[Halld-physics] Random subtraction and uniqueness tracking

[Peter Pauli]

Hello everybody,

I apologise in advance for this lengthy email.
I am trying to understand how to properly do the random subtraction 
while avoiding double counting. After talking to a couple of people at 
the collaboration meeting and during shifts I found that this seems to 
be non trivial and it seemed that some people where not to sure about it 
either.

According to Paul's talk that he gave at the 2016 software workshop the 
rule is to always include all the variables into your uniqueness 
tracking that are used to calculate the histogrammed quantity.
Let's say I look at gp->p pip pim. I want to histogram the pip pim 
invariant mass and do the random subtraction. Although I only use the 
pip and pim tracks to calculate the invariant mass I have to include the 
beam photon in my uniqueness tracking because I also use that quantity 
(timing) in the following step to get the random subtracted histogram. 
But as far as I understand in the voting on the best RF bunch each track 
gets a vote. So do I need to include the proton in the uniqueness 
tracking as well?

What happens if I use the track vectors coming out of the kin fit? The 
standard 4-mom fit that is usually used will include information from 
all tracks in the combo. Does that mean as soon as I plot e.g. the 
invariant mass using kin fitted tracks I need to include everything in 
the uniqueness tracking?

What about binned quantities. Many results are shown in bins of momentum 
transfer squared. In my analysis I look at gp->kp Lambda(->km proton) 
and calculate the momentum transfer as t^2 = (g_P4-kp_P4)^2. If I now 
want to bin the proton Kminus inv mass in t-bins does that mean I need 
to include the beam particle and Kplus in my uniqueness tracking? Aren't 
bins in principle like a 2D plot? Binning means effectively 
histogramming a 2D plot I would say, therefore I need to include them. 
But what is if now make my bins really large (e.g. 0 to -inf)? This 
would effectively be unbinned and I would just track the beam particle, 
proton and km. Does that mean I need uniqueness tracking of beam, km, 
proton for each of my bins individually but not include kp in the tracking?

If there is a document somewhere that clarifies those issues I would be 
happy if you could point me to it. I didn't find anything but maybe I 
missed it.

These are only a couple of questions I have about this but I think it is 
enough for one email. I thought about this stuff for quite some time now 
and feel like I start to confuse myself about some of the issues. 
Therefore I thought I just send it to the physics mailing list. Maybe 
there are straight forward answers and I just don't see them or maybe 
this is worth a discussion at an analysis meeting. Either way I am sure 
this is interesting for more people than just me.

Cheers,
Peter

-- 
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Peter Pauli

Dept. of Physics & Astronomy
University of Glasgow,
Glasgow G12 8QQ.
Scotland. UK.

Tel: +44 (0)141 330 6398
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