Update: Beam Parameters from Dimuons

26 July 2004Josh ThompsonAaron 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– What changes are being implemented– What will be implemented in the future

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

1. Using whole data sample (selection cuts applied):

1. Fit z0, sigmaz to Gaussian2. Fix z0, sigmaz; fit x0, sigmax, y0, sigmay, 3 tilts,

constant background term with a PDF for the doca distribution

2. In bins of z:1. Fit y0, sigmay (optionally x0, sigmax) with other

params fixed from above fit2. Correct sigmay for resolution variation with z (use

doca error vs z plot; details follow)

(Details)

• Tracks in dimuon events are independent (not vertexed)

• Selection cuts:– tan(lambda1) + tan(lambda2) > 0.5 (cut cosmics)– |10.58 GeV - m_| < 0.3 GeV– nDCH >= 20 && nSVT >= 5– cos(phi1 – phi2) < -0.99– cos(theta) < 0.75

First some reviewIs 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 m/m

So the doca error from the fit is likely a good measure of resolution

We will come back to this correlation later

Wid

th o

f m

iss

dist

ance

dis

trib

utio

n (c

m)

sqrt((doca error 1)^2 + (doca error 2)^2) (cm)

Problem 1:Error on doca w.r.t. phi

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

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 distributionthis plot means we can’t cut directly on track quality

Err

or o

n do

ca

phi

(verticality cut applied)

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

(same plot as prev. page but showing only events on “SVT” plot at right)

Color code by doca error: >20umred; <20umgreen mm

Dimuon tracks

SVT structure (II)Color code by doca error: >20umred; <20umgreen

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• 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

doca

err

or (

back

w)

phi (backw)

Eve

nts

Problem 2:Resolution

variation with z

z

doca

err

(forw)

(backw)

• 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 m/cm

• Here: slope (forw) = -0.42 m/cm

• slope (backw) = -0.24 m/cm

Look at doca error in bins of theta

doca

err

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

Total material seen by tracks in first 15cm (x-y) of flight (approx SVT radius)

For simplicity, I will look at the mean of this distribution

cm

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)Mean of distribution from last page, binned in cos(theta) v z

First 15 cm (x-y) of flight First 6 cm (x-y) of flight

(cm) (cm)

Profiles: Material Length v z

15 cm of flight

15 cm of flightcos(theta)>0.65

6 cm of flight

6 cm of flightcos(theta)>0.65

(note suppressed zeros on y axes)

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

-1.2<z<0.93 (cm)0.43<cos(t)<0.50

1.47<z<1.73 (cm)0.69<cos(t)<0.75

1.47<z<1.73 (cm)0.43<cos(t)<0.50

Sample Fits

theta and z dependence of doca error

z (cm)

cos(

thet

a)

Lower m

ean of doca err distribution (cm)

• 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)

Possible band of lower resolution diagonally across plot?

Resolution correction as a function of z only is probably not sufficient

Diagonal Band?

(note expansion in z scale; outer bins statistically limited)

Average number of SVT hits in Layers 1,2,3:

All strips Phi strips only

Missing hit in Layer 1co

s(th

eta)

Fraction of tracks w/a phi side hit in Layer 1

Plug in x-y flight length l = 3.2 cm (min. radius of L1):

zL1 = z0 + l*tan() = z0 + 3.2*tan(/2 – ) ~ 2.5 cm across the band

z (cm)

Where do we go from here?• [GS correction: y,corrected

2 = y,fit2 /

(1+slopefit*z/interceptfit)2 ]

• Incorporate the resolution directly into the PDF:– Replace doca

2 = x2*sin2() + y

2*cos2() with:

– doca2 = x

2*sin2() + y2*cos2() + resolution

2

• resolution 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

• 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 MCno hourglass effect– Generate MC with various beam distributions

to test if fits return expected results

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

Bonding type and SVT resolution

Means from doca error fits

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.)