[Sane-analysis] Scaling fit to neutral pi photoproduction

[O. A. Rondon]

For completeness, and at Whit's request at the last analysis meeting, I
have digitized the H(e,pi-) data and fit form O'Connell's report, and
plotted them along with my PT dependent scaling fit for pion
photoproduction on C (Yerevan data,) normalized by a simple factor of
1/12 for H.

The plots are on my wiki pions section
https://hallcweb.jlab.org/experiments/sane/wiki/index.php/Inclusive_pion_and_nucleon_electroproduction
see(top plot: digitized data vs pion p; bottom: data and fits vs PT)

https://userweb.jlab.org/~rondon/incl-pi_epc-pt_scaling_C_H.pdf
(top plot: digitized data vs pion p; bottom: data and fits vs PT)

As it can be seen, it's comparable to the epc fit for H, for most of the
PT range. The scaling fit clearly works better than epc for the C data.

Keep in mind that the normalization of the photoproduction scaling fit
to the electroproduction data is just a somewhat arbitrary factor of
5.5% (ratio of average electro/photoproduction data cross sections) as
an estimate for the equivalent quanta Q factor needed to convert
from photo to electroproduction.

Agreement with the C(e,pi-) data could be improved by either knowing the
actual C target thickness or by just minimizing the chi-squared of the
scaling fit vs the electroproduction data.

Per my earlier suggestion, I propose we use this scaling fit, based on
actual pion production on nuclei to replace Wiser. The analysis team is
welcome to implement the application. I have no plans for further
improvements.

Cheers,

Oscar

O. A. Rondon wrote:
> To clarify some questions and comments on the scaling fit, I have added
> two items to the wiki section
> https://hallcweb.jlab.org/experiments/sane/wiki/index.php/Inclusive_pion_and_nucleon_electroproduction
> 
> - I have added plots of the pi- digitized data vs p and vs PT. Scaling
> fails again at high momentum for 90 deg, and for 120 deg.
> https://userweb.jlab.org/~rondon/incl-piminus_epc-pt.pdf
> 
> Notice I didn't add the scaling fit on the pi- plot, which is rather
> redundant because the pi+ data looks much like the pi- ones.
> 
> But note that the pi+ fit has somewhat different parameters shown on the
> plot, than the fit to the pi0 cross section shown on the wiki page,
> which is the one we should use to replace Wiser.
> 
> - I have added a page showing the digitized data and the original data
> as published (following the conventions for sharing publications for
> research purposes) to show the units
> https://userweb.jlab.org/~rondon/incl-pi-yerevan.pdf
> 
> The scaling fit cross section follows the units of the fitted
> photoproduction data, invariant cross section
> E d^3s/dp^3 [ub/(sr*(GeV/c)^2)*c/(equiv gamma kV)]
> where the last factor is the so called number of equivalent quanta Q in
> Wiser's thesis.
> 
> The electroproduction data and epc fits are in
> d^2s/dp/dOmega [ub/(sr*GeV/c)].
> 
> The normalized fit plot is to illustrate the scaling fit along with all
> the data (photo and electroproduction). For a better photo- to electro-
> comparison one would need to convert E d^3s/dp^3 to d^2s/dp/dOmega (same
> units for both processes), by multiplying E d^3s/dp^3 times p^2/E, per
> eq. (A-2-1), Wiser thesis.
> 
> This still leaves Q unspecified, but using the 5.5%X0 estimate for the C
> target thickness, the result looks like
> https://userweb.jlab.org/~rondon/incl-pim_epc-C_electrp-u.pdf
> 
> Note that both Alanakyan et al. and O'Connell's data are for nuclear
> cross sections on C, not cross sections per nucleon.
> 
> Cheers,
> 
> Oscar
> 
> 
> 
> 
> 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
>>
>> - 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.
>>
>> 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.
>>
>> 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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