high-occupancy part of the detector. Decays in flight are the main cause of
misidentification of pions and kaons as muons. To a good approximation, the
misidentification rate is the sum of the contribution of decays in flight and
the proton misidentification probability.

The background rejection power can be improved by the computation of a
likelihood for the muon and non-muon hypotheses, based on the pattern of hits
around the extrapolation to the different muon stations of the charged
particles trajectories reconstructed with high precision in the tracking
system. The logarithm of the ratio between the muon and non-muon hypotheses,
$\rm\Delta log\mathcal{L}(\mu)$, is used as a discriminating variable. The
likelihood for the non-muon hypothesis is calibrated using proton data, since
the other charged hadrons (pions or kaons) selected as muons will have a
component identical to the protons and a component very similar to the true
muons, due to decays in flight before the calorimeter. The muon likelihood has
been calibrated with muons from $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays
selected from data, while the non-muon likelihood has been calibrated with a
simulated sample of $\Lambda\rightarrow p\pi^{-}$ decays.

###  4.4 Combined particle identification performance

The PID information obtained separately from the muon, RICH, and calorimeter
systems is combined to provide a single set of more powerful variables. Two
different approaches are used. In the first method the likelihood information
produced by each sub-system is simply added linearly, to form a set of
combined likelihoods, $\Delta{\rm log}{\mathcal{L}}_{comb}(X-\pi)$, where $X$
represents either the electron, muon, kaon or proton mass hypothesis. These
variables give a measure of how likely the mass hypothesis under consideration
is, for any given track, relative to the pion hypothesis. A second approach
has been subsequently developed to improve upon the simple log likelihood
variables both by taking into account correlations between the detector
systems and also by including additional information. This is carried out
using multivariate techniques [84], combining PID information from each sub-
system into a single probability value for each particle hypothesis.

Figure 42: Electron identification performance using the $\Delta{\rm
log}{\mathcal{L}}_{comb}(e-\pi)$ variable, as measured in 8 TeV collision
data, using a tag and probe technique with electrons from the decay
$B^{\pm}\rightarrow(J/\psi\rightarrow e^{+}e^{-})K^{\pm}$. Left, pion
misidentication rate versus electron identification probability when the cut
value is varied. Right, electron identification efficiency and pion
misidentification rate as a function of track momentum, for two different cuts
on $\Delta{\rm log}{\mathcal{L}}_{comb}(e-\pi)$.

To illustrate the improvement made by combining information from different
sub-detectors, the performance of the variable $\Delta{\rm
log}{\mathcal{L}}_{comb}(e-\pi)$ is first considered, using a similar tag and
probe technique to that of Section 4.1.2 in which the calorimeter-only
performance is presented. Figure 42 shows the pion misidentification versus
electron identification probability, for various cuts on $\Delta{\rm
log}{\mathcal{L}}_{comb}(e-\pi)$. Compared to Figure 35 the improvement in the
misidentification rate can clearly be seen, e.g. at $\sim 90\,\%$ electron
efficiency the pion misidentification rate drops from $\sim 6\,\%$ to $\sim
0.6\,\%$.

An improvement in performance can also be seen for the muon identification, as
illustrated by one of the most prominent LHCb results, the measurement of the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ branching fraction and the search for
$B^{0}\rightarrow\mu^{+}\mu^{-}$ decays [8]. The $B^{0}_{(s)}\rightarrow
h^{+}h^{-}$ decay modes, where $h=(K,\pi)$, can fake a signal if both hadrons
are misidentified as muons. Therefore the minimisation of these backgrounds is
of paramount importance for this analysis. This double misidentification
probability has been evaluated by folding the $K\rightarrow\mu$ and
$\pi\rightarrow\mu$ fake rates extracted from a $D^{0}\rightarrow K\pi$ sample
from $D^{*+}\rightarrow D^{0}\pi^{+}$ decays, in bins of $p$ and $p_{\rm T}$,
into the spectrum for selected simulated $B^{0}_{(s)}\rightarrow h^{+}h^{-}$
events. If the tracks identified as muons are also required to satisfy a
selection using the combined PID information ($\Delta{\rm
log}{\mathcal{L}}_{comb}(K-\pi)<10$ and $\Delta{\rm
log}{\mathcal{L}}_{comb}(\mu-\pi)>-5$), the $B^{0}_{(s)}\rightarrow
h^{+}h^{-}$ misidentification probability is reduced by a factor of $\sim 6$,
whilst only $\sim 3\%$ of the $B_{s}\rightarrow\mu^{+}\mu^{-}$ signal is lost.

Figure 43: Background misidentification rates versus muon (left) and proton
(right) identification efficiency, as measured in the $\Sigma^{+}\rightarrow
p\mu^{+}\mu^{-}$ decay study. The variables $\Delta{\rm
log}{\mathcal{L}}(X-\pi)$ (black) and ProbNN (red), the probability value for
each particle hypothesis, are compared for
$5-10$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ muons and
$5-50$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ protons, using data sidebands for
backgrounds and Monte Carlo simulation for the signal.

The possible improvement of the multivariate approach with respect to the
simple log likelihood may also be illustrated by the ongoing search for the
flavour-changing neutral current decay $\Sigma^{+}\rightarrow
p\mu^{+}\mu^{-}$. In Figure 43 the misidentification rates versus efficiency
curves for the $\Delta{\rm log}{\mathcal{L}}(X-\pi)$ and the probability value
for each particle hypothesis variables are shown. The improvement is clearly
visible for both muons and protons. These multivariate variables will be
further developed and utilised more extensively during Run II.

##  5 Trigger

The LHCb trigger consists of two levels; Level-0 (L0) and the High Level
Trigger (HLT). In Run I the trigger reduced the rate of events to be saved for
physics analysis to 2 – 5${\rm\,kHz}$.

The L0 trigger is implemented in hardware and makes decisions based on
information from the calorimeter and muon systems in order to reduce the event
rate to below $1$${\rm\,MHz}$, at which point the whole detector can be read
out. The HLT is a software application running on the event filter farm (EFF).
A fraction of L0 accepted events are deferred to disk for processing by the
HLT during the inter-fill time, optimising the use of available EFF resources.

After the HLT, events are stored and later processed with a more accurate
alignment and calibration of the sub-detectors, and with the reconstruction
software described in Section 2.2. This part of the reconstruction and
subsequent selection of interesting events is referred to as the offline
reconstruction and selection for the remainder of this discussion.

Section 5.1 describes a data-driven method to determine the efficiency and
purity of the signals that are selected by the LHCb trigger. The
implementation of the L0 trigger [25] is briefly summarised in Section 5.2 and
the performance of the HLT [85] is discussed in Section 5.3. The selection
criteria used in the two trigger levels during 2011 and 2012 are described in
detail in Reference [86]. The deferral system is discussed in Section 5.4 and
a short summary of the LHCb trigger is provided in Section 5.5.

The results presented here are based on the configuration and performance of
the LHCb trigger during 2012 when the deferral system was first used and the
majority of the Run I dataset was collected.

###  5.1 Data driven trigger performance determination

The trigger efficiencies are evaluated using events reconstructed with the
full offline software, and are calculated with respect to candidates selected
by the full offline analysis of the respective channel, excluding the trigger.
They therefore quantify the inefficiencies due to the simplified
reconstruction, possible misalignments and reduced resolution, as compared to
the offline reconstruction. They also account for any tighter selection
requirements that are needed to satisfy the rate and processing time
limitations. The following decay channels are chosen to highlight the
performance of the trigger 111Here, and in the following, charge conjugated
decays are implicitly included. :

  * •

$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays,
with ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$.
This decay evaluates the muon trigger efficiency and serves as a proxy for
several key physics decay channels like
$B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$,
$B^{0}\\!\rightarrow K^{*0}\mu^{+}\mu^{-}$ or
$B^{0}_{s}\\!\rightarrow\mu^{+}\mu^{-}$.

  * •

$B^{0}\\!\rightarrow K^{+}\pi^{-}$ as a typical two-body hadronic beauty
decay.

  * •

$B^{0}\\!\rightarrow D^{+}\pi^{-}$ with $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$, as a typical four-body beauty decay.

  * •

$D^{0}\rightarrow K^{-}\pi^{+}$ as a two-body charm decay.

  * •

$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ represents a three-body charm decay.

  * •

$D^{*+}\rightarrow D^{0}\pi^{+}$, followed by the four-body charm decay
$D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$.

These decay channels and their selections are representative of the trigger
needs of the core physics analyses of the LHCb experiment. The selected charm
modes cover the topologies that are most sensitive to $C\\!P$ violating
effects. All samples used in this study carry a large signal to background
ratio. Nevertheless, the yields are determined by fitting the signal peaks in
the invariant mass distributions in order to subtract the residual background.

In the following, the term ‘signal’ refers to a combination of tracks forming
the offline reconstructed and selected $b$\- or $c$-hadron candidates. To
determine the trigger efficiency, trigger objects are associated with signal
tracks. The criteria used to associate a trigger object with a signal track
are as follows. An event is classified as Trigger on Signal (TOS) if the
trigger objects that are associated with the signal candidate are sufficient
to trigger the event. An event is classified as Trigger Independent of Signal
(TIS) if it has been triggered by trigger objects that are not associated with
the signal. Some events can be classified as TIS and TOS simultaneously (${\rm
TIS~{}\&~{}TOS}$), which allows the determination of the trigger efficiency
relative to the offline reconstructed events from data alone. The efficiency
to trigger an event independently of the signal, $\epsilon^{\rm TIS}$, is
given by

$\epsilon^{\rm TIS}=N^{\rm TIS~{}\&~{}TOS}/N^{\rm TOS}\,,$

where $N^{\rm TOS}$ is the number of events classified as TOS. The efficiency
to trigger an event on the signal alone, $\epsilon^{\rm TOS}$, is given by

$\epsilon^{\rm TOS}=N^{\rm TIS~{}\&~{}TOS}/N^{\rm TIS}\,,$

where $N^{\rm TIS}$ is the number of events classified as TIS. This method of
measuring trigger efficiencies is discussed in detail in Reference [87].

###  5.2 Level-0 hardware trigger

The L0 trigger is divided into three independent units; the L0-Calorimeter
trigger, the L0-Muon trigger and the L0-PileUp trigger, the latter being used
only for the determination of the luminosity [27]. The L0 trigger system is
fully synchronous with the 40${\rm\,MHz}$ bunch crossing rate of the LHC. The
latencies are fixed and are independent of the occupancy or the bunch crossing
history.

Table 4: Typical L0 thresholds used in Run I [86]. |  $p_{\rm T}$ or $E_{\rm T}$ |  SPD
---|---|---
|  2011 |  2012 | 2011 and 2012
single muon | 1.48${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | 1.76${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | 600
dimuon $\mbox{$p_{\rm T}$}_{1}\times\mbox{$p_{\rm T}$}_{2}$ | $(1.30\mathrm{\,Ge\kern-1.00006ptV}/c)^{2}$ | $(1.60\mathrm{\,Ge\kern-1.00006ptV}/c)^{2}$ | 900
hadron | 3.50$\mathrm{\,Ge\kern-1.00006ptV}$ | 3.70$\mathrm{\,Ge\kern-1.00006ptV}$ | 600
electron | 2.50$\mathrm{\,Ge\kern-1.00006ptV}$ | 3.00$\mathrm{\,Ge\kern-1.00006ptV}$ | 600
photon | 2.50$\mathrm{\,Ge\kern-1.00006ptV}$ | 3.00$\mathrm{\,Ge\kern-1.00006ptV}$ | 600

The L0-Calorimeter system uses information from the SPD, PS, ECAL and HCAL
detectors, as described in Section 3. It computes the transverse energy,
$E_{\rm T}$, deposited by incident particles in clusters of $2\times 2$ cells.
From these clusters, the following three types of candidates are built.
L0Hadron is the highest $E_{\rm T}$ HCAL cluster, which also contains the
energy of the matching ECAL cluster. L0Photon is the highest $E_{\rm T}$ ECAL
cluster with 1 or 2 PS hits in front of the ECAL cluster and no hit in the SPD
cells corresponding to the PS cells. L0Electron has the same requirements as
L0Photon, with the additional condition of at least one SPD cell hit in front
of the PS cells. The $E_{\rm T}$ of each candidate is compared to a fixed
threshold and events containing at least one candidate above threshold fire
the L0 trigger. The total number of hits in the SPD is also determined, and is
used to veto events that would take a disproportionately large fraction of the
available processing time in the HLT. The SPD hit multiplicity requirements
are listed in Table 4.

The L0 muon processors look for the two highest $p_{\rm T}$ muon tracks in
each quadrant. The position of a track in the first two stations allows the
determination of its $p_{\rm T}$ with a measured momentum resolution of
roughly $25\%$. The trigger considers the eight candidates and sets a single
threshold on either the largest transverse momentum, $\mbox{$p_{\rm T}$}^{\rm
largest}$, or on the product, $\mbox{$p_{\rm T}$}^{\rm
largest}\times\mbox{$p_{\rm T}$}^{\rm 2nd~{}largest}$. These thresholds are
listed in Table 4. The tightening of L0 thresholds in the 2012 configuration
is a consequence of the increased luminosity and beam energy.

The trigger efficiencies are measured on offline selected events, using the
techniques described in Section 5.1. The efficiencies of the L0 muon triggers
evaluated on $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$ events are shown in Figure 44. The majority of events are
accepted by the single muon trigger. The largest inefficiency originates from
the tight muon identification requirements inside the L0 reconstruction
algorithm. The L0 dimuon trigger selects a small fraction of additional
candidates at lower transverse momenta. The combined efficiency for both L0
muon triggers is evaluated to be $89\pm 0.5\%$ [87].

Figure 44:  (left) L0 muon trigger performance: TOS trigger efficiency for
selected $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$ candidates. (right) L0 hadron trigger performance: TOS trigger
efficiency for different beauty and charm decay modes.

The L0 hadron efficiency is shown in Figure 44 for the two- and three-prong
beauty decays $B^{0}\\!\rightarrow K^{+}\pi^{-}$ and $B^{0}\\!\rightarrow
D^{+}\pi^{-}$ and the two-, three- and four-prong charm decays
$D^{0}\rightarrow K^{-}\pi^{+}$, $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ and
$D^{*+}\rightarrow D^{0}\pi^{+}$, as a function of the $B$ or $D$ meson
$p_{\rm T}$. The two-prong beauty decay is triggered with highest efficiency
by the L0 hadron $E_{\rm T}$ criterion ($\epsilon^{\rm TOS}$ = 40%) while the
four-prong charm decay $D^{*+}\rightarrow D^{0}\pi^{+}$ is selected with the
lowest efficiency ($\epsilon^{\rm TOS}$ = 22%). The other modes lie in
between, as shown in Figure 44. With the inclusion of TIS triggers, the total
efficiencies increase significantly, e.g. from 40% to 53% for
$B^{0}\\!\rightarrow K^{+}\pi^{-}$.

The total output rate of the L0 trigger is limited to 1${\rm\,MHz}$, which is
the maximum rate at which the LHCb detector can be read out. This output rate
consists of approximately 400${\rm\,kHz}$ of muon triggers, 500${\rm\,kHz}$ of
hadron triggers and 150${\rm\,kHz}$ of electron and photon triggers, where the
individual triggers have an overlap of about 10%.

###  5.3 High Level Trigger

Events accepted by L0 are transported by the data acquisition network to one
of the processors of the EFF. The HLT is a software application, of which 29
500 instances run on the EFF, and each instance consists of independently
operating trigger “lines”, each of which consists of selection parameters for
a specific class of events.

The HLT is based on the same software framework used throughout LHCb. Given
the available resources in the EFF, the time per event is around fifty times
smaller than in the offline processing. The HLT is divided in two levels. In
the first level (HLT1), a partial event reconstruction is performed. In the
second level (HLT2), the complete event is reconstructed. Where time allows,
the HLT uses the same reconstruction algorithms as employed offline, with some
simplifications that are needed to satisfy the time constraints.

####  5.3.1 First level

The offline VELO reconstruction algorithm which performs a full 3D pattern
recognition is sufficiently fast to be run on all events entering the HLT.
However, the offline algorithm makes a second pass on unused hits to enhance
the efficiency for tracks pointing far away from the beam-line, while in the
HLT this second pass is not used due to CPU constraints. Vertices are
reconstructed from a minimum of five intersecting VELO tracks. Vertices within
a radius of $300$$\,\upmu\rm m$ of the mean position of the $pp$-interaction
envelope are considered to be primary vertices.

HLT1 limits the number of VELO tracks that are passed through the forward
tracking algorithm that searches for matching hits in the tracking stations.
VELO tracks must have a significant IP with respect to all PVs, or be matched
to muon chamber hits by a fast muon identification algorithm. This algorithm
is only run in events that were triggered by a muon line in the hardware step.
To further limit the processing time, the forward track search has a minimum
momentum requirement that varied between 3 and
6${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ during Run I. VELO tracks without
matching muon hits are also subject to a minimum $p_{\rm T}$ threshold that
varied between 0.5 and 1.25${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The
reconstructed forward tracks are fitted using a Kalman filter with a
simplified detector geometry description and fewer iterations than in the
offline configuration. The invariant mass resolution of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$
candidates reconstructed with this procedure is found to be $3\%$ worse than
the 15.1${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ obtained offline. For
tracks identified as muon candidates, the basic offline muon identification
algorithm [83] is applied to increase the purity of the muon sample.

The inclusive beauty and charm trigger is based on the properties of one good
quality track candidate. The selection is based on track $p_{\rm T}$ (typical
value $\mbox{$p_{\rm T}$}>1.6-1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) and
displacement from the primary vertex (typical value IP $>0.1$ mm). This
trigger line produces around 58${\rm\,kHz}$ of output, which is the largest
contribution to the allocated HLT1 bandwidth. It is the most efficient line
for physics channels that do not contain leptons in the final state. The
performance of HLT1 for hadronic signatures is shown in Figure 45 as a
function of the $p_{\rm T}$ of the resonance considered. The inclusive one-
track based trigger also exists in a version for electrons or photons
identified by L0, with reduced thresholds relative to the inclusive version.
The output rate of these lines is around 7${\rm\,kHz}$.

A similar line exists for tracks that are matched to hits in the muon chambers
[88]. This single muon trigger line selects good quality muon candidates that
are displaced from the primary vertex and satisfy $\mbox{$p_{\rm
T}$}>1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Single muon candidates that
satisfy $\mbox{$p_{\rm T}$}>4.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are
selected by a special trigger line without any vertex separation requirements.

Dimuon candidates are either selected based on their mass
($m_{\mu\mu}>2.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$) without any
displacement requirement, or based on their displacement without the mass
restriction. The dominant inefficiency for these lines originates from the
online muon identification algorithms. The performance of HLT1 on muonic
signatures as a function of $p_{\rm T}$ of the $B^{+}$ parent is shown in
Figure 45. The single muon line has an efficiency of around 90% to select
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays,
while the dimuon lines have an efficiency of around 70%. The combination of
muon trigger lines produces an output rate of around 14${\rm\,kHz}$.

Figure 45:  HLT1 inclusive track trigger performance: TOS efficiency for
various channels as a function of $B$ or $D$ $p_{\rm T}$ (left) . HLT1 muon
trigger performance : TOS efficiency for
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$
candidates as function of $B^{+}$ $p_{\rm T}$ (right).

In addition to the trigger lines discussed above, several dedicated lines are
implemented to enhance the trigger performance for events containing
candidates for high $p_{\rm T}$ electrons, di-protons, displaced vertices or
high $E_{\rm T}$ jets. A set of technical lines including selections for
luminosity and beam-gas measurements completes the list of HLT1 triggers.

####  5.3.2 Second level

HLT1 reduces the event rate to about 80${\rm\,kHz}$, which is sufficiently low
to allow the forward tracking of all VELO tracks in HLT2. As described in
Section 2.2, the offline reconstruction uses two complementary tracking
algorithms. Due to the CPU constraints, HLT2 only searches for long tracks
based on VELO seeds. This simplification leads to a lower tracking efficiency
compared to the offline reconstruction of $1-2\%$ per track.

The processing time is further reduced by restricting the search to tracks
with $p>3$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\mbox{$p_{\rm
T}$}>0.3$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Muon identification in HLT2
is performed using the offline muon identification algorithm. Tracks are also
associated to ECAL clusters to identify electrons. Photons and neutral pions
are built starting from the energy clusters reconstructed by the
L0-Calorimeter system.

#### Generic beauty trigger

A significant portion of the output rate of HLT2 is selected by the
‘topological’ lines, which are designed to trigger on partially reconstructed
$b$-hadron decays. These topological lines cover all $b$-hadron decays with at
least two charged particles in the final state and a displaced decay vertex.
The inclusive nature of these lines makes them less susceptible to the $1-2\%$
loss in efficiency per reconstructed track in HLT2. Tracks are selected based
on their track fit $\chi^{2}/\rm ndf$, IP and muon or electron identification.
Two-, three- or four-body vertices are constructed from the selected tracks
with a requirement on their distance of closest approach (DOCA).

Candidate $n$-body combinations are selected based on the following variables:
$\sum|\mbox{$p_{\rm T}$}|,~{}p^{\rm min}_{\rm T}$, $n$-body invariant mass
($m$), DOCA, IP$\chi^{2}$ and flight distance (FD) $\chi^{2}$. In addition,
the corrected mass is defined as $m_{\rm corr}=\sqrt{m^{2}+|p^{\prime}_{\rm
Tmiss}|^{2}}+|p^{\prime}_{\rm Tmiss}|$, where $p^{\prime}_{\rm Tmiss}$ is the
missing momentum transverse to the line of flight between the $n$-body vertex
and the PV to which it has the smallest IP [89]. Figure 47 shows the
reconstructed 2-body and corrected mass distributions for $B^{0}\\!\rightarrow
K^{*0}\mu^{+}\mu^{-}$ events. These variables are combined using a boosted
decision tree trained on simulated signal events and data taken in 2010 [90].
An explicit veto on prompt charm is also applied to reduce its output rate.

Figure 46:  Simulated $B^{0}\\!\rightarrow K^{*0}\mu^{+}\mu^{-}$ events. The
reconstructed 2-body mass is shown in red and the corrected mass ($m_{\rm
corr}$, see text for definition) is shown in black.

Figure 47:  HLT2 inclusive beauty trigger performance as a function of $B$
$p_{\rm T}$. The efficiency for the exclusive $B^{0}\\!\rightarrow
K^{+}\pi^{-}$ trigger line is also given.

Figure 47 shows the efficiency for the topological trigger lines for
$B^{0}\\!\rightarrow K^{+}\pi^{-}$ and $B^{0}\\!\rightarrow D^{+}\pi^{-}$
events as well as the additional efficiency that can be gained by an exclusive
selection for $B^{0}\\!\rightarrow K^{+}\pi^{-}$ in the low $p_{\rm T}$
regime. The output rate of the topological trigger is 2${\rm\,kHz}$, in which
it efficiently selects beauty decays to charged tracks. For example, the
efficiencies for $B^{0}\\!\rightarrow K^{+}\pi^{-}$ and $B^{0}\\!\rightarrow
D^{+}\pi^{-}$ decays are approximately 78% and 76%, respectively.

If one of the tracks forming the generic beauty trigger decision is identified
as a muon, the selection on the boosted decision tree classifier is loosened
which enhances the efficiency for muonic beauty decays like
$B^{0}\\!\rightarrow K^{*0}\mu^{+}\mu^{-}$.

#### Muon triggers

Several trigger lines select events that contain one or two muons. The muon
identification procedure in HLT2 is identical to that which is used offline
[83]. Single muon candidate events are selected if the muon passes a tight
$p_{\rm T}$ requirement ($\mbox{$p_{\rm
T}$}>10{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) or if candidates are
inconsistent with originating from the PV and they satisfy moderate $p_{\rm
T}$ ($\mbox{$p_{\rm T}$}>1.3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) and tight
track quality requirements. Candidates selected with the latter criteria are
prescaled by factor of two.

Dimuon candidate events are selected without a mass requirement if the dimuon
vertex is separated from the primary vertex. If the mass of the muon pair is
within $\pm 100$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ ($\sim 8\sigma$) of
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass, three trigger
selections are considered. Decay-time unbiased
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$
candidates are extensively used for calibration of the LHCb decay time
acceptance. Therefore, all muon pairs with $\mbox{$p_{\rm
T}$}>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are considered, as well as a
fraction of those without any $p_{\rm T}$ requirement. These two prompt
selections are complemented by an additional detached
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ trigger. The separation
requirement of this trigger is looser than that of the generic detached dimuon
trigger described above.

This set of lines is optimised to fully exploit the large physics potential of
both prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X$ decays. Relative
to the offline selection, the trigger efficiencies are typically above 90%.
Figure 48 shows the performance of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ triggers, where the effective prescale of about a factor of two on the
prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ line is visible, as well
as the $p_{\rm T}$ acceptance of the high $p_{\rm T}$ line. The total output
rate of all single and dimuon trigger lines is around $1\,{\rm\,kHz}$.

Figure 48:  HLT2 muon trigger performance for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ trigger lines (left). The
triggers Hlt2DiMuonJPsi and Hlt2DiMuonJPsiHighPT are the two prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ triggers and
Hlt2DiMuonDetachedJPsi is the trigger that selects
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates that are
inconsistent with coming from the primary vertex. HLT2 charm trigger
performance for inclusive and exclusive selections (right). The decay
$D^{*+}\rightarrow D^{0}\pi^{+}$ is followed by $D^{0}\rightarrow
K^{-}\pi^{+}\pi^{+}\pi^{-}$.

#### Charm triggers

In the 2012 running conditions, roughly $600$${\rm\,kHz}$ of $c\bar{c}$-events
are produced within the acceptance of LHCb. This large rate of charm
production means that tight exclusive selections are required in the trigger.
The exception is the decay chain $D^{*+}\rightarrow D^{0}\pi^{+}$, which can
be selected inclusively, i.e. only reconstructing two charged tracks from the
$D^{0}$ decay matched to a slow pion from the $D^{*+}$ decay. The mass
difference between the $D^{*+}$ and $D^{0}$ candidates remains a good
discriminating variable, enabling the rate to be sufficiently reduced. The
$D^{0}$ is partially reconstructed in all combinations containing $\pi^{\pm}$,
$K^{\pm}$, $p$, $\mu^{\pm}$, $K^{0}_{\rm\scriptscriptstyle S}$ or
$\Lambda^{0}$ enabling both rare decay and $C\\!P$ violation measurements.

The dominant exclusive selections for prompt charm are the hadronic two body
and three body lines. The efficiency of these triggers is summarised in Figure
48. Additional selections for hadronic, leptonic and semi-leptonic $D$ and
$\mathchar 28931\relax_{c}^{+}$ decays are implemented. The total output rate
of all charm selections is $\sim 2$${\rm\,kHz}$, but the trigger efficiencies
strongly depend on the offline selection: using a pure sample of
$D^{0}\rightarrow K^{-}\pi^{+}$ events from $D^{*+}$ decays, the HLT2
efficiency is 90%, while the trigger efficiency for the multibody decay
$D^{*+}\rightarrow D^{0}\pi^{+}$ is 26%.

#### Exclusive and technical lines

The HLT incorporates a large number of exclusive and technical trigger lines
to complement the signal selection by the inclusive lines discussed above. For
example, 100${\rm\,Hz}$ of random events are recorded throughout the full data
taking period. These events can be used to understand the trigger system, for
fast monitoring of the data and for luminosity determinations. A number of
trigger lines also exist that maximise the performance for decays with
electrons or photons in the final state [91]. A single muon line with hard
$p_{\rm T}$ requirements is designed to select heavy particles decaying
promptly to one or more muons, like $W^{\pm}$ or $Z^{0}$ for electroweak
measurements.

The remaining lines are required for luminosity measurements, prescaled
physics lines with looser cuts, lines which trigger on low multiplicity events
and lines which look for large transverse momentum jets. The trigger also
contain lines that pass events for monitoring to allow fast feedback on the
quality of the data.

###  5.4 Deferred trigger

The LHC delivers stable beams $\sim 30\%$ of the available time, and thus
unless otherwise occupied the EFF would be idle the remaining $\sim 70\%$ of
the time. Therefore to maximise the use of available resources, LHCb developed
a deferred triggering system for data taking in 2012[92, 93]. Around $20\%$ of
the L0 accepted events are temporarily saved on the EFF node local disks and
these events are subsequently processed by the HLT during the inter-fill
periods. The effective increase in CPU resources this provides was used to
reduce the $p_{\rm T}$ requirement in the forward tracking algorithm and to
include additional tracking algorithms that allow the reconstruction of tracks
from particles that decay beyond the VELO acceptance. These modifications
significantly enhance the efficiency for charm decays.

An additional benefit of this system is that it provides redundancy against
problems downstream in the dataflow. Prior to the adoption of this scheme,
such problems would quickly lead to back-pressure all the way up into the farm
and lead to dead-time. In the deferred trigger scheme, although the fraction
of deferred events would increase, no dead-time would be incurred. The
deferred trigger requires a substantial amount of local disk space, which was
added to the farm before the 2012 run. The requirements on the performance of
the disks are modest222The input data rate per farm-server is about 60 MB/s,
which is significantly lower than the typical disk performance of about 120
MB/s., such that inexpensive desktop hard drives could be used.

###  5.5 Trigger performance summary

The LHCb trigger system has delivered a range of physics modes with high
efficiency in the first running phase of the LHC. It is primarily designed to
select charm and beauty hadrons over a large range of momentum and decay time,
and its efficiency can be determined directly from the data.

The flexible design of the HLT, which is fully deployed in software, allows
for the rapid adaptation to changes in running conditions and physics goals.
Several innovative concepts have been developed that enable inclusive
selections to be utilised in the full trigger chain and thus provide an
efficient trigger for nearly any beauty decay to charged particles. The
deferred triggering permits optimisation of computing resources for mean
instead of peak usage, leading to an effective increase in farm size in 2012
of 20 – 30%. Multivariate selections allow the inclusive triggering of beauty
decays to charged tracks with high efficiency.

Table 5: Efficiencies of selected channels for the whole trigger chain using the 2012 trigger configuration. The efficiencies are normalised to the number of events that are offline selected. channel |  L0 |  HLT1 |  HLT2
---|---|---|---
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$ | 89% | 92% | 87%
$B^{0}\\!\rightarrow K^{+}\pi^{-}$ | 53% | 97% | 80%
$B^{0}\\!\rightarrow D^{+}\pi^{-}$, $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ | 59% | 98% | 77%
$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ | 44% | 89% | 91%
$D^{*+}\rightarrow D^{0}\pi^{+}$, $D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$ | 49% | 93% | 30%

Typical trigger efficiencies for selected signals are summarised in Table 5.
The trigger efficiency is high for muonic $b$-decays. For hadronic $b$-decays,
the hardware trigger stage causes a significant loss of efficiency, but the
software component remains efficient. The trigger efficiency for multibody
charm decays is lower than for $b$-hadron decays, due to the softer momentum
spectra of the final state particles.

The LHCb trigger system also efficiently covers physics beyond the core beauty
and charm programme. This includes $W^{\pm}$ or $Z^{0}$ production, inclusive
particle production, and exotic phenomena, for instance displaced vertices
from heavy long-lived particles.

##  6 Conclusion and outlook

During the first running period of the LHC between 2009 and 2013, the LHCb
experiment recorded a total of about 3.2$\mbox{\,fb}^{-1}$ of integrated
luminosity with $pp$ collisions at centre-of-mass energies of of 0.9, 7 and
8$\mathrm{\,Te\kern-1.00006ptV}$, and 1.6$\mbox{\,nb}^{-1}$ of integrated
luminosity with proton-lead collisions. The majority of the data were recorded
under conditions corresponding to a luminosity of $4\times
10^{32}\mathrm{\,cm^{-2}s^{-1}}$, a bunch spacing of 50${\rm\,ns}$ and a pile-
up of 1.8. Despite the fact that these are significantly more challenging than
the conditions originally foreseen for the experiment, it has been
demonstrated that the performance of each sub-system and the global
performance of the detector are in good agreement with the original
expectations presented in the LHCb detector paper [25]. For some physics
analyses the original expectations are even exceeded, thanks to new ideas and
well understood backgrounds.

During Run II of the LHC, the LHCb experiment expects to collect an additional
5$\mbox{\,fb}^{-1}$ of data, which improves the prospects for observing
physics beyond the Standard Model using heavy quark flavours as a tool.
However, the read-out and trigger scheme of the current LHCb detector limit
the luminosity that can be recorded. To overcome these limitations, the LHCb
experiment will be upgraded [94, 95, 96, 97, 98, 99] to allow the detector to
be read out at the maximum LHC bunch crossing rate of 40${\rm\,MHz}$ with a
flexible software-based trigger. This will not only allow the data rate to be
increased substantially, but will also increase the trigger efficiency,
especially for channels currently triggered at the hardware level by energy
deposits in the calorimeters. In addition to the significant increase in
sensitivity for flavour physics, the experiment will continue to explore other
interesting signatures and thus act as a general purpose detector in the
forward region.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

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Sánchez7, M. Martinelli39, D. Martinez Santos42,38, F. Martinez Vidal64, D.
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Petrolini19,j, E. Picatoste Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25,
A. Pistone19, S. Playfer50, M. Plo Casasus37, F. Polci8, A. Poluektov48,34, I.
Polyakov31, E. Polycarpo2, A. Popov35, D. Popov10, B. Popovici29, C.
Potterat2, E. Price46, J.D. Price52, J. Prisciandaro39, A. Pritchard52, C.
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I. Raniuk43, N. Rauschmayr38, G. Raven42, F. Redi53, S. Reichert54, M.M.
Reid48, A.C. dos Reis1, S. Ricciardi49, S. Richards46, M. Rihl38, K.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
63National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
64Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
65Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41
66Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy