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

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Update beam parameters from dimuons

Update: Beam Parameters from Dimuons

26 July 2004

Josh Thompson

Aaron Roodman

SLAC


Overview
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


Beam parameters from dimuons
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


Gregory schott method
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)


Details
(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


First some review
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)


Problem 1 error on doca w r t phi

(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


Is svt structure the problem
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


Svt structure ii
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


Problem 1 solved
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)


Problem 2 resolution variation with z

(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


Expanded resolution studies
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


Material length
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)


Material length ii
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


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


Material length v z
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


-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


Theta and z dependence of doca error

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?


Diagonal band

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)


Missing f hit in layer 1

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


Where do we go from here
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?)


Test new pdf
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


Summary
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





Track distribution in cos theta z plane
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.)


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