BGV Toy MC 1. Example event retention fractions 2. Aperture: effect - - PowerPoint PPT Presentation

BGV Toy MC

• 1. Example event retention fractions
• 2. Aperture: effect on the performance

Plamen Hopchev

CERN BE-BI-BL

BGV meeting #22

23 Oct 2013

Update to the studies presented in BGV #20

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Interaction rates and retention fractions

The vertex resolution improves with the track multiplicity (NTr)

When measuring the beam profile, select the events with highest multiplicity

What is the expected rate, where should we cut on NTr? Determine the total inelastic interaction rate per bunch

Rinel(in Hz) = 2.5 × 1016 p(in mbar) ∆z(in cm) σpA(in cm2) N frev(in Hz) Assume:

Ne gas p = 6.4 × 10−8 mbar (flat over ∆z) ∆z = 2 m (gas target length) σpA = 243/295 mb (0.45/7 TeV) N = 1.15 × 1011 per bunch Beam has 2808 bunches Per bunch Per beam Ebeam = 450 GeV Ebeam = 7 TeV Ebeam = 450 GeV Ebeam = 7 TeV Rinel [Hz] 100 122 281 000 343 000 Ninel per 3 min 18 × 103 22 × 103 51 × 106 62 × 106 Ncollect events 200 (σstat = 5 %) 20 000 (σstat = 0.5 %) Freduct 90 110 ∼ 2500 ∼ 3000

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Retention fractions and track multiplicity

Freduct indicates what fraction of the events we need to retain in order to get 200 / 20000 events per 3 min

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

Subsequently, we can tell what track multiplicity we can reach

Need to be aware of the large uncertainty associated to the distribution tails (when we select a very small fraction of the events), it will vary between MC event generator

The 5 shown detector geometries are described later

5 10 15 20 25 30 Ntracks ≥X 10

• 4

10

• 3

10

• 2

10

• 1

10 Fraction Fraction of events with at least X charged particles in acceptance; hi_10_450_zRange2m A = 26mm | L2233 A = 26mm | L2000 A = 23mm A = 21mm A = 19mm 5 10 15 20 25 30 Ntracks ≥X 10

• 4

10

• 3

10

• 2

10

• 1

10 Fraction Fraction of events with at least X charged particles in acceptance; hi_10_7000_zRange2m A = 26mm | L2233 A = 26mm | L2000 A = 23mm A = 21mm A = 19mm

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Track multiplicity for the BGV accuracy estimates

Cuts on NTr for the vertex resolution / width accuracy study:

Bunch measurements: NTr ≥ 11 (0.45 TeV); NTr ≥ 18 (7 TeV) Beam measurements: NTr ≥ 15 (0.45 TeV); NTr ≥ 25 (7 TeV)

Note: these estimates can be useful as guidelines, but in some cases (e.g. at 450 GeV) might not be optimal in terms of ratio between σstat and σsyst

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Track multiplicity for the BGV accuracy estimates

Cuts on NTr for the vertex resolution / width accuracy study:

Bunch measurements: NTr ≥ 11 (0.45 TeV); NTr ≥ 18 (7 TeV) Beam measurements: NTr ≥ 15 (0.45 TeV); NTr ≥ 25 (7 TeV)

Note: these estimates can be useful as guidelines, but in some cases (e.g. at 450 GeV) might not be optimal in terms of ratio between σstat and σsyst Next: estimate the resulting vertex resolution and the perfor- mance at 7 TeV Check different minimal BGV apertures

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Setup for the aperture scan

Beam-gas Imaging for LHC 13-Aug-2013 CERN Massimiliano Ferro-Luzzi 1

changing inner radius changing inner radius

 Fix target origin at a single point zt (center of actual target)  Reduce beam pipe inner radius such that it allows the first station to

come closer to the target by a proportional amount

 Find vertex resolution at radii = 25, 23, 21, 19 mm... (for example)  Optionally: parametrize Al window thickness t to be always

proportional to radius r : t = 0.75mm ∙ (r/23mm)

radius R radius R radius R' radius R' θmin zt r

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Example of the resolution dependence on NTr

40 80 120 160 200 240 280 320 x resolution [µm] χ2 / dof = 2.22 A = 577.21 ± 45.56 µm B = 0.35 ± 0.46 C = 0.00 ± 282.07 µm 5 10 15 20 25 30 Ntracks 250 500 750 1000 Entries 40 80 120 160 200 240 280 320 y resolution [µm] χ2 / dof = 2.55 A = 559.74 ± 67.97 µm B = 0.35 ± 0.63 C = 0.00 ± 350.08 µm 5 10 15 20 25 30 Ntracks 250 500 750 1000 Entries 1 2 3 4 5 6 7 8 9 10 z resolution [mm] χ2 / dof = 2.23 A = 17.89 ± 1.40 mm B = 0.37 ± 0.17 C = 0.00 ± 3.44 mm 5 10 15 20 25 30 Ntracks 250 500 750 1000 Entries

PV resolutions fitted to A / N B

tracks + C

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Resolution estimates

Detector layout:

SciFi modules cutout of 80 mm (in principle it should be 65 or 97 mm) For more details of the layout, see slide 3 of

https://indico.cern.ch/getFile.py/access?contribId=1&resId=0&materialId=slides&confId=269648

Exit window: α = 75◦, variable thickness

Assume that we will perform the resolution deconvolution on a sample of events with NTr ≥ X, where X were given on a previous slide Then, σtot = wiσi, where

wi is the relative amount of vertices with i tracks σi is the resolution for a vertex with i tracks

Resolution estimates for 5 geometry configurations. For aperture=26 mm, check both Lgas tank = 2233 mm (keep angle) and 2000 mm

NTr ≥ 18 NTr ≥ 25 zvtx ∈ [mm] [−500; −100] [−100; 300] [300; 700] [−500; −100] [−100; 300] [300; 700] σtot [µm] | Aper26 | L2233 219 209 205 – – – σtot [µm] | Aper26 | L2000 206 210 198 – – – σtot [µm] | Aper23 204 197 195 188 182 179 σtot [µm] | Aper21 191 186 176 179 174 165 σtot [µm] | Aper19 180 174 165 167 162 155

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Achievable accuracy

As expected, the resolution improves with the smaller aperture

The acceptance is approximately the same, but we have a smaller extrapolation distance

Uncertainty estimates not available (expect a few microns) Averaged resolution over z: σvtx.res(≡ σtot):

Aper26 | L2233: 211 µm Aper26 | L2000: 205 µm Aper23: 199 µm Aper21: 184 µm Aper19: 173 µm

Relative uncertainty of the measured beam size: δσbeam σbeam = σ2

vtx.res

σ2

beam

· δσvtx.res σvtx.res The squared ratio R =

• σvtx.res/σbeam

2 is important!

See the last slide (from Colin, BGV kickoff meeting)

For the beam size calculations assume E = 7 TeV and β = 170 m

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Comparison of accuracies (1)

Evaluate R =

• σvtx.res/σbeam

2 for the studied detector layouts ǫn [µm] 1 2 3 σbeam [µm] 151 213 261 R(Aper26|L2233) 1.95 0.98 0.65 R(Aper26|L2000) 1.84 0.93 0.62 R(Aper23) 1.74 0.87 0.58 R(Aper21) 1.48 0.75 0.50 R(Aper19) 1.31 0.66 0.44

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Comparison of accuracies (2)

Assume δσvtx.res/σvtx.res = 10 % The purple squares correspond to A=26 | L2000

19 20 21 22 23 24 25 26 Aperture [mm] 4 6 8 10 12 14 16 18 20

δσbeam/σbeam [%]

BGV resolution systematic. Exit window tapering angle = 75 ◦

ǫn = 1 µm ǫn = 2 µm ǫn = 3 µm

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Systematic compensation with statistics

It is possible to improve the vertex resolution by cutting harder on NTr

Leads to lower rate of useful events, which theoretically can be compensated by longer measurement times or higher gas pressure

Example: require NTr ≥ 20 (iso 18)

σvtx.res gets about 5 % better, giving a 10 % improvement on δσbeam σbeam (effect is comparable to 2-mm aperture reduction) Event rate decreases by a factor of 2 (see the Fgood plots in the beginning of the talk)

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ResoluDon ¡

2012-­‑10-­‑30 ¡ Colin ¡Barschel ¡ 6 ¡ 1 2 3 4 5 0.05 0.10 0.15

σraw

2

= σbeam

2

+σresolution

2

w = σbeam /σresolution δσbeam σbeam = 1 w2 δσresolution σresolution

What ¡is ¡important ¡(and ¡why): ¡

• Know ¡resoluDon ¡to ¡bejer ¡than ¡10% ¡
• True ¡beam ¡width ¡> ¡resoluDon ¡

Beam ¡width ¡= ¡resoluDon ¡ Beam ¡width ¡= ¡2×resoluDon ¡ LHCb ¡3m ¡β* ¡ Beam ¡width ¡< ¡resoluDon ¡

ResoluDon ¡uncertainty ¡

5% ¡ 10% ¡ 5% ¡uncertainty ¡on ¡ Beam ¡width ¡ Beam ¡width ¡≈ ¡5×resoluDon ¡ LHCb ¡10m ¡β* ¡ RelaDve ¡error ¡on ¡beam ¡width ¡

W=σbeam/σresoluDon ¡