whit/SANE/analysis_main/results/cross_sections/inclusive/PionProduction_electro_compare_50_13_-211.png
I haven't gotten around to digitizing the carbon data, but, as I said above, I 
only scale by a factor of two. It is clear the difference between O'Connell's 
proton and carbon data is an order of magnitude (ie about 12). So If I scale my 
result by this I will be on top of the O'Connell data.

>
>I normalized the fit to photoproduction data by the ratio of the
>averages of electro to photoproduction data. I'm sure the normalization
>would agree much better if we knew the actual C target thickness used
>for electroproduction, i.e. probably ~3%, instead of the 5.5% ratio of
>the averages.
>https://userweb.jlab.org/~rondon/incl-pim_epc-C_electrp.pdf
>
>- scaling fit to combined pi+ and pi- to get pi0 cross section. The fit
>form and parameters are given below the figure showing the pi- comparison.
>
>The digitization error of the fit is 5% or less. It only affects the
>cross sections. The kinematics are taken directly from the paper.
>
>I do recommend we forget about Wiser, epc, etc. and just use this fit in
>GEANT. For nitrogen and He we just multiply it by the ratio of atomic
>masses. For H, we can safely assume it's C/12, since our minimum pion
>momentum 500 MeV/c is well above the pion production threshold.

I am hesitant to endorse this procedure because of the discrepancies I have 
seen between the A-dependence of electroproduction and photoproduction data.

Using Wiser's Fit (which was on the proton), why is the electroproduction data  
of O'Connell proportional to A?

Again using Wiser's fit, why is the photoproduction data of Alanakian,et.al., 
not proportional to A?

I should point that when comparing to the pion data on Helium-3 from d2n 
experiment (courtesy of David Flay) I find nice agreement with the simple 
factor of two (ie not proportional to A).
http://quarks.temple.edu/~whit/SANE/analysis_main/results/cross_sections/inclusive/PionProduction_electro_compare_59_45_-211.png

It would be very interesting check to see your scaling fit used to calculate 
the electroprodution cross-section following Tiator and Wright, instead of just 
using the data to normalize it, and get results that agree with the O'Connell 
paper. If I have some time this weekend, I might get around to doing this.

Right now I do not trust the data shown in O'Connell's paper, especially since 
it is of unknown origin.

Cheers,
Whit

>
>To use it, the only thing we need to do is to convert the pion
>kinematics (p, theta, phi) to the corresponding PT and calculate the
>cross section.
>
>To get yields, we use the GEANT bremsstrahlung flux for the real photon
>part times the fit's cross section.
>
>For electroproduction we just replace Wiser with this cross section.
>
>Since the original Yerevan data are in a copyrighted paper, I can't post
>it. Unfortunately, it's not available as a digital file on INSPIRE, but
>the hard copy is available at the JLAB library and at other physics
>dept. libraries.
>
>Cheers,
>
>Oscar
>
>
>
>
>
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