[Halld-physics] Random subtraction and uniqueness tracking

[Peter Pauli]

Hi Thomas,

On 20/03/18 17:42, Thomas Britton wrote:
> My two cents:
>
> It is dependent on WHAT you are trying to do.  The simplest case is to imagine you have 3 tracks (p, K+,K- because I am terribly biased) and 2 Beam Photons (A,B).  If you form all combinations of gamma p -> K+K-p you will get A,K+,K-,p and B,K+,K-,p.  If you want to plot the invariant mass of K+K- then you need uniqueness tracking because both combinations contribute exactly the same data to the invariant mass distribution.
Only if you don't want to do a random subtraction. If you want to random 
subtract (by that I mean a sideband subtraction of out-of-time beam 
photons) you should use uniqueness tracking for kp km or include the 
beam photon in the tracking which will result in the same in you example.
>    What gets odd is if you are plotting the invariant mass of K+K- in bins of beam energy.  In this case A and B have different energies and each combination would contribute the same point...to two different histograms.  Thus you do not need uniqueness tracking.
>
> There are differences between inter event combinations (different beam buckets) and intra event combos which add even more complexity.  My rule of thumb is if you are plotting something and that thing has the same data being plotted (not
> just the same number but really the same underlying objects) multiple times you need uniqueness tracking.
Using your example of km kp p. Let's say you have only one beam photon 
but two tracks that could be your kp. If you want to histogram the km p 
invariant mass one could say that is easy because it does not depend on 
the kp therefore include beam, km and p in your uniqueness tracking and 
only histogram it once. But what if you want to histogram the 
kinematically fitted variables? I would say they are the same underlying 
objects but their numbers (km and p) depend on which kp you use in the 
combo that is fitted. Which one do you pick? Using both doesn't "feel" 
right.
> If that data is plotted to different histograms then it does not need uniqueness tracking.  What this ends up meaning is that a given data set can, in principle, have multiple different uniqueness trackings that are dependent on what exactly you are looking at;  Not a single set for all cases.
I understand that. Still there must be a right way of doing things in a 
more general sense.
>
> I think, technically, for my cross-section measurement, I need to bin in beam energy and internally track the uniqueness of the combinations on a bin by bin basis.  Currently I am not doing that as I found the effect was not too big compared to the missing factors of 2.
>
> Hope this does less harm than helps.  It is certainly not a trivial topic....
>
> Thomas

I know that the bulk of the combinations comes from having more than one 
beam photon in any event. In the reaction I analyse ~97% of the cases 
where I have more than one combination left after all cuts are due to 
multiple beam photons. They are subtracted off by performing a sideband 
subtraction using out of time beam photons. But the remaining 3% are due 
to having multiple possible proton, K- or K+ assignments in one event. 
Therefore this is maybe not the most severe source for errors but I 
would still like to get this right. Also there are probably channels 
where the effect might be stronger (multi-photon states maybe?).

I think Richard's suggestion to have a short series of presentations 
and/or tech notes is very good. This would surely help people to get 
started and help to establish "best practises" as Justin mentioned.

Cheers,
Peter

>
>
> ----- Original Message -----
> From: "Peter Pauli" <ppauli at jlab.org>
> To: "halld-physics at jlab.org Physics" <halld-physics at jlab.org>
> Sent: Tuesday, March 20, 2018 1:18:13 PM
> Subject: [Halld-physics] Random subtraction and uniqueness tracking
>
> 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
>

-- 
================================
Peter Pauli

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

Tel: +44 (0)141 330 6398
================================