[Frost] How do you find the dilution factor?

[Michael Dugger]

Hi,

Barry is right about this. There is too much shape to the division plot 
near the neutron peak. In determining the scale factor you can neglect the 
neutron peak entirely and fit the flat region (perhaps massX between ~0.4 
to ~0.8). This has the benefit of making the analysis a touch easier :)

With regards to the statement "...hydrogen contribution in the carbon 
missing mass spectrum."

One thing that you must be careful about: subtracting the neutron peak 
from the carbon. This is very tricky and you probably don't have to worry 
too much about this for the pi+ n reaction. There is expected to be a 
neutron peak for the carbon target. You can not attribute all of the peak 
to being due to hydrogen vertex leakage. From what we have seen, the 
vertex leakage appears to only play a large role in single proton events 
at forward lab angles and low momentum.

When you do analyze the pi0 reaction, you will have to worry about the 
vertex leakage. The only way I have been able to deal with the leakage 
problem is by using the subtraction method. I don't know how the vertex 
leakage issue can be dealt with using dilution factors. This, of course, 
does not mean that dilution factors can't be used when leakage is a 
problem, it just means that I find the problem difficult :(

Take care,
Michael

On Fri, 25 Feb 2011, Barry Ritchie wrote:

> Jo, just kibitzing here...
>
> In doing your substraction, did you also try having the background be a
> first order (i.e., linear) polynomial rather than a flat background,
> again ignoring the 2pi stuff above the peak? There is clearly a slope to
> the background below the peak, and it is likely that the real shape of
> the background is more complicated, but, in the absence of detailed
> knowledge of that shape, a linear function would be more reasonable.
> Then the two results (flat and linear backgrounds) would help bracket
> the uncertainties in the peak.
>
> ---BGR
>
> Professor Barry G. Ritchie
> Department of Physics
> Arizona State University
> Tempe, AZ  85287-1504
>
> Telephone: (480) 965-4707
> Fax: (480) 965-7954
>
> -----Original Message-----
> From: frost-bounces at jlab.org [mailto:frost-bounces at jlab.org] On Behalf
> Of mcandrew at jlab.org
> Sent: Friday, February 25, 2011 9:19 AM
> To: Michael Dugger
> Cc: frost at jlab.org
> Subject: Re: [Frost] How do you find the dilution factor?
>
> Sung,
>
> I think I used dilution factor = (number of events in butanol - number
> of
> events in carbon)/number of events in butanol.
>
> In order to obtain these values, I use the missing mass histogram from
> butanol and the missing mass histogram from carbon scaled to butanol.
>
> I explain it on this webpage:
>
> http://www2.ph.ed.ac.uk/~s0783525/carbon_background.htm
>
> The method still needs some improvement ie. taking into account energy
> and
> theta and is a first approximation.
>
> Any further questions, let me know.
>
> Have a good weekend,
> Jo.
>
>>
>> Sung,
>>
>> My previous email was wrong. Your dilution factor equation makes sense
>> with the use on the helicity web page. It took me a couple of minutes
> to
>> figure out how you put the dilution factor together.
>>
>> Sorry for the confusion.
>>
>> Take care,
>> Michael
>>
>> On Fri, 25 Feb 2011, Michael Dugger wrote:
>>
>>>
>>> Sung,
>>>
>>> I have been using the subtraction method, so there might be some
> problem
>>> with my understanding on how these dilution factors are put together
> and
>>> used.
>>>
>>> I could be wrong, but I think that your definition of the dilution
>>> factor
>>> might be inverted with respect to what I see on the helicity web
> page:
>>>
> http://clasweb.jlab.org/rungroups/g9/wiki/index.php/Helicity_assignment_
> for_g9a
>>> Also there might be a sign problem.
>>>
>>> You might want to define how you are using the dilution factor. For
>>> example:
>>>
>>> E = (1/(D*P))*[N_a - N_b]/[N_a + N_b],
>>>
>>> Or
>>>
>>> E = (D/P)*[N_a - N_b]/[N_a + N_b],
>>>
>>> where
>>> D = dilution factor
>>> P = beam*target polarizations
>>> ...etc
>>>
>>> -Michael
>>>
>>> On Fri, 25 Feb 2011, Sungkyun Park wrote:
>>>
>>>> Hi Jo,
>>>>
>>>> In your update, I have a simple question.
>>>> How do you find the Dilution Factor?
>>>>
>>>> I define the dilution factor as the ratio between the hydrogen and
> the
>>>> full butanol contribution to the cross section. I used the following
>>>> equation:
>>>>
>>>> (Dilution factor) = 1 - N(carbon)/N(Butanol)*(Scaling Factor)
>>>> where N(carbon) is the number of event in carbon and I count the
> events
>>>> in the missing mass plot of carbon. N(Butanol) is the number of
> event
>>>> in buutanol.
>>>>
>>>> Sung
>>>> Florida State University
>>>>
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