High-resolution measurements with a spaceborne pencil-beam ...
Beam parameters update – the resolution function
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Beam parameters update – the resolution function
J. Thompson, A. Roodman
SLAC
11/19/04
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Beam Parameter Analysis
• Goal is to measure epsilon, beta* (in y) by measuring hourglass effect:– Measure beamspot width as a function of z– Also measure longitudinal lumi distribution
• First attempt (G. Schott) ran into problems– Trying to measure O(1 um) effect on 20 um
resolution– Discovered resolution varies with z
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• Two major effects were not understood:– Variation with phi of predicted error on doca– Variation with z (as mentioned on last page)
• We now know about SVT bonding type
• No answer for z variation
z (cm) z (cm)
docaError(cm)
Track 1 Track 2
Black data
Red MC
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New strategy
• Conclusion: Resolution as a function of detector geometry is complicated
• Incorporate predicted track doca error into the fits and thus fit purely for beam width
• Need a resolution function to correct predicted doca error to actual resolution; convolve it with doca PDF in final fit
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Resolution function
• Each event has two independent tracks (no vertexing)
• doca has been moved into beam coordinates
• Find a function to describe distribution of doca miss distance (sum of signed docas) as a function of sqrt(sigma_doca1^2 + sigma_doca2^2)
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Resolution Function is the sum of 3 Gaussians:
R = f1*G(mu, S1*Sigma) + f2*G(mu, S2*Sigma) + f3*G(0, const), S2>S1
Works OK?; Parameters very correlated; dependence of S1, S2 on choice of width of G3 (originally set to 250um, later adjusted to 125um)
Data:f1=0.92f2=0.08m1=7.0e-5S1=1.09S2=1.94
MC:f1=0.96f2=0.04m1=-8.3e-5S1=1.00S2=2.01
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Resolution fit results in bins of phi and cos(theta)
Better version on next page
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Resolution fit results in bins of phi and cos(theta)
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Sample resolution fits from 2 geometric bins (same theta, adjacent phi)
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SVT bond type largely determines doca error:
Does it affect the scale factors in resolution function widths?
(Scale factors on prev slide mainly varied with phi)
Single-track doca error for all combinations of SVT bond type in layers 1 & 2
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Bonding type combinations from prev slide combined into 4 categories
Doca error (cm)
I will compare resolution function fits to events grouped into combinations of these categories for the 2 tracks in the event (so 16 fits in all)
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Resolution fits by bond type
RR RR:
f1=0.91
f2=0.09
S1=1.04
S2=2.08
SS SS:
f1=0.90
f2=0.09
S1=1.11
S2=1.82
(width3 = 250um)
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Resolution function parameters (in data) by SVT bonding type category
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• Points at each z value are the average of fits to 8 datasets (data)
• Do global sigma_y fits change as we fix res function to these various sets of parameters? eventually a systematic
z (cm)
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3 datasets shown here in color are fits to independent sets of MC events; black is a fit to the 3 datasets combined as one
Width3 = 125um
-0.02cm<miss distance<0.02cm
(removes almost no events)
Generated y width (um)
Blue: 50k events in fit
Red/Green: 70k events in fit
(um)
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Projections of miss distance and doca for a fit similar to those shown on prev page
(no miss distance cut at +-0.02cm)
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Another test2 attempts at floating the width3 in a high-statistics data fit: unrestricted and restricted range in miss distance
(tails look bad on both of the doca distributions also)
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Is fit sensitive to width3 of resolution function?
Fit the same data samples repeatedly with width3 set to varying values
• From left to right at each generated sigmaY:
width3 = 50um
85um
100um
125um
175um
250um
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• Having trouble getting a great fit for resolution function– when statistics are high, tails are hard to model– “outlier” Gaussian seems to play a role in the core
• But sigma_y fit seems rather robust to changes in resolution function
• Is the sigma_y fit biased at low (ie realistic) values?– Need to do more fits to MC at 2-4um
• How many events are needed in a global fit?• How many events will be needed in binned fits?
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Next step: Test fitting in bins of z
Successfully modified generator to create HG effect in y; these plots are made using MC truth
125um
~3um
z (cm)
sigma x sigma y
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Comments
• Compared to GS’s fits:– Resolution function added– Removed/marginalized some parameters (tilts
w/z axis; x0,y0)
• My CM2 ntuples have big improvements – beam info updates >> once per run– MC truth