[Solid_tracking] some initial Qsq / alignment studies

[Robert Michaels]

Thanks for the reply.  Paul Souder explained to me that in order
to get an acceptable error in Qsq it is well-known (by some)
that I need to use a reconstruction based on the GEM hits which
have correction functions that Richard Holmes formulated.

I suppose that using the result of Weizhi's track fitting
would be equivalent and eventually necessary for solving
the pattern-recognition problem in a multitrack situation.

- Bob

On Wed, 17 Jun 2015, Zhiwen Zhao wrote:

> hi, Bob
>
> I am CCing this to solid_tracking at jlab.org because only a few of us are on 
> the list.
> also because the emaillist will keep a copy of email in archive.
>
> The fake hits in space where there's no GEM plane is because current GEMC use 
> the hit processing "flux" to record the hits I gave you.
> If one low energy tracks go forward, then bend back by field and thus pass a 
> GEMC plane twice or more, the hit position will be average out between all 
> hits.
> "flux" is not the real GEM digitization, so just ignore those tracks for now.
>
> I didn't find the comment about pt on 201 page of latest pCDR, but it should 
> be proportional for sure.
>
> So when you fit the helix from the hits on GEM1,2,3 to determine radius of 
> curvature and thus Pt, is field a fitting parameter or is it given as a 
> constant?
> See can see the field variation from plots in pCDR
>
> The file I gave you have particles vertex distributed evenly along 40cm 
> target length.
> When you determine theta by fit to hit on GEM 1,2,3 in r VS z, how did you 
> use the vertex information?
>
> Does thetadiff.gif have 0.36 degree shift you mentioned already? it still 
> doesn't sit at 0 now.
>
> How do you get "systematics are about 3% in Qsq"?
>
> I am not sure if qsq_compare.gif is best way to compare.
> how about Qsq different VS p and theta in 2D plot?
>
> I guess is the final question is
> if GEM alignnment tolerance gives Qsq error larger than tracking error, we 
> don't need very good tracking method for the study.
> if GEM alignnment tolerance gives Qsq error smaller than tracking error, we 
> have push tracking error by using better method in order to see the other 
> effect.
>
> Thanks
>
> Zhiwen
>
> On 6/10/2015 2:57 PM, Robert Michaels wrote:
>> I didn't use the solid_tracking list because I couldn't
>> figure out who is on that list, and I don't think this
>> email needs to go the entire world.  Too many questions.
>> 
>> The goal of this study is to find how the GEM alignnment tolerance
>> affects the systematic error in four-momentum squared Qsq.
>> At this point, I have constructed Qsq, and I mainly need to
>> tweak the GEM positions to measure how it affects the errors.
>> Here is an update.
>> 
>> I use the GEM hits to reconstruct Qsq using two things:
>> 
>> 1. scattering angle theta:
>>     tan(theta) = slope of R vs Z for GEM hits, where R = sqrt(X^2+Y^2).
>>     I restrict the fit to the first 3 GEM chambers where B is uniform.
>> 
>> 2. Transverse momentum Pt is proportional to the radius of curvature
>>     of the helix.  Using the constraint that the beam goes through
>>     the origin, I derived an expression for R based on the GEM hits.
>>     This results in the following correlation, which is admittedly
>>     imperfect:
>> 
>> http://userweb.jlab.org/~rom/solid/ptvsrad.gif
>> 
>> One really silly problem is that the Monte Carlo gives me hits
>> in GEMs for radii like 20 cm and 15 m, but I think these are outside
>> the physical size of the GEM, so there must be a misunderstanding.
>> 
>> Nevertheless, based on 1 and 2, I tried to reconstruct Q^2 and
>> compare to MC as shown below.
>> 
>> First, the scattering angle compared to MC.
>> 
>> http://userweb.jlab.org/~rom/solid/thetadiff.gif
>> 
>> In order to align the peak at zero I had to adjust the reconstructed
>> angle by 0.36 degrees; perhaps because something is unknown about
>> the geometry.
>> 
>> Reconstructed Qsq vs MC Qsq
>> http://userweb.jlab.org/~rom/solid/qsq_compare.gif
>> 
>> The systematics are about 3% in Qsq at the moment.
>> 
>> For the purpose of the study (of GEM alignment) I don't need
>> zero error, I mainly need to look for deviations that occur with
>> misalignments.  Of course, it would be nice if the initial systematics
>> (presently 3%) would be smaller, but I assume these will reduce
>> when we use better track fitting.
>> 
>> I've made an initial study of the sensitivity to the GEM
>> chamber position, but I don't fully trust the results yet,
>> so I'll inform you about that later.
>> 
>> Also, I don't undestand the comment on page 201 of the pre-CDR that
>> the radius is inversely proportional to Pt.  Isn't it proportional,
>> not inversely proportional ?  Am I missing some elementary physics
>> here ?
>> 
>> For example, see this treatise about charge particles moving in a
>> uniform B field:
>> http://www.worldscientific.com/doi/pdf/10.1142/9789812798657_bmatter
>> 
>> -------------------------------------------------------
>> Robert W. Michaels, Staff Scientist
>> http://userweb.jlab.org/~rom    (757) 269 7410
>> Thomas Jefferson National Accelerator Facility
>> 12000 Jefferson Ave, Newport News, VA 23606 USA
>> 
>> 
>> 
>