FIRST ATTEMPT AT FINDING SVT TRACKS

I perform here two analysis: first assuming no a priori knowledge on detector geometry, then using the nominal SVXII geometry. For simplicity I did this in an interactive Mathematica session.

Initialization
[Graphics:Images/SVT_first_gr_5.gif]


Read in data(2382 candidate tracks in 2 wedges)

dat=Table[Read["float_102831.txt",Real],{i,1,2382},{j,1,5}];Close["float_102831.txt"]
[Graphics:Images/SVT_first_gr_6.gif]
[Graphics:Images/SVT_first_gr_7.gif]
[Graphics:Images/SVT_first_gr_8.gif]
[Graphics:Images/SVT_first_gr_9.gif]
[Graphics:Images/SVT_first_gr_10.gif]
I am going to use wedge 3 only, because it has more data
[Graphics:Images/SVT_first_gr_11.gif]
[Graphics:Images/SVT_first_gr_12.gif]
[Graphics:Images/SVT_first_gr_13.gif]
[Graphics:Images/SVT_first_gr_14.gif]
As with the previous smaller sample, the smallest eigenvalue is too big to be just resolution
[Graphics:Images/SVT_first_gr_15.gif]
0.1877440906638008` 0.31033913234003846` 0.5019103800074148` 0.7851928105886267`
[Graphics:Images/SVT_first_gr_16.gif] [Graphics:Images/SVT_first_gr_17.gif] [Graphics:Images/SVT_first_gr_18.gif] 0.45820164928869167`
0.5831392870921455` [Graphics:Images/SVT_first_gr_19.gif] [Graphics:Images/SVT_first_gr_20.gif] 0.3918209464881586`
[Graphics:Images/SVT_first_gr_21.gif] 0.7471787327501067` [Graphics:Images/SVT_first_gr_22.gif] 0.14142080710492277`

I can, however, now  plot the distribution of its projection since I have some more data

[Graphics:Images/SVT_first_gr_23.gif]
[Graphics:Images/SVT_first_gr_24.gif]
[Graphics:Images/SVT_first_gr_25.gif]
[Graphics:Images/SVT_first_gr_26.gif]
[Graphics:Images/SVT_first_gr_27.gif]
[Graphics:Images/SVT_first_gr_28.gif]
[Graphics:Images/SVT_first_gr_29.gif]
[Graphics:Images/SVT_first_gr_30.gif]
[Graphics:Images/SVT_first_gr_31.gif]

The above distribution has a narrower central component over a broader background; this is evidence for some real tracks in the sample !
Its width is about 100 microns.

Now select the cleaner sample in the central peak:
[Graphics:Images/SVT_first_gr_32.gif]
[Graphics:Images/SVT_first_gr_33.gif]
[Graphics:Images/SVT_first_gr_34.gif]
[Graphics:Images/SVT_first_gr_35.gif]
[Graphics:Images/SVT_first_gr_36.gif]
[Graphics:Images/SVT_first_gr_37.gif]
[Graphics:Images/SVT_first_gr_38.gif]
[Graphics:Images/SVT_first_gr_39.gif]
[Graphics:Images/SVT_first_gr_40.gif]
[Graphics:Images/SVT_first_gr_41.gif] [Graphics:Images/SVT_first_gr_42.gif] [Graphics:Images/SVT_first_gr_43.gif] [Graphics:Images/SVT_first_gr_44.gif]
[Graphics:Images/SVT_first_gr_45.gif] [Graphics:Images/SVT_first_gr_46.gif] [Graphics:Images/SVT_first_gr_47.gif] 0.4754713729161473`
0.6070203400012769` [Graphics:Images/SVT_first_gr_48.gif] [Graphics:Images/SVT_first_gr_49.gif] 0.3766605208496238`
[Graphics:Images/SVT_first_gr_50.gif] 0.7516288324672467` [Graphics:Images/SVT_first_gr_51.gif] 0.13457025381347892`

This is (intuitively) the best candidate for the impact parameter wrt to the beam for this sample

[Graphics:Images/SVT_first_gr_52.gif]
[Graphics:Images/SVT_first_gr_53.gif]
[Graphics:Images/SVT_first_gr_54.gif]
[Graphics:Images/SVT_first_gr_55.gif]
Plot its distribution:
[Graphics:Images/SVT_first_gr_56.gif]
[Graphics:Images/SVT_first_gr_57.gif]
[Graphics:Images/SVT_first_gr_58.gif]
[Graphics:Images/SVT_first_gr_59.gif]
[Graphics:Images/SVT_first_gr_60.gif]
This is rather wide, but we used tracks of all Pts. Let's try to use high-Pt only

This is the best candidate for curvature:

[Graphics:Images/SVT_first_gr_61.gif]
[Graphics:Images/SVT_first_gr_62.gif]
[Graphics:Images/SVT_first_gr_63.gif]
[Graphics:Images/SVT_first_gr_64.gif]
[Graphics:Images/SVT_first_gr_65.gif]
[Graphics:Images/SVT_first_gr_66.gif]
[Graphics:Images/SVT_first_gr_67.gif]
[Graphics:Images/SVT_first_gr_68.gif]
[Graphics:Images/SVT_first_gr_69.gif]
Select tracks of high Pt (unclear how much, at this point). Find 123 tracks.
[Graphics:Images/SVT_first_gr_70.gif]
[Graphics:Images/SVT_first_gr_71.gif]
Now plot "impact parameter" for those:
[Graphics:Images/SVT_first_gr_72.gif]
[Graphics:Images/SVT_first_gr_73.gif]
[Graphics:Images/SVT_first_gr_74.gif]
[Graphics:Images/SVT_first_gr_75.gif]
[Graphics:Images/SVT_first_gr_76.gif]
[Graphics:Images/SVT_first_gr_77.gif]


ANALYSIS BASED ON NOMINAL GEOMETRY

Constraint and parameter expressions, generated from nominal geometry (CORRGEN program)
[Graphics:Images/SVT_first_gr_78.gif]
[Graphics:Images/SVT_first_gr_79.gif]
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[Graphics:Images/SVT_first_gr_82.gif]
[Graphics:Images/SVT_first_gr_83.gif]
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[Graphics:Images/SVT_first_gr_86.gif]
[Graphics:Images/SVT_first_gr_87.gif]
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[Graphics:Images/SVT_first_gr_89.gif]
[Graphics:Images/SVT_first_gr_90.gif]
[Graphics:Images/SVT_first_gr_91.gif]
[Graphics:Images/SVT_first_gr_92.gif]
[Graphics:Images/SVT_first_gr_93.gif]
Now plot the (single, because we lack XFT) constraint:
[Graphics:Images/SVT_first_gr_94.gif]
[Graphics:Images/SVT_first_gr_95.gif]
[Graphics:Images/SVT_first_gr_96.gif]
[Graphics:Images/SVT_first_gr_97.gif]
[Graphics:Images/SVT_first_gr_98.gif]
This looks vaguely similar to the one obtained "in the dark" , but much cleaner ! Note it comes out centered at zero without ad-hoc corrections.
NO DOUBT THERE ARE TRACKS HERE !!!!

now select the central peak:

[Graphics:Images/SVT_first_gr_99.gif]
[Graphics:Images/SVT_first_gr_100.gif]
[Graphics:Images/SVT_first_gr_101.gif]
[Graphics:Images/SVT_first_gr_102.gif]
[Graphics:Images/SVT_first_gr_103.gif]
[Graphics:Images/SVT_first_gr_104.gif]
[Graphics:Images/SVT_first_gr_105.gif]
[Graphics:Images/SVT_first_gr_106.gif] [Graphics:Images/SVT_first_gr_107.gif] [Graphics:Images/SVT_first_gr_108.gif] [Graphics:Images/SVT_first_gr_109.gif]
[Graphics:Images/SVT_first_gr_110.gif] [Graphics:Images/SVT_first_gr_111.gif] [Graphics:Images/SVT_first_gr_112.gif] 0.47482059037024443`
0.5804496434264329` [Graphics:Images/SVT_first_gr_113.gif] [Graphics:Images/SVT_first_gr_114.gif] 0.3843728485385215`
[Graphics:Images/SVT_first_gr_115.gif] 0.770647881938822` [Graphics:Images/SVT_first_gr_116.gif] 0.10569412662198875`

Calculate curvature for this cleaned-up sample:

[Graphics:Images/SVT_first_gr_117.gif]
[Graphics:Images/SVT_first_gr_118.gif]
[Graphics:Images/SVT_first_gr_119.gif]
[Graphics:Images/SVT_first_gr_120.gif]
[Graphics:Images/SVT_first_gr_121.gif]
Select a sample of high-Pt tracks:
[Graphics:Images/SVT_first_gr_122.gif]
[Graphics:Images/SVT_first_gr_123.gif]
Plot their impact parameter:
[Graphics:Images/SVT_first_gr_124.gif]
[Graphics:Images/SVT_first_gr_125.gif]
[Graphics:Images/SVT_first_gr_126.gif]
[Graphics:Images/SVT_first_gr_127.gif]
[Graphics:Images/SVT_first_gr_128.gif]
This is kind of wide, but we need to correct for beam position ! Let's plot d vs. phi:
[Graphics:Images/SVT_first_gr_129.gif]
[Graphics:Images/SVT_first_gr_130.gif]
[Graphics:Images/SVT_first_gr_131.gif]
THIS LINEAR RELATIONHIP IS FURTHER CLEAR EVIDENCE WE ARE OBSERVING REAL TRACKS !!!

now I want to fit the beam "by eye", and evaluate d wrt the beam :

[Graphics:Images/SVT_first_gr_132.gif]
[Graphics:Images/SVT_first_gr_133.gif]
[Graphics:Images/SVT_first_gr_134.gif]
[Graphics:Images/SVT_first_gr_135.gif]
[Graphics:Images/SVT_first_gr_136.gif]
[Graphics:Images/SVT_first_gr_137.gif]
OK, so this is the expression of d wrt the beam:
[Graphics:Images/SVT_first_gr_138.gif]
[Graphics:Images/SVT_first_gr_139.gif]
[Graphics:Images/SVT_first_gr_140.gif]
[Graphics:Images/SVT_first_gr_141.gif]
[Graphics:Images/SVT_first_gr_142.gif]
And this is its distribution:
[Graphics:Images/SVT_first_gr_143.gif]
[Graphics:Images/SVT_first_gr_144.gif]
[Graphics:Images/SVT_first_gr_145.gif]
[Graphics:Images/SVT_first_gr_146.gif]
[Graphics:Images/SVT_first_gr_147.gif]
This is rather clean now.
NOTE THAT FULL-WIDTH AT HALF-HEIGHT IS <400 micron

Now I do a crosscheck by replotting the Kernel projection after the beam constraint, restarting from the initial sample, including tracks of all Pt's

[Graphics:Images/SVT_first_gr_148.gif]
[Graphics:Images/SVT_first_gr_149.gif]
[Graphics:Images/SVT_first_gr_150.gif]
[Graphics:Images/SVT_first_gr_151.gif]
[Graphics:Images/SVT_first_gr_152.gif]
[Graphics:Images/SVT_first_gr_153.gif]
[Graphics:Images/SVT_first_gr_154.gif]
This is VERY CLEAN now !!! The beam constraint cleans up the sample a lot !!!
Note that Kernel and d are basically uncorrelated, as they should:
[Graphics:Images/SVT_first_gr_155.gif]
[Graphics:Images/SVT_first_gr_156.gif]
...so there is no trick,the correlation between the two variables is given by physics!!!
 

Finally, select a  sample of good tracks, by cutting both on beam and K:

[Graphics:Images/SVT_first_gr_157.gif]
[Graphics:Images/SVT_first_gr_158.gif]
[Graphics:Images/SVT_first_gr_159.gif]
[Graphics:Images/SVT_first_gr_160.gif]
[Graphics:Images/SVT_first_gr_161.gif]
[Graphics:Images/SVT_first_gr_162.gif]
From this, I get the following estimates:

SILICON DETECTORS RESOLUTION

[Graphics:Images/SVT_first_gr_163.gif]
[Graphics:Images/SVT_first_gr_164.gif]

BEAM WIDTH (transverse direction)

[Graphics:Images/SVT_first_gr_165.gif]
[Graphics:Images/SVT_first_gr_166.gif]

Converted by Mathematica      November 1, 2000