Update beam parameters from dimuons
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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

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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


Update beam parameters from dimuons

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


Update beam parameters from dimuons

-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


Extras

Extras


Bonding type and svt resolution

Bonding type and SVT resolution


Means from doca error fits

Means from doca error fits


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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