Update: Beam Parameters from Dimuons

1. Update: Beam Parameters from Dimuons 26 July 2004 Josh Thompson Aaron Roodman SLAC

2. Overview • Quick summary of the initial analysis: goals and technique • Details about problems that arose during the initial analysis and studies conducted since then • Steps to move forward with the analysis • What changes are being implemented • What will be implemented in the future

3. Beam Parameters from Dimuons • Goal: measure beam parameters epsilon_y and beta*_y (at the IP) • Due to hourglass effect, sigma_y of the interaction region should have a parabolic shape as a function of z, with a central waist • Technique is to fit for sigma_y as a function of z and use this to extract beam parameters

4. Gregory Schott method • Using whole data sample (selection cuts applied): • Fit z0, sigmaz to Gaussian • Fix z0, sigmaz; fit x0, sigmax, y0, sigmay, 3 tilts, constant background term with a PDF for the doca distribution • In bins of z: • Fit y0, sigmay (optionally x0, sigmax) with other params fixed from above fit • Correct sigmay for resolution variation with z (use doca error vs z plot; details follow)

5. (Details) • Tracks in dimuon events are independent (not vertexed) • Selection cuts: • tan(lambda1) + tan(lambda2) > 0.5 (cut cosmics) • |10.58 GeV - m_mm| < 0.3 GeV • nDCH >= 20 && nSVT >= 5 • cos(phi1 – phi2) < -0.99 • cos(theta) < 0.75

6. First some review Is the error on the track doca (from the covariance matrix of the track fit) reliable? Yes: The measured miss distance between the docas of the two tracks in an event does correlate nicely to the combined doca errors for tracks 1 and 2 I get the same slope as in GS’s thesis: 1.2 mm/mm • So the doca error from the fit is likely a good measure of resolution • We will come back to this correlation later Width of miss distance distribution (cm) sqrt((doca error 1)^2 + (doca error 2)^2) (cm)

7. (verticality cut applied) Error on doca phi Problem 1:Error on doca w.r.t. phi • Why do we care? • We need to understand all aspects of the resolution • GS: Integral over a track distribution flat in phi is assumed in the PDF, so cuts must preserve that distributionthis plot means we can’t cut directly on track quality • I had 2 issues with this distribution: • ‘Good’ regions have ~15-20um resolution while ‘bad’ regions have ~20-25um resolution – regions are almost mutually exclusive in doca error • phi distribution of ‘good’ and ‘bad’ regions is unintuitive  Next page

8. Is SVT structure the problem? • Naively: doca resolution dominated by inner SVT layers • Best resolution comes when first hit is as close as possible to IP and track is at a right angle to the SVT plane • Extra material (eg SVT support ribs) degrades resolution Dimuon tracks (same plot as prev. page but showing only events on “SVT” plot at right) Color code by doca error: >20umred; <20umgreen mm

9. SVT structure (II) Color code by doca error: >20umred; <20umgreen • From this (partial and hand-drawn) picture of the SVT: • Each of the 6 modules of the inner SVT layer is split between a green region and red region • No obvious reason why there should be a large resolution shift in the middle of each module, or from one module to the next at the same phi

10. Problem 1 solved • For the phi side only of Layers 1 and 2 of the SVT: • ~Half of each module has every SVT strip connected for readout • The rest of each module has every other strip “floating” (ie not read out) • known as skip bonding • Looking at the info in the SvtHitOnTrk of the Layer 1 phi-side hit: • Blue (solid) histo shows phi distrib of events with regular bonding • Red (dashed) histo shows phi distrib of events with skip bonding Events doca error (backw) phi (backw)

11. (forw) Problem 2:Resolution variation with z doca err • As GS observed, the doca error decreases with increasing z (true for miss distance as well) • [doca error is a single track quantity, so more convenient for detector studies] • GS thesis: slope = -0.385 mm/cm • Here: slope (forw) = -0.42 mm/cm • slope (backw) = -0.24 mm/cm •  Look at doca error in bins of theta z (backw) doca err

12. Expanded resolution studies • How does resolution vary as a function of z and theta together? • Use doca error in bins of theta and z • But this is a two-peaked distribution (due to bonding difference) • Is the mean of the distribution adequate? • Fit to 2 Gaussians • Also look at material length in SVT

13. Material Length Total material seen by tracks in first 15cm (x-y) of flight (approx SVT radius) cm For simplicity, I will look at the mean of this distribution Caveat: This study looks at detector material path length in cm—not g/cm^2. I will work on getting that additional information. (info comes from pathLength() method of DetIntersection)

14. Material Length (II) Mean of distribution from last page, binned in cos(theta) v z (cm) (cm) First 15 cm (x-y) of flight First 6 cm (x-y) of flight

15. Profiles: Material Length v z 6 cm of flight 15 cm of flight (note suppressed zeros on y axes) 15 cm of flight cos(theta)>0.65 6 cm of flight cos(theta)>0.65

16. Material Length v z • Conclusion: All show a negative slope, but very slight and consistent with zero within errors • Material length is not causing the resolution variation w.r.t. z • I need to look at mass thickness to confirm this conclusion

17. -1.2<z<0.93 (cm) 0.69<cos(t)<0.75 1.47<z<1.73 (cm) 0.69<cos(t)<0.75 Sample Fits -1.2<z<0.93 (cm) 0.43<cos(t)<0.50 1.47<z<1.73 (cm) 0.43<cos(t)<0.50

18. cos(theta) Lower mean of doca err distribution (cm) z (cm) theta and z dependence of doca error • In the forward direction, this plot shows the resolution getting better as z increases • At lower cos(theta) this is less pronounced. (NB: transition from forw to backw tracks occurs at cos(theta)~0.5) • Lower mean correlates well with higher mean—high mean plot looks similar (see extra slide) Resolution correction as a function of z only is probably not sufficient Possible band of lower resolution diagonally across plot?

19. Average number of SVT hits in Layers 1,2,3: All strips Phi strips only Diagonal Band? (note expansion in z scale; outer bins statistically limited)

20. Fraction of tracks w/a phi side hit in Layer 1 cos(theta) Missing f hit in Layer 1 z (cm) Plug in x-y flight length l = 3.2 cm (min. radius of L1): zL1 = z0 + l*tan(l) = z0 + 3.2*tan(p/2 – q) ~ 2.5 cm across the band

21. Where do we go from here? • [GS correction: sy,corrected2 = sy,fit2 / (1+slopefit*z/interceptfit)2 ] • Incorporate the resolution directly into the PDF: • Replace sdoca2 = sx2*sin2(f) + sy2*cos2(f) with: • sdoca2 = sx2*sin2(f) + sy2*cos2(f) + sresolution2 • sresolution is the doca error from the track fit adjusted by a resolution function • Resolution function comes from miss distance v doca error • To do: Study this function more completely (e.g. is the miss distance distribution really Gaussian?)

22. Test New PDF • First run simple toys on new PDF: • Generate data samples (Gaussian distributions of the fit parameters) • Make sure fit gives the expected results • In progress now • Next look at MC: • Start with default MCno hourglass effect • Generate MC with various beam distributions to test if fits return expected results

23. Summary • Understand the resolution variation in phi and see that the variation in z is more complicated than just a simple change with z • Strategy: Incorporate doca error directly into the fit (starting from GS’s original fit)  correct for resolution event-by-event • (alternately, use RMS miss distance in bins of theta, phi, and z) • First test in toys and MC, see if fit is stable and unbiased • Then try on data

24. Extras

25. Bonding type and SVT resolution

26. Means from doca error fits

27. Track distribution in cos(theta) – z plane (Note: there may be tracks in bins which show “0” (white) here. Only bins w/ more than a certain threshold of tracks (~50) were filled.)