[Frost] Simple Q-factor example

[Michael Dugger]

Derek,

Thanks for the comments. In the FROST meeting we have been discussing the 
manner that Q-factors are constructed. In particular, we have been talking 
about what would happen if the azimuthal information was neglected when 
constructing the distance to nearest neighbors for Q-factor determination 
and how such an omission would effect the beam asymmetry.

I'm new to the Q-factor stuff and I'm just trying to learn how the 
Q-factors are properly constructed.

Take care,
Michael

On Fri, 12 Aug 2016, Derek Glazier wrote:

> Hi Michael
>  Apologies if I have missed the point of the discussion. I think the 
> behaviour observed in your nice analysis is what would be expected.
>  The Q-factor explicitly requires inclusion of all variables that will be 
> used in further analysis, so in your case certainly phi must be included in 
> the nearest neighbours search. For other reactions also involving fits to 
> decay angles for example, these decay angles must also be included in the 
> nearest neighbour search.
>  If this is not done then it is probably not actually the Q-factor method 
> that is being applied but just a single probabilistic weight function for all 
> events. So if the signal and background ratio change as a function of the 
> variable you are interested in, clearly the single probabilistic weight 
> function will not apply at all values of the variable. Instead the Q-factor 
> is equivalent to making many probabilistic weight functions for events in 
> very small bins of phi so the signal/background is approximately constant for 
> that bin. This also has the implication that if the range of your phi bin for 
> N nearest neighbours is large (e.g. if you have low statistics, or many 
> variables) Q-factor will not work so well.
>  Sorry if this adds to any confusion, but in short I agree with your 
> analysis.
> Cheers
> Derek
>
> On 11/08/16 23:38, Michael Dugger wrote:
>> 
>> Hi,
>> 
>> During our discussion today, regarding the
>> Q-factor dependence on azimuthal angle, it
>> became clear that I needed to have a better
>> explanation. I have created an example that
>> I hope illustrates the point I was trying
>> to make.
>> 
>> A simple Q-factor example can be found at
>> 
>> https://userweb.jlab.org/~dugger/omega/omega6.pdf
>> 
>> Note: The 2nd slide is just a repeat of what
>> I had shown previously. The new information starts
>> on slide 3.
>> 
>> In addition, I have attached the plot
>> (allCos.png) that Barry requested (moment method
>> for integrated polar angle).
>> 
>> Take care,
>> Michael
>> 
>> 
>> 
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>
>