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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