# Further SIMULATION of SMT Detector Performance for run2b  {#further-simulation-of-smt-detector-performance-for-run2b .unnumbered}

> F. Rizatdinova, E. Chabalina, A. Khanov, T. Bolton, R. Demina

## Introduction

This note describes simulation studies of the D0 Run 2b silicon tracker
with changes implemented since the December, 2001 TDR[^1] (hereafter
referred to as "the TDR"). The detector geometry was modified to conform
with the mechanical design, and the intrinsic single hit resolution for
isolated tracks was inflated to 10 microns.

## Overview

The DØ Run 2B group performed a detailed simulation of the Run 2B
silicon microstrip tracker. The simulation included a full Geant
simulation of the underlying physical process, data-tuned models of
detector response, and complete reconstruction of simulated events,
including pattern recognition, within the DØ Run 2B software framework.
Quantitative calculations of occupancy, impact parameter resolution,
momentum resolution, and b-quark tagging efficiency verify substantial
improvements in performance over the presently operating Run 2A silicon
detector. These full Geant results are presented below.

## Silicon Geometry In The Simulation

The Run 2B silicon detector is modeled as a barrel tracker consisting of
six concentric cylindrical layers, numbered from 0 to 5 in going from
the innermost radius of 19 mm to the outermost radius of 164 mm,
respectively. Pseudorapidity coverage extends from -2.5 to +2.5. Each
layer consists of two sub-layers that preserve a six-fold symmetry for
the silicon track trigger. Layers 0 and 1 were simulated with axial
silicon detectors only, while layers 2 through 5 contained axial-stereo
pairs of single-sided detectors in each sub-layer. Figure 1 shows an
*x-y* view of the Run 2B silicon detector geometry as implemented in the
simulations, Figure 2 shows an x-z view, and Table 1 gives positions,
dimensions, and stereo angles of the detector modules used for this
work.

![](media/image1.jpeg){width="4.813194444444444in"
height="4.790972222222222in"}

Figure 1 - Geometric layout used in the Geant simulation of Run 2B
silicon detector.

![](media/image2.wmf)

Figure 2 An xz view of the Run 2b detector as implemented in the Geant
simulation.

![](media/image3.jpeg){width="4.870833333333334in"
height="3.9340277777777777in"}

Figure 3 - Layout of axial and axial-stereo modules.

Barrel modules[^2] are assembled end-to-end on long staves placed on
carbon fiber support cylinders that lie parallel to the z-axis of the
detector. Staves hold six modules each in layers 0-1 and four modules in
layers 2-5. The design of the Run 2B silicon detector requires two kinds
of axial modules and four kinds of axial-stereo \"sandwiches\". The
axial types are simulated as a silicon plates of 1.55 or 2.4972 cm width
(depending on layer, layer 0 has narrow detectors and layer 1 has wider
detectors), 7.94 cm length and 300 m thickness. The design of the Run 2B
silicon detector requires axial modules and two kinds of axial-stereo
"sandwiches". The axial type is simulated as a silicon plate of 1.48 cm
width, 7.84 cm length and 300 m thickness[^3]. A sandwich silicon module
consists of two equivalent silicon sensors, one axially oriented and the
other rotated with respect to the beam axis. The radial distance between
the two silicon planes in the sandwich is 3.094 mm, and the angle of the
rotation is 2.5 degrees for the small sandwiches and 1.25 degrees for
the stereo pairs of ganged detectors. The size of the silicon ladders in
the sandwiches is 4.11 cm 10 cm 300 m. Axial and stereo modules are
shown in Figure 3.

Table 1 - Parameters of the Run 2B silicon tracker used in the GEANT
simulation.

  --------------------------------------------------------------------------
  Layer        Radius (cm)     \# of      Sensor     Sensor    Stereo angle
                               sensors in Length     Pitch (m) (degrees)
                               z          (cm)                 
  ------------ --------------- ---------- ---------- --------- -------------
  0a, 0b       1.780 / 2.465   12         7.94       50        0 / 0

  1a, 1b       3.400 / 4.000   10         7.84       58        0 / 0

  2a, 2b       5.478 / 7.048   10         10.0       60        2.5 / 1.25

  3a, 3b       8.781 / 10.183  10         10.0       60        2.5 / 1.25

  4a, 4b       11.848 / 13.112 12         10.0       60        2.5 / 1.25

  5a, 5b       14.853 / 16.204 12         10.0       60        2.5 / 1.25
  --------------------------------------------------------------------------

All studies assume a functioning CFT in run 2b. Thus, a central track
can have up to 14 hits---six in the SMT and eight in the CFT. The new
layer 0 becomes the innermost hit on the track, and the new layer 5 is
the sixth of fourteen hits.

Low mass readout cables are modeled as copper plates of 1 cm width that
go out of the edge of first and third silicon modules in every layer.

## Simulation Of Signal, Digitization And Cluster Reconstruction

Geant simulates hits in the silicon sensors, and a modified DØ Run 2A
package DØSim[^4] package digitizes signals.

Input for DØSim consists of a bank of GEANT hits, each of which is
described by entry/exit positions and energy deposition in the silicon.
Silicon *dE/dx* is simulated via explicit generation of -rays that
resulted in a Landau distribution of deposited energy. No additional
fluctuations in energy loss were considered.

In order to reproduce the effects of ganging sensors together correctly
in the readout, hits within 1.5 mm of the midpoint in z of long
axial/stereo sandwich modules were discarded at the digitization step.

The total deposited energy is converted into the number of electron-hole
pairs using a coefficient *C*2.77810^8^ GeV^-1^. Charge collection on
strips is computed from a diffusion model with the standard drift and
Hall mobility of the charge carriers in silicon evaluated at the nominal
silicon operating temperature. Charge sharing between strips through
intermediate strip wiring is determined by inter-strip capacitance,
readout-ground capacitance, and the input capacitance of preamplifier,
values of which are taken from Run 2A measurements.

Electronic noise is added to the readout strips after hits have been
digitized. Parameters for noise simulation were extracted from the
readout electronics noise parameterization and silicon detector
prototype studies for Run 2A[^5]. This set of parameters leads to a S/N
ratio of 16:1, and this value is used for all tracking performance
studies. For occupancy studies the average noise was simulated for each
channel according to Gaussian distribution with =2.1 ADC counts that
decreases the signal-to-noise ratio to 10:1, again consistent with the
Run 2A data. A similar signal-to-noise ratio is expected for the end of
Run 2B (see the section on sensors). Only those strips above a threshold
of 4 ADC counts are saved for cluster reconstruction.

The choice of the threshold for the readout and cluster reconstruction
represents a trade-off between efficiency of the cluster reconstruction
and noise suppression. Figure 4 shows the probability to read out a
strip as a function of strip energy deposition in minimum ionizing
particle (MIP) equivalents, and to have a fake hit due to electronic
noise as function of the readout threshold. One can see that a readout
threshold of 6 ADC counts leads to 20% probability of losing a strip
that collects 1/3 MIP while significantly suppressing the noise
contribution.

Reconstruction of one-dimensional clusters was performed using a
modified package for Run 2A cluster finding. The clusters are defined as
a collection of neighbor strips with total charge more than 12 ADC
counts. Only those strips registering above 6 ADC counts are allowed in
the cluster. The position of the cluster is calculated with a center of
mass algorithm independent of the cluster size.

![](media/image4.png)

Figure 4 - Probability to have a hit on strip with different fraction of
MIP\'s charge.

## Analysis Tools

Occupancy and position resolution studies utilize a modified Run 2A DØ
SmtAnalyze package that allows access to raw and digitized Geant hits
and reconstructed clusters. Pattern recognition was performed using the
DØ Run 2A Histogramming Track Finder[^6] (HTF) modified for Run
2B-specific geometric features. The HTF algorithm is based on
pre-selection of hit patterns ("templates") in both the silicon detector
and the DØ fiber tracker with particular r- and z- properties. Hit
patterns are further cleaned and fitted using a standard Kalman
filtering technique. The separation of r- and stereo measuring detectors
in the Run 2B silicon detector by a finite gap required modification to
HTF as the precise z position of hits could be determined only after the
actual track direction was found. After suitable adjustment, HTF
demonstrated the good performance seen for Run 2A. All results assume no
degradation in fiber tracker performance between Run 2A and Run 2B.

The choice of the non-default D0 tracking package HTF was motivated
primarily by the availability of its author to make necessary
modifications in the tracking package to handle the changed run 2b
geometry. The tracking code could be adjusted to read out geometries
directly from GEANT. HTF has been shown to at least match the
performance of the standard D0 tracking package, called GTR, with Run 2a
data, with the added benefit that it could be used in a manner that
decoupled from ongoing Run2a software development.

## Performance Benchmarks

Basic tracker performance was studied with 2000 event single muon
samples generated with transverse momenta of 1, 5, and 50 GeV/c. The
primary vertex was fixed in the transverse plane at x=y=0; and z was
distributed about zero with a 15 cm Gaussian width.

For estimation of the physics performance, representative signal
channels have been chosen and simulated with zero, six, or 7.5 minimum
bias(MB) events overlaid. For the latter sample, the pileup events were
generated with a Poisson distribution with a mean of 7.5. Minimum bias
events were generated in separate runs of Geant. Hits from thse samples
were combined with those of signal processes at the digitization level.
Pattern recognition, track reconstruction in jets, and b-tagging
efficiency were studied by examining associated production of Higgs with
a W-boson. The Higgs boson mass was chosen to be 120 GeV/c^2^, and the
Higgs was forced to decay to a bb pair. The W-boson is forced to decay
leptonically. Z-boson production followed by decay to light (u or d)
quarks was used to estimate the fake rate of the b-tagging algorithm.
Minimum bias events were generated with PYTHIA (version 6.2) using a set
of parameters tuned to CDF run 1 MB data[^7]. Samples of at least 2000
events were processed through the full simulation chain for all studies,
with larger samples of 5000 events used for luminosity and occupancy
studies.

## Results

### Occupancy

Occupancy in the innermost layers is one of the most important issues
for the Run 2B silicon detector operation and performance. Four concerns
related to occupancy impact the design. The first, radiation damage,
limits the lifetime of the sensors; radiation damage and its radial
dependence are discussed in detail in the TDR section devoted to
sensors. Second is the number of hits per module to be read out per
event, which can cause excessive dead time if too large. The
relationship between number of hits and charge collection per strip is
addressed in the TDR electronics section. Another concern is that a high
occupancy in the innermost layer could lead to a significant fraction of
wide clusters formed by overlapping tracks that may worsen spatial
resolution. The occupancy is also an important factor in the pattern
recognition.

Occupancy has been studied in detail using the samples of WH events both
with and without six additional MB events, and with pure MB events. In
all cases, electronic noise was added to physics events. Minimum bias
events were used to estimate the average occupancy as a function of
radius. Peak occupancies occur in the WH with MB events and were
estimated using the the WH plus 6MB sample by looking at the silicon
module with the highest number of fired strips. The highest local
occupancy occurs within a jet. If this value is too high, both pattern
recognition and impact parameter performance will be degraded, resulting
in a loss of b-tagging efficiency and consequent physics reach.

Average occupancy, defined as the number of channels above threshold
divided by the total number of channels in a given layer*,* in MB events
with and without noise as a function of radius is shown in Figure 5. The
plot clearly demonstrates that the average occupancy due to physics
processes in MB events is of about an order of magnitude less than that
due to noise in the system. The occupancy caused by hits from real
particles drops with radius as expected, and the noise occupancy
practically does not change with radius. This behavior is in part due to
the relatively low threshold used for the study.

![](media/image5.png){width="3.248611111111111in"
height="2.9944444444444445in"}

Figure 5 - Mean occupancy as function of radius in minimum bias events
without noise and with average noise.

![](media/image6.jpeg){width="3.0756944444444443in"
height="2.9965277777777777in"}

Figure 6 - Mean occupancy as function of z-position of a silicon module
at different radii. Higher barrel number corresponds to higher z values.

Figure 6 represents the z-dependence of the average occupancy for WH
events without noise in the system. It decreases by 50% for layer 0 away
from *z=0*. At large *z*, two silicon modules in layers 2 through 5 are
bonded to each other ("ganged") to minimize cable count. Occupancy for
these layers clearly increases in the outer barrels where ganging is
applied, but not to a level that harms detector performance.

![](media/image7.png){width="3.3208333333333333in"
height="2.998611111111111in"}

Figure 7 - Mean occupancy in layer 0 without noise and with average
noise as a function of the readout threshold.

![](media/image8.png){width="2.957638888888889in" height="3.0in"}

Figure 8 - Peak occupancy without noise and with average noise at
different readout thresholds as function of the radius.

Dependence of the average occupancy on the readout threshold is shown in
Figure 7 for WH events without pile-up. A reduction factor of 1.8 in the
average occupancy can be obtained by using a threshold of 5 ADC counts.
An additional reduction factor of two can be achieved by using the
readout threshold of 6 ADC counts. This does not significantly affect
the signal readout efficiency while the S/N ratio is higher than 10:1;
but losses of efficiency would be expected for smaller S/N ratios.

![](media/image9.png){width="3.1006944444444446in"
height="3.004861111111111in"}

Figure 9 - Peak occupancy in WH events without pile-up and with 6
minimum bias events as function of the radius.

Peak occupancy as a function of radius for b-jets in WH+0 MB events is
shown in Figure 8. At small radii (less than 5 cm), peak occupancy drops
from 8% in layer 0 to 6% in layer 1b. For larger radii occupancy is
nearly independent of radius since the size of the b-jet is smaller than
the area of a module. Dependence of the peak occupancy on luminosity is
shown in Figure 9. At higher luminosities, corresponding to the
additional 6 MB events, peak occupancy increases by a factor 1.5 in all
layers compared to low luminosity case.

### Cluster size and spatial resolution

Spatial resolution plays an important role in the impact parameter
resolution and in pattern recognition. Factors determining spatial
resolution include detector pitch, presence of intermediate strips,
signal-to-noise ratio, the clustering algorithm, Lorentz angle, and
direction of the track.

The two inner layers are equipped with 50 m pitch sensors, and the outer
four layers contain sensors with 60 m pitch. Figure 10 shows the
fraction of clusters as a function of number of strips for single muons
in the inner and outer layers. Intermediate strips cause two-strip
clusters to dominate, leading to an intrinsic single cluster resolution
of about 6 m. Fractions of one-, two- and three-strip clusters are shown
in Table 2 together with expected spatial resolutions. Resolutions
derived from one- and three-strip clusters are given in Figure 11 and
Figure 12, and are approximately the same for inner and outer layers. No
mis-alignment of the silicon detectors was assumed.

![](media/image10.wmf){width="2.642361111111111in"
height="3.0069444444444446in"}

Figure 10 - Cluster size distribution in layer 0 with 50μm readout pitch
and layer 3 with 60μm readout pitch.

![](media/image11.wmf){width="3.126388888888889in"
height="3.7569444444444446in"}

Figure 11 - Spatial resolution derived from the clusters in the two
innermost layers with readout pitch of 50 μm.

![](media/image12.wmf){width="2.926388888888889in"
height="3.7569444444444446in"}

Figure 12 - Spatial resolution derived from the clusters from four outer
layers with readout pitch of 60 μm.

Table 2 - Position resolutions for various cluster sizes.

+------------+-------+-------+-------+---------+----------+--------+
|            | **L   |       |       | **Layer |          |        |
|            | ayers |       |       | 2-5**   |          |        |
|            | 0,1** |       |       |         |          |        |
+------------+-------+-------+-------+---------+----------+--------+
| ####       | 1     | 2     | 3     | 1       | 2        | 3      |
| # Number o |       |       |       |         |          |        |
| f strips { |       |       |       |         |          |        |
| #number-of |       |       |       |         |          |        |
| -strips .u |       |       |       |         |          |        |
| nnumbered} |       |       |       |         |          |        |
+------------+-------+-------+-------+---------+----------+--------+
| ##         | 0.45  | 0.49  | 0.29  | 0.08    | 0.52     | 0.23   |
| ### Fracti |       |       |       |         |          |        |
| on of clus |       |       |       |         |          |        |
| ters {#fra |       |       |       |         |          |        |
| ction-of-c |       |       |       |         |          |        |
| lusters .u |       |       |       |         |          |        |
| nnumbered} |       |       |       |         |          |        |
+------------+-------+-------+-------+---------+----------+--------+
| **         | 12.7  | 10.9  | 11.7  | 12.9    | 11.1     | 12.8   |
| Resolution |       |       |       |         |          |        |
| (**m**)**  |       |       |       |         |          |        |
+------------+-------+-------+-------+---------+----------+--------+

Figure 13 and Figure 14 show distributions of the number of strips in
clusters for WH and WH events with pile-up. The average number of strips
per cluster for physics events is higher than for single muons.

![](media/image13.png){width="3.0395833333333333in" height="3.0in"}

Figure 13 - Cluster size (number of strips) in WH events without
pile-up.

![](media/image14.png){width="2.921527777777778in"
height="3.004166666666667in"}

Figure 14 - Cluster size (number of strips) in WH events with an
additional 6 minimum bias events.

![](media/image15.wmf){width="2.9972222222222222in"
height="2.9972222222222222in"}

Figure 15 - Hit position resolution in WH events obtained with
non-shared clusters.

![](media/image16.jpeg){width="2.9833333333333334in" height="3.00625in"}

Figure 16 - Hit position resolution in WH events obtained with shared
clusters.

Clusters formed by more than one track are denoted as "shared clusters".
Cluster sharing leads to worse spatial resolution, reduced ability to
find tracks close together, and a drop of impact parameter resolution
and b-tagging efficiency in the end. The spatial resolution for clusters
produced by one track is about 7 m (Figure 15) while the hit position
resolution in the inner layers for WH events for shared clusters is
about 27 m (Figure 16). Figure 17 shows the probability for *N* tracks
to share a reconstructed cluster as a function of *N.* This high
multi-track correlation effect does not easily reveal itself in simple
parametric Monte Carlo studies performed with tools such as MCFast.

![](media/image17.jpeg){width="3.4805555555555556in"
height="3.4972222222222222in"}

Figure 17 - Average multiplicity of the tracks which form a shared
cluster.

The fraction of shared clusters is shown in Table 3 for WH and WH events
with pile-up for different layers. The largest cluster sharing of about
6% is observed in layer 0. The fraction of shared clusters decreases
with radius for the inner layers and is almost constant for the outer
ones since the separation of tracks in b-jets increases modestly over
the silicon detector volume.

Table 3 - Percentage of shared clusters vs. layer for WH events with and
without 7.5 MB events overlaid.

  --------------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- ---------
                  **L0a**   **L0b**   **L1a**   **L1b**   **L2a**   **L2b**   **L3a**   **L3b**   **L4a**   **L4b**   **L5a**   **L5b**

  WH events       7.0       4.6       3.8       3.1       2.6       2.2       1.3       1.5       1.3       1.0       1.1       1.0

  WH with 7.5 MB  7.5       4.7       3.5       3.0       3.0       2.3       2.0       1.8       1.4       1.2       1.3       1.0
  --------------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- ---------

Figure 18, Figure 19, and Figure 20 provide more detail on the spatial
resolution of clusters as a function of the number of tracks in the
cluster. The resolution degrades rapidly as the number of tracks per
cluster increases.

![](media/image18.jpeg){width="4.2972222222222225in"
height="4.454861111111111in"}

Figure 18 - Distributions of reconstructed-true position for simulated
Run 2B SMT clusters for 1, 2, 3, and 4 track clusters.

![](media/image19.jpeg){width="4.627777777777778in" height="4.44375in"}

Figure 19 - Distributions of reconstructed-true position for simulated
Run 2B SMT clusters for 1, 2, 3, and 4 track clusters.

![](media/image20.jpeg){width="4.391666666666667in"
height="2.282638888888889in"}

Figure 20- Distributions of reconstructed-true position for simulated
Run 2B SMT clusters for 9 and 10 track clusters

## Physics Performance Of The Run 2B Tracker

As discussed earlier in this document, the main Run 2B physics goal is
the search for the Higgs boson. Other important investigations will
center on top-quark properties, precision measurements of W-boson mass
and width, b-physics, and searches for supersymmetry and other new
phenomena. All physics would benefit from improved track reconstruction
efficiency and momentum resolution in a Run 2B tracker with an upgraded
silicon detector. However, higher b-tagging efficiency keys new physics
discovery potential in DØ.

It is worth summarizing the essentials of simple cuts-based search for
WH. Requirements include:

1.  A high p~T~ lepton of at least 20 GeV with \|\|\<2 and a missing
    E~T~\>20 GeV. This strongly suppresses all final states without a W
    or Z, selecting ttX, WX, and ZX.

2.  No other isolated tracks with p~T~\>10 GeV. This suppresses events
    with Zll and ttllX.

3.  No more than two central jets with E~T~\>20 GeV. This suppresses
    ttblbjj.

4.  At least two tagged b-jets. This suppresses Wjjljj and WZljj

Note that the suppression of QCD events is largely accomplished [without
b-tagging]{.underline} in this final state. The largest backgrounds turn
out to be contributions from Wbb lbb, WZ lbb, and tt,tb lbb(nj~miss~)
that cannot be reduced by [any]{.underline} improvement in the SMT. The
irreducibility of the backgrounds (at least without a more sophisticated
analysis) implies that S/B will be independent of the b-tagging
efficiency and that S/sqrt(B) will be linear(not quadratic) in single
b-jet tagging efficiency.

The following sections summarize the track reconstruction efficiency,
accuracy of the track parameter measurements, and b-tagging efficiency
obtained from studies of WH events.

### Single track performance

The p~T~ resolution (p~T~) for single muons is shown in Figure 21,
together with (p~T~) calculated for the Run 2A tracker. Resolution is
obtained from a Gaussian fit to q/p~T~, where q is the particle charge.
No tails were observed in this distribution for single muons. For low
p~T~, where the p~T~ resolution is dominated by multiple scattering
there is no difference between run 2A and run 2B trackers. An
improvement at high p~T~ is observed due to larger number of precise
measurements per track. The difference is big at small \|\| and
disappears at \|\| above 1.5, as it is shown in Figure 21(left).

![](media/image21.jpeg){width="2.8090277777777777in"
height="2.745833333333333in"}
![](media/image22.jpeg){width="2.747916666666667in"
height="2.751388888888889in"}

Figure 21 - p~T~-resolution as a function of p~T~ (left) and function of
pseudorapidity (right) for single muons in Run 2A and Run 2B.

Reconstruction efficiency as function of \|\| is shown in Figure 22. It
is fairly flat up to \|\|=1.5 for all transverse momenta. Because tracks
at larger miss the fiber tracker altogether and cannot produce the
minimum four hits required for silicon-only tracking, the reconstruction
efficiency begins dropping above \|\|=1.5, falling to 90% by \|\|=2.

![](media/image23.jpeg){width="3.040277777777778in"
height="3.0055555555555555in"}

Figure 22 - Reconstruction efficiency as function of η of muons with
pT=1,5,and 50 GeV/c.

Impact parameter resolutions in the transverse plane and *z*-direction
are important for heavy-flavor tagging, primary vertex reconstruction
(especially at high luminosity), and detection of secondary vertices. At
high momenta (p~T~\>10 GeV), resolution is determined to a large extent
by the measurements in layer 0. At smaller momenta, it depends on
multiple scattering and therefore the material distribution in the
tracker. Transverse impact parameter resolution as function of p~T~ of
single muons is compared to that in Run 2A in Figure 23. Improvement by
a factor of 1.5 is expected for (d~0~) over the whole p~T~ region. This
can be understood as being due to the closer (to the interaction point)
first measurement in the Run 2B silicon detector and to the larger
number of precision measurements. Indeed, for a simple two layer
detector with measurements of hit resolution ~meas~ at radii R~inner~
and R~outer~, the impact parameter resolution is simply
(d~0~)\~~meas~(1+R~inner~/ R~outer~). The ratio R~inner~/ R~outer~ is
0.27 in Run 2A and 0.11 in Run 2B. This geometric change accounts for
almost all of the impact parameter resolution improvement.

The transverse impact parameter resolution (d~0~) as function of \|\| is
shown in Figure 24 for the Run 2B tracker. For Run 2B, a slight
degradation in (d~0~) is observed for low-p~T~ tracks with increasing
\|\|; for high-p~T~ tracks the distribution of transverse parameter
resolution vs. \|\| is flat. These behaviors are expected from the
enhanced contribution of multiple scattering at large \| and small p~T~

Dependence of the longitudinal impact parameter resolution on p~T~ is
shown in Figure 25. Because of the absence of three-dimensional
measurements in layer 0 and the relatively worsened *z*-resolution
obtained with 2^o^ stereo detectors compared to the 90^o^ detectors in
Run 2A, the resolution in longitudinal impact parameter resolution in
Run 2A degrades to 280 m for high-p~t~ muons.

![](media/image24.jpeg){width="3.9402777777777778in"
height="3.8097222222222222in"}

Figure 23 - Transverse impact parameter resolution as function of pT for
single muons.

![](media/image25.jpeg){width="3.75in" height="3.7465277777777777in"}

Figure 24 - Transverse impact parameter resolutions in Run 2B for low-pT
muons.

![](media/image26.jpeg){width="3.1125in" height="2.995833333333333in"}

Figure 25 - Longitudinal impact parameter resolution as a function of pT
for single muons.

### b-tagging performance

B-tagging is the main tool for searches for the Higgs boson and many
supersymmetric objects, as well as for top physics. The main goal of
b-tagging methods is to reject jets produced by light quarks and gluon
jets while preserving a high efficiency for tagging of the b-jets.
Pre-selection of b-jets is based on the relatively long lifetime of B
hadrons. Rejection of charm jets is limited by the finite lifetime of
charmed hadrons, and rejection of gluon jets is bounded by contributions
from gluon splitting to heavy quarks at branching fractions of a few
percent. Experimental limitations for ideal b-tagging arise from
inefficiencies of the track reconstruction in jets, impact parameter
resolution and secondary vertex resolution.

The overall track reconstruction efficiency in jets together with the
corresponding fake track rate is presented in Table 4 for WH events at
low and high luminosities. There is slight degradation in the track
finding efficiency at high luminosity, but the fake track rate is
negligible in both cases. The average track reconstruction efficiency in
jets ~tr-j~ is consistent with that for Run 2A.

Table 4 - Track reconstruction efficiency ~tr-j~ and fake track rate in
jets in WH events without pile-up and with 7.5 MB events.

  -----------------------------------------------------------------------
                                       ~tr-j~        Fake rate
  ------------------------------------ ------------- --------------------
  WH + 0 min bias events               83%           \<0.01%

  WH + 7.5 min bias events             81%           0.1%
  -----------------------------------------------------------------------

![](media/image27.jpeg){width="3.129166666666667in"
height="2.9944444444444445in"}

Figure 26 - Track reconstruction efficiency in b-jets as function of jet
\|η\|.

Figure 26 shows ~tr-j~ as function of the jet \|\| for WH+0MB and WH+6MB
events. The behavior of ~tr-j~ in jets is similar to the single-track
performance. It is high ( \~88%) in the central region and quickly
degrades beyond the fiber tracker boundary to \~60% at \|\|=2. The
relative drop in efficiency for higher \|\| is more pronounced in jets
than observed for isolated muons. That can be explained by the fact that
the more energetic jets at higher \|\| produce higher track
multiplicity, making pattern recognition more complicated. Taking into
account that b-quarks from Higgs boson decays and top decays produce
mostly central jets, one can expect the overall performance to be
dominated by a track reconstruction efficiency in jets of 85-88%.

A signed impact parameter (SIPtag) method[^8] was used to evaluate
b-tagging performance. A SIPtag requires that:

-   Tracks lie within a cone R \< 0.5 around the jet axis;

-   Selected tracks have p~T~ \> 0.5 GeV/*c*, good reconstruction
    quality, and at least two hits in the silicon;

-   At least two tracks have an impact parameter significance S=
    d~0~/(d~0~)\>3 or at least three tracks have S\>2.

To estimate the \"true\" b-tagging efficiency the numbers of b, c, and s
and u-d quarks with E\>20 GeV and \|\| \<2 were counted; and their
parameters were compared to those of tagged b-jets. If a tagged jet was
within a cone distance R\<0.5 about one of the light quarks, the flavor
of that quark was assigned to the jet.

The b-tagging efficiency ~b~ is defined as the ratio of the number of
jets with assigned b-flavor to the total number of b-quarks in the
considered acceptance. The mis-tagging rate is defined as the ratio of
the number of b-tagged jets originating from light quarks to the total
number of jets produced by light quarks in the considered (E,)~jet~
acceptance.

![](media/image28.jpeg){width="5.246527777777778in"
height="2.607638888888889in"}

Figure 27 - b-tagging efficiency as function of \|η\| of the tagged jet.

![](media/image29.png){width="3.0909722222222222in"
height="2.9944444444444445in"}

Figure 28 - Mis-tagging rate as function of \|η\| of the tagged jet.

Figure 27 shows the b-tagging efficiency ~b~ vs. \|\| of the
reconstructed b-jets in WH +0 MB events. The average ~b~ per jet of 69%
is 19% higher than in Run 2A. This is a consequence of the improved
impact parameter resolution due to the presence of layer 0. The
b-tagging efficiency is above 70% for \|\<1, reflecting the high track
reconstruction efficiency in jets in that region. It decreases with
increasing \|\| to 45% at \|\|=2. Dependence of the mis-tagging rate on
the jet \| was studied using Z-boson decays to first generation quarks;
it is shown in Figure 28. The mis-tagging rate varies between 1% and 2%
over the whole \|\| region. No \|\|-dependence of mis-tagging rate in
run 2B is observed within errors.

![](media/image30.jpeg){width="5.002777777777778in" height="2.425in"}

Figure 29 - b-tagging efficiency as function of the energy of the tagged
jet.

![](media/image31.png){width="3.2215277777777778in"
height="2.9791666666666665in"}

Figure 30 - Mis-tagging rate as function of the energy of the tagged
jet.

Dependencies of the b-tagging efficiency and the mis-tagging rate on
reconstructed jet energy E~j~ are shown in Figure 29 and Figure 30,
respectively. The best performance in terms of b-tagging is expected for
jets with E~j~ \~ 70-100 GeV. The rise of efficiency above 150 GeV is
not statistically significant. Due to insufficient statistics, the
mistagging rate is estimated only up to 140 GeV and is demonstrated to
be about 1.5 % in the whole considered energy scale.

Probabilities to tag an event with one or two b-jets are shown for Run
2A (estimated from Z-boson decays to bb) and Run 2B (from WH events) in
Table 5.

Table 5 - Probabilities to tag an event with one or two b-jets.

  ------------------------------------------------------------------------
                          Run 2A                         Run 2B
  ----------------------- ------------------------------ -----------------
  ***P(n~b~ 1)***         68%                            76%

  ***P(n~b~ 2)***         21%                            33%
  ------------------------------------------------------------------------

One can see from the table that an essential improvement in the
selection of events with b-tagged jets can be achieved with the Run 2B
tracker as compared to the existing tracker. Taking into account the
lower mis-tagging rate obtained in the Run 2B geometry, one can conclude
that the signal-to-background ratio in all analyses involving b-jets
will be significantly better in the next run.

Because of the slight degradation of track reconstruction efficiency in
jets with increasing luminosity, the b-tagging efficiency per jet (~b~)
deteriorates from 69% without pileup to 66% with an additional six MB
events. This leads to the slightly decreased values P(n*~b~* 1)=76% and
P(n*~b~* 2)=33%. Mis-tagging rates were not seen to increase
significantly at higher luminosity.

## Conclusions

The Run 2B silicon detector demonstrates good physics performance in a
realistic simulation that includes detailed physics and detector
response modeling and full pattern recognition. The physics performance
studies prove that the proposed silicon design meets the requirements of
the physics program of DØ Run 2B.

Detailed studies of occupancy in the run 2B silicon detector show the
expected higher rates (about 12% for busy events) in the inner layers.
However, no accompanying worsening in the spatial resolution of hits is
seen. Only 6% of reconstructed clusters in layer 0 are expected to be
shared by more than one track. The remaining single hit clusters
determine a single hit position with an accuracy of 7 m.

The choice of small-degree stereo detectors leads to a significant
decrease in ghost tracks and a consequent improvement in pattern
recognition. The additional layer 5 at radius R=16.4 cm helps to improve
p~T~ resolution for non-central tracks. The new layer 0 at a small
radius results in a factor of 1.5 improvement in impact parameter
resolution. As a consequence the single b-tagging efficiency per jet
improves by 19% compared to that obtained with Run 2A; and the
percentage of events with two b-tagged jets will be 67% higher than in
Run 2A at a fixed mis-tagging rate.

Predictions made for discovery limits of the Higgs boson in Run 2B were
based on the assumption that DØ would have the same performance as in
Run 2A. The proposed silicon detector is shown to deliver even better
performance for high-p~T~ processes.

[^1]: "D0 Run 2B Silicon Detector Upgrade Technical Design Report", D0
    Collaboration,
    http://d0server1.fnal.gov/Projects/run2b/Silicon/TDR/D0_Run2b_Silicon_TDR_11Oct01_v3.pdf

[^2]: "Module" here refers to a geometric unit used in the Geant
    simulation. Readout modules may be different.

[^3]: The actual sensors turn out to be 320 m thick.

[^4]: http://www-d0.fnal.gov/newd0/d0atwork/computing/MonteCarlo/simulation/d0sim.html.

[^5]: J. Ellison and A. Heinson, "Effects of Radiation Damage on the DØ
    Silicon Tracker", DØ note 2679, July, 1995.

[^6]: A. Khanov, R. Demina "Histogramming Track Finding Algorithm
    Performance Study", DØ Note 3845.

[^7]: R. Field, "The Underlying Event in Hard Scattering Processes'',
    http://fnth31.fnal.gov/runiimc.

[^8]: A. Khanov, R. Demina "Histogramming Track Finder: The impact
    parameter b-tagging performance", DØ Note 3855.