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Beam parameters update – the resolution function

Beam parameters update – the resolution function. J. Thompson, A. Roodman SLAC 11/19/04. 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

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Beam parameters update – the resolution function

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  1. Beam parameters update – the resolution function J. Thompson, A. Roodman SLAC 11/19/04

  2. 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

  3. 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 Track 1 Track 2 Black  data Red  MC doca Error (cm) z (cm) z (cm)

  4. 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

  5. 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)

  6. 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=0.92 f2=0.08 m1=7.0e-5 S1=1.09 S2=1.94 MC: f1=0.96 f2=0.04 m1=-8.3e-5 S1=1.00 S2=2.01

  7. Resolution fit results in bins of phi and cos(theta) Better version on next page

  8. Resolution fit results in bins of phi and cos(theta)

  9. Sample resolution fits from 2 geometric bins (same theta, adjacent phi)

  10. SVT bond type largely determines doca error: Single-track doca error for all combinations of SVT bond type in layers 1 & 2 Does it affect the scale factors in resolution function widths? (Scale factors on prev slide mainly varied with phi)

  11. 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)

  12. 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)

  13. Resolution function parameters (in data) by SVT bonding type category

  14. z (cm) • 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

  15. 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 Blue: 50k events in fit Red/Green: 70k events in fit Width3 = 125um -0.02cm<miss distance<0.02cm (removes almost no events) (um) Generated y width (um)

  16. Projections of miss distance and doca for a fit similar to those shown on prev page (no miss distance cut at +-0.02cm)

  17. Another test 2 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)

  18. 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

  19. 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?

  20. Next step: Test fitting in bins of z Successfully modified generator to create HG effect in y; these plots are made using MC truth sigma x sigma y 125um  ~3um z (cm)

  21. 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

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