EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-DP-2013-003 7 January 2013

Performance of the LHCb Outer Tracker

The LHCb Outer Tracker group

R. Arink1, S. Bachmann2, Y. Bagaturia2, H. Band1, Th. Bauer1, A. Berkien1, Ch.
Färber2, A. Bien2, J. Blouw2, L. Ceelie1, V. Coco1, M. Deckenhoff3, Z. Deng7,
F. Dettori1, D. van Eijk1, R. Ekelhof3, E. Gersabeck2, L. Grillo2, W.D.
Hulsbergen1, T.M. Karbach3,4, R. Koopman1, A. Kozlinskiy1, Ch. Langenbruch2,
V. Lavrentyev1, Ch. Linn2, M. Merk1, J. Merkel3, M. Meissner2, J.
Michalowski5, P. Morawski5, A. Nawrot6, M. Nedos3, A. Pellegrino1, G. Polok5,
O. van Petten1, J. Rövekamp1, F. Schimmel1, H. Schuylenburg1, R. Schwemmer2,4,
P. Seyfert2, N. Serra1, T. Sluijk1, B. Spaan3, J. Spelt1, B. Storaci1, M.
Szczekowski6, S. Swientek3, S. Tolk1, N. Tuning1, U. Uwer2, D. Wiedner2, M.
Witek5, M. Zeng7, A. Zwart1.

1Nikhef, Amsterdam, The Netherlands
2Physikalisches Institut, Heidelberg, Germany
3Technische Universität Dortmund, Germany
4CERN, Geneva, Switzerland
5H. Niewodniczanski Institute of Nuclear Physics, Cracow, Poland
6A. Soltan Institute for Nuclear Studies, Warsaw, Poland
7Tsinghua University, Beijing, China

The LHCb Outer Tracker is a gaseous detector covering an area of $5\times 6$
m2 with 12 double layers of straw tubes. The detector with its services are
described together with the commissioning and calibration procedures. Based on
data of the first LHC running period from 2010 to 2012, the performance of the
readout electronics and the single hit resolution and efficiency are
presented.

The efficiency to detect a hit in the central half of the straw is estimated
to be 99.2%, and the position resolution is determined to be approximately 200
$\,\upmu\rm m$. The Outer Tracker received a dose in the hottest region
corresponding to 0.12 C/cm, and no signs of gain deterioration or other ageing
effects are observed.

Published in JINST

© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.

###### Contents

  1. 1 Introduction
  2. 2 Services performance
    1. 2.1 Gas system
    2. 2.2 Gas monitoring
    3. 2.3 Low voltage
    4. 2.4 High voltage
  3. 3 Commissioning and monitoring
    1. 3.1 Quality assurance of detector modules and C-frame services
    2. 3.2 Noise
    3. 3.3 Threshold scans
    4. 3.4 Delay scans
  4. 4 Calibration
    1. 4.1 Distance drift-time relation
    2. 4.2 $t_{0}$ stability
    3. 4.3 Geometrical survey
    4. 4.4 Optical alignment with the Rasnik system
    5. 4.5 Software alignment
  5. 5 Performance
    1. 5.1 Spillover and drift-time spectrum
    2. 5.2 Occupancy
    3. 5.3 Hit efficiency
    4. 5.4 Hit resolution
    5. 5.5 Monitoring of faulty channels
    6. 5.6 Radiation tolerance
  6. 6 Conclusions
  7. Acknowledgements

##  1 Introduction

The LHCb detector [1] is a single-arm forward spectrometer covering the
pseudo-rapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about 4 Tm and three tracking stations
located downstream. The area close to the beamline is covered by silicon-strip
detectors, whereas the large area at more central rapidity is covered by the
Outer Tracker (OT) straw-tube detector.

Excellent momentum resolution is required for a precise determination of the
invariant mass of the reconstructed $b$-hadrons. For example a mass resolution
of 25 MeV/c2 for the decay $B_{s}^{0}\rightarrow\mu^{+}\mu^{-}$ translates
into a required momentum resolution of $\delta p/p\approx 0.4\%$ [2].
Furthermore, the reconstruction of high-multiplicity $B$ decays demands a high
tracking efficiency and at the same time a low fraction of wrongly
reconstructed tracks. To achieve the physics goals of the LHCb experiment, the
OT is required to determine the position of single hits with a resolution of
200 $\mu$m in the $x$-coordinate 111 The LHCb coordinate system is a right-
handed coordinate system, with the $z$ axis pointing along the beam axis, $y$
is the vertical direction, and $x$ is the horizontal direction. The $xz$ plane
is the bending plane of the dipole magnet., while limiting the radiation
length to 3% $X_{0}$ per station (see Fig. 1b). A fast counting gas is needed
to keep the occupancy below 10% at the nominal luminosity of $2\times 10^{32}$
cm-2s-1.

The OT is a gaseous straw tube detector [3] and covers an area of
approximately $5\times 6$ m2 with 12 double layers of straw tubes. The straw
tubes are 2.4 m long with 4.9 mm inner diameter, and are filled with a gas
mixture of Ar/CO2/O2 (70/28.5/1.5) which guarantees a fast drift-time below 50
ns. The anode wire is set to +1550 V and is made of gold plated tungsten of 25
$\mu$m diameter, whereas the cathode consists of a 40 $\mu$m thick inner foil
of electrically conducting carbon doped Kapton-XC 222 Kapton® is a polyimide
film developed by DuPont. and a 25 $\mu$m thick outer foil, consisting of
Kapton-XC laminated together with a 12.5 $\mu$m thick layer of aluminium. The
straws are glued to sandwich panels, using Araldite AY103-1 333Araldite® is a
two component epoxy resin developed by Huntsman.. Two panels are sealed with
400 $\mu$m thick carbon fiber sidewalls, resulting in a gas-tight box
enclosing a stand-alone detector module. A cross-section of the module layout
is shown in Fig. 1(a).

(a)(b) Figure 1: (a) Module cross section. (b) Arrangement of OT straw-tube
modules in layers and stations.

The modules are composed of two staggered layers (monolayers) of 64 drift
tubes each. In the longest modules (type $F$) the monolayers are split in the
middle into two independent readout sections composed of individual straw
tubes. Both sections are read out from the outer ends. The splitting in two
sections is done at a different position for the two monolayers to avoid
insensitive regions in the middle of the module. $F$-modules have an active
length of 4850 mm and contain twice 128 straws, in the upper and the lower
half, respectively. Short modules (type $S$) have about half the length of
$F$-type modules and are mounted above and below the beampipe. They contain
128 single drift tubes, and are read out only from the outer module end. The
inner region not covered by the OT, $|y|<10(20)$ cm for $|x|<59.7(25.6)$ cm,
is instrumented with silicon strip detectors [1]. One detector layer is built
from 14 long and 8 short modules, see Fig. 1(b). The complete OT detector
consists of 168 long and 96 short modules and comprises 53,760 single straw-
tube channels.

The detector modules are arranged in three stations. Each station consists of
four module layers, arranged in an x-u-v-x geometry: the modules in the
$x$-layers are oriented vertically, whereas those in the $u$ and $v$ layers
are tilted by $+5^{o}$ and $-5^{o}$ with respect to the vertical,
respectively. This leads to a total of 24 straw layers positioned along the
$z$-axis.

Each station is split into two halves, retractable on both sides of the beam
line. Each half consists of two independently movable units, known as
C-frames, see Fig. 1(b). The modules are positioned on the C-frames by means
of precision dowel pins. The C-frames also provide routing for all detector
services (gas, low and high voltage, water cooling, data fibres, slow and fast
control). The OT C-frames are sustained by a stainless steel structure (OT
bridge), equipped with rails allowing the independent movement of all twelve
C-frames. At the top the C-frames hang on the rails, while at the bottom the
C-frames are guided, but not supported by the rails, to constrain the movement
in the $z$-coordinate.

(a)(b) Figure 2: (a) Design and (b) photograph of the FE electronics mounted
in a FE box. Only the boards that read out one monolayer of 64 straws are
visible. In addition, the HV boards are not visible in the photograph as they
are hidden by the ASDBLR boards.

The front-end (FE) electronics measures the drift-times of the ionization
clusters produced by charged particles traversing the straw-tubes with respect
to the beam crossing (BX) signal [4]. The drift-times are digitized for each
25 ns (the LHC design value for the minimum bunch crossing interval) and
stored in a digital pipeline to await the lowest-level trigger (L0) decision.
On a positive L0 decision, the digitized data in a window of 75 ns is
transmitted via optical links to TELL1 boards in the LHCb DAQ system [5].

As shown in Fig. 2, the FE electronics has a modular design, consisting of
several interconnected boards housed inside a metallic box (FE box). The main
components of the OT readout electronics are the high voltage (HV) board, the
ASDBLR amplifier board, the OTIS digitization board, and the GOL auxiliary
(GOL/AUX) board. Each ASDBLR board hosts two ASDBLR chips [6]. These are
custom-made integrated circuits, providing the complete analog signal
processing chain (amplification, shaping, baseline restoration, and
discrimination) for the straw tube detectors. The hit outputs of two ASDBLR
boards (32 channels) are connected to one OTIS board, which hosts one
radiation-hard OTIS TDC chip for drift-time digitization [7, 8]. The time
digitization is done through the 25 ns long Delay Locked Loop (DLL) using the
64 delay-stages of the DLL (64 time bins), giving a step size of about 0.4 ns.

The drift-time data is stored in a pipeline memory with a depth of 164 events,
corresponding to a latency of 4.1 $\mu$s. If a trigger occurs, the
corresponding data words of up to 3 bunch crossings are transferred to a
derandomizing buffer, able to store data from up to 16 consecutive triggers.
Only the first hit in the 75 ns wide window of a given channel is stored.
Later signals from multiple ionizations or reflections are thus not recorded.
The OTIS boards in a FE box are connected to one GOL/AUX board. This board [9]
provides the outside connections to the FE box: the power connection, the
interface to the fast-control (beam crossing clock BX, triggers, resets) and
the interface to the slow-control (I2C).

These boxes are mounted at each end of the detector modules. A FE box is the
smallest independent readout unit of the OT: the digitized data of the 128
channels of one module are sent via an optical link and received by the TELL1
board. High- and low-voltage, as well as fast- and slow-control signals are
connected to each FE box individually. In total, 432 FE boxes are used to read
out the OT detector.

This paper describes the detector performance in the first LHC running period
from 2010 to 2012, when the LHCb experiment collected data at stable
conditions, corresponding to a typical instantaneous luminosity of about
$3.5\,(4.0)\times 10^{32}$ cm-2s-1 in 2011 (2012), with a 50 ns bunch crossing
scheme and a proton beam energy of 3.5 (4) TeV. The higher instantaneous
luminosity, and only half of all bunches being filled, translates into a four
times larger occupancy per event as compared to the conditions that correspond
to the design parameters.

In Sec. 2 the performance of the services is described in terms of the gas
quality, and the low and high voltage stability. In Sec. 3 the performance of
the electronics readout is discussed, in particular the noise, amplifier
threshold uniformity and time-linearity. The drift-time calibration and
position alignment is shown in Sec. 4. The final detector performance in terms
of occupancy, single hit efficiency, resolution and radiation hardness is
given in Sec. 5.

##  2 Services performance

###  2.1 Gas system

The counting gas for the straw tube detectors of the OT was originally chosen
as an admixture of Ar/CO2/CF4. Studies on radiation resistance first suggested
to operate without CF4 [10], and subsequently with the addition of O2 [11],
leading to the final mixture Ar/CO2/O2 (70/28.5/1.5). This choice is based on
the requirement to achieve a reasonably fast charge collection to cope with
the maximum bunch crossing rate of 40 MHz at the LHC, a good spatial
resolution and to maximize the lifetime of the detectors.

| typical values | specifications
---|---|---
Gas flow | 800 - 850 l/h |  $<1000$ l/h
Overpressure in detector |  $1.6$ mbar |  $<5$ mbar
Impurity (H2O content) |  $<10$ ppm |  $<50$ ppm
Table 1: Main parameters of the OT gas system.

The gas is supplied by a gas system [12] operated in an open mode, without
recycling of the gas. The gas system is a modular system, with the mixing
module on the surface and two distribution modules, a pump module, an exhaust
module and an analysis module in the underground area behind the shielding
wall to allow access during beam operation. The gas is split between two
distribution modules, each supplying a detector half using 36 individual gas
lines. For each gas line the input flow can be adjusted and is measured
continuously, as well as the output flow. Each distribution module regulates
the pressure in the detector modules. The analysis module allows to sample
each of the 36 lines individually at the detector inlet and outlet. An oxygen
sensor and a humidity sensor are connected to the analysis rack. The
measurement of one gas line takes a few minutes such that each line is
measured approximately once every two hours.

The main operational parameters of the gas system are shown in Table 1. The
gas flow is kept low to prevent ageing effects observed in laboratory
measurements (see Sec. 5.6). The detector modules have been tested to be
sufficiently gas-tight, on average below $1.25\times 10^{-4}$ l/s
(corresponding to 5% gas loss every 2 hours) [13], to prevent the accumulation
of impurities from the environment. The level of impurities is monitored by
measuring the water content in the counting gas, which is at a level below
$10$ ppm.

A system with pre-mixed bottles containing in total about 100 m3 of Ar/CO2/O2,
is automatically activated in case of electrical power failures of the main
gas system, ensuring a uninterupted flow through the detector at all times.
The gas mixture, and the level of impurities (H2O) were stable during the
whole operation from 2010 to 2012.

###  2.2 Gas monitoring

The gas quality for the OT is crucial, as it directly affects the detector
gain and stability, and potentially the hit efficiency and drift-time
calibration. Moreover, a wrong gas mixture can lead to accelerated radiation
damage or dangerously large currents. The gas gain is determined with the help
of two custom built OT modules, of 1 m length, which are irradiated by a 55Fe
source.

LHCb OT Figure 3: Pressure calibration curve of the 55Fe spectrum, obtained
from the dependence of the pulse height $P$ as a function of atmospheric
pressure $p$.

One of the monitoring modules that was used in 2011 was constructed using a
particular glue, Trabond 2115, that does not provoke gain loss after long-term
irradiation with the 55Fe source. The other module was built with the glue
used in mass production, Araldite AY103-1. The modules were half-width modules
containing 32 straw tubes. The readout electronics consists of a high voltage
board carrying a number of single-channel charge pre-amplifiers.

The 55Mn K-$\alpha$ line of the 55Fe source has an energy of 5.9 keV which is
used as calibration reference. Two 55Fe sources with low intensity were used,
resulting in a few events per second for both modules. The data acquisition
system is based on a multi-functional readout box containing two fast ADC
inputs to which the amplified signals are fed. In addition the atmospheric
pressure is recorded. The 55Fe pulses are integrated over 15 minutes, and
subsequently analyzed. A double Gaussian distribution is fitted to the 55Fe
spectrum. The peak position is then corrected for the atmospheric pressure.

The pressure is measured inside a buffer volume at the chambers input. The
pressure correction is determined from a linear fit to the mean pulse-height
as a function of the absolute atmospheric pressure, see Fig. 3. The resulting
stability of the gas gain is within $\pm 2\%$ over 10 days. However, the gain
loss due to ageing of the monitoring modules was about 5% over a period of
about two months. The monitoring modules were therefore replaced at the end of
2011 by stainless steel modules, sealed with O-rings (instead of the standard
construction with Rohacell panels with carbon-fiber facing, glued together to
ensure the gas-tightness). The measurements of the gas gain were stable
throughout the entire running period of 2012.

###  2.3 Low voltage

The function of the low voltage (LV) distribution system is to provide the
bias voltages to the front-end electronics. Each FE box (the GOL/AUX board)
hosts three radiation-hard linear voltage regulators ($+2.5\,\mathrm{V}$,
$+3\,\mathrm{V}$ and $-3\,\mathrm{V}$) biased by two main lines,
$+6\,\mathrm{V}$ and $-6\,\mathrm{V}$. Two distribution boxes per C-frame
split the $+6\,\mathrm{V}$ and $-6\,\mathrm{V}$ supply lines to the 18 FE
boxes at the top and the 18 FE boxes at the bottom; all supply lines to the FE
boxes are individually provided with slow fuses ($4\,\mathrm{A}$ for
$+6\,\mathrm{V}$ and $2\,\mathrm{A}$ for $-6\,\mathrm{V}$) and LED’s showing
their status.

The low-voltage distribution systems worked reliably throughout the 2010 to
2012 data taking periods. In a few cases a single fuse of a FE box broke and
was replaced in short accesses to the LHCb cavern.

###  2.4 High voltage

The anode wires are supplied with +1550 V during operation, which corresponds
to a gas gain of about $5\times 10^{4}$ [14]. Each FE box has four independent
high voltage (HV) connections, one for each 32-channel HV board. Two
mainframes 444CAEN SY1527LC ®., each equipped with four 28-channels supply
boards 555A1833B PLC ®., are used as HV supply. Using an 8-to-1 distribution
scheme a total of 1680 HV connections of the detector are mapped on 210 CAEN
HV channels. The distribution is realized using a patch panel which offers the
possibility to disconnect individual HV boards by means of an HV jumper. Both
components, the HV supply as well as the patch panel, are located in the
counting house. Access to the HV system during data taking is therefore
possible.

The typical current drawn by a single HV channel (supplying 256 detector
channels) depends on the location in the detector and varies between 20 and
150 $\mu$A. The short-circuit trip value per HV channel was set to 200 $\mu$A
with the exception of one channel were the current shows an unstable
behaviour, and where the trip value was increased to 500 $\mu$A. The power
supply can deliver a maximum current of 3 mA for a single HV channel.

In the 2011 and 2012 running periods there were 8 single detector channels
(wires) that showed a short-circuit, either due to mechanical damage, or due
to a broken wire. During technical stops these single channels were
disconnected, to allow the remaining 31 detector channels on the same HV board
to be supplied with high voltage.

##  3 Commissioning and monitoring

Quality assurance tests of the detector modules, the FE-boxes and C-frame
services were performed prior to installation. Faulty components were repaired
whenever possible. During commissioning and operating phases of the LHCb
detector, the stability and the quality of the OT FE -electronics performances
was monitored. Upon a special calibration trigger, sent by the readout
supervisor, the FE -electronics generates a test-pulse injected via the ASDBLR
test input [6, 15]. Test-pulse combinations can be generated, and is
implemented such that only even or only odd numbered channels, or all channels
simultaneously, are injected with charge.

###  3.1 Quality assurance of detector modules and C-frame services

The quality of the detector modules was assured by measuring the wire tension,
pitch, and leakage current (in air) prior to the module sealing. Subsequently,
the gas tightness of the detector module was measured. Finally, the
functionality of each wire was validated in the laboratory immediately after
production, by measuring the response to radioactive sources (55Fe or 90Sr)
[14].

Before and after shipment of the C-frames from Nikhef to CERN, the equipment
of the services were checked, namely the gas tightness of the gas supply
lines, the dark currents on the high-voltage cables, the voltage drop on the
low-voltage supply cables and the power attenuation of the optical fibers [2,
16].

Following the installation of the modules on the C-frames in the LHCb cavern,
the gas tightness of each module was confirmed. The response to 55Fe of
approximately half of the straws was measured again, resulting in 12 noisy
channels, 7 dead channels, and 4 straws with a smaller gas flow [16].

All FE-boxes were measured on a dedicated test-stand in the laboratory, and
the faulty components were replaced. The tests performed on the test-stand are
identical to the tests that are performed regularly during running periods.
Three sequences of test runs are provided:

  * •

runs with a random trigger at varying ASDBLR threshold settings to measure the
noise rate;

  * •

runs with test-pulse injected at the ASDBLR test input, at varying threshold
settings to check the full readout chain for threshold uniformity and cross-
talk;

  * •

runs with test-pulse (at fixed threshold) at increasing test-pulse delay
settings, to determine the time-linearity.

###  3.2 Noise

The noise scan analysis aims at identifying channels that have an “abnormal”
level of noise, which may be due to dark pulses from the detector, bad FE
-electronics shielding, or bad grounding. In each channel the fraction of hits
is determined for increasing values of the amplifier threshold, triggered
randomly. The nominal value of the amplifier threshold is 800 mV, which
corresponds to an input charge of about 4 fC.

(a)(b) Figure 4: The 2d-hitmap histogram showing the noise occupancy, for each
channel, and varying amplifier threshold (1 ADC count $\approx$ 10 mV) [17]
for (a) a typical FE-box with good channels and (b) a FE-box with two groups
of noisy channels.

The typical noise occupancy for 128 channels in one FE box is shown in Fig.
4(a) for increasing amplifier threshold, where the occupancy is defined as the
ratio of the number of registered hits in that channel over the total number
of triggered events. A noise occupancy at the level of $10^{-4}$ is observed
at nominal threshold, as expected from beam tests [18]. These results are
representative for about 98% of all FE boxes in the detector.

An example of a FE box with a few noisy channels is shown in Fig. 4(b), where
two groups of about 5 noisy channels are identified. About 2% of the FE boxes
exhibited this noise pattern during the 2011 running period. At the nominal
threshold of 800 mV (4 fC) only 0.2% of the channels exhibited a noise
occupancy larger than 0.1%. During the 2011/2012 winter shutdown, this noise
pattern was understood and identified to be caused by imperfect grounding, and
was subsequently solved.

###  3.3 Threshold scans

The threshold scan records hits at fixed input charge (given by either a low
or high test-pulse of 4 and 12 fC, respectively) and is aimed at monitoring
the gain of the FE -electronics preamplifier, in order to locate dead
channels, determine gain deteriorating effects and measure cross-talk.

(a)(b) Figure 5: (a) Example of hit-efficiency as function of threshold for a
fixed input charge (“high test-pulse”) [17]. (b) Stability of the half-
efficiency point for channels in one FE-box (1 ADC count $\approx$ 10 mV).

The ASDBLR chip selection prior to assembly of the FE -box components
guarantees a good uniformity of the discriminators, such that a common
threshold can be applied for the entire readout without loss of efficiency or
increased noise levels [2]. An error function produced by the convolution of a
step function (ideal condition in absence of noise) with Gaussian noise, is
used to describe the hit-efficiency as a function of the threshold value. The
stability of the half-efficiency point for all the channels was studied and
the relative variation between channels is expected to be less than $\pm 60$
mV [2].

An example of the fit to the hit efficiency as a function of amplifier
threshold is shown for one channel in Fig. 5(a), and the half-efficiency point
for 128 channels in one FE box is shown in Fig. 5(b). Since the start of the
data taking period in May 2010 the fraction of fully active channels has been
99.5% or more, see Sec. 5.5.

###  3.4 Delay scans

(a)(b) Figure 6: (a) Example of a linear fit of the measured drift-time as a
function of the test-pulse delay [17]. The slope corresponds to unity, if both
axis are converted to ns (1 DAC count $\approx$ 0.1 ns, while 1 TDC count
$\approx$ 0.39 ns). (b) The slope from the linear fit of the timing
measurement for all 128 channels in one FE-box.

The delay scan analysis aims at detecting defects in the timing of the OT
channels, such as time offsets or non-linearities. An example of the time
measurement as a function of the test-pulse delay is shown in Fig. 6(a), where
each measurement corresponds to the average of 10,000 time measurements at a
given test-pulse delay. The corresponding slope for all 128 channels of one FE
box is shown in Fig. 6(b). No anomalous behaviour in the time measurement has
been observed. Approximately 96% of all channels have a slope between 0.983
and 1.024 times the average value. Most of the remaining 4% of the channels
suffer from insufficient test-pulse stability rather than from pre-amplifier
or TDC shortcomings.

##  4 Calibration

The position of the hits in the OT is determined by measuring the drift-time
to the wire of the ionisation clusters created in the gas volume. The drift-
time measurement can in principle be affected by variations in the time offset
in the FE electronics, and is regularly monitored. The spatial position of the
OT detector also affects the hit position, and the correct positioning of the
detector modules is ensured by periodic alignment campaigns.

###  4.1 Distance drift-time relation

The OT detector measures the arrival time of the ASDBLR signals with respect
to the LHC clock, $T_{\mathrm{clock}}$, and is referred to as the TDC time,
$t_{\mathrm{TDC}}$. This time is converted to position information to
reconstruct the trajectory of the traversing charged particle, by means of the
drift-time–distance relation, or TR-relation. The arrival time of the signal
corresponds to the time of the $pp$ collision, $T_{\mathrm{collision}}$,
increased by the time-of-flight of the particle, $t_{\mathrm{tof}}$, the
drift-time $t_{\mathrm{drift}}$ of the electrons in the straw, the propagation
time of the signal along the wire to the readout electronics,
$t_{\mathrm{prop}}$, and the delay induced by the FE electronics,
$t_{\mathrm{FE}}$. The various contributions to the TDC time are schematically
shown in Fig. 7, and can be expressed as

$t_{\mathrm{TDC}}=(T_{\mathrm{collision}}-T^{\mathrm{FE}}_{\mathrm{clock}})+t_{\mathrm{tof}}+t_{\mathrm{drift}}+t_{\mathrm{prop}}+t_{\mathrm{FE}}.$
(1)

The phase of the clock at the TDC input, $T^{\mathrm{FE}}_{\mathrm{clock}}$,
can be adjusted with a shift $t^{\mathrm{FE}}_{\mathrm{clock}}$. The
expression for $t_{\mathrm{TDC}}$ can be rewritten as

$t_{\mathrm{TDC}}=(T_{\mathrm{collision}}-T_{\mathrm{clock}})+t_{0}+t_{\mathrm{tof}}+t_{\mathrm{drift}}+t_{\mathrm{prop}},$
(2)

where $t_{0}=t_{\mathrm{FE}}-t^{\mathrm{FE}}_{\mathrm{clock}}$. Variations in
$t_{0}$ are discussed in the next section. The difference
$t_{\mathrm{clock}}=T_{\mathrm{collision}}-T_{\mathrm{clock}}$ accounts for
variations of the phase of the LHC clock received at the LHCb experiment
control and is kept below 0.5 ns.

(b)(a) Figure 7:  (a) Sketch of the various contributions to the measured TDC
time [19], as explained in the text. (b) Picture of a charged particle that
traverses a straw.

The TR-relation is the relation between the measured drift-time and the
closest distance from the particle trajectory to the wire. The TR-relation is
calibrated on data by fitting the distribution of drift-time as a function of
the reconstructed distance of closest approach between the track and the wire,
as shown in Fig. 8(a). At the first iteration the TR-relation obtained from
beam tests was used. The line shows the currently used TR-relation [19], which
has the following parameterization:

(a)(b)(c) Figure 8:  The (a) TR-relation distribution follows the shape of a
second order polynomial distribution, which leads to a (b) falling drift-time
spectrum (black), which, smeared with the time resolution (blue), leads to the
shape of the (c) measured drift-time distribution.

$t_{\mathrm{drift}}(r)=20.5\,\mathrm{ns}\cdot\frac{|r|}{R}+14.85\,\mathrm{ns}\cdot\frac{r^{2}}{R^{2}}\text{,}$
(3)

where $r$ is the closest distance between the track and the wire and $R=2.45$
mm is the inner radius of the straw. This TR-relation is compatible with the
one obtained from the beam test of 2005 [18],
$t(r)=20.1\,\mathrm{ns}\cdot\frac{|r|}{R}+14.4\,\mathrm{ns}\cdot\frac{r^{2}}{R^{2}}$.
The maximum drift-time extracted from the parameterization of the TR-relation
is 35 ns. Due to the average drift-time resolution of 3 ns, and due to the
variation in time-of-flight of the traversing particles, the drift-time
distribution broadens, as illustrated in Fig. 8(b). The measured drift-time
spectrum after $t_{0}$ calibration is shown in Fig. 8(c), and the start of the
drift-time spectrum is thus set to 0 ns by construction. During operation, the
start of the 75 ns wide readout gate was set to approximately $-9$ ns, to
ensure that also the earliest hits are recorded. The varying number of entries
in the subsequent time bins is a characteristic of the OTIS TDC chip known as
the differential non-linearity (caused by variations of the digital delay bin
sizes) and does not significantly affect the drift-time resolution [16].

###  4.2 $t_{0}$ stability

LHCb OT Figure 9:  $t_{0}$ stability versus run number. Every point
corresponds to one run that typically lasts one hour. The arrows indicate the
adjustment of the $t_{clock}$ time.  Figure 10:  Distribution of differences
between $t_{0}$ constants per FE box, for two different calibrations. The mean
shift originates from a change of the overall $t_{clock}$ time, whereas the
spread shows the stability of the delay $t_{\mathrm{FE}}$ induced by the FE
electronics.

The $t_{\mathrm{FE}}$ values need to be stable to a level better than the time
resolution. There are two factors that contribute to the stability of $t_{0}$,
usually referred to as the $t_{0}$ constants: one is the drift of the global
LHCb clock and the second is the drift of FE electronic delays. The first can
be extracted from the average over the whole OT of the drift-time residual
distribution calculated for every run separately. The second can be estimated
from the difference of $t_{0}$ values for two different calibrations, for each
FE-box.

Figure 9 shows the variation of the LHCb clock as a function of the run
number, for the data taking period between May and July 2011\. The global LHCb
clock is adjusted if it changes by more than 0.5 ns. As a result, the average
value of the drift-time residual stays within the range of $\pm 0.5$ ns.

Figure 10 shows the difference of the $t_{0}$ values per FE-box, for two
different calibrations performed on runs 89350 and 91933, respectively. These
runs correspond to the beginning of two data taking periods in May and July
2011. For most FE boxes the spread of the $t_{0}$ constants is smaller than
0.1 ns. The overall shift of 0.4 ns is due to the change of the global LHCb
clock. The variation of $t_{0}$ is well below the time resolution of 3 ns and
does therefore not contribute significantly to the detector resolution.

###  4.3 Geometrical survey

The correct spatial positioning of the OT modules is ensured in three steps.
First, the design and construction of the OT detector guarantees a mechanical
stability of 100 (500) $\mu$m in the $x$($z$) direction. Secondly, an optical
survey determined the position of all modules after installation. Finally, the
use of reconstructed tracks allows to measure the position of the detector to
the highest accuracy.

By construction the anode wire is centered within 50 $\mu$m with respect to
the straw tube. The detector modules are fixed with dowel-pins to the C-frames
at the top and the bottom, with tolerances below 50 $\mu$m. The modules are
not fixed at the center, making larger variations possible (see Sec. 12).
Finally, the C-frames are mounted on rails, which fixes the $z$-coordinate at
the top and at the bottom.

First, the survey confirmed that the rails were straight within the few
millimeters tolerance. Then, after installation, the position of the four
corners of the C-frames were adjusted until all measured points on the dowel-
pins at the top and bottom of the modules, and on the surface at the center of
the modules, were within $\pm 1$ mm of their nominal position. The final
survey coordinates provided the corrections to the nominal coordinates of the
C-frames and modules [20]. The C-frames can be opened for maintenance, and the
reproducibility of the C-frame positioning in the $x$-coordinate was checked
to be better than the 200 $\mu$m precision of the optical survey. The shape of
the modules in the $x$-coordinate is finally determined using reconstructed
tracks, see Sec. 12.

###  4.4 Optical alignment with the Rasnik system

The stability of the C-frame relative position during data taking is monitored
by means of the Rasnik system [21, 22]. The Rasnik system consists of a CCD
camera that detects a detailed pattern. The pattern, or “mask”, is mounted on
the C-frame and a movement is detected by the CCD camera as a change of the
pattern position. All four corners of the 12 C-frames are equipped with a
Rasnik system. Together with two additional Rasnik lines to monitor movements
of the suspension structure, this leads to a total of 50 Rasnik lines. Due to
mechanical conflicts in the installation, only about 2/3 of the lines are
used. The intrinsic resolution of the system perpendicular (parallel) to the
beam axis is better than 10 (150) $\mu$m. The Rasnik measurements showed that
the position of the C-frames is unchanged after opening and closing within
$\pm 10$ $\mu$m, and unchanged within $\pm 20$ $\mu$m for data taking periods
with opposite polarity of the LHCb dipole magnet.

###  4.5 Software alignment

(a)LHCb OT(b)LHCb OT Figure 11: (a) Displacement of modules relative to the
survey and (b) hit residuals in the first X-layer of station T2 before (dashed
line) and after (continuous line) offline module alignment.

To achieve optimal track parameter resolution the position and orientation of
the OT modules must be known with an uncertainty that is negligible compared
to the single hit resolution.

The OT C-frames hang on rails and can be moved outside the LHCb acceptance to
allow for maintenance work during technical stops of the LHC. Since no survey
is performed after such operations, the reproducibility of the nominal
position is important. Using track based alignment the reproducibility has
been established to be better than 100 $\,\upmu\rm m$, consistent with the
measurements done with the Rasnik system.

The most precise alignment information is obtained with a software algorithm
that uses charged particle trajectories [23]. For each module and C-frame the
alignment is parametrized by three translations and three rotations. The
algorithm selects high quality tracks and subsequently minimizes the total
$\chi^{2}$ of those tracks with respect to the alignment parameters. Only a
subset of parameters needs to be calibrated to obtain sufficient precision.
For the alignment of modules inside each C-frame only the translation in $x$
and the rotation in the $xy$ plane are determined. For the C-frames themselves
only the translations in $x$ and $z$ are calibrated. To constrain redundant
degrees of freedom the survey measurements are used as constraints in the
alignment procedure.

Figure 11 illustrates the result of an alignment of module positions. For this
alignment, tracks were fitted using only the OT hits. At least 18 hits per
track were required. To remove poorly constrained degrees of freedom, modules
in the first $x$ and stereo ($u$) layers of stations T1 and T3 were all fixed
to their nominal position. Figure 11(a) shows the difference between the
$x$-position of the module center relative to the survey. Statistical
uncertainties in alignment parameters are negligible and the alignment is
reproducible in data, taken under similar conditions, within about 20
$\,\upmu\rm m$. Figure 11(b) shows the hit residuals in one layer before and
after alignment. A clear improvement is observed.

The module displacements in Fig. 11 are larger than expected, based on the
expected accuracy of the dowel pins that keep the modules in place. It is
assumed that the disagreement can at least partially be explained by degrees
of freedom that are not yet corrected for, such as module deformations and the
positioning of straws within each module. Figure 12 shows an example of the
average hit residual as a function of the coordinate along the wire for one
module. A relative displacement of the two monolayers is observed, as well as
jumps at the wire locators, which are placed at every 80 cm along the wire
length. The effect on the final hit resolution is discussed in Sec. 5.4.

LHCb OT Figure 12: Average hit residual as function of $y$ coordinate in one
particular module (labelled T3L3Q1M7). The four curves show residuals for the
four groups of 32 channels within one FE-module. The round markers correspond
to one monolayer of 64 straws, whereas the square markers show the residuals
of the second monolayer. The vertical dashed lines indicate the position of
the wire locators, at every 80 cm along the wire [19].

##  5 Performance

The performance of the OT detector was stable in the entire first running
period of the LHC between 2010 and 2012, as was shown in the previous
sections. No significant failures in the LV, HV and gas systems occurred. The
details of the data quality in terms of resolution and efficiency are
described below.

###  5.1 Spillover and drift-time spectrum

In order to register all charged particle hits produced in the $pp$
interaction, three consecutive intervals of $25\,\mathrm{ns}$ are readout upon
a positive L0-trigger. Only the first hit in the readout window is recorded,
as the first hit typically corresponds to the ionization cluster closest to
the wire, and it is thus the best estimate for the radial distance to the
wire.

In the following, data are studied that are recorded in $75\,\mathrm{ns}$,
$50\,\mathrm{ns}$ and $25\,\mathrm{ns}$ bunch-spacing data taking periods of
the LHC. These varying conditions show the effect of so-called spillover hits
on the drift-time spectrum and straw occupancies. Distributions obtained in
the $75\,\mathrm{ns}$ bunch-crossing period are close to those observed with
only one single bunch crossing in LHCb, and therefore they will be considered
free of spillover.

The drift-time spectrum and the occupancies presented here correspond to
events with an average number of visible $pp$ interactions per bunch crossing
of about 1.4, in accordance with the typical run conditions in 2011 and 2012.
The events are triggered by any physics trigger, implying that most events
contain $B$ or $D$-decays. The drift-time distributions for the
$75\,\mathrm{ns}$, $50\,\mathrm{ns}$ and $25\,\mathrm{ns}$ bunch-spacing
conditions are shown in Fig. 13.

(a)LHCb OT(b)LHCb OT Figure 13: (a) Drift-time distribution in module 8, close
to the beam, for $75\,\mathrm{ns},50\,\mathrm{ns},25\,\mathrm{ns}$ bunch-
crossing spacing in red, black and blue, respectively. The vertical lines at
64 and 128 TDC counts correspond to 25 and 50 ns, respectively. The
distributions correspond to all hits in 3000 events for each bunch-crossing
spacing, recorded with an average number of overlapping events of
$\mu=1.2,1.4$ and 1.2, for $75\,\mathrm{ns},50\,\mathrm{ns}$ and
$25\,\mathrm{ns}$ conditions, respectively. (b) The drift-time distribution
for empty events illustrates the contribution from spillover hits from “busy”
previous bunch-crossings (red). The naive expectation of the spillover
distribution is shown in black, and is obtained by shifting the nominal drift-
time spectrum by $-50\,\mathrm{ns}$.

The typical drift-time spectrum from the (spillover-free) distribution from
the 75 ns running can be understood by inspecting Fig. 8 in Sec. 4.1. The
projection of the TR-relation results in a linearly decreasing drift-time
spectrum, assuming a flat distribution of the distance between the tracks and
the wires. In addition, the number of earlier hits is slightly enhanced in the
drift-time distribution, since late hits are hidden by earlier hits on the
same straw, as only the first hit is recorded. The recording of the first hit
only, induces a “digital dead-time” starting from the first hit until the end
of the readout window at 192 TDC counts, or 75 ns. A second source of dead-
time originates from the recovery time required by the amplifier. This “analog
dead-time” lasts between 8 ns and 20 ns, depending on the signal pulse height,
and is usually hidden by the digital dead-time.

The black line in Fig. 13(a) correspond to the data recorded in the
$50\,\mathrm{ns}$ bunch-spacing period. The contribution from hits from the
next bunch-crossing, 50 ns later, is visible between 128 and 192 TDC counts.
The relative contribution of these late hits from the next bunch crossing is
determined by the average occupancy in the next bunch crossing, and thus
depends on the run conditions. In principle it also depends on the occupancy
of the triggered event, and thus on the trigger configuration, but in practice
that is quite stable. The shape of the drift-time distribution of the late
spillover hits corresponds to the nominal, spillover-free (i.e. 75 ns) drift-
time spectrum, with a shift of $+50\,\mathrm{ns}$.

The drift-time shape of the spillover hits from the previous
$-50\,\mathrm{ns}$ bunch-crossing is more complex. It contains the late hits
of the drift-time distribution from the previous bunch-crossing. Naively, the
drift-time spectrum of these early hits can be modelled by a shift of the
spillover-free distribution by $-50\,\mathrm{ns}$, as illustrated by the black
line in Fig. 13(b). However, a traversing track can give rise to multiple
hits, which are usually not detected due to the digital “dead-time”. These
multiple-hits, or “double pulses” from the previous bunch-crossing now become
visible, when they fall inside the readout window of the triggered bunch-
crossing.

In 30 to 40% of all hits, the first arriving ionization cluster produces a
second hit that arrives about $30\,\mathrm{ns}$ later. Several effects, such
as multiple ionizations, reflections [24] or photon feedback [25], can produce
such a double pulse. The time-spectrum of late hits from the previous bunch-
crossing, observed in the triggered bunch crossing, is clearly isolated by
studying “empty” bunch-crossings with “busy” previous bunch-crossings. The
empty and busy bunch-crossings are selected using the total activity in the
calorimeter in the subsequent bunch-crossings. The resulting drift-time
spectrum of late hits from busy previous bunch-crossings in empty triggered
events is shown as the red line in Fig. 13(b). The large number of double-
pulses around 40 TDC counts, or 15 ns explains the enhancement of hits between
$0$ and $25\,\mathrm{ns}$ in the $50\,\mathrm{ns}$ bunch-crossing drift-time
spectrum compared to the spillover-free drift-time spectrum from the
$75\,\mathrm{ns}$ data, see Fig. 13(a).

Finally, the drift-time spectrum corresponding to the 25 ns bunch spacing
conditions (recorded in Dec 2012) is also overlayed in Fig. 13(a). An overall
increase of the number of hits is seen for a comparable number of overlapping
events, compared to the 50 and 75 ns running conditions.

###  5.2 Occupancy

The occupancy per straw is shown in Fig. 14 for typical run conditions in 2011
and 2012, triggered by any physics trigger. The occupancy is shown for events
with 25, 50 and 75 ns bunch-crossing conditions. In absence of spillover (i.e.
the 75 ns case), the occupancy varies from about $15\%$ in the innermost
modules to about $3\%$ in the outermost modules. For the data taken with
$50\,\mathrm{ns}$ bunch-crossing spacing, about 30% of all hits originate from
spillover, i.e. from the previous bunch crossing.

Monte Carlo simulations demonstrate that most of the hits originate from
secondary charged particles, produced in interactions with material. Figure 15
shows the fraction of hits that originate from a particle created at a given
$z$ coordinate. The hits from tracks that originate from the genuine $pp$
interaction or a subsequent particle decay, are predominantly located close to
the interaction region. They represent $27.7\%$ (resp. $27.1\%$ and $25.7\%$)
of all hits seen in station T1 (resp. T2 and T3). The remaining hits originate
from charged particles created in secondary interactions, mainly in the
support of the beam pipe situated in the magnet or in the detectors located
upstream of the detector layer (Vertex Locator, Ring Imaging Detector, Tracker
Turicensis (TT), Inner Tracker (IT) and OT).

LHCb OT Figure 14: Straw occupancy for
$75\,\mathrm{ns},50\,\mathrm{ns},25\,\mathrm{ns}$ bunch-crossing spacing in
red, black and blue, respectively, for typical run conditions with on average
1.2, 1.4 and 1.2 overlapping events per bunch crossing, respectively. One
module contains in total 256 straws, whereas the width of one module is 340
mm. The steps in occupancy at the center of the detector correspond to the
location of the shorter S-modules, positioned further from the beam in the
$y$-coordinate. The data corresponding to $25\,\mathrm{ns}$ bunch-crossing
spacing, was recorded with opposite LHCb-dipole polarity, as compared to the
other two data sets shown here.  (a)(b)LHCb OTLHCb OT Figure 15: Coordinate of
the origin of charged particles that produce a hit in the OT detector. (a) The
blue histogram peaks at $z=0$ and corresponds to hits from particles produced
at the $pp$ interaction point and their daughters, while the hits from
particles produced in secondary interactions (red) predominantly originate
from $z>0$. (b) The longitudinal and transverse position of the origin of
charged particles produced in secondary interactions, showing the structure
corresponding to the material in the detector.

###  5.3 Hit efficiency

A high single-hit efficiency is crucial, as it affects the tracking
efficiency, and eventually the physics performance of the LHCb experiment. The
efficiency is defined as the number of observed hits in a particular detector
region over the number of expected hits in the same region. The number of
expected hits is estimated by considering charged particle tracks in $pp$
collision data and extrapolating the charged particle trajectory to the
monolayer under study.

In order to determine the hit efficiency, good quality tracks have been
selected, requiring a $\chi^{2}/ndf$ (where $ndf$ are the number of degrees of
freedom) less than 2 and a minimum number of 21 hits in the OT detector. This
corresponds to accepting about 87% of all good tracks. For each track, every
OT monolayer has been considered, and a hit has been searched in the straw
closest to the charged particle trajectory. Since a track is reconstructed by
the same hits that are subsequently used for the efficiency estimation, the
large number of required hits could bias the efficiency determination. This
has been corrected for by not considering the monolayer under study, when
counting the minimum number of hits per track.

The hit efficiency is studied as a function of the distance between the
predicted track position and the center of the considered straw. The resulting
single-hit-efficiency profile is shown in Fig. 16(a), summed for all straws in
the long modules closest to the beam-pipe (module 7).

(a)(b)LHCb OTLHCb OT Figure 16: (a) Efficiency profile as a function of the
distance between the predicted track position and the center of the straw, for
straws in the long F-modules closest to the beampipe (module 7). The vertical
lines represent the straw tube edge at $|r|=2.45$ mm. (b) Histogram of the
average efficiencies per half module (128 channels), at the center of the
straw, $|r|<1.25$ mm, for runs 96753, 96763 and 96768 on 22 July 2011.

The shape of the efficiency profile can be understood by considering two
effects. Near the straw tube edge, the path length of ionizing particles
inside the gas volume is limited, resulting in a sizeable probability for not
ionizing the gas. This can be described with a Poissonian distribution for the
single-hit probability. Secondly, the finite track resolution smears the
distribution at the edge of the straw tube, lowering the efficiency inside and
increasing the efficiency outside of the straw. The finite probability to
detect a hit outside straw tube originates from random hits unrelated to the
track under study, and is proportional to the average occupancy in that part
of the detector.

The straw tube profile can thus be fitted with the following line shape, which
describes the efficiency as a function of the distance $r$ from the center of
the straw,

$\displaystyle p(r)$ $\displaystyle=$ $\displaystyle
1-\Big{(}1-\varepsilon(r)\otimes\rm{Gauss}(r|0,\sigma)\Big{)}\cdot(1-\omega),$
(4) $\displaystyle\mathrm{with}\,\,\,\,\,\,\varepsilon(r)$ $\displaystyle=$
$\displaystyle\varepsilon_{0}\left(1-e^{\frac{-2\sqrt{R^{2}-r^{2}}}{\lambda}}\right),$

where $R=2.45$ mm is the inner radius of the straw, $\omega$ is the average
occupancy, $\lambda$ is the effective ionization length of a charged particle
in the gas volume, and $\sigma$ is the track resolution.

The deviation from the perfect efficiency is quantified in Eq. (4) by
$\varepsilon_{0}$. However, in the following, an operationally straightforward
definition of the single-hit efficiency is used. The single-hit efficiency per
straw is defined as the average hit efficiency $\varepsilon_{hit}$ in the
limited range close to the wire, $|r|<1.25$ mm. The inefficient regions
between two straws lead to the maximum efficiency of 93%, integrated over the
monolayer, and is calculated by taking the ratio of the straw diameter of 4.9
mm over the pitch, 5.25 mm. The inefficient regions are covered by the
neighbouring monolayer in the same module, which is staggered by half a straw
pitch.

Table 2: Average single-hit efficiencies $\varepsilon_{hit}$ near the center of the straws, $|r|<1.25$ mm, for different module positions of the OT detector. Module position | Efficiency (%)
---|---
1 | $98.085\pm 0.011$
2 | $99.130\pm 0.005$
3 | $99.279\pm 0.003$
4 | $99.277\pm 0.003$
5 | $99.282\pm 0.002$
6 | $99.342\pm 0.002$
7 | $99.286\pm 0.002$
8 | $99.200\pm 0.002$
9 | $99.351\pm 0.003$

A fit to the straw efficiency profile, using Eq. (4), separately for the
profiles of the nine module positions, yields the following average
parameters, $\langle\lambda\rangle=0.79\pm 0.09$ mm,
$\langle\varepsilon_{0}\rangle=0.993\pm 0.003$, $\langle\sigma\rangle=0.26\pm
0.06$ mm, $\langle\omega\rangle=0.07\pm 0.02$, where the quoted uncertainty is
the standard deviation from the values obtained for the nine different module
positions. Note that these parameters are averaged over the different module
positions, corresponding to different conditions. For example, the measured
occupancy $\omega$ varies from $4.7\%$ to $9.7\%$ depending on the distance of
the module to the beam. Fits to the single-hit efficiency profiles show that
the efficiency is close to maximal, i.e. the value for $\varepsilon_{0}$ is
consistent with unity.

For each half-module, corresponding to one FE box, the average single-hit
efficiency $\varepsilon_{hit}$ has been calculated and the result is shown in
Fig. 16(b). The efficiency distribution peaks around 99.5%, consistent with
the measurements from beam tests [18]. The average of the distribution is
about 99.2%. This value is consistent with the fit to the straw tube profile,
shown in Fig. 16(a). The large hit efficiency is a prerequisite for large
efficiency to reconstruct charged particle’s tracks in LHCb. The average
tracking efficiency is approximately 95% in the region covered by the LHCb
detector [26].

The modules that are located at the edge of the geometrical acceptance of
LHCb, in particular the outermost modules in the first station, detect a
relatively small number of tracks. All eight FE boxes in Fig. 16(b) with a
value of the efficiency exactly equal to 1, and 11 out of the 14 FE boxes with
$\varepsilon_{hit}<96\%$, are attached to modules located most distant from
the beampipe (module 1), and suffer from few tracks in the efficiency
determination. The remaining three FE boxes with $\varepsilon_{hit}<96\%$
suffer from hardware problems, representing $3/432=0.7\%$ of all FE boxes.

In order to calculate the average efficiency for each module position, modules
with few tracks, ie. with an efficiency lower than 96%, or with an efficiency
equal to unity, have been discarded. The average efficiency thus obtained for
each module position is listed in Table 2 where the reported uncertainties are
statistical.

As shown above, the decrease of the hit efficiency close to straw edge is
partially due to the fact that the charged particle traverses a short distance
through the straw volume. Hence, the probability to not form an ionization
cluster increases towards the straw edge. Alternatively, the effective
ionization length $\lambda$ can be probed by selecting only those tracks that
pass close to the wire. In contrast to the first method exploiting Eq. 4, here
the determination of the ionization length is not affected by absorption of
drifting electrons. The larger the ionization length, the more hits will
exhibit a large drift-time, as the ionization does not necessarily occur close
to the wire. The effective ionization length $\lambda$ extracted from
particles traversing the straw within $|r|<0.1$ mm amounts to about 0.7 mm
[19, 27], consistent with $0.79\pm 0.09$ mm, as obtained above.

###  5.4 Hit resolution

The single hit resolution is determined using good quality tracks, selected by
requiring a momentum larger than 10 GeV, at least 16 OT hits and a track-fit
$\chi^{2}/ndf<2$ (excluding the hit under study, and excluding any hit in the
neighbouring monolayer in the same module). For a given track, the drift-time
and the hit position in a straw are predicted, and compared with the measured
drift-time and position, respectively. The resulting distribution of the
drift-time residuals and hit position residuals are shown in Fig. 17.

(a)(b) Figure 17:  (a) Drift-time residual distribution and (b) hit distance
residual distribution [19]. The core of the distributions (within $\pm
1\sigma$) are fitted with a Gaussian function and the result is indicated in
the figures.  (a)(b) Figure 18:  Improvement in (a) drift-time residual
distribution and (b) hit distance residual distribution, (red) before and
(blue) after allowing for a different horizontal displacement per half
monolayer, corresponding to 64 straws [19].

The drift-time residual distribution has a width of 3 ns which is dominated by
the ionization and drift properties in the counting gas. The granularity of
the step size of the TDC of 0.4 ns has a negligible impact on the drift-time
resolution. The hits in the left tail of the drift-time residual distribution
are early hits, that do not originate from the track under study, but instead
are a combination of noise hits, hits from different tracks in the same bunch
crossing, and hits from tracks from previous bunch crossings (spill-over
hits).

The hit distance residual distribution has a width of about 205 $\mu$m, which
is close to the design value of 200 $\mu$m. An improvement of the hit position
resolution is foreseen when the two monolayers within one detector module are
allowed to be relatively displaced to each other in the global LHCb alignment
procedure. By allowing a different average horizontal displacement per half
monolayer, containing 64 straws, a single hit resolution of approximately 180
$\mu$m is in reach, see Fig. 18. Also allowing for a rotation of each half
monolayer, improves the single hit resolution further to 160 $\mu$m. These
values refer to a Gaussian width of the resolution, determined from a fit to
the residual distribution, within two standard deviations of the mean. This is
in good agreement with the hit resolution below 200 $\mu$m, as obtained in
beam tests [18].

###  5.5 Monitoring of faulty channels

LHCb OT Figure 19: The evolution of number of dead and noisy channels as
function of run number in the 2011 and 2012 running periods. The definition of
dead and noisy channels is given in the text. The three periods with larger
number of dead channels, correspond to periods with a problem affecting one
entire front-end box.

Noisy or dead channels due to malfunctioning front-end electronics are timely
identified through the analysis of the calibration runs as described in Sec.
3. With the full offline data set available, the performance of individual
channels is also monitored by comparing the occupancy to the expected value.
First, the performance of entire groups of 32 channels is verified. Then,
within a group of 32 channels, the occupancy is compared to the truncated
mean, after correcting for the dependence of the occupancy on the distance to
the beam. If the occupancy is above (below) 6 standard deviations from the
truncated mean, the channel is declared “noisy” (“dead”). For a typical run
recorded at the end of 2012 (run 133785), when all front-end modules were
functioning properly, the OT contained 52 dead channels and 8 noisy channels,
evenly distributed over the detector. The evolution of the number of bad
channels throughout the 2011 and 2012 running periods is shown in Fig. 19.
666The three periods with larger number of dead channels correspond to a
broken laser diode (VCSEL) between September and December 2011 at location
T1L3Q0M2, a broken fuse in May 2012 at location T3L3Q0M8, and
desynchronization problems between July and September 2012 at location
T2L2Q0M9. Note that the front-end box at location M9 on the C-side reads out
only 64 straws.

###  5.6 Radiation tolerance

It was discovered that, in contrast to the excellent results of extensive
ageing tests in the R&D phase, final production modules suffered from gain
loss after moderate irradiation (i.e. moderate collected charge per unit time)
in laboratory conditions. The origin of the gain loss was traced to the
formation of an insulating layer on the anode wire [11], that contains carbon
and is caused by outgassing inside the gas volume of the plastifier contained
in the glue [28]. Remarkably, the gain loss was only observed upstream of the
source position with respect to the gas flow.

A negative correlation was observed between the ageing rate and the production
of ozone [11], which suggests that the gain loss is prevented under and
downstream of the source due to the formation of ozone in the avalanche
region. As a consequence it was decided to add 1.5% O2 to the original gas
mixture of Ar/CO2, to mitigate possible gain loss. In addition, a beneficial
effect from large induced currents was observed, which removed the insulating
layers from irradiation in the laboratory. These large currents can either be
invoked by large values of the high voltage in the discharge regime (dark
currents), or by irradiating the detector with a radioactive source [28].

(a)(b)LHCb OTAug 2010LHCb OTDec 2012 Figure 20: Hit efficiency as a function
of amplifier threshold in (a) August 2010 and (b) December 2012 for the inner
region, defined as $\pm 60\,\mathrm{cm}$ in $x$ and $\pm 60\,\mathrm{cm}$ in
$y$ from the central beam pipe, summed over all OT layers. Note that the
threshold value of 1350 mV, where the efficiency is 50%, is much higher than
the operational threshold of 800 mV, and is equivalent to multiple times the
corresponding average hit charge.

No signs of gain loss have been observed in the 2010 to 2012 data taking
period of LHCb, corresponding to a total delivered luminosity of 3.5 fb-1.
Most of the luminosity was recorded in 2011 and 2012, corresponding to about
$10^{7}$ s of running at an average instantaneous luminosity of $3.5\times
10^{32}$ cm-2s-1, and the region closest to the beam accumulated an integrated
dose equivalent to a collected charge of 0.12 C/cm. Possible changes in the
gain are studied by increasing the amplifier threshold value during LHC
operation, and comparing the value where the hit efficiency drops, see Fig.
20. This value of the amplifier threshold can be converted to hit charge,
which provides information on the change of the detector gain. This method to
measure the gain variations is outlined in detail in Ref. [29].

##  6 Conclusions

The Outer Tracker has been operating in the 2010, 2011 and 2012 running
periods of the LHC without significant hardware failures. The low voltage,
high voltage and gas systems showed a reliable and stable performance.
Typically 250 channels out of a total of 53,760 channels were malfunctioning,
resulting in 99.5% working channels. The missing channels were mainly caused
by problems in the readout electronics, whereas only a handful channels could
not stand the high voltage on the detector.

The occupancy of the Outer Tracker detector of typically 10% was larger than
anticipated, due to twice larger instantaneous luminosity at LHCb with half
the number of bunches in the LHC, compared to the design specifications.
Despite these challenging conditions, the Outer Tracker showed an excellent
performance with a single-hit efficiency of about 99.2% near the center of the
straw, and a single hit resolution of about 200 $\mu$m. No signs of
irradiation damage have been observed.

## Acknowledgements

We wish to thank our colleagues of the CERN Gas Group for their continuous
support of the Outer Tracker gas system. We also express our gratitude to our
colleagues in the CERN accelerator departments for the excellent performance
of the LHC. We thank the technical and administrative staff at the LHCb
institutes. We acknowledge support from CERN and from the national agencies:
CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and Region
Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN
(Italy); FOM and NWO (The Netherlands); SCSR (Poland); MEN/IFA (Romania);
MinES, Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGal
and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC
(United Kingdom); NSF (USA). We also acknowledge the support received from the
ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France),
KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC
(Spain), GridPP (United Kingdom). We are thankful for the computing resources
put at our disposal by Yandex LLC (Russia), as well as to the communities
behind the multiple open source software packages that we depend on.

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