Vertex Reconstruction studies

Inclusive electron GEMC 2.4 & Coatjava 2.4

LB_GEMC2.4CJ2.4_Vertex

Summary

Set all histogram ranges to -6,6 cm  and bin sizes of 0.1 cm

Point target X,Y,Z=0 cm

Below are examples of the reconstruction for several line targets as seen in the CED

We should change it to +30,150,210, and 330 degrees so the electron is not going in between two drift chambers but rather into the center, keep 90 and 270.

6cm Z Target, No Rotation	6cm Z Target, 270 Degree Rotation	6cm Z Target, 90 Degree Rotation	2cm Y Target, 30 Degree Rotation	2cm Y Target, 180 Degree Rotation	2cm X Target, 90 Degree Rotation	2cm X Target, 270 Degree Rotation

The histograms below are using a 6 GeV electron fired at an angles of 25 degrees in theta and 0 degrees in phi.

	No Rastering
Vx Difference
Vy Difference
Vz Difference
X Resolution (cm)	0.2362 +/- 0.0008
Y Resolution(cm)	0.09809 +/- 0.00033
Z Resolution (cm)	0.05435 +/- 0.00017

These histograms raise some questions. To begin I created a LUND file with 6 GeV incident electrons at 25 degrees in theta and 0 degrees in phi. All of the vertex positions were set to 0. I then ran GEMC 2.4 using the command line ~/src/CLAS/GEMC/source/gemc -USE_GUI=0 -INPUT_GEN_FILE="LUND,No_Raster.LUND" -N=75000 eg12_sol_No_Raster.gcard

which created an output file called eg12_sol_75k_No_Raster.ev. After that the reconstruction command line used was

~/src/CLAS/coatjava-2.4/bin/clas12-reconstruction -i eg12_sol_75k_No_Raster.ev-config GEOM::new=true -config MAG::torus=-1.0 -config MAG::solenoid=1.0 -o eg12_sol_75k_No_Raster_rec.evio -s DCHB:DCTB:EC:FTOF:EB -config DATA::mc=true -config DCTB::useRaster=true

After the reconstruction a root file was created using

~/src/CLAS/evio2root/bin/evio2root eg12_sol_75k_No_Raster_rec.evio eg12_sol_75k_No_Raster_rec.root 75000

A plot was then created to show the X Vertex and Y Vertex Differences

The first question is why is there a shift in the Y Difference. What would make X more centered around 0? The next question is when rastering begins, why do the resolutions in the X Vertices remain unchanged while the resolutions in the Y Vertices change?

Point in 2-D but extended target in 1-D

Two vertex variables are fixed at zero and the third vertex variable is altered. A 6 GeV electron was fired at angles of 25 degrees in theta and 0 degrees in phi.

	2cm X Raster, Y=0,Z=0	2 cm Y Raster, X=0,Z=0	2 cm Z Raster ,X=0,Y=0	6 cm Z Raster ,X=0,Y=0
Vx Difference
Vy Difference
Vz Difference
X Resolution (cm)	0.2658 +/- 0.0010	0.2531 +/- 0.0009	0.2544 +/- 0.0009	0.2539 +/- 0.0009
Y Resolution(cm)	0.1728 +/- 0.0007	0.2368 +/- 0.0007	0.2644 +/- 0.0007	0.6191 +/- 0.0013
Z Resolution (cm)	0.1792 +/- 0.0006	0.1998 +/- 0.0004	0.4318 +/- 0.0009	1.105 +/- 0.002

Extended target -3 < Z < 3 cm

	1cm X Raster	1 cm Y Raster	1 cm X & Y Raster
X Resolution (cm)	0.2696 +/- 0.0009	0.2588 +/- 0.0009	0.2734 +/- 0.0009
Y Resolution (cm)	0.6234 +/- 0.0014	0.6851 +/- 0.0014	0.6927 +/- 0.0013
Z Resolution (cm)	1.136 +/- 0.002	1.361 +/- 0.002	1.381 +/- 0.003
Generated Vx (cm)
Generated Vy (cm)
Generated Vz (cm)
Reconstructed Vx (cm)
Reconstructed Vy (cm)
Reconstructed Vz (cm)
Vx Difference (cm)
Vy Difference (cm)
Vz Difference (cm)

Extended target in Z. Vy shift analysis

All Histograms below were created by simply making the target longer along the Z axis. Each case uses vertex points for X and Y ranging from -1cm to 1cm

	0.5cm Z Target	1cm Z Target	2cm Z Target	3cm Z Target	4cm Z Target	5cm Z Target
X Resolution (cm)	0.2705 +/- 0.0010	0.2726 +/- 0.0010	0.2716 +/- 0.0010	0.2731 +/- 0.0010	0.2702 +/- 0.0009	0.2736 +/- 0.0010
Y Resolution (cm)	0.2041 +/- 0.0010	0.2282 +/- 0.0011	0.3152 +/- 0.0014	0.433 +/- 0.002	0.5584 +/- 0.0018	0.6454 +/- 0.0015
Z Resolution (cm)	0.28 +/-0.00	0.3582 +/- 0.0013	0.5659 +/- 0.0018	0.7927 +/- 0.0023	1.034 +/- 0.003	1.253 +/-0.003
X Mean (cm)	0.0139 +/- 0.001	0.0139 +/- 0.00107	0.01436 +/- 0.00104	0.01217 +/- 0.00107	0.00991 +/- 0.00104	0.009022 +/- 0.00105
Y Mean (cm)	-0.1893 +/- 0.0011	-0.2004 +/- 0.0012	-0.2379 +/- 0.0016	-0.2936 +/- 0.0022	-0.3648 +/- 0.0027	-0.3871 +/- 0.0026
Z Mean (cm)	0.0928 +/- 0.0014	0.06464 +/- 0.0013	-0.0337 +/- 0.0028	-0.1582 +/- 0.0040	-0.3016 +/- 0.0053	-0.486 +/- 0.006
Generated Vx (cm)
Generated Vy (cm)
Generated Vz (cm)
Reconstructed Vx (cm)
Reconstructed Vy (cm)
Reconstructed Vz (cm)
Vx Difference (cm)
Vy Difference (cm)
Vz Difference (cm)

It would seem that increasing the length of the target in the Z direction has an effect on the resolution of the Y vertex position along with how far the center of the Gaussian peak will shift for the Y vertex differences.

Localized Vertex Resolution Investigation of Line Targets

GEMC was ran to create electrons being produced in a line along certain axes. These include three separate 2cm targets centered at (0,0,0) in the X, Y , and Z directions. The final target is a line along the Z axis centered at (0,0,0) that is 6cm long. The generated electrons were shot at 25 degrees in theta and 0 degrees in phi at an energy of 6GeV.

Here is an example of how the cuts were made. Consider the case of a 2cm line target in the Z direction centered at (0,0,0). Closed intervals begin at the end of the target and are 0.1cm long. So the first interval would be [-1.0,-0.9], then the next would be [-0.9, -0.8] and so on until the entire target is covered. The events in the EVENTHB bank were cut so that in any given interval there would be a margin of +/- 1cm to remove any outliers that may cause the histograms to have long tails.

Below are the histograms for the 2cm line target in Y,X=0,Z=0. The electrons were fired with an energy of 6 GeV at 25 degrees in theta at 0 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vy Difference	***	Interval	Resolution (cm)	Vy Difference
[-1.0,-0.9]	0.09406 +/- 0.00128		***	[0.9,1.0]	0.1001 +/- 0.0016
[-0.9,-0.8]	0.0868 +/- 0.0013		***	[0.8,0.9]	0.1221 +/- 0.0018
[-0.8,-0.7]	0.08961 +/- 0.00128		***	[0.7,0.8]	0.1144 +/- 0.0017
[-0.7,-0.6]	0.09853 +/- 0.00148		***	[0.6,0.7]	0.169 +/- 0.003
[-0.6,-0.5]	0.1038 +/- 0.0016		***	[0.5,0.6]	0.171 +/- 0.003
[-0.5,-0.4]	0.1202 +/- 0.0018		***	[0.4,0.5]	0.1105 +/- 0.0016
[-0.4,-0.3]	0.1755 +/- 0.0026		***	[0.3,0.4]	0.09508 +/- 0.00137
[-0.3,-0.2]	0.1847 +/- 0.0028		***	[0.2,0.3]	0.09065 +/- 0.0140
[-0.2,-0.1]	0.1255 +/- 0.0019		***	[0.1,0.2]	0.093002 +/- 0.0013
[-0.1,0.0]	0.09663 +/- 0.00160		***	[0.0,0.1]	0.09008 +/- 0.0012

Below are the histograms for a 2cm target along the Y axis, X = 0 Z = 0. The electrons were fired with an energy of 6 GeV at 25 degrees in theta and 180 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vy Difference	***	Interval	Resolution (cm)	Vy Difference
[-1.0,-0.9]	0.07741 +/- 0.00166		***	[0.9,1.0]	0.2319 +/- 0.0189
[-0.9,-0.8]	0.0976 +/- 0.0017		***	[0.8,0.9]	0.2147 +/- 0.0185
[-0.8,-0.7]	0.09924 +/- 0.00150		***	[0.7,0.8]	0.2364 +/- 0.0188
[-0.7,-0.6]	0.1386 +/- 0.0024		***	[0.6,0.7]	0.2323 +/- 0.0189
[-0.6,-0.5]	0.1278 +/- 0.0027		***	[0.5,0.6]	0.06016 +/- 0.00299
[-0.5,-0.4]	0.09882 +/- 0.00142		***	[0.4,0.5]	0.3986 +/- 0.00104
[-0.4,-0.3]	0.09322 +/- 0.0013		***	[0.3,0.4]	0.3056 +/- 0.0047
[-0.3,-0.2]	0.09399 +/- 0.00145		***	[0.2,0.3]	0.1097 +/- 0.0029
[-0.2,-0.1]	0.08935 +/- 0.00131		***	[0.1,0.2]	0.1146 +/- 0.0025
[-0.1,0.0]	0.08913 +/- 0.00130		***	[0.0,0.1]	0.09557 +/- 0.0015

Below are the Histograms for a 2cm long target in the X Direction with a 6GeV electron fired at 25 degrees in theta and 90 degrees in phi

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vx Difference	***	Interval	Resolution (cm)	Vx Difference
[-1.0,-0.9]	0.1341 +/- 0.0140		***	[0.9,1.0]	0.01572 +/- 0.0002
[-0.9,-0.8]	0.1304 +/- 0.0051		***	[0.8,0.9]	0.01844 +/- 0.00031
[-0.8,-0.7]	0.1182 +/- 0.0036		***	[0.7,0.8]	0.01722 +/- 0.0028
[-0.7,-0.6]	0.09062 +/- 0.0031		***	[0.6,0.7]	0.02386 +/- 0.00088
[-0.6,-0.5]	0.06816 +/- 0.00191		***	[0.5,0.6]	0.024 +/- 0.001
[-0.5,-0.4]	n/a		***	[0.4,0.5]	0.04406 +/- 0.00182
[-0.4,-0.3]	0.0635 +/- 0.0013		***	[0.3,0.4]	0.04517 +/- 0.00118
[-0.3,-0.2]	0.0618 +/- 0.0012		***	[0.2,0.3]	0.04722 +/- 0.00107
[-0.2,-0.1]	0.07473 +/- 0.00178		***	[0.1,0.2]	0.05667 +/- 0.00106
[-0.1,0.0]	0.08787 +/- 0.00132		***	[0.0,0.1]	0.08356 +/- 0.00159

Below are the Vx Differences using a 2cm target in X with incident 6 GeV electrons at 25 degrees in theta and 270 degrees in phi

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vx Difference	***	Interval	Resolution (cm)	Vx Difference
[-1.0,-0.9]	0.01571 +/- 0.0002		***	[0.9,1.0]	0.1257 +/- 0.0100
[-0.9,-0.8]	0.0163 +/- 0.0003		***	[0.8,0.9]	0.112 +/- 0.004
[-0.8,-0.7]	0.01821 +/- 0.0003		***	[0.7,0.8]	0.1162 +/- 0.0034
[-0.7,-0.6]	0.03065 +/- .000163		***	[0.6,0.7]	0.08958 +/- 0.00316
[-0.6,-0.5]	0.02109 +/- 0.00217		***	[0.5,0.6]	0.07347 +/- 0.00210
[-0.5,-0.4]	0.03772 +/- 0.00133		***	[0.4,0.5]	0.07271 +/- 0.00159
[-0.4,-0.3]	0.04817 +/- 0.00125		***	[0.3,0.4]	0.06196 +/- 0.00146
[-0.3,-0.2]	0.05154 +/- 0.00113		***	[0.2,0.3]	0.06087 +/- 0.00114
[-0.2,-0.1]	0.05677 +/- 0.00106		***	[0.1,0.2]	0.07298 +/- 0.00149
[-0.1,0.0]	0.08348 +/- 0.00144		***	[0.0,0.1]	0.09017 +/- 0.00128

Below are the histograms for a 6cm target in the Z direction using a 6 GeV electron fired at 25 degrees in theta and 0 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vz Difference	***	Interval	Resolution (cm)	Vz Difference
[-3.0,-2.5]	0.1427 +/- 0.0009		***	[2.5,3.0]	0.1467 +/- 0.0008
[-2.5,-2.0]	0.1412 +/- 0.0008		***	[2.0,2.5]	0.1419 +/- 0.0009
[-2.0,-1.5]	0.1365 +/- 0.0007		***	[1.5,2.0]	0.1372 +/- 0.0008
[-1.5,-1.0]	0.1439 +/- 0.0008		***	[1.0,1.5]	0.1394 +/- 0.0008
[-1.0,-0.5]	0.1429 +/- 0.0008		***	[0.5,1.0]	0.1584 +/- 0.0010
[-0.5,0.0]	0.1332 +/- 0.0007		***	[0.0,0.5]	0.1378 +/- 0.0009

Below are the histograms for a 6cm target in the Z direction using a 6 GeV electron fired at 25 degrees in theta and 90 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vz Difference	***	Interval	Resolution (cm)	Vz Difference
[-3.0,-2.5]	0.1192 +/- 0.0005		***	[2.5,3.0]	0.1211 +/- 0.0005
[-2.5,-2.0]	0.1205 +/- 0.0005		***	[2.0,2.5]	0.1251 +/- 0.0005
[-2.0,-1.5]	0.122 +/- 0.001		***	[1.5,2.0]	0.1312 +/- 0.0006
[-1.5,-1.0]	0.1249 +/- 0.0006		***	[1.0,1.5]	0.1233 +/- 0.0005
[-1.0,-0.5]	0.1278 +/- 0.0006		***	[0.5,1.0]	0.1254 +/- 0.0005
[-0.5,0.0]	0.1289 +/- 0.0006		***	[0.0,0.5]	0.1237 +/- 0.0005

Below are the histograms for a 6 GeV electron fired at angles 25 degrees in theta and 270 degrees in phi. The target was 6cm in the Z direction.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vz Difference	***	Interval	Resolution (cm)	Vz Difference
[-3.0,-2.5]	0.1171 +/- 0.0008		***	[2.5,3.0]	0.1186 +/- 0.0008
[-2.5,-2.0]	0.1162 +/- 0.0008		***	[2.0,2.5]	0.1226 +/- 0.0009
[-2.0,-1.5]	0.1207 +/- 0.0009		***	[1.5,2.0]	0.1317 +/- 0.0010
[-1.5,-1.0]	0.1294 +/- 0.0010		***	[1.0,1.5]	0.1239 +/- 0.0009
[-1.0,-0.5]	0.131 +/- 0.001		***	[0.5,1.0]	0.1256 +/- 0.0009
[-0.5,0.0]	0.131 +/- 0.001		***	[0.0,0.5]	0.1261 +/- 0.0010

Below are the histograms for a 6 GeV electron fired at 25 degrees in theta and 0 degrees in phi. The target is 2cm long on the Y axis.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vy Difference	***	Interval	Resolution (cm)	Vy Difference
[-1.0,-0.9]	0.09406 +/- 0.00128		***	[0.9,1.0]	0.1001 +/- 0.0016
[-0.9,-0.8]	0.0868 +/- 0.0013		***	[0.8,0.9]	0.1221 +/- 0.0018
[-0.8,-0.7]	0.08961 +/- 0.00128		***	[0.7,0.8]	0.1144 +/- 0.0017
[-0.7,-0.6]	0.09853 +/- 0.00148		***	[0.6,0.7]	0.169 +/- 0.003
[-0.6,-0.5]	0.1038 +/- 0.0016		***	[0.5,0.6]	0.171 +/- 0.003
[-0.5,-0.4]	0.1202 +/- 0.0018		***	[0.4,0.5]	0.1105 +/- 0.0016
[-0.4,-0.3]	0.1755 +/- 0.0026		***	[0.3,0.4]	0.09508 +/- 0.00137
[-0.3,-0.2]	0.1847 +/- 0.0028		***	[0.2,0.3]	0.09065 +/- 0.0140
[-0.2,-0.1]	0.1255 +/- 0.0019		***	[0.1,0.2]	0.093002 +/- 0.0013
[-0.1,0.0]	0.09663 +/- 0.00160		***	[0.0,0.1]	0.09008 +/- 0.0012

Below are the histograms for a 2cm target along the Y axis, X = 0 Z = 0. The electrons were fired with an energy of 6 GeV at 25 degrees in theta and 30 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vy Difference	***	Interval	Resolution (cm)	Vy Difference
[-1.0,-0.9]	0.069 +/- 0.002		***	[0.9,1.0]	0.04936 +/- 0.00068
[-0.9,-0.8]	0.08185 +/- 0.00218		***	[0.8,0.9]	0.05797 +/- 0.00094
[-0.8,-0.7]	0.08764 +/- 0.00212		***	[0.7,0.8]	0.05896 +/- 0.00086
[-0.7,-0.6]	0.09158 +/- 0.00258		***	[0.6,0.7]	0.05895 +/- 0.00091
[-0.6,-0.5]	0.07913 +/- 0.00166		***	[0.5,0.6]	0.05943 +/- 0.00096
[-0.5,-0.4]	0.0774 +/- 0.0014		***	[0.4,0.5]	0.06227 +/- 0.00118
[-0.4,-0.3]	0.07978 +/- 0.00157		***	[0.3,0.4]	0.08115 +/- 0.00186
[-0.3,-0.2]	0.08193 +/- 0.00235		***	[0.2,0.3]	0.01028 +/- 0.0029
[-0.2,-0.1]	0.1812 +/- 0.0025		***	[0.1,0.2]	0.136 +/- 0.003
[-0.1,0.0]	0.1503 +/- 0.0021		***	[0.0,0.1]	0.2052 +/- 0.0033

Below are the histograms for a 2cm Y target with an incident electron energy of 6 GeV. The angles were theta = 25 degrees and phi = 210 degrees

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Interval	Resolution (cm)	Vy Difference	***	Interval	Resolution (cm)	Vy Difference
[-1.0,-0.9]	0.04815 +/- 0.00067		***	[0.9,1.0]	0.07184 +/- 0.00181
[-0.9,-0.8]	0.05734 +/- 0.00091		***	[0.8,0.9]	0.08837 +/- 0.00268
[-0.8,-0.7]	0.05873 +/- 0.00085		***	[0.7,0.8]	0.0982 +/- 0.0024
[-0.7,-0.6]	0.05868 +/- 0.00089		***	[0.6,0.7]	0.09622 +/- 0.00305
[-0.6,-0.5]	0.05962 +/- 0.00098		***	[0.5,0.6]	0.08028 +/- 0.00156
[-0.5,-0.4]	0.0645 +/- 0.0014		***	[0.4,0.5]	0.07917 +/- 0.00163
[-0.4,-0.3]	0.0861 +/- 0.0020		***	[0.3,0.4]	0.08056 +/- 0.00159
[-0.3,-0.2]	0.1003 +/- 0.0024		***	[0.2,0.3]	0.08939 +/- 0.00201
[-0.2,-0.1]	0.1305 +/- 0.0024		***	[0.1,0.2]	0.186 +/- 0.003
[-0.1,0.0]	0.2042 +/- 0.0033		***	[0.0,0.1]	0.1476 +/- 0.0021

Localized Vertex Resolution Investigation of 2 Dimensional Targets

The histograms below were created using a 6 GeV electron fired at 25 degrees in theta and 30 degrees in phi. To make the cuts I simply made circles of increasing radius centered at the origin. I used 0.1cm increments to make the 10 histograms for each vertex position.

Below are the Vx and Vy Differences for a 2cm XY target, Z=0.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Radius (cm)	Resolution (cm)	Vx Difference	***	Radius (cm)	Resolution (cm)	Vx Difference
0.1	0.2309 +/- 0.0091		***	0.6	0.259 +/- 0.001
0.2	0.235 +/- 0.004		***	0.7	0.2769 +/- 0.0014
0.3	0.2242 +/- 0.0028		***	0.8	0.2927 +/- 0.0013
0.4	0.2272 +/- 0.0020		***	0.9	0.3074 +/- 0.0013
0.5	0.2422 +/- 0.0016		***	1.0	0.3237 +/- 0.0014

Radius (cm)	Resolution (cm)	VyDifference	***	Radius (cm)	Resolution (cm)	Vy Difference
0.1	0.162 +/- 0.006		***	0.6	0.1733 +/- 0.0020
0.2	0.1798 +/- 0.0031		***	0.7	0.1661 +/- 0.0017
0.3	0.1947 +/- 0.0028		***	0.8	0.1615 +/- 0.0015
0.4	0.1959 +/- 0.0033		***	0.9	0.1578 +/- 0.0013
0.5	0.1861 +/- 0.0027		***	1.0	0.4832 +/- 0.0035

Below are the Vy and Vz differences for a 2cm target in Y and Z, X=0. The electrons were fired with an energy of 6 GeV and angles of 25 degrees in theta and 30 degrees in phi.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Radius (cm)	Resolution (cm)	Vy Difference	***	Radius (cm)	Resolution (cm)	Vy Difference
0.1	0.1722 +/- 0.0065		***	0.6	0.1806 +/- 0.0017
0.2	0.1773 +/- 0.0037		***	0.7	0.1868 +/- 0.0015
0.3	0.1781 +/- 0.0031		***	0.8	0.1974 +/- 0.0014
0.4	0.1734 +/- 0.0024		***	0.9	0.2028 +/- 0.0013
0.5	0.1764 +/- 0.0020		***	1.0	0.221 +/- 0.001

Radius (cm)	Resolution (cm)	Vz Difference	***	Radius (cm)	Resolution (cm)	Vz Difference
0.1	0.07095 +/- 0.00239		***	0.6	0.261 +/- 0.001
0.2	0.1063 +/- 0.0015		***	0.7	0.2874 +/- 0.0010
0.3	0.146 +/- 0.001		***	0.8	0.3232 +/- 0.0011
0.4	0.1833 +/- 0.0012		***	0.9	0.3528 +/- 0.0010
0.5	0.2222 +/- 0.0012		***	1.0	0.3847 +/- 0.0010

Below are the Vx and Vz differences for a 2cm XZ target, Y = 0. The electrons were fired with an energy of 6 GeV at angles theta = 25 degrees and phi = 30 degrees.

GenPart.x	GenPart.y	GenPart.z	Event.x	Event.y	Event.z

Radius (cm)	Resolution (cm)	Vz Difference	***	Radius (cm)	Resolution (cm)	Vz Difference
0.1	0.06193 +/- 0.00199		***	0.6	0.2495 +/- 0.0012
0.2	0.1059 +/- 0.0015		***	0.7	0.2862 +/- 0.0011
0.3	0.1412 +/- 0.0013		***	0.8	0.3172 +/- 0.001
0.4	0.1704 +/- 0.0012		***	0.9	0.3512 +/- 0.0012
0.5	0.2183 +/- 0.0013		***	1.0	0.4066 +/- 0.0013

Radius (cm)	Resolution (cm)	Vx Difference	***	Radius (cm)	Resolution (cm)	Vx Difference
0.1	0.2125 +/- 0.0090		***	0.6	0.2365 +/- 0.0016
0.2	0.2392 +/- 0.0044		***	0.7	0.2307 +/- 0.0013
0.3	0.251 +/- 0.003		***	0.8	0.2251 +/- 0.0012
0.4	0.2494 +/- 0.0023		***	0.9	0.222 +/- 0.001
0.5	0.2439 +/- 0.0019		***	1.0	0.2193 +/- 0.0010

Localized Vertex Resolution of 3 Dimensional targets

For this section I created a target that is 2cm in X and Y, and 6cm in Z. To produce the histograms I made a cut in the radius of a cylinder (R=0.1cm, R=0.2cm, .... , R=1.0cm) and also cut Z (Z=1cm, Z=2cm,...,Z=6cm) so that for each fixed radius there will be 6 histograms corresponding to changes in Z. For example, assume I am using R=0.1cm. There will be 6 histograms for X,Y,and Z corresponding to changing Z from 1cm to 6cm in 1cm increments. I also placed a cut for the reconstructed events using the commands abs(Event.z) <= 4.0 and sqrt(Event.x*Event.x+Event.y*Event.y) <=1.

Below are the Vx Differences for R=1.0cm

Z (cm)	Resolution (cm)	Vx Difference	***	Z (cm)	Resolution (cm)	Vx Difference
1.0	0.305 +/- 0.003		***	4.0	0.3459 +/- 0.0018
2.0	0.307 +/- 0.003		***	5.0	0.3688 +/- 0.0016
3.0	0.3214 +/- 0.0021		***	6.0	0.3877 +/- 0.0015

Below are the histograms for R=0.9cm

Z (cm)	Resolution (cm)	Vx Difference	***	Z (cm)	Resolution (cm)	Vx Difference
1.0	0.2979 +/- 0.0032		***	4.0	0.3331 +/- 0.0018
2.0	0.2979 +/- 0.0025		***	5.0	0.3551 +/- 0.0016
3.0	0.3106 +/- 0.0021		***	6.0	0.3728 +/- 0.0015

Below are the histograms for R=0.8cm

Z (cm)	Resolution (cm)	Vx Difference	***	Z (cm)	Resolution (cm)	Vx Difference
1.0	0.2827 +/- 0.0031		***	4.0	0.3184 +/- 0.0017
2.0	0.2863 +/- 0.0024		***	5.0	0.3388 +/- 0.0016
3.0	0.2974 +/- 0.0020		***	6.0	0.3556 +/- 0.0015

Below are the histograms for R=0.7 cm.

Z (cm)	Resolution (cm)	Vx Difference	***	Z (cm)	Resolution (cm)	Vx Difference
1.0	0.273 +/- 0.003		***	4.0	0.3077 +/- 0.0017
2.0	0.2775 +/- 0.0024		***	5.0	0.3292 +/- 0.0017
3.0	0.2883 +/- 0.0020		***	6.0	0.3292 +/- 0.0017