EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-LHCb-DP-2014-001

Performance of the LHCb Vertex Locator

LHCb VELO Group†††Authors are listed on the following page.

The Vertex Locator (VELO) is a silicon microstrip detector that surrounds the
proton-proton interaction region in the LHCb experiment. The performance of
the detector during the first years of its physics operation is reviewed. The
system is operated in vacuum, uses a bi-phase $\rm CO_{2}$ cooling system, and
the sensors are moved to 7$\rm\,mm$ from the LHC beam for physics data taking.
The performance and stability of these characteristic features of the detector
are described, and details of the material budget are given. The calibration
of the timing and the data processing algorithms that are implemented in FPGAs
are described. The system performance is fully characterised. The sensors have
a signal to noise ratio of approximately 20 and a best hit resolution of
4$\,\upmu\rm m$ is achieved at the optimal track angle. The typical detector
occupancy for minimum bias events in standard operating conditions in 2011 is
around 0.5%, and the detector has less than 1% of faulty strips. The proximity
of the detector to the beam means that the inner regions of the
$\rm{\it{n^{+}}}\mbox{-}on\mbox{-}{\it{n}}$ sensors have undergone space-
charge sign inversion due to radiation damage. The VELO performance parameters
that drive the experiment’s physics sensitivity are also given. The track
finding efficiency of the VELO is typically above 98% and the modules have
been aligned to a precision of 1$\,\upmu\rm m$ for translations in the plane
transverse to the beam. A primary vertex resolution of 13$\,\upmu\rm m$ in the
transverse plane and 71$\,\upmu\rm m$ along the beam axis is achieved for
vertices with 25 tracks. An impact parameter resolution of less than
35$\,\upmu\rm m$ is achieved for particles with transverse momentum greater
than 1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

To be submitted to Journal of Instrumentation

LHCb VELO group

R. Aaij1, A. Affolder2, K. Akiba3, M. Alexander4, S. Ali1, R.B. Appleby5, M.
Artuso6, A. Bates4, A. Bay7, O. Behrendt8, J. Benton9, M. van Beuzekom1, P.M.
Bjørnstad5, G. Bogdanova10, S. Borghi5, A. Borgia6, T.J.V. Bowcock2, J. van
den Brand1, H. Brown2, J. Buytaert8, O. Callot11, J. Carroll2, G. Casse2, P.
Collins8, S. De Capua5, M. Doets1, S. Donleavy2, D. Dossett12, R. Dumps8, D.
Eckstein13, L. Eklund4, C. Farinelli1, S. Farry2, M. Ferro-Luzzi8, R. Frei7,
J. Garofoli6, M. Gersabeck5, T. Gershon12, A. Gong14, H. Gong14, H. Gordon8,
G. Haefeli7, J. Harrison5, V. Heijne1, K. Hennessy2, W. Hulsbergen1, T.
Huse15, D. Hutchcroft2, A. Jaeger16, P. Jalocha17, E. Jans1, M. John17, J.
Keaveney18, T. Ketel1, M. Korolev10, M. Kraan1, T. Laštovička19, G. Lafferty5,
T. Latham12, G. Lefeuvre6, A. Leflat10, M. Liles2, A. van Lysebetten1, G.
MacGregor5, F. Marinho20, R. McNulty21, M. Merkin10, D. Moran22, R. Mountain6,
I. Mous1, J. Mylroie-Smith2, M. Needham23, N. Nikitin10, A. Noor2, A.
Oblakowska-Mucha24, A. Papadelis1, M. Pappagallo4, C. Parkes5, G.D. Patel2, B.
Rakotomiaramanana7, S. Redford8, M. Reid12, K. Rinnert2, E. Rodrigues5, A.F.
Saavedra25, M. Schiller1, O. Schneider7, T. Shears2, R. Silva Coutinho12, N.A.
Smith2, T. Szumlak24, C. Thomas17, J. van Tilburg1, M. Tobin7, J. Velthuis9,
B. Verlaat1, S. Viret26, V. Volkov10, C. Wallace12, J. Wang6, A. Webber5, M.
Whitehead12, E. Zverev10.

1Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
2Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
3Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
4School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
5School of Physics and Astronomy, University of Manchester, Manchester, United
Kingdom
6Syracuse University, Syracuse, NY, United States
7Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
8European Organization for Nuclear Research (CERN), Geneva, Switzerland
9H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
10Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
11LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
12Department of Physics, University of Warwick, Coventry, United Kingdom
13Deutsches Elektronen-Synchrotron, Hamburg, Germany
14Center for High Energy Physics, Tsinghua University, Beijing, China
15Department of Physics, University of Oslo, Oslo, Norway
16Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
17Department of Physics, University of Oxford, Oxford, United Kingdom
18Vrije Universiteit Brussel, Brussel, Belgium
19Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic
20Universidade Federal do Rio de Janeiro, Campus UFRJ - Macaé, Rio de Janeiro,
Brazil
21School of Physics, University College Dublin, Dublin, Ireland
22Universidad Autónoma de Madrid, Spain
23School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
24AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
25School of Physics, University of Sydney, Sydney, Australia
26Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3, Institut
de Physique Nucléaire de Lyon, Villeurbanne, France

###### Contents

  1. 1 Introduction
  2. 2 Subsystem performance
    1. 2.1 Commissioning results
    2. 2.2 Vacuum stability
    3. 2.3 Cooling performance
    4. 2.4 Low voltage and high voltage
    5. 2.5 Motion performance
    6. 2.6 Material description
  3. 3 Calibration, monitoring and simulation
    1. 3.1 Data acquisition system
    2. 3.2 Timing and gain
      1. 3.2.1 ADC sampling time
      2. 3.2.2 Gain
      3. 3.2.3 Timing to the beam
    3. 3.3 FPGA data processing algorithms
      1. 3.3.1 Pedestal subtraction
      2. 3.3.2 Mean common mode suppression
      3. 3.3.3 Topological strip channel reordering
      4. 3.3.4 Zero suppression and clusterisation
    4. 3.4 Error identification
      1. 3.4.1 Single event upsets
    5. 3.5 Monitoring
    6. 3.6 Simulation
  4. 4 Overall system performance
    1. 4.1 Signal size and noise rate
    2. 4.2 Resolution
    3. 4.3 Occupancy
    4. 4.4 Beam backgrounds and high multiplicity events
    5. 4.5 Efficiency and faulty channel analysis
    6. 4.6 Radiation damage studies
      1. 4.6.1 Current measurements
      2. 4.6.2 Effective doping concentration
      3. 4.6.3 Charge loss to second metal layer
  5. 5 Physics performance
    1. 5.1 Pattern recognition and tracking
    2. 5.2 Alignment
      1. 5.2.1 Optical and mechanical measurements
      2. 5.2.2 Track-based alignment methods
      3. 5.2.3 Mechanical measurement of closing
      4. 5.2.4 Alignment performance
    3. 5.3 Primary vertex resolution
    4. 5.4 Impact parameter resolution
    5. 5.5 Decay time resolution
  6. 6 Conclusions
  7. 7 Acknowledgements

##  1 Introduction

LHCb [1] is an experiment dedicated to heavy flavour physics at the LHC. Its
primary aim is to discover new physics through precision studies of CP
violation and rare decays of beauty and charm hadrons. The detector is
comprised of the Vertex Locator (VELO), silicon strip and straw chamber
trackers, a warm dipole magnet, ring imaging Cherenkov particle identification
systems, calorimeters and a muon detection system.

The LHCb Vertex Locator [2] is a silicon microstrip detector positioned around
the proton-proton interaction region. The VELO provides measurements of track
coordinates which are used to identify the primary interaction vertices and
the secondary vertices that are a distinctive feature of $b$\- and $c$-hadron
decays. The VELO was designed to optimise the LHCb physics programme in the
following ways:

  * •

Angular coverage. The VELO is designed to cover the forward region, such that
all tracks inside the nominal LHCb acceptance of 15–300$\rm\,mrad$ cross at
least three VELO stations. In this way the detector fully reconstructs roughly
$27\%$ of $b\overline{}b$ production for 7$\mathrm{\,Te\kern-1.00006ptV}$
proton-proton centre-of-mass collisions, while covering just $1.8\%$ of the
solid angle [3, 4]. The VELO also reconstructs tracks in the forward direction
and backward directions which do not have momentum information, but are useful
to improve the primary vertex reconstruction.

  * •

Triggering. The reconstruction of the primary vertex and the displaced
secondary decay vertex of a heavy flavour hadron in the VELO is a key
ingredient of the high level trigger which reduces the event rate from a
1${\rm\,MHz}$ event rate to a few kHz [5].

  * •

Efficient reconstruction. LHCb has studied decay modes with up to six charged
tracks in the final state [6]. This relies on the highly efficient cluster
reconstruction in the VELO since track reconstruction efficiency losses are
transmitted as the sixth power. The cluster reconstruction efficiency in the
VELO is paramount, both for the selection of those tracks, as six measurements
per track are required, and for efficient pattern recognition and fake track
rejection.

  * •

Displaced tracks and vertices. Excellent vertex resolution is essential to the
LHCb physics programme. Most analyses rely heavily on selection cuts on the
distance with which tracks approach the primary vertex (impact parameter) and
on the displaced vertex reconstruction with the VELO to identify the signal
channels. The impact parameter resolution was optimised by positioning the
VELO sensors as close to the LHC beam as permitted by safety consideration,
having a small inter-strip pitch at the inside of the sensors, and minimising
the amount of material traversed by a particle before the first measured hits
in the VELO.

  * •

Decay time. The decay time of a particle is obtained from the measurement of
its flight distance in the VELO. This is required for lifetime measurements
and, critically, for time-dependent measurements in the rapidly oscillating
$B^{0}_{s}$–$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ meson
system [7, 8].

Figure 1:  (top left) The LHCb VELO vacuum tank. The cut-away view allows the
VELO sensors, hybrids and module support on the left-hand side to be seen.
(top right) A photograph of one side of the VELO during assembly showing the
silicon sensors and readout hybrids. (bottom) Cross-section in the $xz$ plane
at $y=0$ of the sensors and a view of the sensors in the $xy$ plane. The
detector is shown in its closed position. $R$ ($\Phi$) sensors are shown with
solid blue (dashed red) lines. The modules at positive (negative) $x$ are
known as the left or A-side (right or C-side).

The VELO contains a series of silicon modules arranged along the beam
direction, see Fig. 1. A right-handed co-ordinate system is defined with $z$
along the beam-axis into the detector, $y$ vertical and $x$ horizontal.
Cylindrical polar co-ordinates ($r,\theta,\phi$) are also used. The region of
the detector at positive (negative) $z$ values is known as the forward
(backward) or downstream (upstream) end.

The sensors are positioned only 7$\rm\,mm$ from the LHC beams. This is smaller
than the aperture required by the LHC beam during injection. Hence, the
detector is produced in two retractable halves. There is a small overlap
between the two detector halves when closed. This aids alignment and ensures
that full angular coverage is maintained. The position of the VELO halves are
moveable in $x$ and $y$ and the VELO is closed at the beginning of each fill
such that it is centred on the interaction region.

Figure 2:  Schematic representation of an $R$ and a $\Phi$ sensor. The $R$
sensor strips are arranged into four approximately $45^{\circ}$ segments and
have routing lines perpendicular to the strips. The $\Phi$ sensor has two
zones with inner and outer strips. The routing lines of the inner strips are
orientated parallel to the outer strips.

Approximately semi-circular silicon sensors are used. Each module contains one
$r$ and one $\phi$ coordinate measuring sensor, known as $R$ and $\Phi$
sensors and shown schematically in Fig. 2. The inter-strip pitch varies from
approximately 40 to 100$\,\upmu\rm m$ across the sensor. The strips are read
out from around the circumference of the sensor through the use of routing
lines on the sensor. The sensors are read out using the Beetle [9] analogue
front-end ASIC, operated with a 40${\rm\,MHz}$ input event sampling rate. The
signals are digitised and processed to form clusters in an FPGA-based readout
board known as the TELL1 [10], before being passed to the high level trigger.
More details on the readout chain are given in Sect. 3.1

There are 21 standard modules in each VELO half. Two further modules, known as
the pile-up system, containing $R$ sensors only are located in the most
upstream positions.

Owing to the proximity of the detector to the beam, the VELO is exposed to a
high radiation fluence and radiation tolerant oxygenated
$\rm{\it{n^{+}}}\mbox{-}on\mbox{-}{\it{n}}$ sensors, consisting of an $n$-type
implant on an $n$-type bulk with a backplane $p^{+}$-type implant, are
employed. One of the most upstream modules uses
$\rm{\it{n^{+}}}\mbox{-}on\mbox{-}{\it{p}}$ silicon (one $R$ and one $\Phi$
sensor pair). These are the only $\rm{\it{n^{+}}}\mbox{-}on\mbox{-}{\it{p}}$
sensors in operation at the LHC and were installed as this technology is a
leading candidate for use in the LHC upgrades. All sensors were fabricated by
Micron Semiconductor.111Micron Semiconductor Ltd., 1 Royal Buildings,
Marlborough Road, Lancing Business Park, Lancing, Sussex, BN15 8SJ, UK.

The detectors are mounted in a vacuum vessel and are located in a secondary
vacuum separated from the LHC machine vacuum by an RF-box. The surfaces facing
the beam are 0.3$\rm\,mm$ thick corrugated sheets, known as the RF foil. These
RF-boxes and foil provide three functions: they provide shielding against RF
pickup from the LHC beams, guide wakefields to prevent impedance disruptions
to the LHC beams, and protect the LHC vacuum from outgassing of the detector
modules. The detector is located upstream of the LHCb dipole magnet in a
region with a negligible magnetic field.

This paper reports on the performance of the VELO detector over the first
period of LHC physics operation. The first proton-proton collisions occurred
in November 2009 at beam energies of 450$\mathrm{\,Ge\kern-1.00006ptV}$, with
the first 3.5$\mathrm{\,Te\kern-1.00006ptV}$ beam collisions occurring in
March 2010. The beam energy was raised further to
4$\mathrm{\,Te\kern-1.00006ptV}$ in April 2012. All physics data were recorded
with a 50${\rm\,ns}$ minimum bunch spacing. LHCb recorded integrated
luminosities of 0.04$\mbox{\,fb}^{-1}$ in 2010, 1.11$\mbox{\,fb}^{-1}$ in 2011
and 2.08$\mbox{\,fb}^{-1}$ in 2012. The first period of LHC operations ended
in February 2013, when the LHC entered a shutdown for an upgrade to increase
the beam energy. The LHCb VELO performance results in this paper are primarily
given on 2011 data, the first year in which the instantaneous luminosity
reached, and exceeded, the nominal design value. Section 2 describes the
performance of the component subsystems in the VELO. The calibration of the
timing, gain and processing parameters is described in Sect. 3, along with the
detector monitoring strategy and the simulation and reconstruction software.
Sections 4 and 5 provide the system performance results, with the former
section providing detector performance related results and the latter results
on quantities more directly related to physics performance.

##  2 Subsystem performance

The performance of individual subsystems from the VELO are described in this
section. The section starts with a description of the commissioning stages of
the detector and then describes the performance of the vacuum, cooling, low
and high voltage and motion systems. The section ends with information on the
material budget of the VELO.

###  2.1 Commissioning results

The subsystems and overall operations of the VELO were extensively
commissioned before the first LHC beam collisions. After production, the
commissioning of the VELO consisted of four main stages: testing during
assembly, operation in a test beam, commissioning post-installation at the
LHCb experimental area, and testing with beam-absorber collisions.

The detectors underwent extensive quality assurance tests at the production
sites and after delivery for system assembly, utilising components of the
final readout system [11]. During detector assembly (Fig. 1 shows a photograph
of the system at this stage) each module was operated with a complete readout
slice, simulating as closely as possible the final vacuum, cooling, and
powering conditions of the VELO. The main mechanical difference from the final
system was the absence of the RF foil. This first testing step allowed a
complete “fingerprint” of the pedestal and noise map of each module to be
produced, along with the commissioning of the zero suppression algorithms
running in the TELL1 DAQ boards (see Sect. 3.3).

In the second step, a partially assembled VELO half was taken to the
120$\mathrm{\,Ge\kern-1.00006ptV}$ pion/muon beam at the North area SPS test
beam facility at CERN. Complete track and vertex reconstruction was performed,
using the products of interactions of the beam in lead targets placed in
similar positions to that of the LHC beam interaction region [12]. This
allowed the data acquisition and software chain to be debugged, in addition to
performing a full speed test of significant components of the LHCb readout
chain. It also served as a “dress rehearsal” for the transportation of the
VELO using a truck with special traction and speed control. The VELO half was
mounted on four shock absorbers on a trailer with special suspension, and the
transport motion was fully logged using accelerometers.

The third stage of the commissioning was carried out after the installation of
the VELO at the LHCb experimental area. Due to the proximity of the silicon
sensors ($\leq 1$$\rm\,mm$) to the 1$\rm\,m$ long corrugated RF foil, and the
insertion procedure of the detector halves into the RF foil relying purely on
the manufacturing and assembly tolerances, it was necessary to employ special
monitoring procedures. Each module slot was tested with an oversized dummy
sensor model for contact with the foil, and a test insertion was performed
with a genuine module. Characteristic IV curves of all sensors were taken at
several occasions during the transport, movement and installation procedures,
and it was verified that no damage had occurred. Following this, the cabling
of the detector was verified by applying custom test-pulse patterns to each of
the 5632 readout links, and verifying the correct pattern was read back. Each
link was tuned to select the optimal ADC sampling point using test-pulses (see
Sect. 3.2.1). The digitisation uniformity was confirmed by injecting sine wave
pulses with an amplitude close to the full dynamic range and a period matching
the pulse train from the front-end ASICs. In addition, the noise and pedestals
were measured, and compared with the “fingerprint” recorded during the
assembly and commissioning process.

In the fourth and final commissioning step, a special method was found to
study genuine tracks in the detector before the start of LHC collisions. The
synchronisation tests of the LHC beam were utilised in which, during the
initial phase of each test, the LHC proton beam was collided with a beam
absorber at the end of the transfer line between the CERN SPS and the LHC
about 340$\rm\,m$ from the LHCb cavern. This allowed the VELO to reconstruct
the first tracks from the LHC machine [13]. The particles produced by the
proton interactions in the absorber, and by their re-interaction, were
detected by the LHCb experiment and were used to commission the detector.
These injection tests were performed in 2008 before the first circulating beam
in the LHC and in 2009 before the first proton-proton collisions. These data
were used to set up the timing and the alignment of the system, and for
commissioning of the control, reconstruction and monitoring software. They
were of particular importance to the VELO as it is not possible to collect
sufficient cosmic ray data for commissioning due to the horizontal geometry,
and hence provided the first full system test of the VELO. With this method
about 50k tracks were reconstructed in LHCb. This was sufficient to determine
that the modules were displaced by less than 10$\,\upmu\rm m$ from their
surveyed positions (see Sect. 5.2). The alignment of the modules was
determined with 5$\,\upmu\rm m$ precision for $x$ and $y$ translation and
200$\,\upmu\rm rad$ for the rotations around the $z$-axis [14]. In addition,
the tracks traversing from one VELO half to the other could be used, by
evaluating the mismatch of the two segments, to measure the distance between
the halves to a precision of 100$\,\upmu\rm m$. The time alignment of the VELO
was determined to a precision of 2${\rm\,ns}$, and measurements made of the
signal to noise and cluster finding efficiency. These commissioning stages
allowed LHCb to be ready for an immediately successful start to physics data
taking after the first LHC beams collided in November 2009.

###  2.2 Vacuum stability

The VELO vacuum vessel is composed of two sections: the first is part of the
beam volume of the LHC, and the other contains the detector modules. The two
sections are separated by a vacuum tight RF-box, welded from a 0.3$\rm\,mm$
thick corrugated AlMg3 foil with 0.5$\rm\,mm$ thick side walls which
encapsulates each detector half. The differential pressure between the beam
and detector volume should always remain below 5$\rm\,mbar$ to protect the
foil against irreversible deformation. Consequently, the pump-down and gas
venting procedures are very delicate operations that are controlled by a
programmable logic controller (PLC), based on the readings from three membrane
switches that have preset trigger values. The PLC continuously monitors the
performance of the system and takes, when needed, appropriate actions. A
PVSS222PVSS is a Supervisory Control and Data Acquisition software package
developed by ETM professional control GmbH. project monitors and archives all
relevant system variables in a database, that is common to the whole LHCb
experiment [15]. For redundancy purposes, two sets of roughing, turbo-
molecular and ion pumps are implemented in the system. The pressure in the
detector volume is around $2\times 10^{-7}$$\rm\,mbar$, while the beam volume
is at $1\times 10^{-9}$$\rm\,mbar$ in the absence of circulating beams. Under
the influence of 1380 bunches per beam this pressure can rise to $5\times
10^{-9}$$\rm\,mbar$. The influence of the proton beams on the pressure of the
beam volume can clearly be seen in Fig. 3.

Figure 3:  Illustration of the influence of the proton beams on the beam
volume pressure. The readings of the beam volume (PE 412) and detector volume
(PE 422) are shown, and the increase in pressure in the beam volume coinciding
with the beam injections (each containing $2\times 10^{14}$ protons) at
$t=6~{}\mathrm{hours}$ can be seen. The beams were dumped 24 hours later.

###  2.3 Cooling performance

The VELO modules are cooled by means of an evaporative system using CO2 as
coolant. The cooling plant, which is located outside the radiation zone, has
two chillers filled with hydrofluorocarbon (R507a): a 2.5 kW water-cooled main
chiller and a 1 kW air-cooled backup chiller, operating at $-40$ and
$-25^{\circ}C$, respectively (see Ref. [16]). The actual cooling system of the
detector consists of two parallel, largely independent, loops: one for each
detector half. The CO2 is subcooled by the main chiller and subsequently
pumped to the corresponding detector via a 55$\rm\,m$ long transfer line. The
operation principle is that of a bi-phase accumulator controlled loop, in
which the evaporative temperature in the detector is regulated by controlling
the pressure of the saturated mixture of vapour and liquid in the accumulator.
The cooling system is controlled by a PLC. In total 31 pressure and 192
temperature sensors are installed throughout the system. The PLC controls the
system via 24 proportional, integrating and differentiating loops based on a
subset of these readings. Alarm handling tasks are executed continuously and
if appropriate the system switches to the backup chiller or a spare pump. A
PVSS project monitors and archives all relevant system variables in an Oracle
database that is common to the whole LHCb experiment. A separate heating
system takes care of maintaining the temperature of the module base at 20∘C to
minimise deformations.

The default evaporator temperature is $-28$∘C. Due to thermal gradients
between the cooling blocks and the components of the hybrid the silicon
temperatures are $(-7\pm 2)$∘C. From the moment the front-end electronics is
switched on, it takes 3 minutes till the hybrid temperatures have stabilised.
The hybrid temperatures have been shown to be stable within 0.1∘C over a
period of four weeks.

The operation of the cooling system has been very smooth. The only major
intervention required was the replacement of the insulation of the transfer
lines in 2011 to eliminate the formation of ice. During operations in both
2009 and 2011 an increase of $\sim$1∘C was observed in one detector half and
found to be due to clogging of filters: the filters were replaced during the
following winter shutdowns.

During injection and ramp of the beams, the temperatures of the RF-boxes
increase by 0.5∘C. Subsequently the temperatures of the RF-boxes decrease by
1.5∘C when the VELO is closed.

###  2.4 Low voltage and high voltage

Each silicon sensor has its own hybrid with separate low voltage (LV) and high
voltage (HV) supplies. In addition, repeater boards are located directly
outside the VELO vacuum tank, which have their own positive and negative
supplies. Both the LV and HV power supplies are inside the counting-house
shielded from the radiation zone of the detector.

The LV system is based on the A3009 EASY low voltage module, with compatible
crates and mainframe controller, manufactured by CAEN.333CAEN S.p.A., Via
Vetraia 11, 55049 - Viareggio (LU) - Italy. The main system performance issue
has been with the LV Anderson connectors used in the system. Due to oxidation
a voltage drop across the connector can occur. This requires careful
monitoring as the dissipated power caused severe thermal damage on one of the
connectors during operation. The connectors were replaced by CAEN during the
shutdown at the end of 2011.

The HV system is based on the EHQ F607n-F 16-channel HV module from
Iseg.444Iseg Spezialektronik GmbH, Bautzner Landstr. 23, 01454 Radeberg / OT
Rossendorf, Germany. Careful monitoring of the HV parameters is a key
requirement as the current and depletion voltage change with radiation damage
(see Sect. 4.6). The main performance issue was with the control of the HV
supplies. The supplies occasionally get stuck when ramping in voltage,
requiring the software commands to be resent or control software restarted.

Voltage and current monitoring are implemented for both LV and HV systems and
they are connected to an FPGA based interlock safety system. All HV and LV
modules can have their channels switched off quickly ($<1$ s) by the interlock
system in case of problems. The primary uses of the interlock system have been
in the case of power cuts or disruptions, and interruptions to the chilled
water supply that is used by the cooling system.

###  2.5 Motion performance

The first active silicon strips are brought to within 8.2$\rm\,mm$ of the LHC
beams, with the inner surface of the RF foil at a 5.5$\rm\,mm$ radius. To
ensure detector safety during beam injection and adjustments, each VELO half
is retracted $\sim 29\rm\,mm$ in the horizontal plane and is only closed once
stable-beam conditions are declared. The VELO halves are moved using radiation
hard stepper motors, and the motion towards the final position is always done
from the same direction in order to minimise the effects of mechanical
backlash. The position is read from resolvers mounted on the motor axes. The
reproducibility of the position has been measured to be better than
10$\,\upmu\rm m$. The motion system is controlled by a PLC which performs many
safety checks to prevent unwanted movements due to hardware failures or
corruption of the destination position calculated by the closing procedure.

An automated closure procedure has been developed to position the VELO halves
around the beams, whilst taking into account the current beam conditions. It
uses information about the background level, the response of the hardware and
the positions of the beams to make informed decisions. During closure, the
LHCb trigger accepts 500${\rm\,Hz}$ of events which are required to contain at
least one track in the VELO. This rate ensures that a new beam-position
measurement, consisting of 400 reconstructed vertices, can be acquired in 1–2
s, even in the most open position. Figure 4 shows an example of the
distribution of vertices during a typical closure.

Figure 4: The horizontal position of LHC collision vertices as reconstructed
by the A-Side (left) and C-Side (right). These online screenshots of data
illustrate the “stop-measure-move” cycle of the closing procedure, where each
peak in the distribution corresponds to a “stop”, as well as the degradation
of vertex resolution with opening distance.

Upon receiving notification of stable beams, the two VELO halves are moved in
a series of “stop-measure-move” steps from open to closed. A vertical
adjustment is also made at each of the steps, if the movement required to
centre the VELO around the beams is greater than 20$\,\upmu\rm m$. Three
criteria are checked at all times during and after closure:

  1. 1.

the total silicon bias current from the 44 sensors in each half of the VELO is
less than 1000$\rm\,\mu A$ above the dark current. This limit corresponds to
10% occupancy of ionising particles in all sensors for several seconds;

  2. 2.

the Beam Conditions Monitors [17] — each consisting of eight CVD-diamond
radiation monitors placed adjacent to the beam pipe — are all functional and
reporting fluences less than 5% of the threshold which triggers an LHC beam
dump;

  3. 3.

the reconstructed beam position in $x$ and $y$, as measured by the two halves,
agree given the known opening distance at any given step. The observed beam
width must be acceptable given the opening distance and the expected
resolution thereof.

By considering the two independent beam profiles compiled by each half, the
VELO is observed to close symmetrically to an accuracy of better than
4$\,\upmu\rm m$.

Once closed the monitoring continues throughout the data taking. Apart from
requiring the above conditions, a slow drift of the beams is protected against
by prompting the VELO to open if the beams move by more than 300$\,\upmu\rm
m$. The LHC beam orbit has shown excellent stability. Consequently, the VELO
is permitted to remain closed for up to 20 minutes if the reconstruction of
the beam profiles is interrupted. This happens, for example, if the LHCb data
acquisition is paused (e.g. for a run change or reconfiguration). During this
grace period, movement of the beam is monitored by the LHC beam position
monitors which are horizontal and vertical wire pickups located at $z=\pm
22\rm\,m$ of the collision region. A deviation of 200$\,\upmu\rm m$ in any of
these readings will trigger the VELO to open.

The initial use of the system was performed with careful manual checking and
control of the closings. The automated closing procedure was then put in
place. From the declaration of stable beams the VELO takes, on average, 210 s
to close. Of this 160 seconds is due to the motion from the open to closed
positions. During the operations in 2010–2012 approximately 750 closing
procedures were performed and 0.9% of the stable-beam integrated luminosity
delivered by the LHC was lost due to this detector-safety procedure. This
number is in line with the expectation. Only minor performance problems have
been encountered and these have been addressed with changes to the closing
procedure, safety checks and motion PLC code.

###  2.6 Material description

The minimisation of the material budget of the detector is important for the
physics performance of the experiment in order to reduce the amount of
multiple scattering and particle interactions with material. An accurate
description of the material is also required for the simulation of the
experiment and for estimating the amount of multiple scattering that particles
undergo when performing track reconstruction. The material description is
implemented using the basic volumes in Geant4 [18] and there are limits on the
accuracy that is achievable, both from the range of basic volumes (and
combinations thereof) that are available and from the CPU time taken to
process very complex composite volumes. The appropriate balance must therefore
be obtained between accuracy and simplicity for each element of the
description. This is particularly an issue for the description of the complex
RF foil shape (see Fig. 6 below).

A comparison has been made between the measured masses of the various elements
of the detector, as determined at production, and their simulated
counterparts, which in general shows very good agreement, e.g. the average
mass of the sensors is $(2.17\pm 0.03)\rm\,g$, compared with the simulated
mass of $2.14\rm\,g$. Similarly the mass of the dominant component of the
material, the RF foil, is reproduced to within 2%. The RF foil was
manufactured as a single sheet of aluminium magnesium alloy and then pressed
into its rather complex shape. So while the agreement of the total material
may be good, the distribution of that material might not be so well described.
Tests were performed by measuring the thickness of an RF foil and it was found
that the amount of material was too low in regions around the beam in the
description used up till 2012 and this has now been improved. While this has
only a small effect on the total material it does contribute significantly to
the material before the first measured point, which is important for the
impact parameter performance with lower momentum tracks (see Sect. 5.4).

The simulated detector description can be used to estimate the material
traversed by a particle as it moves through the VELO. Figure 5 (left) shows
the amount of material along the trajectory of a particle, which originates
from the interaction point, before it reaches the radius of the first active
strip on the detector ($8.2\rm\,mm$), as a function of pseudorapidity and
azimuthal angle. The amount of material is expressed in terms of the fraction
of a radiation length ($X_{0}$) and the average material in the VELO
acceptance passed through before reaching this radius is $0.042\,X_{0}$. The
average amount of material traversed before a particle leaves the VELO at
$z=835\rm\,mm$ is $0.227\,X_{0}$. The breakdown of this total material budget
into the components of the VELO system inside the acceptance is shown in Fig.
5 (right). The VELO design means that much of the electronics and services are
outside the detector acceptance. The RF foil dominates with $\sim 43\%$ of the
material, and the next largest component is the active silicon sensors.
Considering the uncertainty on all components of the VELO, the material
traversed by a typical particle is estimated as being known to an accuracy of
$\pm 6\%$.

Figure 5: (left) Material passed through on trajectories originating from the
interaction point and terminating at the radius of the first active strip in
the detector expressed in terms of the fraction of a radiation length
($X_{0}$) and as a function of pseudorapidity ($\eta$) and azimuthal angle
($\phi$). The material is higher in the regions around $\pm 90^{\circ}$ where
the two halves of the detector overlap. (right) Breakdown of the total
material budget by component of the VELO. The number given for each component
is the percentage of the total average VELO material budget ($0.227\,X_{0}$).

A particle traversing the VELO can interact with the material, potentially
producing a number of other particles in the interaction. If some or all of
these particles are charged and their trajectories are within the VELO
acceptance they can be tracked and the vertex of the interaction
reconstructed. By examining the density distribution of these reconstructed
vertices the material distribution can be studied. The procedure is applied to
a sample of data arising from interactions of the beam with gas molecules in
the beam pipe as this provides a more uniformly distributed flux of
interactions than in collision events.

Figure 6 shows the distribution of vertices in a cross-section of the VELO
between $y=-5\rm\,mm$ and $y=+5\rm\,mm$. The vertices are plotted in the
$r^{\prime}z$ plane, where $r^{\prime}$ is the radial distance from the beam
axis of the vertex multiplied by either $1$ or $-1$ depending on the sign of
the $x$ coordinate to separate the left and right halves of the detector.
Vertices with a radius less than $5\rm\,mm$ are not plotted. The top right and
bottom left components of the figure focus on a more restricted region in $z$,
just downstream of the interaction point in data and simulation. The main
features of the $R$ and $\Phi$ sensors in each module and the undulating form
of the RF foil can clearly be seen. The most striking difference between data
and simulation is the more angular form of the simulated RF foil.

Figure 6: Vertices of hadronic interactions in the LHCb VELO material. (top
left) Full VELO system with entrance and exit regions visible in data. (top
right) Zoom in to a group of sensors downstream from the interaction point in
data. (bottom left) the same region reconstructed using simulation events.
(bottom right) Zoom onto an pile-up module consisting of a single R-sensor to
check the distance between the sensor and foil.

Another useful feature of these vertex distributions is that they allow checks
to be performed of the relative positions of the various VELO components. The
proximity of the sensors to the RF foil is of particular interest since if
these were to touch it could lead to an electrical short or damage to the RF
foil. Figure 6 (bottom right) shows the material interactions in the region
around one of the pile-up veto stations which have a single sensor. It is
clear that in this pile-up station the sensor is quite close to, though not
actually touching, the foil. All of the VELO stations have a greater clearance
from the foil.

These data can also be used to make a determination of the aperture available
to the beam due to the mechanical tolerances of the RF foil construction and
positioning. This information is of particular interest for the upgrade of the
VELO in which the radius of the detector, and hence of the RF foil, is to be
reduced [19]. The vertices attributed to interactions in the RF foil in the
$z$ regions around the sensors where the foil is at its smallest radius are
selected. Information can be obtained on the available beam aperture by
fitting the data with a circle and extracting the variations [20].
Conservatively assuming a foil thickness of 300$\,\upmu\rm m$, an aperture of
4.9$\rm\,mm$ is obtained, to be compared with the nominal value of
5.5$\rm\,mm$. This is further reduced to 4.5$\rm\,mm$ by the weld of the foil
to the RF box but is still well within the tolerance of 2.4$\rm\,mm$ that was
reserved for mechanical imperfections of the foil with regard to the beam
aperture.

##  3 Calibration, monitoring and simulation

The performance of the VELO depends critically on its calibration. This
section describes the calibration of the timing and gain of the detector, and
the data processing algorithms that are executed in FPGAs. The determination
and verification of the parameters of these algorithms are discussed. The
section starts with a brief description of the data acquisition system (DAQ).
The simulation of the detector is also described at the end of the section.

###  3.1 Data acquisition system

The silicon sensor’s strips are connected to the Beetle front-end ASICs [9] on
the hybrid circuit boards of the VELO modules. The ASIC samples data with the
LHC bunch crossing frequency and stores them in an analogue pipeline, with a
length of 160 events, awaiting the decision of the first level trigger. Both
the shape of the Beetle front-end amplifier pulse response and the sampling
time can be tuned in order to get the best performance; the tuning procedure
for the sampling time is described in Sect. 3.2.3.

After a positive trigger decision is obtained, the data from the Beetle ASIC
are read out on analogue links [21]. Each 128 channel Beetle ASIC provides
four-output ports. The signals of 32 channels of the sensor and four channels
of header information are sent serially at 40${\rm\,MHz}$ rate. The system has
a maximum readout rate of 1.1${\rm\,MHz}$. The data are sent out from the
hybrid circuit board of the module on kapton cables, via vacuum feedthroughs
to the repeater boards that are located outside the VELO tank. The analogue
data are then transmitted over a 60$\rm\,m$ long differential link (twisted
pair) to the TELL1 DAQ boards. The TELL1 boards are located in the counting
rooms outside the radiation zone.

The TELL1 DAQ boards digitise the analogue signals and process the data in
FPGAs. The adjustment of the sampling phase is described in Sect. 3.2.1. The
processing algorithms and the tuning of their parameters are described in
Sect. 3.3. The TELL1 boards output the processed data to the high level
trigger system [5]. The primary output from the TELL1 boards is zero-
suppressed (ZS) data. For monitoring and tuning purposes, a number of special
output data types can also be transmitted. The raw ADC values (non-zero
suppressed, NZS) are sent out at a low rate of approximately 1${\rm\,Hz}$. The
data formats also contain the header data from the Beetle ASICs. The headers
are used for the gain and error bank studies (described in Sects. 3.2.2 and
3.4 respectively).

###  3.2 Timing and gain

The ADC sampling time for the digitisation of the analogue data needs to be
determined, as does the input gain of the digitisation boards. The ADC
sampling time is set for each link to account, for example, for the slight
differences in cable lengths. The gain in the ADCs is particularly important
for the uniformity of the noise and signal levels measured subsequently. Then,
the timing of the pulse sampling in the Beetle ASIC with respect to the LHC
beam collisions needs to be setup. These three calibration procedures are
described below.

####  3.2.1 ADC sampling time

As described in Sect. 3.1, one triggered event of a VELO sensor is fully read
out through 64 analogue links, that each carry 36 analogue voltage levels
spaced by 25${\rm\,ns}$ each. The first four levels in this readout block are
encoded header bits, which have their heights calibrated to be slightly ($\sim
30\%$) larger than one MIP. On the receiving end, the TELL1 boards are
equipped with cards that digitise the 36 consecutive levels, sampling every
25${\rm\,ns}$. The sampling can be delayed by several clock cycles
(25${\rm\,ns}$) and fine time adjustments made with steps 1/16th of a clock
cycle. The optimisation procedure first consists of roughly aligning the
readout of the front-end signals to the digitising window. This is performed
by sending internally generated signals, test-pulses, on known channels in the
Beetle ASICs and adjusting the sampling so that the header bits are obtained
in the correct positions. A scan is then performed over the fine time steps in
order to get the final setting for each analogue link. The analysis of the
scan data finds the optimal sampling point based on two conditions: the best
signal to noise ratio and the minimal inter-symbol cross-talk. The inter-
symbol cross-talk is defined as the fraction of the signal spilling over to
the channel transmitted in the previous or next clock cycle on the same
analogue link. A plot of the delay scan analysis is shown in Fig. 7, where the
measured signal at each timing step is shown. The selected sampling point of
the channels is indicated by the solid vertical line, while the small inter-
symbol cross-talk at the sampling point of the previous and next channels is
indicated with the dashed lines.

Figure 7: An example of the scan over the digitisation phases (see text). Data
for 16 analogue links are shown. The horizontal axis represents the sampling
time, where the integer numbers indicate the location of the serially
transmitted Beetle channels, and between two channels there are 16 bins. The
solid red vertical line indicates the chosen sampling point and the dashed red
lines the position of the previous and next samples.

####  3.2.2 Gain

Each strip has a different capacitance, depending on its size and state of
depletion, and the length of its routing line. This, in addition to the range
of variances in the Beetle pipeline, cause links to have a range of signal
sizes for a given deposited charge. The _gain_ is normalised with a method
that is independent of these variations and is stable as the VELO undergoes
radiation damage. Here, gain refers to the conversion factor that relates a
certain Beetle output voltage to an ADC value. The gain factor can be varied
using a hardware setting on each digitisation card. This setting controls the
upper limit of the voltage range digitised by the ADC and hence the
proportionality of an input voltage to ADC counts.

The four bits of header information, which precede the 32 strip signals output
on each link, encode the pipeline column number of the event. The headers are
added to the link output in the Beetle, so they are not affected by strip
capacitance or by non-uniformities in the Beetle pipeline. They are digital
bits, which are subsequently sent over an analogue link, so can act as
standard candles during the gain normalisation.

Depending on whether these digital bits corresponds to a ‘0’ or ‘1’, a header
is classified as ‘Header High’ or ‘Header Low’, which when uncalibrated,
typically have output values of around 560 and 460 ADC counts respectively.
The distributions of high and low headers for each link are Gaussian in shape,
and we define the full header swing (FHS) as the difference between the two
means. To calibrate the VELO, the gain of each link is set to a value where
FHS is equal to 100 ADC counts. The effect of a gain calibration on the FHS is
shown in Fig. 8.

With the gain normalised, the most probable value of the Landau distributions
and average noise values of each link are more uniform than for the
uncalibrated VELO. The gain has been found to be fairly stable and the
calibration procedure is repeated every six months or after the replacement of
TELL1 digitisation cards or changes to the FPGA firmware.

Figure 8: The FHS distribution before and after the first gain calibration.
The data were taken two months apart in late 2009. One entry is made in the
histogram for each link.

####  3.2.3 Timing to the beam

After performing the digitisation and gain determination, a tuning is required
to synchronise the front-end amplifier sampling to the signals generated in
the silicon by particles from beam collisions. The signal left by a particle
passing through a strip is pre-amplified and shaped in the Beetle ASIC. The
level of this pulse is sampled every 25${\rm\,ns}$ and stored in a pipeline
position. When a trigger command is received the Beetle outputs the data from
the amplified signals that were sampled 4$\,\upmu{\rm s}$ earlier; this
trigger latency corresponds to 160 clock cycles. The time alignment adjusts
the Beetle sampling time to the time that the particles pass through the
detector, which is synchronous to the LHC bunch crossing time plus the time of
flight of the particle to that sensor.

The time alignment is performed by scanning the clocks of the front-end
readout in steps of 1${\rm\,ns}$. Data from a few thousand collision events
are stored for each step and the pulse-shape is reconstructed offline. The
pulse-shape is fitted with a bifurcated Gaussian function, where the two
halves have different widths but are constrained to have the same amplitude at
the peak; this accounts for the difference in the rise and fall time of the
pulses. This simple function does not fully describe the peak or the tails of
the distribution, most notably the undershoot after the pulse, but gives good
agreement in the rising and falling edges, and hence allows a quick and
reliable way to optimise the sampling time. Conventionally the sampling time
would be set to sample on the peak of the distribution, which would maximise
the signal to noise distribution. However, we choose instead to minimise the
contamination into the previous (pre-spill) or next (spillover) bunch
crossing. This is obtained by setting a sampling time that equalises the
spillover and pre-spill. As the rise time of the pulse is faster than the fall
time this corresponds to sampling a few nanoseconds after the peak, and
corresponds to a loss of about 4% in the optimal signal size. Figure 9 shows
the result of a scan, with the simple function that is fitted shown and the
optimal sampling time marked.

Figure 9: Pulse-shape obtained by combining data from all sensors, with a
1${\rm\,ns}$ time step and after applying for each sensor the time shift
determined by the procedure. The plot on the left shows the ADC spectra versus
time. The plot on the right shows the most probable value for each time bin
obtained from a fit of a Landau convolved with a Gaussian function. A
bifurcated Gaussian function is fitted to this distribution from which the
rise and the fall widths are obtained. The fitted function also predicts the
amount of pre-spill (25${\rm\,ns}$ before the chosen point) and the spillover
(25 ns after), which are marked with red vertical dotted lines. The chosen
sampling time is also marked with a red vertical dotted line.

###  3.3 FPGA data processing algorithms

After digitisation the data are processed in a series of FPGA algorithms
performed on the TELL1 board. Each TELL1 processes the output from one sensor,
and contains four FPGAs each of which independently processes 512 channels of
data.

A full bit-perfect emulation of the FPGA processing algorithms was implemented
in C-code at the same time as the VHDL code for the FPGAs was developed.
Extensive checks of the bit-perfectness are performed before any firmware
changes, running both the TELL1 and C-code software on the same data samples
and ensuring that bit-perfect agreement is obtained. The C-code emulation is
then encapsulated, in a software project known as Vetra [22] used by both the
VELO and LHCb Silicon Tracker, and run inside the main software framework of
the experiment. This allows the algorithms to be fully tested with data before
being deployed in operation for collision data. This also allowed the
algorithms to be fully tested and debugged during the commissioning period. In
operation, the ability to fully emulate the processing steps allows the output
of any processing stage to be monitored, which is used for assessing the data
quality and fully understanding the system performance.

The algorithms described below require a set of tuneable parameters to be
determined and uploaded to the FPGAs. The parameter values used are stored in
XML files and recorded in a database. The parameters are primarily based on
the analysis of NZS data using the Vetra package. For example, the pedestal
values are determined and the cluster thresholds are optimised. In total 550k
parameters are stored in the XML files for operation of the system.

####  3.3.1 Pedestal subtraction

Significant variation in the average raw ADC values (pedestals) are observed
for each Beetle ASIC. Variations in pedestal from link-to-link and channel-to-
channel for the raw NZS data are also seen, as shown in Fig. 10. Hence, the
pedestal values must be determined for each channel of the system
individually, and thus 180k 10-bit pedestal values are required.

Figure 10: Typical raw (Non-Zero Suppressed) data ADC values. Data from two
ASICs, each with four analogue links, is shown. Variations in the pedestal
values at the ASIC, analogue link, and channel level are seen.

The pedestal values are determined offline using NZS data collected when there
are no collisions. The values are then uploaded to the FPGAs, and are
subtracted from the raw ADC when processing each event. Operational experience
has shown that the pedestal values remain relatively stable and a pedestal
retuning is made once the pedestal subtracted ADC values of more than a few
percent of channels are more than 2 ADC counts away from 0. A retuning
typically happens every two months, and is usually performed during technical
stops of the LHC. A retuning is also required after the replacement of a TELL1
digitisation card or a change to the firmware. In addition to the pedestal
subtraction, channels in the system that are known to be faulty are masked at
this stage of the data processing.

####  3.3.2 Mean common mode suppression

The 128 channels of the sensor that share the same Beetle ASIC, and the 32
channels of one analogue link may be subject to the same sources of signal
fluctuation, known as common mode (CM) noise. The CM noise is suppressed in
the FPGAs with a Mean Common Mode Suppression (MCMS) algorithm which operates
on each analogue link, correcting any baseline offset in each event.

In the algorithm, first the average pedestal-subtracted ADC value of the
channels in a link is calculated for that event. Using this mean value a
search for particle hits is performed for each channel. All channels with hits
are masked, and a new mean value is calculated for each link. This value is
then used to correct the ADC values in all channels of the link.

This algorithm would not fully correct common mode sources from the silicon
sensor, for example from noise pickup from the proton beams. This is because
consecutive channels on the sensor are not read out on consecutive inputs of
the front-end ASIC (see Sect. 3.3.3). A second common mode algorithm was
originally foreseen for use after channel reordering. However, studies
performed by monitoring the noise level as a function of the VELO opening
distance, showed that this source of noise pickup was small, and this second
common mode algorithm has not been used in operation.

Figure 11 shows the distribution of the CM noise measured in the system. It
peaks at 0 and has a sigma of 1.74 ADC counts. Furthermore, out of the 1.74
ADC counts link CM noise, there is a common fluctuation among all 5376 links,
introduced by the common power supply and environment. This global common mode
noise is 1.47 ADC counts, meaning the intrinsic link common mode noise is 0.93
ADC counts. For comparison the average incoherent (CM suppressed) noise is
1.91 ADC counts.

Figure 11: Distribution of common mode noise per link. The blue histogram is
for all links. The green histogram is for links in a ASIC that has large
signals (see text).

The common mode distribution has a long tail on the negative side, where all
four links from the same ASIC have a coherent baseline shift. The effect is
illustrated in an event snapshot in Fig. 12 (left). Accompanying the baseline
shift are a few channels with very large signals that reach the saturation
point of the electronics, most likely arising from soft tracks at large
angles. In Fig. 11 the green distribution corresponds to links that have at
least two channels with signal more than 180 ADC counts above the baseline.
The large energy deposition hypothesis was confirmed in a test-pulse
calibration procedure. A controllable amount of charge is injected to a few
selected Beetle ASIC channels using test-pulse calibration capacitors. The
baseline shift is proportional to the injected charge as shown in Fig. 12
(right). These baseline shifts are corrected by the CM correction algorithm.

Figure 12: (left) Event snapshot for an ASIC that has large signals (channels
1024-1152). The blue dots are the raw ADC values. The red lines are the
pedestals. (right) ASIC baseline shift in response to injected charge in units
of the most probable charge deposited by a MIP in 300$\,\upmu\rm m$ thick
silicon.

####  3.3.3 Topological strip channel reordering

As a consequence of the layout of the routing of the channels from the VELO
$R$ and $\Phi$ sensors on the second metal layer, neighbouring channels on the
sensor are not necessarily read out consecutively. In the $\Phi$ sensor strips
from the inner region of the sensor are routed out over strips in the outer
region, and the readout is thus intermingled between inner and outer region
strips, as shown in Fig. 2. Therefore the electronic readout ASIC channel
numbering does not correspond to the physical (strips) channels on the
sensors. The zero-suppression and clusterisation must be performed in terms of
physically neighbouring channels, and thus a translation algorithm is
necessary. The reordering procedure is performed separately for $R$ and $\Phi$
type sensors. The implementation of this algorithm consumes a significant
amount of the FPGA resources.

####  3.3.4 Zero suppression and clusterisation

The final data processing algorithm on the TELL1 produces the raw cluster bank
which is sent out to the high level trigger. This processing reduces the data
size by only transmitting channels that have significant signals present. It
also groups together neighbouring hits that may be due to single particles and
produces a first estimate of the centre of this cluster.

In the first step, hit detection is performed by finding signals above seeding
thresholds. The current seeding threshold in each channel is set to be six
times higher than the measured noise in that channel, rounded to the nearest
ADC count. This limits fake noise hits while not significantly reducing the
selection efficiency of true signal clusters in fully depleted sensors (see
Sect. 4.1).

In the second step, the algorithm attempts to include adjacent strips in the
cluster. Strips are added to the cluster if they pass an inclusion threshold,
which is currently set at 40% of the seeding threshold. By setting a lower
inclusion threshold than the seeding threshold additional charge is added to
the cluster, which helps improve the resolution on the particle position. The
maximum number of strips per cluster is four.

The centre of the cluster is calculated from a pulse-height weighted average
of the strips contributing to the cluster. This is calculated with a precision
of an eighth of a strip (3-bits). This calculation is used to save time in the
trigger; it is recalculated with floating point precision for use in the
offline tracking. The resolution and cluster detection efficiency are
discussed in Sect. 4.

Finally, each cluster is encoded into a bit structure that contains
information on the cluster position, cluster size, and the charge measured on
each strip that contributes to this cluster. The size of the raw cluster bank
varies depending on the event’s occupancy, and the typical size of this bank
for the full VELO is about 20$\rm\,kB$.

###  3.4 Error identification

Information is sent out from the Beetle in the header bits that allow a number
of consistency checks to be performed. Error banks are then produced by the
TELL1s when the data of a link is internally inconsistent, or there is
inconsistency between data from various links. They aim to contain the
required information to trace down the origin of the error and take
appropriate measures. The most commonly occurring errors relate to the
verification of the pipeline column number. This number records in which
column of the Beetle pipeline the data are stored while awaiting a first level
trigger acceptance signal. The pipeline column number is reset periodically by
a broadcast command and hence verifying that it is identical for all front-end
ASICs ensures the synchronicity of the detector. Elements of the binary value
of the pipeline column number are transmitted as an analogue signal preceding
the data from each link of the ASICs. Gain variations and inter-symbol cross-
talk can cause the analogue values to end up in between the corresponding low
and high bit thresholds, and consequently make the bit assignment ambiguous.
Calibration and verification procedures that are executed regularly, have
managed to control these effects to a satisfactory level and errors now occur
at the level of a few in every ten thousand events.

####  3.4.1 Single event upsets

One error type of particular interest is a single event upset (SEU). Since the
Beetle ASIC is exposed to ionising radiation charge will be liberated in its
electronic circuits. Most particles will however not generate enough charge to
influence the operation of the devices. Occasionally a highly ionising
particle can cause a change in the logic state of one of the flip-flops in the
Beetle ASIC. These SEU can affect the performance on the ASIC if they occur
for instance in one of the configuration registers. Therefore all critical
flip-flops are implemented in a triple redundant way, featuring majority
voting and auto-correction. To monitor the rate of SEU, all bit-flips are
counted in a dedicated counter. The two least significant bits of this counter
are sent with the data for every trigger as part of the header bits. By
analysing the transitions of these counter bits, an average of 2.9 SEU per
$\mbox{\,pb}^{-1}$ of delivered integrated luminosity for all 1344 Beetle
ASICs combined is observed.

###  3.5 Monitoring

The VELO monitoring infrastructure is used to ensure that any degradation in
data quality is observed and can be followed up quickly. It is complementary
to the LHCb monitoring which is split in two components: online and offline
monitoring. The LHCb online monitoring analyses a fraction of the ZS data
sample that has been selected by the trigger. The LHCb offline monitoring uses
a number of lightweight algorithms to monitor a sample of all data that are
processed for physics analyses. The VELO monitoring adds two components: an
analysis of NZS data and a detailed analysis of the ZS data. Experience shows
that many data quality problems are spotted first in the detailed checks
performed by the dedicated VELO monitoring team.

The NZS data are recorded in a special data stream which is stored separately
from the physics data at a rate of 1${\rm\,Hz}$. Events directed to this
stream contain NZS data from all VELO sensors. This allows the analysis of
pedestals, common mode suppression, cross-talk effects and noise to be made
for each run. The NZS readout has also been used to study correlations between
different sensors in the same event (see Sect. 3.3.2).

The VELO monitoring also analyses ZS data which have not been biased by any
trigger selection. This sample of events is thus representative of the data
being recorded by the detector, and allows the detector performance to be
monitored independent of changes to the trigger. These data are recorded at a
rate of 10${\rm\,Hz}$ and stored in a separate data stream to increase the
efficiency of the data analysis.

All data in the ZS and NZS streams used by the VELO monitoring are processed
automatically by monitoring algorithms shortly after they have been recorded.
The output of the monitoring algorithms are analysed daily by VELO data
quality shifters. These are people on call who analyse the incoming data and
alert experts of problems if necessary. These analyses include information on
pedestals, noise, common mode, cluster signal distributions, occupancy,
tracking and alignment. Separate monitoring is implemented for all slow
control data such as voltages, currents, temperatures and pressures.

Figure 13: Example of the graphical user interface used in the VELO
monitoring. Shown are distributions of the number of hits per VELO track
segment (top left), the track angle with respect to the beam axis (top right),
and the ADC counts of $R$ and $\Phi$ sensor clusters associated to a track
(bottom left and right, respectively). The results of the current run are
shown in red filled symbols and the reference data for comparison are shown as
black open symbols.

A graphical user interface has been developed to facilitate the analysis of
the output of the regular monitoring algorithms. An example of its usage is
shown in Fig. 13. The same tool also produces trend and correlation plots of
the relevant quantities, which are used to track the detector stability over
time. Summary tables of representative values to assess data quality, for
example numbers of high occupancy channels, for each run are also made. The
summary values and comments from the analyst of the data are stored in a
dedicated electronic logbook.

Data are also taken under special conditions to cover aspects that cannot be
easily accessed with physics data. Dedicated monitoring is in place for these
periodic performance checks. These include sensor current versus voltage,
current versus temperature, noise versus voltage, and charge collection
efficiency versus voltage data which are performed to monitor radiation damage
(see Sect. 4.6).

###  3.6 Simulation

The LHCb simulation is based on Monte-Carlo event generators and the use of
the Geant4 toolkit [18]. A detailed model of the detector material in the VELO
has been produced, through which the simulated particles are propagated (see
Sect. 2.6). The entry and exit points of the simulated particles in the
silicon sensors are obtained from Geant4. A thin silicon sensor is expected to
have an energy deposition distribution that can be described by a Landau
function convolved with a Gaussian distribution. The charge deposited by a
particle in the silicon sensor is calculated using the form from theory and
previous experiment [23].

The total deposited charge is distributed at uniformly spaced nodes along the
particle path in the silicon, with the energy fluctuations along the path
simulated. The diffusion of the charge as it drifts in the electric field of
the silicon is simulated through a Gaussian smearing whose width is dependent
on a bias voltage parameter. Cross-talk between the charge attributed to the
strips is then added to model capacitive coupling. Noise is added to the
strips following the measured values in the data. The measured pulse-shape of
the front-end electronics is also simulated, and corrections are applied for
the time of flight of the particles. The electronics response from the
previous and the next events are also simulated by applying the pulse-shape to
simulated events. Pedestal offsets and common mode noise are not normally
simulated as they are removed effectively in the real data by the FPGA
processing algorithms. This simulation stage results in a model of the amount
of charge collected on a sensor’s strips. The model has the bias voltage and
capacitive coupling as free parameters which are tuned to obtain agreement
with the measured data resolution as a function of pitch and track angle and
typically agree to within 5%. This simple algorithm is fast and sufficiently
accurate for the simulation required for physics analyses.

The next stage of the simulation models the processing in the TELL1 board.
First, the signal is digitised. At this point the DAQ emulation produces an
output format that corresponds to the raw non-zero suppressed data. The
simulated data are then passed through the bit-perfect emulation of the TELL1
clusterisation algorithm (see Sect. 3.3). Identical clusterisation thresholds
are used to those in the data taking. The output data bank is then produced in
the same format as that produced by the TELL1 boards. A global scaling, the
gain (electron to ADC conversion), is applied to normalise the observed signal
in simulation, with a correction for the variation in signal size with radius
(see Sect. 4.1). The trigger, pattern recognition and track reconstruction
algorithms are applied identically for real and simulated data.

##  4 Overall system performance

This section characterises the VELO system performance, including the signal
to noise ratio, hit resolution, occupancy, and efficiency studies. Beam
backgrounds are also discussed. The results presented use data before
appreciable effects of radiation damage were observed, results on the observed
radiation damage are reported at the end of this section.

###  4.1 Signal size and noise rate

The observed total signal from the clusters is determined by fitting a Landau
convolved with a Gaussian function around the peak region. The deposited
charge for each track is corrected for the track’s angle to give a result
corresponding to a path length in the silicon of the nominal 300$\,\upmu\rm m$
thickness of the sensor. An example fit is shown in Fig. 14 (left). The
function provides a good description of the rising edge and peak region, but
undershoots the data in the high energy deposition region. This is in part due
to the presence of photon conversions to electron positron pairs which, in the
absence of an appreciable magnetic field in the VELO, can remain merged into a
single cluster. The tuned simulation is in good agreement with the data
distribution, including in the high energy deposition region, and the FWHM
does not require any additional smearing of the detector response. The most
probable value (MPV) of the Landau distribution varies as a function of track
radius, as shown in Fig. 14 (right).

Figure 14: (left) Fit of the signal distribution for Sensor 104 (a $\Phi$
sensor) for clusters on long tracks with a track intercept point on the sensor
$10<r(\rm\,mm)<15$. (right) The most probable value of the fits to sensors 40
and 104, the $R$ and $\Phi$ sensor of the same module respectively, as a
function of the track intercept point radius. The cluster ADC counts were
normalised to a track crossing 300$\,\upmu\rm m$ of silicon.

The noise of the front-end ASIC depends on the strip capacitance. On the $R$
sensors the inner radius strips have the lowest capacitance due to their
shorter length though this is partially compensated due to the inner strips
having longer routing lines. Still, the dependence of the noise on the strip
length is visible when comparing Fig. 15 (left) with the sensor layout shown
in Fig 2. The $R$ sensor is divided into four approximately $45^{\circ}$
segments, and the strip length increases with increasing strip number in each
segment. The $\Phi$ sensor has two zones with inner and outer strips. The
inner strips are shorter but have additional routing line contributions to
their capacitance. In the outer zone every alternate strip is under the
routing line for an inner strip so the capacitance for these strips is larger.
The noise in these three types of $\Phi$ sensor strips is shown in Fig. 15
(right). Larger noise is also clearly visible in both the $R$ and $\Phi$
sensors every 32 channels, this is due to inter-symbol cross-talk from the
digital header information into the first channel in each analogue readout
link. A suppression algorithm for this inter-symbol cross-talk has been
implemented in the FPGAs, but is not currently used due to the small size of
this cross-talk and the large signal to noise ratio.

Figure 15: Noise in ADC counts averaged across the 42 installed R (left) and
$\Phi$ (right) sensors, with the error bars indicating the RMS of the
distribution.

The average signal to noise ratio, computed as the average MPV of single strip
clusters divided by their strip noise, for the VELO is around 20:1. It is
higher for the $\Phi$ sensors than the $R$ sensors and shows a variation on
the sensor radius as shown in Fig. 16.

Figure 16: Signal to noise (S/N) ratio from the MPV of the signal for single
strip clusters on tracks divided by the noise of that strip. Shown are the S/N
values for sensor 40 (R) and sensor 104, the $\Phi$ sensor of the same module,
as a function of impact point radius.

###  4.2 Resolution

The hit resolution in silicon devices depends on the inter-strip readout pitch
and the charge sharing between strips. The charge sharing varies with
operational bias voltage and the projected angle of the track. The bias
voltage was 150$\rm\,V$ throughout the physics data taking in 2010–2012. The
projected angle provides information on the number of strips that the particle
crosses while it traverses the thickness of the silicon sensor. It is defined
as the angle between the track and the perpendicular to the sensor, in the
plane perpendicular to the sensor and containing the perpendicular to the
strip. Initially the resolution improves with increasing angle, due to the
charge sharing between strips allowing more accurate interpolation of the hit
position. The optimal resolution is obtained when the tracks cross the width
of one strip when traversing the 300$\,\upmu\rm m$ thickness of the sensor.
For the VELO the optimal projected angle varies between about 7∘ at the lowest
inter-strip pitch of 40$\,\upmu\rm m$, to about 18∘ for the largest
100$\,\upmu\rm m$ pitch strips. Above the optimal angle the resolution begins
to deteriorate due to the fluctuations in the charge on the strips and because
the signal to noise ratio on individual strips may drop below the clustering
threshold.

The clustering algorithm and charge interpolation method is described in Sect.
3.3. The VELO reads out analogue pulse-height information from the strips, and
this information is used offline to calculate the cluster position using the
weighted average of the strip ADC values. Including the track angle dependence
in the clustering algorithm is found to give a small improvement in precision.
The results presented here rely on the offline recalculation of the position,
while the trigger relies on the lower resolution (3-bits) calculation (see
Sect. 3.3.4). The estimated resolution in the simulation is parameterised and
fitted as a function of both track angle and strip pitch. This resolution
estimate for each hit is then used in the Kalman fit tracking algorithm.

The hit resolution is determined from the hit residuals which are evaluated
using the LHCb Kalman filter track fit [24] and include a correction for
multiple scattering and energy loss dependent on the track momentum. The
residual is defined by the distance between the hit measurement and the
extrapolated point of the fitted track to that sensor. As the hit for which
the residual is being determined is included in the track fit this gives rise
to a bias in the residual which must be corrected for. The bias correction
used to determine the residual is $\sqrt{V_{M}/V_{R}}$ [25] where $V_{M}$ is
the variance of the measurement and $V_{R}$ is the variance of the residual.
The evaluation of this correction is implemented in the Kalman fit.

The resolution has been determined as a function of the strip pitch and of the
projected angle. For each bin, the resolution has been determined from the
sigma of the fit of a Gaussian function to the distribution of the corrected
residuals. The resolution is evaluated using tracks that have hits in the
tracking stations behind the magnet and hence for which the momentum
measurement is available. The tracks are required to have a momentum greater
than 10${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to reduce the dependence on the
estimation of the multiple scattering effect, and a number of other track
quality criteria are applied to reject fake tracks. The results are presented
here for the $R$ sensor. The $\Phi$ sensor results are compatible but the
almost radial geometry of the strips means that tracks primarily have small
projected angles.

The measured hit resolution has a linear dependence on the strip pitch in
projected angle bins, as shown in Fig. 17 (left). The hit resolution at small
projected angles, almost perpendicular to the sensor, has a resolution which
is close to that which would be obtained from a binary system. This is to be
expected as the charge sharing between strips at this angle is minimal. A
significantly better resolution is obtained for larger projected angles, where
the fraction of two strip clusters increases and the analogue readout of the
pulse height in each strip is of benefit. The hit resolution as function of
the projected angle is shown in Fig. 17 (right) and the fraction of one and
two strip clusters as a function of the projected angle and strip pitch are
shown in Fig. 18. The best hit precision measured is around 4$\,\upmu\rm m$
for an optimal projected angle of 8∘ and the minimum pitch of 40$\,\upmu\rm
m$.

Figure 17: (left) The VELO resolution for two projected angle bins for the $R$
sensors as a function of the readout pitch compared with binary resolution.
(right) Resolution divided by pitch as function of the track projected angle
for four different strip pitches.

Figure 18: The percentage of one (left) and two (right) strip clusters as a
function of the track projected angle for four different strip pitches.

###  4.3 Occupancy

The detector occupancy is a key parameter in the performance of the pattern
recognition and tracking algorithms of the experiment. High occupancy can lead
to the mis-identification of hits on tracks and increase the number of hit
combinations decreasing the speed of the algorithms. The occupancy shown here
is for clusters. The cluster seeding thresholds and masking of noisy strips in
the FPGA data processing algorithms ensure that the contribution to the
occupancy from noise is negligible compared with that from particles; in the
absence of circulating beams the observed occupancy is below 0.01%. The
typical cluster occupancy during 2011 operations is shown in Fig. 19 (top
plots). Only events from particle beam crossings are utilised in the
computation, and this data sample has an average number of visible
interactions per beam crossing, $\mu$, of 1.7. The occupancy is shown computed
with data collected using two different triggers. Data from a random trigger
on beam crossings are used as this represents the average occupancy in the
events observed by the detector. The occupancy for events passing the high
level trigger is also given, this is higher as events with heavy flavour
production are typically of higher multiplicity than the average. The
distribution for events passing the high level trigger is not fully symmetric
around the collision point due to the preference of selecting events in the
LHCb acceptance.

LHCb VELO

Figure 19: Cluster occupancy in the VELO silicon strip detectors. (left plots)
Average occupancy in the sensor as a function of the position of the sensor
along the beam-line. (right plots) Occupancy as a function of the local radius
of strips on the $R$ sensors, with a negative sign applied to sensors on one
half. The upper plots show the occupancy when fully closed using 2011 data
with a $\mu$ of 1.7 and for events selected using a random trigger or with
events passing the high level trigger. The lower plots show the occupancy as a
function of closing distance with fully closed labelled as 0$\rm\,mm$, the
points below then follow in order of the retraction distance indicated in the
key.

The cluster occupancy has a dependence on the position of the sensors along
the beam-line, as shown in Fig. 19 (left). The location of the interaction
region is clearly visible from the dip in the occupancy distribution. The
highest occupancy of 1.1% for events passing the trigger is at around the end
of the closely spaced region of sensors in the VELO, where the occupancy is
44% larger than at its minimum.

The occupancy also varies across the sensor, increasing closer to the beam as
seen in Fig. 19 (top right). The maximum occupancy is 83% higher than the
minimum as a function of $R$. This is a much weaker dependence than might
naively be expected since the inner strips are five times closer to the beam
than the outer strips. However, the semi-circular sensor geometry means that
the strip length naturally reduces with decreasing radius on the $R$ sensors,
and the inter-strip pitch also reduces with decreasing radius on both the $R$
and $\Phi$ sensors. The occupancy reduces in the smallest radius region on the
$R$ sensors as these strips are shorter due to having the corners cut off.

Figure 19 (lower plots) also shows how the occupancy varies across the sensor
at a range of closing distances. These data do not have a well defined $\mu$
as the luminosity levelling (see Ref. [26]) had not yet been performed. The
minimum average sensor occupancy drops from around 0.4% when closed to around
0.1% when the VELO sensors are fully retracted by 29$\rm\,mm$ from the beam.
Even in the fully retracted position the number of particles that can be
reconstructed in the detector allows the performance of the system to be
determined and the primary vertex to be fitted to allow the detector to be
safely closed (see Sect. 2.5).

###  4.4 Beam backgrounds and high multiplicity events

Studies have been performed of beam-related backgrounds in the VELO, and a
number of sources of hits have been identified: beam-gas interactions;
instrumental effects triggered by the presence of beam; and beam interactions
with collimators. The rate of these effects is sufficiently low to not have a
significant detrimental effect on physics or to contribute significantly to
radiation damage in the detector.

The interaction of beams with residual gas in the LHC vacuum pipe and VELO
vacuum vessel provides a useful data sample for alignment and luminosity
studies. Simulations of beam-gas interactions in the VELO vacuum vessel and
the long straight section of the LHC have been performed [27], with the latter
including particle fluxes from beam-gas interactions in the long straight
section and from proton interactions in collimators. Tracks arising from these
beam-gas interactions provide a complementary sample to tracks from beam-
collisions due to their very forward angular distribution. Many of these
tracks pass through all VELO sensors and this provides useful additional
constraints for alignment (see Sect. 5.2). The reconstruction of the beam-gas
interaction vertices in the VELO region is illustrated in Fig. 20 (left). The
blue and red points are obtained from events in which only one beam passed
through LHCb, and vertices with at least five tracks are reconstructed from
interactions of the beam with residual gas. The horizontal crossing angle of
the beams is apparent. The downstream beam (red) interactions are limited in
their extent in the negative direction along the beam-line by the
predominantly forward acceptance of LHCb. This reconstruction of beam-gas
interactions allows a measurement of the transverse bunch profile along the
beam trajectory to be obtained and allows the beam angles, profiles and
relative positions to be determined. The beam-overlap integral can then be
obtained from the extracted beam profiles and has been used to obtain a
measurement of the luminosity [28]. The precision of the VELO allows this
luminosity determination to be performed with a comparable precision to that
obtained from the well-known van der Meer scan method. The rate of beam-gas
interactions can also be increased in the VELO by the use of a gas injection
system, which was commissioned in 2011 [29].

Events containing a collimated spray of background hits are also observed, as
shown in Fig. 20 (right). These events are characterised by high occupancy in
local regions of the sensor, and they are correlated with activity in other
tracking detectors. The rate of events is proportional to the beam intensity
in the LHC, and typically constituted 0.03% of events passing the high level
trigger in 2011. A possible origin for these events is beam interactions with
collimators.

Figure 20: (left) Imaging of the LHC beams through the reconstruction of the
production vertex of tracks in 2010. The vertices from beam-gas interactions
with the beam travelling in the $+z$ ($-z$) direction in LHCb are shown in
blue (red). Vertices arising from beam-beam interactions are in green. The
vertical axis represents the horizontal direction ($x$) and the horizontal
axis the beam direction ($z$). (right) An event display image showing clusters
in $R$ and $\Phi$ sensors with a high occupancy in a localised region assumed
to be due to a beam background splash event.

###  4.5 Efficiency and faulty channel analysis

Studies have been performed of the charge collection efficiency and cluster
finding efficiency of the detector. The detector is initially operated at a
bias voltage sufficient to obtain the full charge from the sensors, and the
charge collection efficiency and cluster finding efficiency as a function of
radiation are reported in Sect. 4.6. In addition faulty channels have been
identified through the study of the cluster finding efficiency, occupancy and
noise spectrum.

The cluster finding efficiency is a useful measure of the performance of the
detector. This is determined by excluding a sensor in the pattern recognition,
and interpolating tracks to this sensor. The tracks are required to have hits
in both the $R$ and $\Phi$ sensors in the two modules before the test sensor
and in the two modules after the test sensor. These requirements place some
restrictions on the sensors that can be probed and the regions analysed within
the studied sensors. Tracks that have intercept points inside the active
region of the sensor are then considered. Track quality selection cuts are
applied to remove fake tracks and track isolation cuts to prevent a cluster
from another track being selected. The efficiency with which clusters are
found near the track intercept points is then determined. The efficiency for
finding a cluster depends on the applied bias voltage and the thresholds
applied in the cluster making algorithms. The standard operational settings
are used for the studies presented here.

The region boundary between the inner and outer strips of the $\Phi$ sensor
and the middle region boundary of the $R$ sensor both contain a 79$\,\upmu\rm
m$ wide region with the HV bias resistors. This region and the region of the
guard ring around the sensor are excluded in the efficiency calculation.
Averaging across sensors, cluster finding efficiencies of $99.45\%$ sensors
were obtained at the start of operation as shown in Fig. 21. Bad strips are
identified with the cluster finding efficiency analysis described below. When
these bad strips are neglected the cluster finding efficiency rises to
$99.97\%$. The system contains only a single front-end ASIC that is not
functioning, the failure of which occurred after production and before the
start of physics operations, this is visible in the reduced efficiency of the
$\Phi$ sensor of module 21 in Fig. 21 (left).

Figure 21: The cluster finding efficiency for each sensor with all strips
(left) and when identified bad strips are excluded (right).

During the production of the modules faulty channels were identified through
the application of three techniques: high resolution visual microscope
inspections, the response of the modules to scans of a laser, and the analysis
of noise data. A total of only 0.6% of the VELO sensor strips were found to be
faulty, see Table 1. The analysis of noise data can also be performed on the
installed experiment. The measured noise on a functioning channel will
decrease once it is biased above its depletion voltage, since its capacitance
will decrease: unbonded strips or faulty ASIC channels will not display this
dependence. However, it was found that the tuning of the selection was highly
detector and condition sensitive and hence this method of faulty channel
identification is less accurate for repeated semi-automatic analysis than
those discussed below.

Table 1: Fraction of faulty strips classified as dead or noisy. The results are obtained from the methods used at production, occupancy spectrum studies, and a cluster finding efficiency analysis. Values are given at the time of production or start of operations in 2010, at the end of 2011, and at the end of 2012. Delivered Int. Luminosity | 0 $\mbox{\,fb}^{-1}$ | 1.2 $\mbox{\,fb}^{-1}$ | 3.3 $\mbox{\,fb}^{-1}$
---|---|---|---
Dead Strips |  |  |
Production Tests | 0.6% | – | –
Occupancy | 0.7% | 0.7% | 0.6%
Cluster Finding Efficiency | 0.8% | 1.1% | –
Noisy Strips |  |  |
Production Tests | 0.02% | – |
Occupancy | 0.01% | 0.02% | 0.02%

The cluster finding efficiency analysis can also be used to determine the
number of dead channels in the detector. A track is extrapolated to the
detector and clusters searched for in the channels around the intercept point.
A channel is identified as dead if tracks extrapolated to this strip show four
times more missed clusters than the mean of the $30$ nearest neighbours.
Examples of the locations of strips in which clusters are not found are shown
in Fig. 22, which shows the boundary region on the $\Phi$ sensor between the
inner and outer strips and the location of bad strips. This method identifies
89% of the channels found in the dead channel list made at production. Only
0.8% of channels were identified as dead at the start of operations by the
cluster finding analysis method. At the end of 2011, after two years of
operation and a delivered fluence of 1.2$\mbox{\,fb}^{-1}$, the fraction had
increased to 1.1% of channels.

Figure 22: The intercept position of an extrapolated track when a cluster is
not found for two example $R$ (left) and $\Phi$ (right) sensors. The bad
channels are clearly visible.

Two classes of faulty strips, dead and noisy, are also identified through the
analysis of the channel occupancy spectra (see Sect 4.3). Faulty channels are
usually masked in the FPGA data processing algorithms, and hence would not
show up in the occupancy spectra. Therefore, the analysis is performed using
NZS data and emulating the data processing, but without the faulty channel
mask applied. Channels with less than $10\%$ of the average occupancy are
identified as dead, and those with greater than three times the average
occupancy as noisy. The results are compared with those found at production
and with the cluster finding efficiency method in Table 1, and seen to be in
good agreement. The level of dead and noisy strips is shown to have remained
at a low level throughout the operations.

###  4.6 Radiation damage studies

The proximity of the silicon sensors to the LHC beam results in a high
particle fluence of up to $5\times 10^{13}$ 1$\mathrm{\,Me\kern-1.00006ptV}$
neutron equivalents / $\rm\,cm^{2}$ ($\rm\,n_{eq}$) per $\mbox{\,fb}^{-1}$ of
delivered integrated luminosity for the most irradiated sensor regions,
varying by approximately a factor of two as a function of the position of the
sensors along $z$. The VELO geometry, with the sensors placed perpendicular to
the beam, gives rise to a highly non-uniform radiation dose across the sensors
with the fluence falling off with radius $r$ as approximately $r^{-1.9}$. The
estimated fluence is obtained from the LHCb simulation and using measured
values of displacement damage in silicon. Particle irradiation gives rise to
both bulk and surface damage effects in the silicon. The bulk radiation damage
is primarily caused by the displacement of atoms in the silicon sensors from
their lattice sites, and induces changes in the leakage current and effective
doping concentration of the material. Consequently, radiation damage
monitoring was put in place from the start of operations. The leakage
currents, noise and charge collection efficiency (CCE) of the sensors are
studied regularly, with dedicated data taking scan procedures having been
developed. Detailed studies of radiation damage in the VELO based on 2010 and
2011 data taking have been reported in Ref. [30]. Further results, based on
the 2012 and 2013 data taking periods, are summarised here.

####  4.6.1 Current measurements

Sensor currents are studied as a function of both voltage and temperature.
Current-voltage scans are taken with an automated procedure on a weekly basis.
The shapes are analysed to look for signs of gradient changes that could
indicate the onset of breakdown, and the values at the operational voltage of
150$\rm\,V$ are compared to the expected currents. Current-temperature scans
are taken a few times a year by controlling the temperature of the cooling
system. The current-temperature scans allow the surface and bulk current
components to be measured separately. More details of these studies are
available in Refs. [31, 32].

The expected increase in the bulk current in each sensor due to radiation
damage is calculated using the predicted fluences and the measured temperature
history of the sensor and the relation [33]

$\Delta I=\alpha\phi\rm{V_{Si}},$

where $\alpha$ is the annealing parameter in units of A/$\rm\,cm$, which
depends on the temperature history, $\phi$ is the fluence in particles per
$\rm\,cm^{2}$ and $\rm{V_{Si}}$ is the silicon volume in $\rm\,cm^{3}$. The
evolution of the observed currents in the sensors with delivered integrated
luminosity are in good agreement with the expectation (see Fig. 23).

Figure 23: Currents measured for each sensor as a function of time (bottom).
The integrated luminosity delivered to LHCb and the average sensor temperature
is shown over the same time scale (middle and top). Increases in the delivered
luminosity are matched by increases in the sensor currents. The evolution of
the mean measured current agrees well with the prediction from simulation. The
mean measured value excludes sensors that are surface-current dominated.

####  4.6.2 Effective doping concentration

The $n$-bulk sensors undergo space-charge sign inversion under irradiation,
and hence their depletion voltage initially reduces with irradiation. This
continues until type inversion occurs, after which it increases with further
irradiation. In order for the charge collection efficiency of the sensors to
remain reasonably high, the sensors must be close-to or fully depleted during
operation. As all of the VELO sensors are operated at a constant voltage over
long periods, monitoring the sensor depletion voltages is a useful
experimental technique for ensuring that the CCE for a particular sensor does
not decrease significantly due to the sensor being under-depleted. In
practice, this is achieved by monitoring the effective depletion voltage
(EDV), which is derived using the following method. Here we report results for
the $n$-type sensors, but note that one $p$-type module is also installed in
the VELO and is studied in Ref. [30].

Sensors are grouped into a 1–in–5 pattern, where four of the sensors are
operated at the nominal operation voltage (150$\rm\,V$ throughout 2010–2013)
whilst a single sensor, referred to as the test sensor, has a range of bias
voltages applied to it. Using only the sensors at the nominal operation
voltage, a track is then fitted and extrapolated to the test sensor, where the
amount of collected charge at the intercept is determined. The distribution of
collected charge arising from repeating this process for many tracks is fitted
with a Landau distribution convolved with a Gaussian distribution to obtain
the MPV of the Landau distribution. The EDV is then determined as the voltage
at which the MPV of the charge distribution is equal to $80\%$ of the MPV
obtained at the maximum test voltage (currently 200$\rm\,V$). This value of
$80\%$ provides good agreement between the depletion voltage measured from
this method prior to irradiation and that obtained from the capacitance-
voltage measurements performed on the sensors at production. It also
represents a voltage above which the sensors must be operated to ensure
significant signal charge is extracted. This process then repeats via an
automated procedure for a range of patterns such that all of the sensors are
tested. As this procedure requires beam time that would otherwise be used for
physics data taking, it is currently only performed around three times per
year.

Figure 24 shows the measured EDV values using all the VELO sensors, and
dividing them into radial regions with reasonably constant fluence. The
delivered integrated luminosity at each CCE scan has been combined with the
expected fluence per $\mbox{\,fb}^{-1}$ to give the fluence for each radial
region of each sensor. The sensors exhibit an overall decrease in EDV with
fluence followed by an increase in EDV until the most recent CCE scan (after a
delivered integrated luminosity of 3.4$\mbox{\,fb}^{-1}$). As a result of the
radiation damage that had occurred by the start of 2013, many of the sensors
now have EDVs significantly higher than before irradiation. On average, type
inversion of the silicon occurs around $20\times 10^{12}$ $\rm\,n_{eq}$, after
which the EDV increases linearly with fluence. This behaviour can therefore be
used to predict the operational voltages required to give maximal CCE for a
given fluence and hence a delivered integrated luminosity. It can also be
noted that a minimum EDV of $\sim 20$$\rm\,V$ is observed for all sensors,
this is assumed to be a result of the finite integration time of the front-end
electronics.

Figure 24: The effective depletion voltage versus fluence for all VELO sensors
up to 3.4$\mbox{\,fb}^{-1}$ delivered integrated luminosity.

####  4.6.3 Charge loss to second metal layer

The cluster finding efficiency in the sensors is studied using the same
technique of track extrapolation as that used to study the CCE (see Sect.
4.6.2). These studies have shown an unexpected radiation induced charge loss
due to the presence of the second metal layer on the sensors. The second metal
layer on the sensors is used to route signals from inner strips to the outer
radius of the sensor. Particles that pass close to a second metal layer trace,
but away from the shielding effect of the first metal layer on the strip, have
a reduced charge collected on this strip and additionally induce charge on the
second metal layer. This gives rise to a reduction in cluster finding
efficiency on this strip, and additional noise clusters located on the strip
connected to the second metal layer track. This degradation has been observed
to continue throughout the 2012 data taking period, although there is some
evidence to suggest the rate of change with fluence is decreasing. Currently
studies of the VELO tracking efficiency show no degradation associated with
this effect within the errors of $\pm 0.3\%$. This effect is discussed in
detail in Ref. [30].

##  5 Physics performance

The performance of the VELO on more directly physics analysis related
parameters is reviewed in this section. The performance of the pattern
recognition, track reconstruction and the alignment of the detector are
discussed. The impact parameter, primary vertex (PV) resolution and decay time
resolution of the detector are then presented.

###  5.1 Pattern recognition and tracking

Obtaining a high efficiency for reconstructing the trajectories of charged
particles is particularly important for the analysis of many-body final states
since the selection efficiency scales with the track finding efficiency to the
power of the number of tracks. An accurate knowledge of the tracking
efficiency is also important in many other physics analyses, especially those
that aim to measure a production cross-section or a branching fraction. The
track finding algorithms in LHCb start with a search in the VELO detector for
straight lines. These tracks are then combined with hits in the tracking
stations to produce the “long” tracks that are used for most physics analyses.
The track fit is performed using a Kalman fit. In the trigger a simplified
model of the detector material and a single direction Kalman fit are used in
order to reduce CPU consumption. A full bi-directional Kalman fit is performed
offline using a detailed model of the detector material.

The VELO pattern recognition algorithm requires a minimum of three $R$ sensor
and three $\Phi$ sensor clusters to reconstruct a trajectory. The basic
algorithm collects sets of $R$ clusters consistent with being on a straight
line from the interaction point, then looks for a set of compatible $\Phi$
sensor clusters to confirm the trajectory. The alternating stereo angles of
the $\Phi$ sensor strips resolves the stereo ambiguities when combining the
$R$ and $\Phi$ sensor clusters. A second pass is made combining the unused
clusters to find tracks not from the interaction region. The number of
clusters on a VELO track ranges from six (the minimum requirement is three on
$R$ and three on $\Phi$ sensors) up to the full 42, with an average of 11. An
additional algorithm, that only runs when the detector is closing, makes 3D
space points from the $R$ and $\Phi$ sensor clusters in a module and forms
tracks from these having no assumptions about the track directions.

The efficiency of the track reconstruction in the VELO has been measured using
a tag-and-probe method. Samples of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ decays into two muons are used where the track of one of the muons is
fully reconstructed (tag-muon), while the other muon is only partially
reconstructed using hits in the other tracking stations (probe-muon). The
momenta of the tag- and probe-muon are used to reconstruct the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate mass and hence
confirm the selection. It is required that the trigger has not selected the
event based on the probe muon track to prevent any potential trigger bias. The
VELO tracking efficiency is obtained by matching the partially reconstructed
probe muon to a long track (which has a VELO track segment).

The measured VELO tracking efficiency for long tracks is shown in Fig. 25 for
data and simulation, and is typically 98% or higher in the data. The
simulation is weighted by the number of tracks observed in the data. The
efficiency for the VELO pattern recognition is weakly dependent on the
multiplicity of the event, as the pattern recognition becomes more complex in
a higher occupancy environment. The dips in efficiency at $|\phi|\approx\pi/2$
are caused by the extra multiple scattering from the material of the RF foil
in the vertical plane, see Fig 5 (left). The discrepancy between data and
simulation in these bins is partially explained by the effect of assumptions
made in the tracking: the beam is centred in the coordinate system in the
simulation while it is offset by 0.4$\rm\,mm$ in data; and the distance
between the two halves when the system is fully closed differ at the
150$\,\upmu\rm m$ level between data and simulation. The discrepancy is taken
into account in physics analyses by applying a reweighting procedure that
ensures data and simulation agreement, and a procedure for determining the
systematic uncertainties due to this correction is also in place.

Figure 25: Tracking efficiency for the 2011 data and simulation for the VELO
as a function of the momentum, p (top left), the pseudorapidity, $\eta$ (top
right), the azimuthal angle $\phi$ (bottom left) and the total number of
tracks in the event, $N_{track}$ (bottom right). The simulation has been
reweighted to the number of tracks observed in data for the p,$\eta$ and
$\phi$ plots. The error bars indicate the statistical uncertainty.

Another important measure of the tracking performance is the number of poor
quality or “ghost” tracks that are produced. Defining a ghost track as one in
which less than 70% of the VELO clusters on the track are from the same
simulated particle, the fraction of ghost tracks is shown in Fig. 26 (left) as
a function of the total number of VELO clusters. These tracks become more
frequent as the detector occupancy rises, with typical occupancies being 0.5%
for randomly triggered events and 1% for HLT triggered events (see Sect. 4.3).

Figure 26: (left) Fraction of ghost tracks versus number of VELO clusters in
simulation. (right) VELO pattern recognition timing versus number of clusters,
the pattern recognition alone (magenta triangles), the raw data decoding (blue
squares) and the combined (red circles) timings are shown. The times are
scaled to a 2.8${\rm\,GHz}$ Xeon processor.

The CPU resources consumed by the VELO tracking in the high level trigger are
substantial and the algorithms have been optimised for speed. For example, to
minimise the time taken in decoding the clusters, the 3-bit cluster centre
position computed in the TELL1 FPGAs is used (see Sect. 3.3). The time taken
for the decoding and pattern recognition algorithms is shown in Fig. 26
(right).

###  5.2 Alignment

The VELO has extremely stringent alignment requirements to ensure that the
intrinsic hit resolution of the detector (see Sect. 4.2) and the impact
parameter and decay time resolution (see below) of the experiment are not
adversely affected. Furthermore, as described in Sect. 2.5, the VELO halves
are inserted and centred around the beams in each LHC fill. Consequently the
high level trigger requires an immediate update of the alignment parameters.
These parameters are also required for the offline reconstruction. The
alignment of the detector is thus separated into two elements: the underlying
system alignment, and the updates required in each fill.

The underlying alignment of the VELO relies on three components: the precise
construction and assembly of the detector, the mechanical and optical survey
of each part of the detector, and the software alignment of the system using
tracks. The updates for each fill are then added to this: mechanical
measurements of the position to which the detector is closed are used to
determine these.

####  5.2.1 Optical and mechanical measurements

Each component of the detector was surveyed at the various stages of the
assembly using a smart-scope for the individual modules, and a coordinate
measuring machine with optical and touch probe heads for the modules and for
each half of the assembled system. The relative position of the $\Phi$ sensor
with respect to the $R$ sensor in each module was measured with an accuracy of
about 3$\,\upmu\rm m$ for the $x$ and $y$ translation and with an accuracy of
about 20$\,\upmu\rm rad$ for rotations around the $x$ and $y$ axis. The
relative module positions within each half of the detector were measured with
a precision of about 10$\,\upmu\rm m$ for the translations along $x$ and $y$.
Measurements of the mounting frame were made with a coordinate measuring
machine during production, and then prior to, and after, installation
measurements were made using photogrammetry, theodolites, mechanical gauges
and levelling instruments. The position of the two VELO halves was determined
with an accuracy of 100$\,\upmu\rm m$ for the translations and 100$\,\upmu\rm
rad$ for the rotations. These survey measurements are used as a starting point
for the track-based software alignment, and remain important for the final
alignment quality as some degrees of freedom (see below) are difficult to
align with tracks.

####  5.2.2 Track-based alignment methods

The track-based alignment relies on minimising the residuals between the
fitted tracks and the measured cluster positions. The alignment can be
considered in terms of three different stages:

  1. 1.

the relative alignment of each $\Phi$ sensor with respect to the $R$ sensor in
the same module. This allows the $x$ and $y$ translations of the sensors to be
determined;

  2. 2.

the relative alignment of the modules within each VELO half. This alignment is
primarily sensitive to the $x$ and $y$ translations of the modules and their
rotations around the $z$ axis. Only the $\Phi$ sensors are sensitive to this
rotation due to the strip geometry and hence this rotation must be determined
at the module level. The misalignment due to the other three degrees of
freedom (the $z$ translation and the rotations around the $x$ and $y$ axis)
cause second order effects to which sensitivity can only be obtained with $R$
sensors from using a large data sample with a wide range of track angles;

  3. 3.

the relative alignment of one VELO half with respect to the other half. The PV
position can be used as a constraint since tracks reconstructed in each half
originate from this common point. This method is sensitive to the $x$, $y$ and
$z$ translations and the rotations around the $x$ and $y$ axis. In addition,
tracks that cross both halves of the detector are used. There is a small
overlap between the sensors in the left and right halves of the VELO when the
detector is fully closed, and tracks that traverse the VELO in this overlap
region are particularly important. The alignment using these tracks is mainly
sensitive to the misalignment of $x$ and $y$ translations and the rotation
around the $z$ axis.

Two methods were developed and used for performing the track-based software
alignment. The first method [34, 35] performs the $\Phi$ sensor alignment by
fitting an analytical form to the residuals as a function of $\phi$, and
performs the remaining alignment stages using a matrix inversion method, based
on Millepede [36], which performs a $\chi^{2}$ minimisation that depends upon
both the track and alignment parameters. This alignment method is fast but the
implementation fits straight line tracks in the VELO. The second method uses a
global $\chi^{2}$ minimisation based on Kalman track fit residuals [25]. This
method uses an iterative procedure, that could be time consuming in the case
of a large misalignment. However, the Kalman filter fit takes into account the
corrections for multiple scattering, energy loss effects and the weak magnetic
field in the VELO region. The results from both methods are in agreement [14].

The alignment is performed using a specially selected data sample which
improves the sensitivity to all degrees of freedom and better constrains the
upstream and downstream of the PV regions of the VELO. This sample includes a
mixture of tracks from collisions with a wide range of angles, and tracks from
beam-gas interactions. The beam-gas interactions are roughly parallel with the
beam-axis, giving tracks that cross many modules.

Correlated module misalignments which are poorly constrained in the track-
based alignment, known as weak modes, can bias physics quantities like the
impact parameter or the invariant mass. The most important weak mode in the
VELO is the twist of the modules around the $z$-axis. This misalignment can
distort the impact parameter measurement by several tens of microns as a
function of the azimuthal direction of the track. The effect is limited by
using the alignment track sample with a range of track types, and by applying
constraints in the alignment procedure from the survey measurements.

####  5.2.3 Mechanical measurement of closing

The VELO halves are moved independently horizontally ($x$) and together
vertically ($y$) during the closing procedure and the motion is measured to an
accuracy of a few$\,\upmu\rm m$ with mechanical position sensors. These
measure the revolutions of the spindle that controls the displacement. The
position of the two VELO halves is updated for each fill using these
mechanical system measurements in $x$ and $y$ by adding these changes to the
underlying system alignment.

Performing the track-based alignment of the VELO halves using data collected
at different opening positions (distance between the two halves of 0,
$\pm$5$\rm\,mm$, $\pm$10$\rm\,mm$, $\pm$29$\rm\,mm$) allows a calibration of
the motion system measurements to be performed. This shows a calibration
accuracy of $0.6\%$ of the motion system along the $x$ direction is achieved.

####  5.2.4 Alignment performance

The track-based alignment results are in good agreement with the lower
precision survey results, within the uncertainties, apart from the effect due
to the change in temperature of the system. The system was surveyed at room
temperature, but is normally operated with the cooling system operated at
-30∘C. Comparing track-based alignments performed with the cooling temperature
set to +8∘C and -30∘C a change of distance between the two halves of about
170$\,\upmu\rm m$ was measured. Laboratory measurements were also made by
heating individual modules and an expansion of approximately 1$\,\upmu\rm m$
per degree along the $x$ direction of the carbon fibre that supports the
modules was found. Hence, even when using materials with a low coefficient of
thermal expansion it is important to control temperature changes when aiming
for $\,\upmu\rm m$ level precision. This is achieved in the VELO by
maintaining the mounting base plate of each VELO half at 20∘C and operating
with a stable cooling system temperature.

The improvement obtained after the track-based alignment procedure over the
precision of the survey is illustrated in Fig. 27. The shapes of the residual
distributions as a function of the azimuthal coordinate are characteristic of
particular sensor misalignments. The precision obtained after the track-based
alignment is better than the best hit resolution of the detector with an
alignment at the few $\,\upmu\rm m$ level obtained for the $x$ and $y$ module
translations.

Fitting the position of the PV separately with tracks in the two halves of the
VELO allows the misalignment between the two halves to be determined. This is
shown in Fig. 28 over a period of four months of operation. The variation
between runs shows the accuracy with which the position in each fill is
measured. The excellent stability of the alignment of the system is also
clear.

Figure 27: Example unbiased sensor residuals as a function of the $\phi$
coordinate using only the survey information (left) and using the track-based
software alignment (right). Results are given for two different example
sensors. (top) A significant improvement in the residuals is seen in this
sensor with the track-based alignment. (bottom) In this sensor the alignment
quality using the survey information is already good.  Figure 28: Misalignment
between the two VELO halves in each run, evaluated by fitting the PV
separately with tracks in the two halves of the VELO. The run numbers shown
here span the period of the last four months of operations in 2010.

###  5.3 Primary vertex resolution

The accurate measurement of decay lifetimes is required for the primary
physics aims of the LHCb experiment in CP violation and rare decay studies.
Precise vertex reconstruction is therefore of fundamental importance, in order
to resolve production and decay vertices.

The PV resolution is strongly correlated to the number of tracks $N$ used to
reconstruct the vertex. The analysis is performed on an event-by-event basis.
The principle is to reconstruct the same PV twice, and to determine the
difference between these two PV positions. This is achieved by splitting the
track sample of each event into two and making vertices from each independent
set of tracks. The method was verified in the simulation by comparing the
reconstructed and generator level information.

The track splitting is done entirely at random, with no ordering of tracks and
no requirement that the same number of tracks is put into each set. The vertex
reconstruction algorithm is applied to each set of tracks. Vertices are
‘matched’ between the two sets by requiring that the difference in their $z$
position is $<2$$\rm\,mm$. Then, if the number of tracks making a pair of
matched vertices is the same, the residual is calculated. Repeating for many
events yields a series of histograms of residuals in $(x,y,z)$ for varying
track multiplicity.

In practice, the number of tracks making a vertex ranges from $5$ (the
required minimum) to around $100$. However, given the track splitting method
roughly divides the total number of tracks in two, it is difficult to measure
the resolution past $40$ tracks. Each residual histogram is fitted with a
Gaussian distribution. The resolution for each particular track multiplicity
is calculated as the $\sigma$ of the fitted Gaussian divided by $\sqrt{2}$, as
there are two uncorrelated resolution contributions in each residual
measurement.

The resolution is fitted with a function which parametrises it in terms of $N$
as follows:

$\sigma_{PV}=\frac{A}{N^{B}}+C,$ (1)

where $A,B,C$ are constants.

In 2011 data it was found that a 25-track vertex has a resolution in the
transverse plane of 13$\,\upmu\rm m$, while the resolution in $z$ is
71$\,\upmu\rm m$, as shown in Fig. 29. The 2011 simulation had a resolution
approximately 2$\,\upmu\rm m$ better than in the data. For data with an
average number of visible proton-proton interactions per bunch crossing of
around 1.3, the average number of tracks in a minimum bias event containing
one PV is 55. The equivalent number in an event in which a candidate $B$ decay
has been reconstructed is 120. As the number of reconstructed PVs in the event
increases, the resolution degrades. The rate of degradation is approximately
5–10% per additional vertex. The vertex resolution results for 2012 data are
very similar.

Figure 29: PV Resolution of events with exactly one PV in 2011 data as a
function of track multiplicity. (left) $x$ (red) and $y$ (blue) resolution and
(right) $z$ resolution. The fit parameters $A$, $B$ and $C$ for each
coordinate are given.

The stability of the PV position has also been studied. In a single fill the
PV position was found to move in $x$ and $y$ by not more than 4$\,\upmu\rm m$
and 2$\,\upmu\rm m$ respectively. Based on analysing a three-month data sample
from 2012, the PV position in the LHCb coordinate system was found to move by
a maximum of 50$\,\upmu\rm m$ (RMS=16$\,\upmu\rm m$). The VELO is centred
around the beam with a maximum variation of 20$\,\upmu\rm m$ in $x$ and
40$\,\upmu\rm m$ in $y$. For a conservative estimate we apply a safety factor
of two to the total variation, and determine that the beam stability with
respect to the VELO is better than 100$\,\upmu\rm m$.

###  5.4 Impact parameter resolution

The impact parameter (IP) of a track is defined as the distance between the
track and the PV at the track’s point of closest approach to the PV. The $B$
and $D$ mesons studied in many LHCb analyses are long lived particles and
hence their decay vertex is generally displaced from the PV. The tracks made
by particles coming from the decay of long lived particles therefore tend to
have larger IPs than those made by particles produced at the PV. Consequently,
cuts on the IP are very effective at excluding prompt backgrounds, and
maximising the signal content of a data set. It is thus of great importance
for an experiment like LHCb to be able to measure IPs to a high precision, and
to have a good understanding of the effects contributing to the resolution of
IP measurements.

The IP resolution is governed by three main factors: multiple scattering of
particles by the detector material; the resolution on the position of hits in
the detector from which tracks are reconstructed; and the distance it is
required to extrapolate a track from its first hit in the detector to the PV.
An approximate analytical expression can be derived [12],

$\displaystyle\sigma_{IP}^{2}$ $\displaystyle=$
$\displaystyle\left(\frac{0.0136}{\mbox{$p_{T}$}}\sqrt{x/X_{0}}[1+0.038\ln(x/X_{0})]\right)^{2}r_{1}^{2}+\frac{\Delta_{02}^{2}\sigma_{1}^{2}+\Delta_{01}^{2}\sigma_{2}^{2}}{(\Delta_{02}-\Delta_{01})^{2}},$
(2)

where the first term is due to multiple scattering and the second term due to
the detector resolution. The particle has a transverse momentum $p_{T}$ and it
passes through a piece of material, of thickness $x$, and with radiation
length $X_{0}$. The track is extrapolated over a distance $\Delta_{01}$
between the first hit on a track and the PV, and the distance from the PV to
the second hit is $\Delta_{02}$. The resolution of the first and second hits
on the track are $\sigma_{1}$ and $\sigma_{2}$. This expression applies to a
1D IP measurement. Parametrising the resolution in the plane perpendicular to
the beam, $IP_{x}$ and $IP_{y}$, as a function of $1/p_{T}$ one expects
identical, roughly linear distributions with an $x$ or $y$-intercept dependent
on the detector resolution, and a gradient proportional to the material
budget. In 3D geometry an IP has two degrees of freedom: three as it is a
distance in 3D space, minus one from the requirement of being calculated at
the point of closest approach to the PV. Due to the forward geometry of LHCb
the $z$ component is negligible, and the IP measurement in 3D space is thus
simply the sum in quadrature of its $x$ and $y$ components. The mean offset of
such a measurement from its true value is given by the resolution on the 1D
components multiplied by $\sqrt{\pi/2}$.

The vast majority of tracks reconstructed at LHCb are made by particles
produced promptly at the PV. The measured IP of such tracks is non-zero only
due to the measurement resolution. Thus, the IP resolution can be measured by
examining the width of the $IP_{x}$ and $IP_{y}$ distributions for all tracks.
To do this, only good quality long tracks from events with only one
reconstructed PV are used. The PV is required to have at least 25 tracks
included in its fit to minimise the contribution of the vertex resolution to
the measured IP. Furthermore, the PV is refitted excluding each track in turn
before its IP is calculated so the track has no influence on the PV position.
The $IP_{x}$ and $IP_{y}$ are then plotted in bins of the variable of
interest, such as $1/p_{T}$, and a fit of a Gaussian function performed in
each bin. The width of the fitted Gaussian is taken as the resolution.

Figure 30:  $IP_{x}$ and $IP_{y}$ resolution as a function of momentum (left)
and $IP_{x}$ as a function of $1/p_{T}$ and compared with simulation (right).
Determined with 2012 data.

Figure 30 shows plots of the IP resolution versus momentum and $1/p_{T}$. The
resolution of $IP_{x}$ and $IP_{y}$ is almost identical. They are asymptotic
at high $p_{T}$, tending to $\sim$12$\,\upmu\rm m$, and depend roughly
linearly on $1/p_{T}$. The performance of the VELO in this respect is
excellent, achieving IP resolutions of $<$35$\,\upmu\rm m$ for particles with
$p_{T}$ $>$1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Figure 31: $IP_{x}$ resolution as a function of azimuthal angle $\phi$,
measured on 2011 data and compared to simulation.

The distribution of material in the VELO is non-uniform, and this also affects
IP resolutions. The excellent agreement with simulation shown in Fig. 30 was
only obtained after careful study of the material distribution in the RF foil.
In the region in which the two halves of the VELO overlap the two sides of the
RF foil also overlap, greatly increasing the material density. This can be
seen by measuring the IP resolution in bins of the azimuthal angle $\phi$, as
is shown in Fig. 31. The increase in material is reflected in the increase in
IP resolution about $\phi=\pm\pi/2$, i.e. in the overlap region.

Thus, it can be seen that the VELO provides accurate IP measurements on which
the LHCb physics programme relies for the rejection of prompt backgrounds to
long-lived heavy flavour hadron decays. The IP resolution behaves as expected,
with a roughly linear dependence on $1/p_{T}$, and a clear dependence on both
the hit resolution and the distribution of material.

###  5.5 Decay time resolution

The reconstructed decay time of strange, charm and beauty hadrons is used in
offline event selections and in precise measurements of lifetimes. However,
the most stringent demands on the decay time resolution stem from the
requirement to resolve the fast oscillations induced by $B^{0}_{s}$–$\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ mixing. Consequently, we
illustrate the performance of the VELO with an analysis of the decay time
resolution of $B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\phi$ decays.

The reconstructed decay time in the rest frame of the decaying particle can be
expressed in terms of the reconstructed decay length $l$, momentum $p$ and
mass $m$ of the particle in the LHCb frame as

$t\;=\;\frac{m\>l}{p}.$ (3)

The decay time is computed with a vertex fit that constrains the decaying
particle to originate from the PV. The decay time uncertainty is a function of
the actual decay time. For small decay times it is dominated by the resolution
on the decay length $l$, which in turn is dominated by the secondary vertex
resolution of the VELO. For large decay times, it is dominated by the
momentum, which is mostly determined by the tracking stations before and after
the LHCb magnet. The two contributions are approximately equal at several
times the $B$ hadron lifetime. Therefore, the momentum resolution plays only a
small role.

Time dependent $CP$ violation effects are measured as the amplitude of an
oscillation in the $B$ decay time distribution. The size of the observed
amplitude is damped by a dilution factor from the finite decay time
resolution. For a resolution function that is a single Gaussian function with
RMS $\sigma_{t}$, the dilution is

$D\;=\;\exp\left[-\frac{1}{2}\Delta m^{2}\sigma_{t}^{2}\right],$ (4)

where $\Delta m$ is the mixing frequency.

The sensitivity to the oscillation amplitude is proportional to the dilution.
Therefore, for optimal sensitivity the dilution must be as close to unity as
possible. However, even more important is the understanding of the dilution
itself, since a bias in the estimated dilution leads to a bias in the
measurement of a $CP$ violating effect.

The decay time resolution depends on the topology of the decay and is
calibrated for each final state on data. The calibration method uses prompt
combinations that fake signal candidates. Ignoring the small contribution from
signal candidates and long-lived background, the shape of the prompt peak is
determined only by the resolution function. Figure 32 (left) shows the decay
time distribution for fake
$B^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\phi\rightarrow\mu^{+}\mu^{-}K^{+}K^{-}$ decays in data and simulation.
The $B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$
candidate selection is described in Ref. [8]. The contribution from signal
decays (which would result in a tail on the right of the distribution) is
removed. The RMS values quoted in the figure are computed using events with
negative decay time or decay length only, to reduce the sensitivity to a small
contribution from other $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}X$ decays. For a mixing frequency of 17.7${\rm\,ps^{-1}}$, the decay
time resolution corresponds to a dilution of about $0.7$.

Figure 32: Decay time (left) and decay length (right) distribution for fake,
prompt $B^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\phi\rightarrow\mu^{+}\mu^{-}K^{+}K^{-}$ candidates in 2011 data (black
points) and simulation (solid red histogram). Only events with a single PV are
used. The simulated data are generated inclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ events from which signal
$B^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$ are
removed. In the data contributions from
non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ di-muon combinations and
from true $B^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip