2.3 Tracking Detectors

The trajectory of charged particles may be determined by their ionizing effects on the material they pass through. The track curvature in a magnetic field can be used to determine a particle's momentum (and charge), which in DELPHI's central uniform 1.2 T field is given in $\ensuremathbox{\mathrm{GeV}/c}$ by $p = 0.0036 \rho / \sin\theta$, where $\rho$ is the radius of curvature in cm.

Tracking of charged particles in the barrel is provided by the Inner Detector (ID), TPC, and Outer Detector (OD). The forward chambers (FCA and FCB) are used in the endcaps. All these detectors use gases as ionizing media. Additional extremely precise measurements are made close to the interaction point by the silicon Vertex Detector (VD). See table 2.2 for a comparison of these detectors' specifications.

Table 2.2: Some characteristics of the DELPHI tracking and particle identification detectors: Vertex Detector (VD), Inner Detector (ID), TPC, Outer Detector (OD), Forward Chambers A and B (FCA and FCB respectively), Barrel and Forward RICHes (RIB and RIF), and Barrel, Forward, and Surround Muon Chambers (MUB, MUF, and MUS).

2.3.1 Vertex Detector (VD)

A recognition of the importance of precise measurements close to the interaction region to identify and reconstruct short-lived particles, particularly given the emphasis on particle identification prompted by the RICHes, led to the inclusion of a high-precision silicon Vertex Detector in the design of DELPHI.

2.3.1.1 Geometry

After initial tests during the pilot run of 1989, two layers of single-sided detectors (measuring only the azimuthal coordinate) at 9 and 11 cm radii (designated inner and outer respectively) were installed in 1990. This was the first use of this technology in a collider [24].

In 1991 an additional (closer) layer was added at 6.3 cm, when experience with LEP operation allowed a reduction of the beampipe radius from 7.9 to 5.6 cm. The new beampipe is composed of beryllium, rather than aluminium to reduce multiple scattering.

For the 1994 run, the closer and outer layers were replaced with double-sided detectors [25], which are capable of measuring both the azimuthal and longitudinal coordinates. The inner layer remained of the old design (and in fact used modules scavenged from the inner and outer layers of the previous detector).

The geometry of the 1994 detector is shown in figure 2.5.

Figure 2.5: Schematic layout of the 1994 Vertex Detector in a) perspective and b) $\ensuremathbox{R\phi}$ views. The scale is in cm. The geometry of the 1991-3 detector was similar, except that it did not have the longer innermost layer, and the modules of the outer two layers had a `paddle wheel' arrangement.

a) b)

Each shell consists of 24 modules with a 10-20% overlap in $\phi$ between modules. The 12 modules in the three layers on each side ($+x$ and $-x$) are assembled into two half-shells, which are independently installed into DELPHI. Each module consists of 4 silicon detectors (plaquettes), bonded together end-to-end for a total length of 24 cm for the inner and outer layers, and 22 cm (1991-3) / 28 cm (1994-5) for the closer layer.

2.3.1.2 Detectors

The single-sided detector plaquettes consist of 285 $\ensuremathbox{\mu\mathrm{m}}$-thick phosphorous-doped n-type silicon with 7 $\ensuremathbox{\mu\mathrm{m}}$-wide boron-doped p$^{+}$ strips parallel to the $z$-axis spaced at intervals of 25 $\ensuremathbox{\mu\mathrm{m}}$. By applying a reverse bias of $\sim 60$ V to these diodes, the n-type silicon is depleted of charge carriers. The passage of a charged particle through the detector liberates electron-hole pairs. The holes drift to the diodes where the deposited charge is detected.

Every other diode (i.e. at 50 $\ensuremathbox{\mu\mathrm{m}}$ intervals) is read out via capacitive coupling: the aluminium readout strip is separated from the p$^{+}$ silicon by a 0.23 $\ensuremathbox{\mu\mathrm{m}}$ layer of silicon dioxide insulator. Capacitive coupling, rather than direct charge readout, is used to reduce the leakage current and hence detector noise. Each unconnected strip is capacitively coupled to the readout strips on either side of it. This causes the deposited charge to be distributed over several readout strips (most often two), allowing the position measurement to be improved over simple strip enumeration by using the relative charge deposits on each strip.

As shown in figure 2.6,

Figure 2.6: Cross section of a Vertex Detector double-sided plaquette.

the double-sided detector has n$^{+}$ strips running across its other side, allowing the $z$-coordinate to be measured by picking up the electron signal. A layer of metal readout lines, orthogonal to those running along the n$^{+}$ strips, allows the signals from the n-side to be read out at the end of the detector.

In order to improve the signal-to-noise ($S/N$) ratio in $z$, the n$^{+}$ strip pitch is increased at the ends of the module, where the larger incidence angle of the tracks spreads the charge over a larger area. The two plaquettes on each side of a module are bonded such that the n-side of one is joined to the p-side of the other, further improving the ($S/N$) of the $z$-measurement. The opposite polarities of signals from the two plaquettes also alleviates the ambiguity produced by multiplexing (3:1 in the closer and 2:1 in the outer layer) the connections between the two metal layers on the n-side.

2.3.1.3 Readout

Pairs of plaquettes are wire-bonded in series to form half-modules, which are read out at either end by onboard CMOS chips, which each preamplify and multiplex the charges from 128 channels. 4-10 chips are read out serially at 2.5 MHz on a single twisted pair cable connected via a line driver and repeater to the data acquisition crates (in the counting houses, $\sim 25$ m away). 36 (1991-3) or 48 (1994-5) SIROCCO^2.5Fastbus modules, each with two readout units consisting of a flash ADC and digital signal processor are used to digitize the signal stream and perform pedestal and noise calculations and zero suppression. A total of 73,728 (1991-3) or 125,952 (1994-5) strips are read out.

Temperature and humidity variations (which are monitored as described in sections 3.2.3 and 3.2.10) as well as detector interventions can affect the alignment. Until 1995, the stability of the outer layer position relative to the ID was monitored (every 64th beam crossing) to a 1 $\ensuremathbox{\mu\mathrm{m}}$ precision using lasers.

2.3.1.4 Reconstruction

Channels passing a $S/N$ cut (in 1994, 2.5 on the p-side and 1.4 on the n-side) are grouped into clusters, which are accepted if their total $S/N>5$. The hit position is calculated from the pulse-height weighted position of the cluster maximum and its largest neighbour ( $\eta= S_{i+1} / (S_i + S_{i+1})$), corrected for nonlinear charge sharing between the two strips. n-side clusters with a large incidence angle ( $>15\ensuremathbox{^\circ}$ from the normal) where the charge is spread over several strips use the strips on the edge of the cluster.

The local $x$ or $z$ coordinates cannot be converted into global DELPHI coordinates without additional information (usually external tracks). Before 1994, no $z$ coordinate was available, and even since then there is no reliable way of directly associating the p-side hit with its n-side counterpart. Although the plaquettes are aligned closely with the $z$-axis, this is not perfect, so even a precise separate measurement of $\ensuremathbox{R\phi}$ or $z$ cannot be made. For these reasons, it is necessary to associate initial track measurements from the ID, TPC, and OD with individual VD hits before conversion to the DELPHI coordinate system and inclusion into the global track fit. First $\ensuremathbox{R\phi}$ and then (using the resultant precision improvement) $z$ hits are associated with each track. Remaining unassociated hits are checked for the possibility of VD-only tracks (perhaps due to material interaction outside the VD) using the beamspot position as the external constraint.

In order to obtain the full precision of the Vertex Detector, the relative positions of the plaquettes as well as the global alignment of the VD within DELPHI must be accurately measured [26]. The relative position of each module within a half-shell is determined to 25 $\ensuremathbox{\mu\mathrm{m}}$ before insertion into DELPHI with a combination of microscope (for the strip positions relative to the module) and mechanical probe (relative module positions) measurements. The 2 $\ensuremathbox{\mu\mathrm{m}}$ (1994-5) microscope measurement precision is sufficient for plaquette-plaquette alignment. Tracks passing through the regions where two modules overlap, 3-hit tracks, and dimuon ( $\ensuremathbox{\mathrm{Z^0}}\rightarrow \ensuremathbox{\mu^+ \mu^-}$) events are used to improve the module-module alignment, align the two half-shells relative to each other, and align the VD with respect to the rest of DELPHI. An overall alignment precision of the order of half the intrinsic hit precision is obtained.

All these tasks are performed by a single software library, VDCLAP^2.6 [28], which was the first detector physics package in DELPHI to be used at all levels of the reconstruction (DELANA, DSTFIX, as well as analysis programs). VDCLAP operates on VD hit, track, alignment, association, efficiency, dead strip, and beamspot data held in standard COMMON blocks.

2.3.1.5 Performance

Minimum ionizing particles at normal incidence give (1994-5) $S/N$ between 11 (closer $z$) and 17 (outer, $\ensuremathbox{R\phi}$ and $z$), producing a single-hit efficiency of 98-99% and, as shown in figure 2.7,

Figure 2.7: Vertex Detector intrinsic hit resolutions. Shown on the left are the $\ensuremathbox{R\phi}$ residuals for tracks passing through the overlap regions in the a) closer, b) inner, and c) outer layers ( $\sigma / \sqrt{2}$ gives the single hit resolution). d) shows the inner-layer residuals for tracks with hits in all three layers (single hit resolution = $\sigma / \sqrt{1.5}$).
In $z$ the resolution depends on the track incidence angle, as shown for the outer layer on the right. The closed circles represent the region where the readout pitch was doubled. The inset shows the $z$ hit residuals for normally incident tracks (single hit resolution = $\sigma / \sqrt{2}$).

an intrinsic resolution of 8-9 $\ensuremathbox{\mu\mathrm{m}}$ (7.6 $\ensuremathbox{\mu\mathrm{m}}$ in the outer layer) in $\ensuremathbox{R\phi}$ and 9-40 $\ensuremathbox{\mu\mathrm{m}}$ in $z$ (9 $\ensuremathbox{\mu\mathrm{m}}$ for perpendicular tracks passing through the outer layer).

The overall precision of a vertex detector may be described in terms of track impact parameters (see definition in appendix B) with respect to the production vertex, usually the primary vertex (see section 2.11.3). There are two components to the impact parameter error (excluding the uncertainty in the production vertex, which does not concern us here): the intrinsic precision of the VD hits, extrapolated to the vertex; and the uncertainty due to multiple scattering in the beam pipe and VD material. In the $\ensuremathbox{R\phi}$ and $\ensuremathbox{R z}$ planes these may be parameterized with

$$\sigma_{\ensuremathbox{R\phi}} = \frac{\alpha_{\mathrm{MS}}}{p\sin^{3/2}\theta} \oplus \sigma_{0,\ensuremathbox{R\phi}}$$ (2.3)

and

$$\sigma_z = \frac{\alpha'_{\mathrm{MS}}}{p\sin^{5/2}\theta} \oplus \sigma_{0,z} \,,$$ (2.4)

where the constants $\alpha_{\mathrm{MS}}$ (multiple scattering) and $\sigma_0$ (intrinsic precision) are best fitted from the data as shown in figure 2.8.

Figure 2.8: Track impact parameter errors as a function of momentum in (a) the $\ensuremathbox{R\phi}$ plane and (b) the $Rz$ plane (lower curve: $80\ensuremathbox{^\circ}< \theta < 90\ensuremathbox{^\circ}$, upper curve: $45\ensuremathbox{^\circ}< \theta < 55\ensuremathbox{^\circ}$). Fits to parameterizations 2.3 and 2.4 are shown. The error due to uncertainty in the primary vertex position (shown on the lower curve in (a)) has been removed.

(a) (b)

The fitted curves give $\alpha_{\mathrm{MS}} = 65$ $\ensuremathbox{\mu\mathrm{m}}$$\cdot$ $\ensuremathbox{\mathrm{GeV}/c}$ and $\sigma_{0,\ensuremathbox{R\phi}} = 20\ \ensuremathbox{\mu\mathrm{m}}$ in equation 2.3 and $\alpha'_{\mathrm{MS}} = 71$ $\ensuremathbox{\mu\mathrm{m}}$$\cdot$ $\ensuremathbox{\mathrm{GeV}/c}$ and $\sigma_{0,z} = 39\ \ensuremathbox{\mu\mathrm{m}}$ ( $80\ensuremathbox{^\circ}< \theta < 90\ensuremathbox{^\circ}$) or 96 $\ensuremathbox{\mu\mathrm{m}}$ ( $45\ensuremathbox{^\circ}< \theta < 55\ensuremathbox{^\circ}$) in equation 2.4.

2.3.2 Inner Detector (ID)

The Inner Detector [29] consists of two components: the jet chamber is a high-resolution drift chamber providing $\ensuremathbox{R\phi}$ tracking information, while the trigger layers provide a rapid readout in both $\ensuremathbox{R\phi}$ and $z$.

The jet chamber consists of 24 azimuthal sectors, each with a plane of 24 axial wires down its centre. A variation in the drift field (and hence drift velocity) with $R$ allows for constant drift time for all measurements of radial tracks, and hence a rapid trigger.

Outside this, the trigger layers consist of 5 layers of 192 multiwire proportional chambers (MWPC; before 1995) or straw tubes (1995 [30]). As well as measuring the $z$-coordinate, the $\ensuremathbox{R\phi}$ measurement can be used to help resolve the left-right ambiguity of the jet chamber.

2.3.3 Time Projection Chamber (TPC)

The TPC [31] is the main tracking detector in DELPHI, providing three-dimensional position information, a momentum measurement (from the track curvature in the magnetic field), and some particle identification based on the specific ionization in the detector.

The layout of the TPC is shown in figure 2.9.

Figure 2.9: Schematic layout the the TPC.

The cylindrical vessel is divided in two by a cathode plane at $z=0$ producing a uniform drift field of 187 V/cm. Primary electrons liberated by the passage of charged particles drift to the two ends of the detector. These are each divided into 6 azimuthal sectors, acting as MWPCs, each with 16 azimuthal cathode pad rows 4 mm behind 192 sense wires. The charge avalanche initiated on the anode wires by the primary electrons induces a signal on the pads, giving the $\ensuremathbox{R\phi}$-coordinate. The drift time to the sense wires gives the $z$-coordinate. The pulse height is a measure of the initial ionization ( $\ensuremathbox{\mathrm{d}E / \mathrm{d}x}$), which can be used for particle identification.

2.3.4 Outer Detector (OD)

The size of the the TPC is constrained by the Barrel RICH surrounding it. The Outer Detector [32] provides an additional track measurement outside this to extend the distance over which the track curvature is measured and hence improve the overall momentum resolution.

The OD consists of 24 overlapping planks, each of 145 drift tubes, arranged into 5 staggered layers. The $\ensuremathbox{R\phi}$-coordinate is obtained from the drift time, and $z$ (3 layers only) from the relative timings of the signal at the two ends of the anode wires.

2.3.5 Forward Chambers A (FCA)

The Forward Chambers A are mounted on either end of the TPC, and are thus mechanically part of the barrel. Each side consists of three modules each of two staggered layers of drift tubes, operating in limited streamer mode. The wire orientation of each module is 120 $\ensuremathbox{^\circ}$ from the other two, providing two measurements of each of three non-orthogonal coordinates $(x, u, v)$.

2.3.6 Forward Chambers B (FCB)

The Forward Chambers B are positioned outside the Forward RICH. Each endcap consists of two semicircular modules, each with 12 planes of wires. Pairs of staggered wire planes are orientated 120 $\ensuremathbox{^\circ}$ from their neighbours, providing four measurements of each of the same $(x, u, v)$ coordinates used in the FCA.