BGV Vertex Resolution First Analysis Vertex Resolution as Function of Aperture

LHC

BGV Vertex Resolution First Analysis

Vertex Resolution as Function of Aperture

M. Kuhn, P. Hopchev

Maria Kuhn - BGV Meeting #20 - 25.9.2013

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Introductiono Actual transverse beam size for Gaussian shaped beams

is broadened by vertex resolution

o When : goal for final BGV!

o Motivation:

− Measurement at 7 TeV most challenging, as the beam is smallest

− Goal of initial BGV system: demonstrate the principle

• vertex resolution ~7 TeV beam (150-200 mm) would be sufficient

o Analyse vertex resolution as function of

− Beam pipe radius: 23 mm, 21 mm and 19 mm aperture

− Exit window tapering angle: 45º and 75º


aim at 0.2 aim at 10 %

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Input for MC Simulation and Vertex Reconstruction

o See talk in BGV meeting #17 (14/08/2013)

− Proton beam – neon gas target interactions simulated with HIJING

− Flat distribution of events in z-range [-500;1100] mm

− Process ~ 73000 events with large number of high multiplicity tracks

o 2 detector modules at z = 1591 mm and z = 2611 mm with 2 space point measurements per station

− Variable exit window thickness

• Thickness with R = 23 mm : 0.75 mm, thickness with R = 106 mm: 3.5 mm, linear interpolation in between


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BGV sche-matic detector layout

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o Vertex Resolution improves with track multiplicity (NTr)

− When measuring the beam profile, select events with high #tracks

o What is the expected rate, where we should cut on the NTr?

o Determine total inelastic interaction rate per bunch:

− Assuming: 2808 bunches per beam ()

• Ne gas flat over (gas target length)

• (0.45/7 TeV)

Cut on Track Multiplicity NTr (I)

4Maria Kuhn - BGV Meeting #20 - 25.9.2013

P. Hopchev

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Cut on Track Multiplicity NTr (II)

o Freduct indicates what fraction of the events is needed to retain in order to get 200/20000 events per 3 min

− i.e. to get 5/0.5 % statistical error on the beam profile fit (assuming Gaussian)

o Subsequently, we can tell what NTr can be reached

− Caveat: large uncertainty associated to the distribution tails (when a very small fraction of events is selected)


P. Hopchev

LHC

Cut on Track Multiplicity NTr (III)o Guidelines for BGV vertex resolution study with toy MC:

− For detector layout with SciFi modules cut-out of 65 mm

− Choose only events with high track multiplicity

− For bunch measurements: NTr ≥ 11 (0.45 TeV); NTr ≥ 18 (7 TeV)

− For beam measurements: NTr ≥ 15 (0.45 TeV); NTr ≥ 25 (7 TeV)

o In the following:

− Estimates of the relative uncertainty on the beam width at 7 TeV

(always worse than at 450 GeV, because transverse beam size is smaller)

• As function of aperture

• And for different tapering angles


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Vertex Resolution Definitiono Define and track true MC vertex xMC with BGV toy MC Simulation

− Sort events per number of tracks/vertex (NTr)

o Reconstruct primary vertex with LHCb algorithm xrec

o For each NTr plot histogram with residuals: xMC – xrec

o Fit histogram with 3 parameter Gauss Function to obtain s


= s vertex resolution

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Vertex Resolution versus NTr

o Divide original vertices from MC simulation in 4 z-position intervals

− [-500;-100], [-100;300], [300,700], [700,1100] mm

− Sort residuals accordinglyo Fit the x and y resolution with function:

− Fit convergences very sensitive to the initially given parameter values need to improve fitting method


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Vertex Resolution versus NTr (II)

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Vertex Resolution versus NTr (III)

o Repeated vertex resolution calculation for all apertures with 75º tapering angle

− “Nominal” aperture (23mm)

− 2 mm reduced aperture (21 mm)

− 4 mm reduced aperture (19 mm)

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Weighted Vertex Resolution

o Choose events with NTr ≥ 18

o Weighted resolution:

− With and weights

o Vertex resolution improves when going closer to detector

− But less high-multiplicity events


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detector

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Summary Resolution for NTr ≥ 18o Comparison of weighted vertex resolution for different

apertures

− resolution error obtained from Gauss fit of histogram (statistical)

o Choose events with NTr ≥ 18

− Weighted vertex resolution for each NTr ≥ 18

− Results for x and y resolutions are similar, quoting the average of x and y

− To do: get resolution from curve fit and not from histogram


z range[mm]

Weighted resolution

“Nominal” aperture (23 mm)

2 mm reduced aperture (21 mm)

4 mm reduced aperture(19 mm)

700;1100 svtx [mm] 178 ± 6 164 ± 9 147 ± 10

300;700 svtx [mm] 192 ± 5 175 ± 5 165 ± 5

-100;300 svtx [mm] 192 ± 6 183 ± 5 175 ± 5

-500;-100 svtx [mm] 200 ± 6 187 ± 6 180 ± 5

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Conclusion - enorm = 1 mmo Reminder: with

o at 7 TeV for enorm = 1 mm & b = 170 m


z range[mm]




700;1100 0.141 0.119 0.096

300;700 0.163 0.136 0.120

-100;300 0.164 0.148 0.136

-500;-1000.176 0.154 0.144

Gain 10 – 15 % 20 – 30 %

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Conclusion - different enorm

o for enorm = 1.5 [2.,2.5] mm

− 7 TeV & b = 170 m

o Average over z range from [-500;700] mm (discard first z bin)


e [mm]




1.0 0.168 0.146 0.133

1.5 0.116 0.102 0.09

2.0 0.085 0.075 0.068

2.5 0.065 0.057 0.052

Gain 10 – 15 % 20 – 30 %

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for Different Emittanceso Relative uncertainty on the transverse beam size

− See table on previous slide

o Better accuracy for larger transverse beam sizes

o Smaller relative beam size uncertainty for smaller aperture

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Vertex Resolution for 45º Tapering Angle

o Repeated these studies with different tapering angle

− 45º instead of 75º

− 23 mm aperture

− NTr ≥ 18

o Conclusions:

− For every z-position interval the vertex resolution is worse for the smaller tapering angle

− The relative uncertainty of the measured beam size improves by 9 % when choosing a larger tapering angle (75º)

• Again assuming

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P. Hopchev

LHC

Summaryo The expected vertex resolution is estimated from the BGV toy

MC

− For 3 different apertures: 23 mm, 21 mm, 19 mm (75º tapering angle)

− And for 2 different tapering angles: 45º and 75º (23 mm aperture)

o The improvements on are

− 10 – 15 % better resolution for 2 mm reduced aperture

− 20 – 30 % better resolution for 4 mm reduced aperture

• With respect to 23 mm aperture

− 9 % better resolution for 75º tapering angle

• With respect to 45º

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Additional Slides


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Vertex Resolution for 2 mm Reduced Aperture

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Vertex Resolution Nominal Aperture

o Scatter plot: vertex resolution per z and #tracks bin

− Colour represents vertex resolution for x and y position

− Circle size represents #events per bin (see previous slide)

o Best x and y vertex resolution for large #tracks!o Weighted resolution =


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Nominal aperture = 23 mm

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2mm Reduced Apertureo Aperture = 21 mm

o Vertex resolution improves


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4 mm Reduced Apertureo Aperture = 19 mm

o Vertex resolution even better


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NTr ≥ 25


Not very useful to analyse – not enough statistics in high track multiplicity bin

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Documents

BGV Vertex Resolution First Analysis Vertex Resolution as Function of Aperture