[Halld-cal] Fwd: Re: Curvature

[beattite]

Re-sending.  Some people missed it.  I'll shove it on DocDB at some 
point as well, I suppose.


-------- Original Message --------
Subject: Re: Curvature
Date: 13.07.2015 14:51
 From: beattite <beattite at uregina.ca>
To: <halld-cal at jlab.org>

Accidentally sent the e-mail before attaching things.  Here you are.


On 13.07.2015 14:48, beattite wrote:
> Hello.
>
> Last week, Mark asked for some sort of plot showing the effects of
> the shower curvature for why we might want to be doing a correction 
> to
> the IU shower code, since it's been a while since Andrei's original
> work and we all want to be on the same page.
>
> The attached picture (15degrees.jpg) is point r vs. point z for a 
> simulated 5 GeV
> photon gun at 15 degrees.  The picture shows all reconstructed points
> in the run.  It gives the point z distribution for an incident photon
> at 15 degrees (I chose such a large energy, 5 GeV, so that there are
> enough points in layer 4 to talk about).
>
> If we expect the centroid of the point z distribution to lie along
> the trajectory of the photon, we would expect the centroid in the 
> four
> layers to be r/tan(15):
>   Layer 1 - 242 cm
>   Layer 2 - 256 cm
>   Layer 3 - 274 cm
>   Layer 4 - 302 cm
>
> What we actually see are centroids in the four layers of:
>   Layer 1 - ~253 cm
>   Layer 2 - ~257 cm
>   Layer 3 - ~260 cm
>   Layer 4 - ~265 cm
>
> This is similar to what Andrei's plots from a lot time ago show, as
> in, the centroid in layer one is shifted in the positive z-direction
> from the photon trajectory while the centroids in layers three and
> four are shifted in the negative z-direction from the photon
> trajectory.  The centroid of layer two lines up nicely with the
> trajectory.
>
> The IU code uses the Moliere radius around the trajectory to include
> points.  At low angles like 15 degrees, the spread of the cone in z 
> is
> something like +\- 75 cm.  That is to say, the code is looking for
> points in the shower between z = 230 and z = 370 or so in layer four.
> While this does actually cover the shower including the curvature (in
> this case), it also has a huge acceptance in the positive z-direction
> that is unneeded and which possibly catches points which belong to a
> different shower.  So, the idea is to take the initial energy 
> estimate
> from the IU shower along with the angle estimate of the IU shower
> (which is based off points in layers 1, 2, and 3, and so should be
> close to the angle of the actual incident particle), then use the
> curvature tables provided by Andrei which simulated in more detail 
> the
> energy deposition of an incident photon in the BCAL at different
> angles and energies.  The tables give energy deposition centroids in
> each layer which we can then use to fill the showers with points
> rather than the Moliere radius that the IU code used.
>
> The effect is less pronounced at, say, 50 degrees (50degrees.jpg).
> Here, the centroid in layer four should be around 68, but it lies
> more around 65, for instance.
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