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BGV Toy MC 1. Example event retention fractions 2. Aperture: effect on the performance Update to the studies presented in BGV #20 Plamen Hopchev CERN BE-BI-BL BGV meeting #22 23 Oct 2013 Interaction rates and retention fractions The vertex

  1. BGV Toy MC 1. Example event retention fractions 2. Aperture: effect on the performance Update to the studies presented in BGV #20 Plamen Hopchev CERN BE-BI-BL BGV meeting #22 23 Oct 2013

  2. Interaction rates and retention fractions The vertex resolution improves with the track multiplicity ( N Tr ) When measuring the beam profile, select the events with highest multiplicity What is the expected rate, where should we cut on N Tr ? Determine the total inelastic interaction rate per bunch R inel (in Hz) = 2 . 5 × 10 16 p (in mbar) ∆ z (in cm) σ pA (in cm 2 ) N f rev (in Hz) Assume: Ne gas p = 6 . 4 × 10 − 8 mbar (flat over ∆ z ) ∆ z = 2 m (gas target length) σ pA = 243 / 295 mb (0 . 45 / 7 TeV ) N = 1 . 15 × 10 11 per bunch Beam has 2808 bunches Per bunch Per beam E beam = 450 GeV E beam = 7 TeV E beam = 450 GeV E beam = 7 TeV R inel [Hz] 100 122 281 000 343 000 18 × 10 3 22 × 10 3 51 × 10 6 62 × 10 6 N inel per 3 min N collect events 200 ( σ stat = 5 % ) 20 000 ( σ stat = 0 . 5 % ) F reduct 90 110 ∼ 2500 ∼ 3000 2 / 12

  3. Retention fractions and track multiplicity F reduct 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 Fraction of events with at least X Fraction of events with at least X charged particles in acceptance; hi_10_450_zRange2m charged particles in acceptance; hi_10_7000_zRange2m 0 0 10 10 -1 -1 10 10 Fraction Fraction -2 -2 10 10 A = 26mm | L2233 A = 26mm | L2233 -3 -3 10 10 A = 26mm | L2000 A = 26mm | L2000 A = 23mm A = 23mm A = 21mm A = 21mm -4 -4 10 10 A = 19mm A = 19mm 0 5 10 15 20 25 30 0 5 10 15 20 25 30 N tracks ≥ X N tracks ≥ X 3 / 12

  4. Track multiplicity for the BGV accuracy estimates Cuts on N Tr for the vertex resolution / width accuracy study: Bunch measurements: N Tr ≥ 11 (0.45 TeV); N Tr ≥ 18 (7 TeV) Beam measurements: N Tr ≥ 15 (0.45 TeV); N Tr ≥ 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 σ stat and σ syst 4 / 12

  5. Track multiplicity for the BGV accuracy estimates Cuts on N Tr for the vertex resolution / width accuracy study: Bunch measurements: N Tr ≥ 11 (0.45 TeV); N Tr ≥ 18 (7 TeV) Beam measurements: N Tr ≥ 15 (0.45 TeV); N Tr ≥ 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 σ stat and σ syst Next: estimate the resulting vertex resolution and the perfor- mance at 7 TeV Check different minimal BGV apertures 4 / 12

  6. Setup for the aperture scan changing inner radius changing inner radius r θ min z t radius R radius R' radius R radius R'  Fix target origin at a single point z t (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) 1 Beam-gas Imaging for LHC 13-Aug-2013 CERN Massimiliano Ferro-Luzzi 5 / 12

  7. Example of the resolution dependence on N Tr PV resolutions fitted to A / N B tracks + C 320 320 10 9 280 280 8 240 240 7 z resolution [mm] x resolution [ µ m ] y resolution [ µ m ] 200 200 6 160 160 5 4 120 120 3 80 80 χ 2 / dof = 2.22 χ 2 / dof = 2.55 2 χ 2 / dof = 2.23 A = 577.21 ± 45.56 µ m A = 559.74 ± 67.97 µ m A = 17.89 ± 1.40 mm 40 40 1 B = 0.35 ± 0.46 B = 0.35 ± 0.63 B = 0.37 ± 0.17 C = 0.00 ± 282.07 µ m C = 0.00 ± 350.08 µ m C = 0.00 ± 3.44 mm 0 0 0 1000 1000 1000 750 750 750 Entries Entries Entries 500 500 500 250 250 250 0 0 0 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 N tracks N tracks N tracks 6 / 12

  8. 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 N Tr ≥ X , where X were given on a previous slide Then, σ tot = � w i σ i , where w i is the relative amount of vertices with i tracks σ i is the resolution for a vertex with i tracks Resolution estimates for 5 geometry configurations. For aperture=26 mm, check both L gas tank = 2233 mm (keep angle) and 2000 mm N Tr ≥ 18 N Tr ≥ 25 z vtx ∈ [ mm ] [ − 500; − 100] [ − 100; 300] [300; 700] [ − 500; − 100] [ − 100; 300] [300; 700] σ tot [ µ m ] | Aper26 | L2233 219 209 205 – – – σ tot [ µ m ] | Aper26 | L2000 206 210 198 – – – σ tot [ µ m ] | Aper23 204 197 195 188 182 179 σ tot [ µ m ] | Aper21 191 186 176 179 174 165 σ tot [ µ m ] | Aper19 180 174 165 167 162 155 7 / 12

  9. 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 : σ vtx . res ( ≡ σ tot ) : Aper26 | L2233: 211 µ m Aper26 | L2000: 205 µ m Aper23: 199 µ m Aper21: 184 µ m Aper19: 173 µ m Relative uncertainty of the measured beam size: σ beam = σ 2 δσ beam · δσ vtx . res vtx . res σ 2 σ vtx . res beam � 2 is important! The squared ratio R = � σ vtx . res /σ beam See the last slide (from Colin, BGV kickoff meeting) For the beam size calculations assume E = 7 TeV and β = 170 m 8 / 12

  10. Comparison of accuracies (1) � 2 for the studied detector layouts Evaluate R = � σ vtx . res /σ beam ǫ n [ µ m ] 1 2 3 σ beam [ µ m ] 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 9 / 12

  11. Comparison of accuracies (2) Assume δσ vtx . res /σ vtx . res = 10 % The purple squares correspond to A=26 | L2000 BGV resolution systematic. Exit window tapering angle = 75 ◦ 20 ǫ n = 1 µ m ǫ n = 2 µ m 18 ǫ n = 3 µ m 16 δσ beam /σ beam [%] 14 12 10 8 6 4 19 20 21 22 23 24 25 26 Aperture [mm] 10 / 12

  12. Systematic compensation with statistics It is possible to improve the vertex resolution by cutting harder on N Tr Leads to lower rate of useful events, which theoretically can be compensated by longer measurement times or higher gas pressure Example: require N Tr ≥ 20 (iso 18) σ vtx . res gets about 5 % better, giving a 10 % improvement on δσ beam (effect is comparable to σ beam 2-mm aperture reduction) Event rate decreases by a factor of 2 (see the F good plots in the beginning of the talk) 11 / 12

  13. ResoluDon ¡ 2 2 2 What ¡is ¡important ¡(and ¡why): ¡ σ raw = σ beam + σ resolution • Know ¡resoluDon ¡to ¡bejer ¡than ¡10% ¡ w = σ beam / σ resolution • True ¡beam ¡width ¡> ¡resoluDon ¡ δσ beam = 1 δσ resolution 0.15 w 2 σ beam σ resolution RelaDve ¡error ¡on ¡beam ¡width ¡ ResoluDon ¡uncertainty ¡ 0.10 10% ¡ 5% ¡ 5% ¡uncertainty ¡on ¡ 0.05 Beam ¡width ¡ 1 2 3 4 5 W=σ beam /σ resoluDon ¡ Beam ¡width ¡< ¡resoluDon ¡ Beam ¡width ¡≈ ¡5×resoluDon ¡ Beam ¡width ¡= ¡resoluDon ¡ LHCb ¡10m ¡β* ¡ Beam ¡width ¡= ¡2×resoluDon ¡ LHCb ¡3m ¡β* ¡ 2012-­‑10-­‑30 ¡ Colin ¡Barschel ¡ 6 ¡ 12 / 12

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