Updated impact parameter resolutions of the ATLAS Inner Detector
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1 Updated impact parameter resolutions of the ATLAS Inner Detector ATLAS Internal Note Inner Detector ATL-INDET /10/2000 Szymon Gadomski, CERN 1 Abstract The layout of the ATLAS pixel system has changed twice since the physics TDR was published. This note presents updated impact parameter resolutions calculated using a simple program that models geometry, detector resolutions and multiple scattering. The results can be used for physics simulations using parameterised tracker resolutions. 1 Inner Detector layouts As the detailed engineering work on the Inner Detector is progressing, the layout is being constantly modified. Most of the changes introduced since the physics TDR [1] imply relatively small shifts in positions of the SCT and TRT wheels. Changes like that have practically no impact on the vertex resolutions. Only the changes of the pixel system, particularly those affecting the B-layer, can have a significant effect. The pixel layout was changed twice since the TDR. In June of 1999 the Prague layout was introduced [2]. Compared to the TDR layout, the changes were: new layout of the forward disks: now 5 disks, closer to the barrel in Z, pixel size increased from µm 2 to µm 2 except in the B-layer. In May of this year a change of the beam pipe of ATLAS has been adopted [3]. The pipe in its innermost part has changed in the following way: Physics TDR: 50 mm outer diameter, 1 mm thick Be wall after May 2000: inner diameter 58 mm, double wall mmofbewith4mmvacuum gap for bake out, outer diameter 69.2 mm The change of the beam pipe is being justified by the need to heat it for out-gassing while the B-layer will already be in place. An increase of the outer radius of the beam pipe has made it necessary to increase the radius of the B-layer. The new layout, which is called here the Dubna layout, is the current ATLAS baseline. Compared to the Prague layout the following changes have been made [5, 6]: 1 on leave of absence from the INP Cracow 1
2 an increase of the average radius of the sensors in B-layer from 4.30 cm to 5.05 cm, an increase of material in pixel layers from 5.3% to 6.2% of X/X 0 (counting 3 pixel layers at η =0), cm shifts of the SCT disk positions. An updated layout is being introduced into the full GEANT3 model of the ATLAS detector [7]. While this work is progressing, it was necessary to have an estimate of the impact of changes that could be available on a shorter time scale. In addition to the Prague and Dubna layouts introduced above, a third case named Dubna 400 was studied. This case is identical to the Dubna layout except for the size of pixels in the B-layer, which is made identical to that in the rest of the pixel system µm 2. The Dubna 400 layout is an academic study of what would happen if the B-layer was made of the same modules as the rest of the pixel system. 2 Calculation method The resolutions were calculated using a toy Monte-Carlo program developed in 1992 and used several times since to study the ID layouts. The model is characterised by the following features: tracking layers are represented as perfect disks and cylinders, invariance in φ is assumed, geometry, resolutions and material are defined in a custom-format file, a track is extrapolated from layer to layer as if in vacuum, uniform 2T magnetic field is assumed, space points on a track are smeared with given resolutions, multiple scattering is simulated using a thin layer approximation[8], only one track is treated at a time, no need of pattern recognition, a helix is fitted to the collection of points, the measured track parameters are returned. Figure 1 shows the simplified layout of the Inner Detector as implemented in the simulation. The continuous tracking of the TRT is approximated using four discreet layers. It should be noted that the interaction of particles with detector material is limited to multiple scattering. There is no Bremsstrahlung and no nuclear interactions. This approximation is known to reproduce the Gaussian parts of all resolutions. Each resolution is calculated as RMS of the measured track parameters using many tracks. This method is inefficient compared to using the error returned by the fitter, but 2
3 Figure 1: The simplified layout of the Inner Detector used to calculate the impact parameter resolutions. Symmetry in φ is assumed. The TRT is approximated using four discreet layers. 3
4 it allows to treat cases close to edges of cylinders and disks. Due to multiple scattering, and to the spread of primary vertices, two tracks with identical p T and η can pass through different combinations of detector layers and have different errors returned by the track fitter. A parameterised resolution, on the other hand, needs to be represented by a single number for a given p T and η. The RMS of the fitted track parameters is a choice of that number. Special care was applied to the track point resolutions in the pixel system. The point resolutions both in Rφ and in Z are dependent on the track-sensor angle and therefore on track rapidity. The results of full GEANT simulation of the pixel sensors [4] were used to parameterise the track point resolutions of the pixel system separately in the B-layer, the other two barrel layers and in disks. The code is based on an even earlier simulation program developed by Allan Poppleton. Several cross-checks with full simulation were done during the lifetime of the code. In the framework of this study the results of the fast simulation were also compared with full simulation results where available (see the end of section 3). 3 Results The resolutions as a function of p T, for tracks at η = 0 are shown in Fig.2. Top plot shows the resolutions in the transverse impact parameter d 0. An increase of multiple scattering from Prague layout to the Dubna layout is visible. The Dubna 400 layout is identical to the Dubna layout when considered in the XY plane, the resolutions are equal as expected. The bottom plot of Fig.2 shows the resolutions in the Z of the closest approach of the fitted helix to the beam line. Again an increase of the multiple scattering term is visible when comparing Prague and Dubna layouts. The curve for the Dubna 400 layout presents the deterioration that would be due to longer pixels, visible both at low and at high p T. It should be noted that the vertical scale on the plot does not start at zero, making the relative deterioration seem more significant. It is conventional, if not always very accurate, to parameterise the impact parameter resolutions over the entire (η, p T ) space using two constants. The parameterisations that can be obtained from Fig.2 are: 88 σ(d 0 )=12 p T sinθ µm (1) 160 σ(z 0 )=95 p T sin3 θ µm (2) where p T is in GeV/c. The formulas are for the Dubna layout, the current ATLAS baseline. The dependence of the resolutions on η is shown in Fig.3 for all the three layouts and for two very different track momenta. 4
5 Figure 2: Impact parameter resolutions calculated for the Prague, Dubna and Dubna 400 layouts. The resolutions in the transverse impact parameters d 0 (top)andinthe Z of the closest approach of the track to beam line Z 0 are shown as a function of p T at η =0. 5
6 Figure 3: Impact parameter resolutions calculated for the Prague, Dubna and Dubna 400 layouts. The resolutions in the transverse impact parameters d 0 andinthe Z of the closest approach of the track to beam line Z 0 are shown as a function of η for track p T of 1 and 200 GeV/c. 6
7 The curves are also available as parameterisations that can be used in ATLFast, ATL- Fast++ or other fast simulation programs. The files are called /afs/cern.ch/user/g/- gadomski/public/impres00/results/*.vtxres, where * is Prague, Dubna or Dubna400. The resolutions are given in mm for each point on the grid of (p T,η)points that is used by ATLFast++ (p =0.5, 1.0, 1.5, 2, 3, 4, 5, 10, 20, 40, 100, 200, 500, 1000 GeV, η = 0.0, 0.1, , 2.5). If you would like to use the points for physics simulations, please feel welcome and do not hesitate to ask questions or report problems to szymon.gadomski@cern.ch. Some cross-checks with full simulations are already available. For the Prague layout the full simulation results are available in [2] for low and high momentum tracks. The track momenta and the layout of the plots in Fig. 3 were made identical to those in [2] to facilitate comparisons. For the Dubna layout some full simulation results, limited to high p T tracks, are available in [7]. In almost all cases the resolutions compare with an accuracy that is better than the size of a point in the plots. 4 Conclusions In order to keep up with the changes of the Inner Detector layout, particularly with those affecting the beam pipe and the pixel system, a set of impact parameter resolutions was produced using a fast simulation program. The resolutions where checked against the full GEANT3 model implemented in DICE where the results of the latter were available. The Prague layout has impact parameter resolutions close to those from the Physics TDR, because the B-layer did not get changed. The Dubna layout (current baseline) has worse resolutions, as can be expected from an increase of B-layer radius. An increase of material in the pixel layers as well as in the beam pipe also contributes to the deterioration. The Dubna 400 layout would represent further deterioration of the resolution in the RZ plane. The three resolutions defined on a grid of points in (p T,η) are accessible and can be used for physics and detector performance simulations using fast simulation, at least until a parameterisation derived from the full GEANT model becomes available. References [1] ATLAS Collaboration, ATLAS Detector and Physics Performance Technical Design Report, CERN/LHCC/99-14, 25 May [2] Dario Barberis, ATLAS Inner Detector Developments, presentation at the BEAUTY 99 conference, 24 June [3] Presentations from a review of beam pipe held at CERN in May 2000 are available under EDMS. 7
8 [4] Alexandre Rozanow, Summary of 300 versus 400 µm pixels studies available, presentation at the pixel software meeting in Praha, 2 June 99. [5] Dario Barberis, private communication. [6] Geoff Tappern, technical drawings of the Inner Detector layout. [7] Alexandre Rozanow, Preparation of the Dubna layout, presentation at the pixel software meeting at CERN, 12 June [8] Particle Data Group, Review of Particle Physics, e.g. The European Physical Journal C, Volume 3,
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