[Frost] Dilution method

[Volker Crede]

Hi Michael,

thanks for the nice summary, I fully agree with your email below. Just a brief comment: we noticed that the Carbon statistics for the two-pion channel is only about 10-15% of the Butanol statistics. For this reason, subtracting the Carbon distributions introduces huge statistical errors without even considering the error of the scaling factor. Since the helicity difference is likely small (at least for the most part) for ppi+pi- , we conclude that the subtraction method is not applicable for us; the final errors of the observables after the subtraction (dominated by the statistical fluctuations of Carbon) wash out any polarization effect we see for the Butanol alone. I guess that all of us have more or less the same problem.

The determination of the dilution factor also depends on the Carbon statistics, but our hope is that we can extract sort of a function which smoothly describes the dilution factor. This will probably include some assumptions on the dependence of the dilution factor on certain kinematic variables. At the moment, we see that we are limited by the Carbon statistics and to a somewhat lesser extent by the Butanol statistics.

Best wishes

       Volker


On Feb 28, 2011, at 2:51 PM, Michael Dugger wrote:

> 
> Hi,
> 
> There are two common methods of dealing with the bound nucleons:
> 1) Subtraction method
> 2) Dilution method.
> 
> Either method should produce final results that are consistent with one 
> another. I want to make sure that we are all in agreement as to the use of 
> the dilution method. (the subtraction method is very simple and probably 
> does not need much in the way of explanation.)
> 
>> From my discussion with Ken, I understand that (please correct me if I am 
> wrong) the dilution method can be summarized through the equation:
> 
> O_free = [O_butanol*N_butanol - N_bound*O_carbon]/N_free,
> 
> where
> O_free = Observable on the free proton
> O_butanol = Observable on the butanol
> O_carbon = Observable on the carbon
> N_free = Number of events on free proton
> N_butanol = Number of events of interest on butanol
> N_bound = Number of events of interest on bound nucleons within butanol
> 
> If we introduce the dilution factor D = N_free/N_butanol, then we can 
> rewrite O_free as
> 
> O_free = O_butanol/D - O_carbon*(1-D)/D
> 
> There are two observables and a dilution factor that make up the 
> observable for free protons.
> 
> For the special case where O_carbon = 0, we get the nice result that
> O_free = O_butanol/D.
> 
> The scale factor can be connected to the dilution factor through the 
> equation
> D = 1 - sf*N_carbon/N_butanol,
> as Sung does.
> 
> It is important to note that for the Sigma, Cz and Cx observables O_carbon 
> is not expected to be = 0.
> This means that for these observables you must use the full equation:
> O_free = O_butanol/D - O_carbon*(1-D)/D
> 
> Liam: It looks like it is possible for an incorrect dilution factor to 
> cause a sign change in observables. Perhaps you can vary the dilution 
> factors and see if you can get Cz and Cz observables to better agree with 
> the g1c data.
> 
> Take care,
> Michael
> 
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