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Update: Beam Parameters from Dimuons

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Update: Beam Parameters from Dimuons

26 July 2004

Josh Thompson

Aaron Roodman

SLAC

- 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

- 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

- 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)

- 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

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)

(verticality cut applied)

Error on doca

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 distributionthis 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

- 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: >20umred; <20umgreen

mm

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

- 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)

(forw)

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

- 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

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)

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

- 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

cos(theta)

Lower mean of doca err distribution (cm)

z (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)

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

Possible band of lower resolution diagonally across plot?

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

All strips

Phi strips only

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

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

cos(theta)

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

- [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?)

- Resolution function comes from miss distance v doca error

- 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

- 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

(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.)