# The LHCb Trigger and its Performance in 2011

R. Aaijo J. Albrechtm F. Alessiom S. Amatoa E. Aslanidesd I. Belyaevi M. van
Beuzekomo E. Bonaccorsim R. Bonnefoyc L. Brardam O. Callote M. Cattaneom H.
Chanalc M. Chebbim X. Cid Vidall M. Clemencicm J. Closierm V. Cocoo J. Cogand
O. Deschampsc H. Dijkstram Corresponding author. C. Drancourtb R. Dzhelyadinj
M. Frankm M. Gandelmana C. Gasparm V.V. Gligorovm C. Göbelv L.A. Granado
Cardosom Yu. Guzj C. Haenm J. Hee E. van Herwijnenm W. Hulsbergeno R.
Jacobssonm B. Jostm T.M. Karbachm U. Kerzelm P. Koppenburgo G. Krockerf C.
Langenbruchm I. Laxg R. Le Gacd R. Lefèvrec J. Lefrançoise O. Leroyd L. Li
Gioic G. Lium F. Macheferte I.V. Machikhiliyanb,i M. Magnec G. Mancinellid U.
Marconig A. Martín Sáncheze M.-N. Minardb S. Monteilc N. Neufeldm V. Niessc S.
Oggeroo A. Pérez-Calero Yzquierdok P. Perretc M. Perrin-Terrind B. Pietrzykb
A. Puig Navarron G. Ravenp P. Robbee H. Ruizk M.-H. Schunee R. Schwemmerm J.
Serranod I. Shapovalq,m T. Skwarnickiu B. Souza De Paulaa P. Spradlinr S.
Stahlf V.K. Subbiahm S. T’Jampensb F. Teubertm C. Thomast M. Vesterinenm M.
Williamss,1 M. Witekh A. Zvyaginm
aUniversidade Federal do Rio de Janeiro (UFRJ)
Rio de Janeiro  Brazil
bLAPP  Université de Savoie  CNRS/IN2P3
Annecy-Le-Vieux  France
cClermont Université  Université Blaise Pascal  CNRS/IN2P3  LPC
Clermont-Ferrand  France
dCPPM  Aix-Marseille Université  CNRS/IN2P3
Marseille  France
eLAL  Université Paris-Sud  CNRS/IN2P3
Orsay  France
fPhysikalisches Institut  Ruprecht-Karls-Universität Heidelberg
Heidelberg  Germany
gSezione INFN di Bologna
Bologna  Italy
hHenryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences
Kraków  Poland
iInstitute of Theoretical and Experimental Physics (ITEP)
Moscow  Russia
jInstitute for High Energy Physics (IHEP)
Protvino  Russia
kUniversitat de Barcelona
Barcelona  Spain
lUniversidad de Santiago de Compostela
Santiago de Compostela  Spain
mEuropean Organization for Nuclear Research (CERN)
Geneva  Switzerland
E-mail<EMAIL_ADDRESS>
nEcole Polytechnique Fédérale de Lausanne (EPFL)
Lausanne  Switzerland
oNikhef National Institute for Subatomic Physics
Amsterdam  The Netherlands
pNikhef National Institute for Subatomic Physics and VU University Amsterdam
Amsterdam  The Netherlands
qNSC Kharkiv Institute of Physics and Technology (NSC KIPT)
Kharkiv  Ukraine
rSchool of Physics and Astronomy  University of Glasgow
Glasgow  United Kingdom
sImperial College London
London  United Kingdom
tDepartment of Physics  University of Oxford
Oxford  United Kingdom
uSyracuse University
Syracuse  NY  United States
vPontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)
Rio de Janeiro  Brazil  associated to a
1Massachusetts Institute of Technology
Cambridge  MA  United States

###### Abstract

This paper presents the design of the LHCb trigger and its performance on data
taken at the LHC in 2011. A principal goal of LHCb is to perform flavour
physics measurements, and the trigger is designed to distinguish charm and
beauty decays from the light quark background. Using a combination of lepton
identification and measurements of the particles’ transverse momenta the
trigger selects particles originating from charm and beauty hadrons, which
typically fly a finite distance before decaying. The trigger reduces the
roughly $11$ MHz of bunch-bunch crossings that contain at least one inelastic
$pp$ interaction to 3 kHz. This reduction takes place in two stages; the first
stage is implemented in hardware and the second stage is a software
application that runs on a large computer farm. A data-driven method is used
to evaluate the performance of the trigger on several charm and beauty decay
modes.

###### keywords:

Trigger algorithms; Trigger concepts and systems (hardware and software)

##  1 Introduction

The LHCb detector [1] is a single-arm spectrometer that has been optimised to
perform flavour physics measurements at the LHC. LHCb has a pseudorapidity
acceptance of $2<\eta<5$. The detector layout is shown in Fig. 1.

Figure 1: Layout of the LHCb detector.

It consists of a silicon vertex detector surrounding the $pp$ interaction
region (VELO); a silicon strip detector (TT); a dipole magnet; two Ring
Imaging Cherenkov detectors (RICH 1$\&$2); tracking detectors (T1-T3), which
consist of silicon strip detectors (IT) near the beam and straw tubes (OT)
further out; a calorimeter system consisting of a Scintillating Pad detector
(SPD), an electromagnetic calorimeter with pre-shower (ECAL, PS) and a
hadronic calorimeter (HCAL); and muon chambers (M1-M5).

The LHCb trigger uses all of the above sub-systems. Its architecture consists
of two levels, the first level trigger (L0) and the High Level Trigger (HLT).
L0 is implemented in hardware and uses input from the calorimeter and muon
systems. L0 reduces the rate of crossings with at least one inelastic $pp$
interaction to below 1.1 MHz, at which the whole detector can be read out.
This maximum rate is imposed by the front-end (FE) electronics. The
implementation of L0 is only described briefly in Section 2; a fuller
treatment can be found in reference [1]. The HLT consists of a software
application that runs on a farm of Personal Computers (PCs). It has evolved
significantly compared to reference [1], in which it is assumed that the LHC
machine would operate with a 25 ns bunch separation [2], and that LHCb would
limit the number of visible $pp$ interactions111A visible interaction is
defined as one in which at least two tracks are reconstructed in the VELO,
that both point to the interaction envelope. such that the average number of
visible interactions per bunch crossing $\mu\simeq 0.4$. However, the smallest
bunch separation of the machine was 50 ns in the 2011 physics runs. To
compensate for the loss in number of bunches, and combined with the fact that
the LHCb detector performance did not degrade up to $\mu\approx 2.5$, LHCb
decided to run at $\mu\approx 1.4$. Therefore the HLT had to adapt to running
conditions rather different from those described in reference [1].

The HLT is described in detail in Section 3. The HLT reduces the rate of
accepted events to $\sim 3$ kHz, and all such events are written to storage.
The events written to storage are processed with a more accurate alignment and
calibration of the sub-detectors, and with reconstruction software that is
more elaborate and allows for more redundancy than is possible in the HLT.
This part of the reconstruction and subsequent event selection will henceforth
be referred to as the off-line reconstruction and selection.

The method used to obtain a data-driven determination of the trigger
performance is described in Section 4. Section 5 describes the performance of
the trigger in 2011 relative to off-line reconstruction and selection. Section
6 concludes with a summary of the trigger performance.

##  2 First Level Trigger

L0 is divided into three independent triggers; the L0-Calorimeter trigger, the
L0-Muon trigger and the L0-PileUp trigger. The last of these is not used to
select flavour physics events, but instead aids the determination of the
luminosity [5], and will not be further described in this paper.

The L0 system is fully synchronous with the 40 MHz bunch crossing signal of
the LHC. The latencies are fixed and depend neither on the occupancy nor on
the bunch crossing history. All of the L0 electronics are implemented in
custom-designed hardware that makes use of parallelism and pipelining to do
the necessary calculations within the maximum latency of $4\,\mu$s. The
trigger decisions are combined in a single L0 decision, which is transferred
to the Readout Supervisor board (RS). The RS generates in addition a small
rate of random (NoBias) triggers taking into account the bunch filling scheme
of the machine222Not all of the 3564 slots available for proton bunches around
the machine are filled with protons. Most of the luminosity in 2011 was
collected with 1296 bunches colliding in LHCb.. The RS emulates the state of
the FE buffers to protect against their overflow. It also has information on
the state of the buffers in the readout boards of all sub-detectors and the
availability of the PCs in the farm. Based on this information it can retain
or throttle a bunch crossing.

###  2.1 L0-Calorimeter Trigger Implementation

The L0-Calorimeter system uses information from the SPD, PS, ECAL and HCAL.
These four detectors are stacked along the beam axis ($z$-axis) and their
longitudinal segmentation offers the possibility to distinguish between
photon, electron and hadron showers. Transverse to the beam axis ($x$-$y$
plane) the detectors are segmented into square cells. SPD, PS and ECAL are
divided into three zones with ECAL cell rib sizes of 40.4 mm in the inner zone
close to the beam pipe, 60.6 mm and 121.2 mm further out. HCAL is divided into
two zones with rib size 131.3 mm and 262.6 mm. The SPD, PS and ECAL have the
same geometry and are projective, i.e. the sizes of the cells in the SPD and
PS are adjusted to take into account the different $z$ positions of the
detectors. The HCAL cells are larger but their boundaries always correspond to
the boundaries of the ECAL cells. The L0-Calorimeter system computes the
transverse energy deposited in clusters of $2\times 2$ cells, using only cells
located in the same zone. Hence the cluster energy of showers with energy
deposits in two adjacent zones will be too low. The transverse energy of a
cluster is defined as:

$\mbox{$E_{T}$}=\sum_{i=1}^{4}E_{i}\rm{sin}\theta_{\it i}\,,$ (1)

where $E_{i}$ is the energy deposited in cell $i$ and $\theta_{i}$ is the
angle between the $z$-axis and a neutral particle assumed to be coming from
the mean position of the interaction envelope hitting the centre of the cell.
The ECAL and HCAL signals are read out and processed in FE boards (FEB) that
cover an area of $(8+1)\times(4+1)$ cells, such that the (+1) cells are shared
between neighbouring FEB. Each FEB selects the highest $E_{T}$ cluster among
its 32 clusters. From these clusters, three types of candidates are built
combining information as follows:

  1. 1.

Hadron candidate (L0Hadron): the highest $E_{T}$ HCAL cluster. If there is a
highest $E_{T}$ ECAL cluster located in front of the HCAL cluster, the $E_{T}$
of the hadron candidate is the sum of the $E_{T}$ of the HCAL and ECAL
clusters.

  2. 2.

Photon candidate (L0Photon): the highest $E_{T}$ ECAL cluster with 1 or 2 PS
cells hit in front of the ECAL cluster and no hit in the SPD cells
corresponding to the PS cells. In the inner zone of the ECAL, an ECAL cluster
with 3 or 4 PS cells hit in front of it is also accepted as photon. The
$E_{T}$ of the candidate is the $E_{T}$ deposited in the ECAL alone.

  3. 3.

Electron candidate (L0Electron): same requirements as for a photon candidate,
with in addition at least one SPD cell hit in front of the PS cells.

The $E_{T}$ of the candidates is compared to a fixed threshold and events
containing at least one candidate above threshold are retained by L0.

###  2.2 L0-Muon Trigger Implementation

The muon system contains five muon stations (M1-M5) consisting of pads in the
high occupancy regions and horizontal and vertical strips elsewhere. Strips
are combined to form logical pads for the muon trigger. The pad sizes are
chosen to obtain projectivity towards the interaction region in the $y$-$z$
plane. Each quadrant of the muon detector is connected to a L0 muon processor.
There is no exchange of information between quadrants, hence muons traversing
quadrant boundaries cannot be reconstructed in the trigger. Each of the four
L0 muon processors tries to identify the two muon tracks with the largest and
second largest momentum transverse to the $z$-axis ($p_{T}$) in their
quadrant. The processors search for hits that define a straight line through
the five muon stations and that points towards the interaction point in the
$y$-$z$ plane. In the $x$-$z$ plane the search is limited to muons with
$\mbox{$p_{T}$}\gtrsim 0.5$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The
position of a track in the first two stations allows the determination of its
$p_{T}$ with a measured resolution of $\sim 25\,\%$ relative to off-line
reconstructed muon tracks. The trigger sets a single threshold on either the
largest $\mbox{$p_{T}$}^{\rm largest}$ of the eight candidates (L0Muon), or a
threshold on $\mbox{$p_{T}$}^{\rm largest}\times\mbox{$p_{T}$}^{\rm
2nd~{}largest}$ (L0DiMuon).

##  3 High Level Trigger

The HLT runs on the Event Filter Farm (EFF) that is a farm of multiprocessor
PCs. The HLT is a program written in C++, and 26110 copies of it run in the
EFF. An event that is accepted by L0 is transferred by the on-line system from
the FEB to the EFF and is assembled by one of the event builder programs that
run on one of the cores of each multicore node. The assembled events are
placed in a buffer that is accessed by the HLT programs that run on the cores
of the node. A detailed description of this process can be found in reference
[1] and references therein.

The HLT is based on the same software as used throughout LHCb data processing
and simulation [3]. The off-line event reconstruction and selection requires
about 2 s per event. During 2011 the L0 rate was about 870 kHz. Given the
available resources in the EFF this limits the time per event in the HLT to
$\sim$30 ms. The HLT is divided into two stages. The first stage (HLT1)
processes the full L0 rate and uses partial event reconstruction to reduce the
rate to 43 kHz. At this rate the second stage (HLT2) performs a more complete
event reconstruction.

A "trigger line" is composed of a sequence of reconstruction algorithms and
selections. The trigger line returns an accept or reject decision. An event
will be accepted by L0, HLT1 or HLT2 if it is accepted by at least one of its
trigger lines at the relevant stage. Combinations of trigger lines, together
with a L0 configuration, form a unique trigger with its associated Trigger
Configuration Key (TCK). The TCK is a 32 bit label pointing to a database that
contains the parameters that configure the trigger lines. The TCK is stored
for every event in the raw data, together with information on which trigger
lines accepted the event. During 2011 running, the HLT contained 38 HLT1 and
131 HLT2 lines. The trigger lines that cover the main physics goals of LHCb
[4], and accept the majority of events stored, are described below in addition
to the common reconstruction algorithms. The corresponding selection
parameters and their performance are given in Section 5.

The remaining trigger lines consist of lines for luminosity measurements, pre-
scaled physics trigger lines with looser cuts, lines that select very low
multiplicity events and lines that identify large transverse momentum jets.
The trigger also contains lines designed to accept NoBias events, lines that
monitor events with inconsistent raw data or other errors during the HLT
processing, lines that allow the VELO to monitor the position of the $pp$
interaction envelope and lines selecting calibration and monitoring data for
fast feedback on the quality of the data.

###  3.1 HLT1

The off-line VELO reconstruction software is fast enough to permit the full 3D
pattern recognition of all events that enter the HLT. In the off-line VELO
pattern recognition a second pass is made on unused hits to enhance the
efficiency for tracks that point far away from the beam-line, but in the HLT
this search is not executed. At the start of each LHC fill, the mean position
of the $pp$ interaction envelope in the $x$-$y$ plane,
$\rm{PV}_{\rm{xy}}^{\rm{mean}}$, is determined using VELO tracks. This
position is measured to be stable to within a few $\rm\mu m$ per fill. The
VELO tracks are used to construct vertices with at least 5 tracks originating
from them, and those vertices within a radius of $300~{}\mu\rm m$ of $\rm
PV_{xy}^{mean}$ are considered to be primary vertices (PV).

While in the off-line pattern recognition all VELO tracks are considered to
identify the corresponding hits in the tracking stations downstream of the
magnet, the pattern recognition in HLT1 limits the execution time by selecting
VELO tracks that have a larger probability to originate from signal decays.
HLT1 lines that do not require muons select VELO tracks based on their
smallest impact parameter (IP) to any PV. In addition, cuts are applied to the
quality of each VELO track based on the number of hits on a track and the
expected number of hits.

For events triggered by L0Muon or L0DiMuon, a fast muon identification is
performed in HLT1 to select VELO tracks that are muon candidates using the
following procedure. For every VELO track, a search window is defined in the
M3 station by extrapolating the VELO track in a straight line. The magnet does
not bend tracks in the vertical plane, and multiple scattering dominates the
vertical size of the search window. A muon candidate is required to have a
momentum of at least 6 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, hence the
horizontal search window size corresponds to the deflection of a 6
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ track. Hits found inside the search
window are combined with the VELO track to form candidate tracks that are used
in a search for additional muon hits in stations M2, M4 and M5. A candidate
track is provisionally accepted if it contains at least one hit in addition to
the M3 hit. In the final step of the algorithm, a linear $\chi^{2}$ fit of the
candidate track (containing both the VELO track and the muon hits) in the
horizontal plane is performed and the $\chi^{2}~{}\rm
divided~{}by~{}the~{}number~{}of~{}degrees~{}of~{}freedom~{}(ndf)$ is required
to be less than 25\. As soon as the first candidate is found, the algorithm
stops and the VELO track is tagged as a muon candidate.

For the VELO tracks that are selected by either their IP or by being tagged as
a muon candidate, the track-segments in the OT and IT-stations are
reconstructed to determine their momentum in a procedure known as forward
tracking. Imposing a minimum momentum and transverse momentum
($p,~{}\mbox{$p_{T}$}$) in the forward tracking significantly reduces the
search windows that have to be opened in the IT and OT tracking stations
thereby reducing the required processing time. Each reconstructed track is
fitted using a Kalman filter [6] based track fit to obtain its $\chi^{2}$ and
a full covariance matrix at the start of the track. Compared to off-line
reconstruction, this fit uses a simplified material geometry description, it
makes fewer iterations and consequently it performs a less sophisticated
removal of outlier hits. The invariant mass resolution of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$
determined in the HLT is measured to be $3\,\%$ larger than the 14
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ obtained off-line. This shows that
the resolution of the track parameters obtained in the HLT is sufficiently
close to off-line to allow selective cuts in IP, momentum and mass. For tracks
that are tagged as muon candidates, the off-line muon identification algorithm
[7] is applied to the tracks to improve the purity of the muon sample.

###  3.2 HLT2

As mentioned above, HLT1 reduces the rate from 870 kHz to 43 kHz. At this rate
forward tracking of all VELO tracks can be performed in HLT2. While the off-
line reconstruction uses two tracking algorithms, HLT2 only employs the
algorithm based on seeding the search with VELO tracks. This leads to a lower
efficiency compared to off-line of $1-2~{}\%$ per track. To further limit the
processing time only tracks with $p>5$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and $\mbox{$p_{T}$}>0.5$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are
reconstructed by limiting the search windows.

Muon identification is performed using the off-line algorithm on all tracks
from the forward tracking. Tracks are also associated to ECAL clusters to
identify electrons.

A large share of the 3 kHz output rate of HLT2 is selected by "topological"
trigger lines, which are designed to trigger on partially reconstructed
$b$-hadron decays. The topological trigger lines in principle cover all
$b$-hadrons with at least two charged particles in the final state and a
displaced decay vertex. The efficiencies are less dependent on reconstruction
inefficiencies imposed by the minimum ($p,~{}\mbox{$p_{T}$}$) requirements and
loss due to the single, non-redundant, track reconstruction mentioned above.
In the following two sections the topological trigger lines are described in
more detail.

While the topological trigger lines target inclusive $b$-hadrons, a number of
dedicated "exclusive" trigger lines are also implemented in HLT2. These
require all decay particles to be reconstructed in HLT2 and use narrow mass
windows to reduce their rate. These exclusive trigger lines either target
prompt $c$-hadron production, or allow triggering on hadronic $b$-hadron
decays without the necessity to use lifetime-biasing selections to reduce the
rate. These lines are described in Section 3.2.3.

####  3.2.1 Topological Trigger Lines

The decisions of the topological trigger lines are based on the properties of
combinations of 2, 3, or 4 “Topo-Tracks”. Topo-Tracks are a subset of HLT2
tracks selected with additional requirements on their track fit quality
($\chi^{2}/\rm ndf$), IP, and muon or electron identification. N-body (i.e. an
n track combination) candidates are built as follows: two Topo-Tracks are
combined into a 2-body object, requiring that their distance of closest
approach (DOCA) is less than 0.2 mm. A 3(4)-body object is made by combining a
2(3)-body object and another Topo-Track with the same DOCA <0.2 mm cut, where
the DOCA is calculated between the 2(3)-body object and the additional Topo-
Track. This sequence of DOCA selections enhances the efficiency of the
topological trigger lines on $B\rightarrow DX$ decays. Not all of the
$b$-hadron final state particles need to satisfy these criteria. The trigger
is designed to allow for the omission of one or more final state particles
when forming the trigger candidate.

If an n-body candidate only contains a subset of the daughter particles, its
invariant mass ($m$) will be less than the mass of a $b$-hadron. Thus, a mass
window would need to be very loose if the trigger is to be inclusive. Instead
a corrected mass ($m_{\rm corr}$) is used that is defined as:

$m_{\rm corr}=\sqrt{m^{2}+|p^{\prime}_{T\rm miss}|^{2}}+|p^{\prime}_{T\rm
miss}|,$ (2)

where $p^{\prime}_{T\rm miss}$ is the missing momentum transverse to the
direction of flight, as defined by the PV and the n-body vertex [8]. In case
of multiple PVs, the PV with respect to which the n-body combination has the
smallest IP is used. The quantity $m_{\rm corr}$ would be the minimal mass of
the parent if a massless particle was omitted from the trigger candidate.
Prompt $c$-hadrons that are erroneously combined with another track constitute
a significant fraction of the n-body candidates. These candidates are rejected
by requiring that all (n-1)-body objects used by a n-body trigger line either
have a mass greater than 2.5 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ or
that they have a significant IP to all PVs.

To select a n-body candidate, cuts are applied to the following variables:
$\sum|\mbox{$p_{T}$}|,~{}p^{min}_{T}$, $m$, $m_{\rm corr}$, DOCA, IP
significance (IP$\chi^{2}$) and flight distance significance (FD$\chi^{2}$).
Using NoBias events for background and Monte Carlo (MC) simulated signal
events, we find that a larger rejection power is achieved for the same signal
efficiency by combining the above variables in a multivariate selection.

####  3.2.2 Topological Multivariate Lines

To combine the variables mentioned above a boosted decision tree (BDT) was
chosen; this classifier has already been successfully used elsewhere [9]. All
multivariate classifiers select n-dimensional regions of a multivariate space
by learning from the training samples provided to them. If selected regions
are small relative to the resolution of the detector, the signal could
oscillate between regions resulting in, at best, a less efficient trigger or,
at worst, a trigger that is very difficult to understand. To avoid this, all
of the variables are mapped onto discrete variables. The application of the
BDT to discrete variables is henceforth referred to as Bonsai BDT (BBDT).

The BBDT ensures that the smallest interval that can be used satisfies $\Delta
x_{\rm min}>\delta_{x}$ for all $x$ values, where $\delta_{x}={\rm
MIN}\\{|x_{i}-x_{j}|:~{}x_{i},~{}x_{j}\in x_{\rm discrete}\\}$. The
constraints governing the choice of $x_{\rm discrete}$ are then as follows:
firstly $\delta_{x}$ should be greater than the resolution on $x$ and be large
with respect to the expected variations in $x$, and secondly the
discretisation should reflect common $b$-hadron properties.

The discretisation scheme for each variable was determined by first training a
BBDT with a very large number of discretisation values and then gradually
decreasing this number while maintaining near optimal performance. The
training signal samples were MC simulated data that contained as signal
$B^{+},~{}B^{0},~{}B_{s}$ or $\Lambda_{b}$ decays333Charge conjugate hadrons
are always implied. with decay modes as given in Table 1, while the background
sample was NoBias data recorded in 2010.

Table 1: MC signal samples used to train the BBDT, where $K$ means $K^{\pm}$ and $\pi$ means $\pi^{\pm}$. Parent | Daughters
---|---
$B^{+}$ | $K\pi\pi,D_{[K\pi]}\pi,D_{[hhhh]}K,D_{[K_{S}\pi\pi]}K,D_{[K\pi\pi]}K\pi$
$B^{0}$ | $K^{*}_{[K\pi]}\mu\mu,K^{*}_{[K\pi]}ee,D_{[K\pi\pi]}\pi,K\pi,D_{[K\pi]}K\pi,D^{*}_{[D(K\pi)\pi]}\mu\nu,D_{[K\pi\pi]}K\pi\pi$
$B_{s}$ | $D_{s[KK\pi]}\pi,D_{s[KK\pi]}K\pi\pi,K^{*}_{[K\pi]}K^{*}_{[K\pi]}$
$\Lambda_{b}$ | $\Lambda_{c[pK\pi]}\pi,\Lambda_{c[pK\pi]}K\pi\pi$

Table 2 shows the discretisation scheme for each of the variables used in the
BBDT.

Table 2: Allowed mapping points in the BBDT. The variables are explained in the text. Variable | Cuts(2, 3, 4-body) | Intervals used in the BBDT
---|---|---
$\sum|p_{T}|$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] |  $>3$, 4, 4 | 3.5, 4, 4.5, 5, 6, 7, 8, 9, 10, 15, 20
$p_{T}^{\rm min}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>0.5$ | 0.6, 0.7, 0.8, 0.9, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 4, 5, 10
$m$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ ] | $<7$ | 2.5, 4.75
$m_{\rm corr}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ ] |  | 2, 3, 4, 5, 6, 7, 8, 9, 10, 15
${\rm DOCA}$ [mm] | $<0.2$ | 0.05, 0.1, 0.15
${\rm IP}\chi^{2}$ |  | 20
${\rm FD}\chi^{2}/100$ | $>1$ | 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 100

####  3.2.3 Exclusive Lines

In the topological trigger described in the previous section there is an
explicit veto on prompt charm. The selection of prompt charm decays is
achieved by HLT2 lines that require a reconstruction of all the decay
products, and have tight cuts on the invariant mass of the reconstructed
candidates. While HLT2 reconstruction and selection efficiencies for
$b$-hadrons are good, the $\mbox{$p_{T}$}>0.5$
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ constraint reduces the efficiency for
the exclusive selection of charm decays with more than two final state
particles. To enhance the reconstruction efficiency for these exclusive
trigger lines, the trigger lines first try to identify a two-prong secondary
vertex. Selection cuts are imposed on the maximum invariant mass of the two
tracks, the quality of their vertex, the sum of the transverse momenta of the
tracks and $m_{\rm corr}$. These initial cuts reduce the rate sufficiently to
allow for the forward tracking of the remaining VELO tracks, but now with a
relaxed $\mbox{$p_{T}$}>0.25$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
constraint and only using the hits in the tracking system that have not been
used by the previous pass in forward tracking. Two-prong candidates are
subsequently combined with other tracks, which now include the low $p_{T}$
tracks, to form exclusively reconstructed candidates. The combinatorial
background is reduced by tight requirements on the mass and on the angle
between the momentum of the $D$ and the vector connecting the PV with the $D$
vertex. HLT2 contains 28 trigger lines dedicated to selecting prompt charm.

Another example of an exclusive trigger is a dedicated trigger line selecting
the decay $B_{s}\rightarrow\,K^{+}K^{-}$ while avoiding cuts that bias the
$B_{s}$ lifetime. This implies that a cut on IP, a powerful variable to reject
combinatorial background, cannot be used. In order to enrich the $B_{s}$
candidates two dedicated neural networks based on the NeuroBayes neural
network package [10] are used. In a first step, kinematic constraints such as
the transverse momentum of the final state particles and the helicity angle in
the rest frame of the $B_{s}$ candidate are used to reduce the rate. This
allows running the comparatively slow particle identification algorithm using
the RICH sub-detector on the events selected by the first neural network. This
information is then included in a second neural network that uses both
kinematic and particle ID information to make the final selection.

##  4 Data-driven Trigger Performance Determination

The trigger performance is evaluated relative to offline reconstruction and
selections, and thus contains only the additional inefficiency due to
simplifications used in the trigger, possible alignment inaccuracies, worse
resolution than the offline reconstruction or harder cuts imposed by rate
and/or processing time limitations. The following channels have been chosen to
show the performance of the trigger: $D^{0}\rightarrow K^{-}\pi^{+}$,
$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$,
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})K^{+}$, $B^{0}\rightarrow
D^{-}(K^{+}\pi^{-}\pi^{-})\pi^{+}$, $B^{-}\rightarrow
D^{0}(K^{-}\pi^{+})\pi^{-}$,
$B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(e^{+}e^{-})K^{\ast 0}(K^{+}\pi^{-})$ and $B^{0}\rightarrow
K^{*0}(K^{+}\pi^{-})\gamma$. These channels and their selections are
representative for those used in most analyses. In all off-line selected
signal samples the level of background is significantly lower than the signal.
Substantial differences in trigger efficiency, however, are observed for true
signal and background. The trigger performance on each channel is measured by
determining the signal component using fits to the invariant mass
distributions, hence avoiding any background contamination.

In what follows, the term “signal” refers to a combination of tracks that form
the off-line reconstructed and selected $b$ or $c$-hadron candidate. To
determine the trigger efficiency, trigger objects are associated to signal
tracks. The trigger records all the information needed for such an
association. All strips, straws, cells and pads of the sub-detectors have a
unique identifier, and these identifiers are written in a trigger report in
the data stream for every trigger line that accepts an event. The criteria
used to associate a trigger object with a signal track are as follows:

  * •

L0-Calorimeter: the off-line track is extrapolated to the $z$-position of the
calorimeter (ECAL or HCAL), and the cells intersecting with the track and its
eight neighbours are considered signal cells. If any of the $2\times 2$ cells
of a L0-Calorimeter cluster above the threshold coincides with a signal cell,
this cluster is associated with the off-line track. If none of the cells
overlap, the cluster is not associated with the off-line track.

  * •

L0-Muon: the trigger records the M1, M2 and M3 hits used to form the L0 muon
candidate. If at least two of the three hits are shared with an off-line
reconstructed muon the L0 muon is associated with the off-line track. Non-
associated L0 muons have no hits overlapping between the L0 muon and the muon
hits of the off-line track.

  * •

HLT tracks: a HLT track has VELO hits and hits in the OT and/or the IT. In
addition it can have TT hits and hits in the muon chambers M2-M5. Associated
tracks require that the fraction of HLT track hits that overlaps with the off-
line track is at least $70~{}\%$ in the VELO, $70~{}\%$ in the TT if
applicable and $70~{}\%$ of the OT and IT combined. For muons the association
requirement is that at least $60~{}\%$ of the HLT muon hits overlap with the
off-line muon. Non-associated HLT tracks share no hits with the off-line
track.

An event is classified as TOS (Trigger on Signal) if the trigger objects that
are associated with the signal are sufficient to trigger the event. An event
is classified as TIS (Trigger Independent of Signal) if it could have been
triggered by those trigger objects that are not associated to the signal.
Global event variables, such as the number of primary vertices or the SPD
multiplicity, are not considered in this classification. A number of events
can be classified as TIS and TOS simultaneously ($N^{\rm TIS\&TOS}$), which
allows the extraction of the trigger efficiency relative to the off-line
reconstructed events from data alone. The efficiency to trigger an event
independently of the signal, $\epsilon\rm^{\rm TIS}$, 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, $\epsilon\rm^{\rm TOS}$, 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. The total trigger efficiency for events containing the signal can then
be computed as $\epsilon^{\rm TIS}\times N^{\rm Trig}/N^{\rm TIS}$, where
$N^{\rm Trig}$ is the total number of triggered signal events.

The phase-space distribution of the signal is affected by the TIS requirement.
This is illustrated in Fig. 2, which shows the $p_{T}$ distribution of
$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ candidates selected from NoBias and TIS
events.

Figure 2: Comparison of the $p_{T}$ distributions of $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$ selected in NoBias and TIS events.

The $p_{T}$ of TIS events is harder, which would result in a too large signal
efficiency when integrated over all phase-space. This bias in phase-space can
be understood considering that $c\bar{c}$, or $b\bar{b}$, pairs are correlated
in phase-space at production, and TIS events are predominantly triggered by
the decay products of the hadron that contains the other heavy quark. Another
example of bias is that for charm decays TIS events could enhance the non
prompt charm component by triggering on the other decay products of a $B$ to
$D$ decay. These biases can only be evaluated individually for each analysis.
Therefore the trigger performance is presented as a function of the signal
$p_{T}$ and its lifetime ($\tau$).

##  5 Trigger Performance

For each channel $\varepsilon^{\rm TOS}$ is determined relative to the off-
line selection efficiency of a channel. $\varepsilon^{\rm TOS}$ for the
HLT1(2) performance is given for off-line selected events that have also been
classified as TOS in the previous trigger level(s), unless mentioned
otherwise.

At each trigger level the different trigger lines compete for their share of
the available resources. To determine the different selections for the trigger
lines, a "bandwidth division" procedure has been adopted, which is described
in the next section. The performance of the different trigger lines with the
thresholds as determined by the bandwidth division will be presented for L0,
HLT1 and HLT2 in the next sections for the channels listed in Section 4.

###  5.1 Bandwidth Division Procedure

The bandwidth division minimises the overall loss in efficiency by minimising
the following:

$\sum_{\rm signal}\left(\sum_{\rm lines}{\left(1-\frac{\varepsilon^{\rm
signal,~{}line}}{\varepsilon_{\rm max}^{\rm
signal,~{}line}}\right)}\right)^{2},$ (3)

where $\varepsilon^{\rm signal,~{}line}$ is the L0$\times$HLT trigger
efficiency obtained using a set of selections (corresponding to a single set
of cut values) for all signal channels and trigger lines simultaneously and
$\varepsilon_{\rm max}^{\rm signal,~{}line}$ is the maximum of
$\varepsilon^{\rm signal,~{}line}$ with the full computing resources dedicated
to that signal and specific trigger line alone. The score is evaluated for
each set of cuts by running an emulation of the L0 trigger and executing the
HLT application. This emulation includes FE-buffer overflow emulation, the
available processing power in the EFF and the maximal HLT2 output rate to disk
as boundary conditions. The configuration with the minimum score is found by
varying the cuts and running the trigger software for each variant.

For signal the following MC generated and off-line reconstructed and selected
channels have been chosen to represent both the main physics goals of LHCb and
to cover all the trigger components that need to be tuned: $B_{s}\rightarrow
J/\psi(\mu^{+}\mu^{-})\phi(K^{+}K^{-})$, $B_{s}\rightarrow\mu^{+}\mu^{-}$,
$B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$, $B_{(s,d)}\rightarrow\mu^{+}X$,
$D^{*+}\rightarrow D(\mu^{+}\mu^{-})\pi^{+}$, $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$, $B^{0}\rightarrow K^{*0}\gamma$, $B^{0}\rightarrow
K^{+}\pi^{-}$, $B^{0}\rightarrow K^{*0}e^{-}e^{+}$, $B^{+}\rightarrow
K^{+}\pi^{-}\pi^{+}$, $B_{s}\rightarrow D_{s}^{-}(K^{+}K^{-}\pi^{-})K^{+}$,
$B^{+}\rightarrow\bar{D^{0}}(K_{S}(\pi^{+}\pi^{-})\pi^{+}\pi^{-})K^{+}$ and
$D^{0}\rightarrow K^{-}\pi^{+}$ with $K^{\ast 0}\rightarrow K^{+}\pi^{-}$.
NoBias events from 2010 with $\mu=1.4$ are used as background. Rather than
introducing weights favouring some channels, we have chosen to emphasize the
main physics goals by the number of channels included in the bandwidth
division procedure. For example, channels decaying with muons in the final
state are more abundant.

All performance results are given for 1296 colliding bunches in LHCb, which
corresponds to a bunch crossing rate with at least one visible $pp$
interaction of $\sim 11$ MHz. The bandwidth division yields the following
rates for NoBias events: 870 kHz for L0, 43 kHz for HLT1 and 3 kHz for HLT2.

###  5.2 L0 Performance

Events with a large occupancy in the OT and IT consume a disproportionately
large fraction of the available processing time in the HLT. The SPD
multiplicity measured at L0 is a good measure of this occupancy, permitting an
early rejection of events that require a relatively large processing time.
Using the bandwidth division the optimal SPD cut is determined to be $<~{}900$
for events triggered by L0DiMuon and $<~{}600$ for all other L0 triggers. On
average, events with a SPD multiplicity larger than 600 consume four times
more time in the HLT than events with less than 600 SPD hits. The fraction of
events rejected due to these cuts has been determined from real data for charm
hadron production to be $7.4\pm~{}0.3~{}(0.05\pm 0.01)\,\%$ for a cut on 600
(900) in SPD multiplicity. Similarly for $b$-hadron production the fraction of
events with a SPD multiplicity $>600~{}(900)$ is found to be $8.8\pm
0.6~{}(0.5\pm 0.2)\,\%$. All efficiencies quoted below are given relative to
the sample after the SPD multiplicity cut.

Table 3 lists the L0 cuts. About $20~{}\%$ of the events accepted by L0 are
selected by more than one trigger line, giving a total L0 rate of 870 kHz
prior to throttling.

Table 3: Cuts of L0 lines and their rates prior to throttling. The definition of the trigger lines is given in Section 2. | Threshold | SPD Multiplicity | Rate
---|---|---|---
L0Muon |  $\mbox{$p_{T}$}>1.48$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | $<600$ | 340 kHz
L0DiMuon |  $\sqrt{\mbox{$p_{T}$}^{\rm largest}\times\mbox{$p_{T}$}^{\rm 2nd~{}largest}}>1.296$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ | $<900$ | 75 kHz
L0Hadron |  $E_{T}>3.5$ $\mathrm{\,Ge\kern-1.00006ptV}$ | $<600$ | 405 kHz
L0Electron |  $E_{T}>2.5$ $\mathrm{\,Ge\kern-1.00006ptV}$ | $<600$ | 160 kHz
L0Photon |  $E_{T}>2.5$ $\mathrm{\,Ge\kern-1.00006ptV}$ | $<600$ | 80 kHz

L0Muon is the main trigger for particle decays with one or more muons in the
final state. L0DiMuon recovers part of the events with a SPD multiplicity
$>600$ for a small increase in rate. The performance of L0Muon and L0DiMuon
are shown in Fig. 4 for $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})K^{+}$ as a function of $p_{T}$
(${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$). L0DiMuon increases the
number of signal events by $4.9~{}\%$, of which $87~{}\%$ have a SPD
multiplicity larger than 600 hits. The remaining $13~{}\%$ is due to the lower
$p_{T}$ cut in L0DiMuon. L0 requires a muon candidate to have a hit in all
five muon stations, while off-line as few as two stations are sufficient to
identify a muon. As a result L0DiMuon has a maximum efficiency of $\sim
80~{}\%$ even for a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ with large
$p_{T}$. L0Muon recovers this loss for lower SPD multiplicities and decays
with more muons at large $p_{T}$.

Figure 3: Efficiency $\epsilon^{\rm TOS}$ of
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})K^{+}$ as a function of $p_{T}$
(${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$) for L0Muon and L0DiMuon
lines.

Figure 4: The efficiency $\epsilon^{\rm TOS}$ of L0Hadron is shown for
$B^{0}\\!\rightarrow D^{-}\pi^{+}$, $B^{-}\\!\rightarrow D^{0}\pi^{-}$,
$D^{0}\rightarrow K^{-}\pi^{+}$ and $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ as
a function of $p_{T}$ of the signal $B$ and $D$ mesons.

L0Hadron selects heavy flavour decays with hadrons in the final state. The
performance of L0Hadron is shown in Fig. 4 for $B^{0}\\!\rightarrow
D^{-}\pi^{+}$, $B^{-}\\!\rightarrow D^{0}\pi^{-}$, $D^{0}\rightarrow
K^{-}\pi^{+}$ and $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ as a function of
$p_{T}$ of the signal $B$ and $D$ mesons. At low $p_{T}$, L0Hadron has a
better efficiency for $b$-hadrons than for $c$-hadrons due to the larger
$b$-hadron mass. Once the $p_{T}$ of the hadron is above the $b$-hadron mass,
the decays with fewer final state tracks have a higher efficiency.

L0Electron selects decays with electrons in the final state. It also triggers
on radiative decays, with the photon being either converted, or with photon
clusters with SPD hits in front due to overlapping charged particles. The
performance of L0Electron is shown in Fig. 5 for ${B}^{0}\rightarrow
J/\psi{(\rm e^{+}e^{-})}K^{*0}$ as a function of
$\mbox{$p_{T}$}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$. Contrary to
L0Muon, L0Electron is not fully efficient for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ with large $p_{T}$. This is due
to the hardware implementation (see Section 2.1) that prevents energy
deposited in different ECAL zones from being combined into one cluster.

Figure 5: The efficiency $\epsilon^{\rm TOS}$ of L0Electron is shown for
${B}^{0}\rightarrow J/\psi{(\rm e^{+}e^{-})}K^{*0}$ as a function of $p_{T}$
(${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$).

The performance of the trigger for high-energy photons from radiative penguin
decays is measured with the channel $B^{0}\rightarrow K^{*0}\gamma$. The
number of TIS events in this channel is insufficient to study the efficiency
as a function of $p_{T}$ of the $B^{0}$. The mean efficiency for the L0Photon
line integrated over $p_{T}$ is $50\pm 4~{}\%$. Selecting events with either
L0Photon or L0Electron gives an efficiency of $88\pm 5~{}\%$ .

###  5.3 HLT1 Performance

HLT1 muon lines are only executed for events that have been triggered by
L0Muon or L0DiMuon, and the lines require their tracks to be validated as a
muon candidate as described in Section 3.1. Table 4 gives the names of the
HLT1 muon lines and their cuts.

Table 4: HLT1 muon lines and their cuts. The rate is measured on events accepted by L0Muon or L0DiMuon.  Hlt1line | TrackMuon | SingleMuon | DiMuon | DiMuon
---|---|---|---|---
|  | HighPT | HighMass | LowMass
Track IP [mm] | $>0.1$ | - | - | -
Track IP$\chi^{2}$ | $>16$ | - | - | $>3$
Track $p_{T}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>1$ | $>4.8$ | $>0.5$ | $>0.5$
Track $p$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>8$ | $>8$ | $>6$ | $>6$
Track $\chi^{2}/\rm ndf$ | $<2$ | $<4$ | $<4$ | $<4$
DOCA [mm] | - | - | $<0.2$ | $<0.2$
$\chi_{\rm vertex}^{2}$ | - | - | $<25$ | $<25$
Mass [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ ] | - | - | $>2.7$ | $>1$
Rate [kHz] | 5 | 0.7 | 1.2 | 1.3

Hlt1TrackMuon accepts events with $B$, $D$ or $\tau$ decays with at least one
muon in its final state by identifying and accepting events with muon
candidates that have significant IP with respect to all PVs. To trigger on
muons originating from heavy particles with a negligible lifetime, like
$W^{\pm}$ or $Z^{0}$, an alternative line, Hlt1SingleMuonHighPT, is
implemented. It does not have any requirements on IP, but requires a hard
$p_{T}$ cut to reduce the rate. Hlt1DiMuonHighMass is complementary to
Hlt1TrackMuon in that it allows $b$-hadron decays to be selected without
imposing lifetime related cuts, and thus allows the lifetime acceptance bias
of the larger efficiency Hlt1TrackMuon line to be determined. Finally
Hlt1DiMuonLowMass allows triggering on final states with two muons with a
relatively small invariant mass. To reduce the rate the line requires that
both muons are not prompt.

The performance of the HLT1 muon lines is evaluated using
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays.
Figure 6 shows the performance of Hlt1TrackMuon, Hlt1DiMuonHighMass and
Hlt1DiMuonLowMass as a function of the $p_{T}$ and $\tau$ of the $B^{+}$.
Hlt1TrackMuon gives the best performance overall, except at low lifetimes,
where Hlt1DiMuonHighMass recovers events. Hlt1DiMuonLowMass loses $\sim
10~{}\%$ in efficiency compared to Hlt1TrackMuon for
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ due to
the requirement to have at least two muon candidates, but its cuts on IP and
$p_{T}$ are significantly relaxed to allow the selection of candidates with
the muon pair mass down to 1 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, which
is designed to select $b\rightarrow s\mu\mu$ decays like $B\rightarrow
K^{*}\mu^{+}\mu^{-}$.

The performance of Hlt1SingleMuonHighPT is not properly assessed using
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays
because it is designed to accept events with decays of particles with a mass
larger than that of $b$-hadrons. Instead
$Z^{0}~{}\rightarrow~{}\mu^{+}~{}\mu^{-}$ events are used to measure the
efficiency, by requiring one of the two muons to be TIS. This yields an
efficiency of $77.1\pm 0.2~{}\%$ for the Hlt1SingleMuonHighPT line per single
muon, implying an efficiency for $Z^{0}~{}\rightarrow~{}\mu^{+}~{}\mu^{-}$ of
$95~{}\%$. The fast HLT1 muon reconstruction, as described in Section 3.1,
applies more stringent cuts than the off-line muon identification to keep
misidentification and as a consequence the rate and CPU time consumption under
control.

Figure 6: Efficiency $\epsilon^{\rm TOS}$ of Hlt1TrackMuon, Hlt1DiMuonHighMass
and Hlt1DiMuonLowMass for
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})K^{+}$ as a function of the $p_{T}$ and lifetime of the
$B^{+}$.

In addition to the muon lines mentioned above, HLT1 also contains a line that
is executed for all events accepted by L0, Hlt1TrackAllL0. It is designed to
select hadron decays which are significantly displaced from a PV. A trigger
line called Hlt1TrackPhoton is only executed for events that have a L0Photon
or a L0Electron with $E_{T}>4.2$ $\mathrm{\,Ge\kern-1.00006ptV}$. This trigger
line is designed to enhance the trigger efficiency for radiative $b$-hadron
decays with a high $p_{T}$ photon. The corresponding selection cuts are given
in Table 5. Both trigger lines require at least one track with sufficient IP
and $p_{T}$. Hlt1TrackPhoton is designed to select lower $p_{T}$ tracks, and
correspondingly also has relaxed track quality requirements compared to
Hlt1TrackAllL0.

Table 5: The cuts applied in Hlt1TrackAllL0 and Hlt1TrackPhoton lines. The rate is measured on events accepted by L0. Hlt1 line | Hlt1TrackAllL0 | Hlt1TrackPhoton
---|---|---
Track IP [mm] | $>0.1$ |  $>$0.1
Number VELO hits/track | $>9$ | $>6$
Number missed VELO hits/track | $<3$ | $<3$
Number OT+IT$\times$2 hits/track | $>16$ | $>15$
Track IP$\chi^{2}$ | $>16$ |  $>$16
Track $p_{T}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>1.7$ | $>1.2$
Track $p$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>10$ | $>6$
Track $\chi^{2}/\rm ndf$ | $<2.5$ | $<2.5$
Rate [kHz] | 33 | 4.2

Figure 7 shows the performance of Hlt1TrackAllL0 as a function of
$\mbox{$p_{T}$}\rm~{}and~{}\tau$ for channels with hadronic decays.

Figure 7: Efficiency $\epsilon^{\rm TOS}$ of Hlt1TrackAllL0 is shown for
$B^{-}\\!\rightarrow D^{0}\pi^{-}$, $B^{0}\\!\rightarrow D^{-}\pi^{+}$,
$D^{0}\rightarrow K^{-}\pi^{+}$ and $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ as
a function of $p_{T}$ and $\tau$ of the $B$-meson and prompt $D$-meson
respectively.

Hlt1TrackAllL0 provides a very efficient trigger for all heavy flavour decays
with a significant flight distance from their PV, reducing the rate from 870
kHz to 33 kHz. At low $p_{T}$ the requirement of at least one decay particle
with $p_{T}$ $>1.7$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ results in
selecting $b$-hadrons with a larger efficiency than $c$-hadrons, and low
multiplicity decays with a larger efficiency than higher multiplicity decays.
At large $p_{T}$ this condition favours the decays with larger multiplicities.
While in L0 special lines are used to select $b$-hadron decays with electrons
in the final state, in HLT1 these decays are covered by Hlt1TrackAllL0.

There are insufficient radiative $B$-decays to extract the performance of
Hlt1TrackPhoton as a function of $p_{T}$ in a data-driven way. Hlt1TrackPhoton
uses the same tracks as Hlt1TrackAllL0, but with a relaxed set of requirements
as shown in Table 5. The yield increase in $B^{0}\rightarrow K^{*0}\gamma$
events obtained by including Hlt1TrackPhoton in addition to Hlt1TrackAllL0 is
measured to be $12\pm 2~{}\%$.

###  5.4 HLT2 Performance

Similar to HLT1, HLT2 has lines that select events with one or two identified
muons in the final state. In HLT2 the muon identification is identical to the
off-line algorithm. The cuts corresponding to lines that are purely based on a
single identified muon are given in Table 6.

Table 6: HLT2 lines based on one identified muon.  Hlt2Single | Muon | MuonHighPT
---|---|---
Hlt1TrackMuon | TOS | -
Track IP [mm] | $>0.5$ | -
Track IP$\chi^{2}$ | $>200$ | -
Track $p_{T}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>1.3$ |  $>$10
Track $\chi^{2}/\rm ndf$ | $<2$ | -
Pre-scale | 0.5 | 1.
Rate [Hz] | 480 | 45

Hlt2SingleMuon selects semileptonic $b$ and $c$-hadron decays. To minimise the
bias on the hadronic part of the decay the $p_{T}$ cut is set low, in
combination with scaling the rate down by a factor two, rather than tightening
the cut to reduce the rate. This trigger line also provides a large yield for
$J/\psi\rightarrow\mu\mu$ events that are selected by one of the two muons,
while the other muon is used for calibration of tracking and muon
identification efficiencies. Hlt2SingleMuonHighPT is designed to select heavy
particles decaying promptly to one or more muons, like $W^{\pm}$ or $Z^{0}$.
Contrary to Hlt2SingleMuon the rate is not a problem so there is no HLT1
requirement imposed. As for HLT1, $Z^{0}\rightarrow\mu^{+}\mu^{-}$ decays are
used to measure an efficiency of over $99\%$ for Hlt2SingleMuonHighPT per
muon. This small loss in efficiency is attributed to different alignment
constants and the non-redundant track reconstruction used in HLT2 as described
in Section 3.2.

The HLT2 lines that are based on two identified muons are grouped into two
categories. Those that are dedicated to prompt decays use the mass as the main
discriminant, while "detached" lines use the separation between the dimuon
vertex and the PV as the main discriminant. The names and corresponding cuts
of the prompt decay selections are given in Table 7.

Table 7: HLT2 lines based on two identified muon.  Hlt2DiMuon | JPsi | Psi2S | B | JPsiHighPT | Psi2SHighPT
---|---|---|---|---|---
Track $\chi^{2}/\rm ndf$ | $<5$ | $<5$ | $<5$ | $<5$ | $<5$
Mass [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ ] | M${}_{J/\psi}\pm 0.12$ | M${}_{\psi{(2S)}}\pm 0.12$ | $>4.7$ | M${}_{J/\psi}\pm 0.12$ | M${}_{\psi{(2S)}}\pm 0.12$
$\chi_{\rm vertex}^{2}$ | $<25$ | $<25$ | $<10$ | $<25$ | $<25$
$\mbox{$p_{T}$}^{\mu\mu}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | - | - | - | $>2$ | $>3.5$
Pre-scale | 0.2 | 0.1 | 1. | 1. | 1.
Rate [Hz] | 50 | 5 | 80 | 115 | 15

Hlt2DiMuonJPsi(Psi2S) and Hlt2DiMuonJPsi(Psi2S)HighPT all select a mass region
around ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}(\psi{(2S)})$.
Hlt2DiMuonJPsi(Psi2S) avoids explicit $p_{T}$ requirements but as a
consequence needs to be pre-scaled to reduce the rate.
Hlt2DiMuonJPsi(Psi2S)HighPT reduces the prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}(\psi{(2S)})$ rate by applying
a $p_{T}$ cut on the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}(\psi{(2S)})$ candidate. Hlt2DiMuonB has its mass cut set high enough
to have an acceptable rate.

The names and corresponding cuts of the detached decay selections are given in
Table 8.

Table 8: HLT2 lines based on two identified muons.  Hlt2DiMuon | Detached | DetachedHeavy | DetachedJPsi
---|---|---|---
Track $\chi^{2}/\rm ndf$ | $<5$ | $<5$ | $<5$
Track IP$\chi^{2}$ | $>9$ | - | -
Mass [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ ] | $>1$ | $>2.95$ | M${}_{J/\psi}\pm 0.12$
${\rm FD}\chi^{2}$ |  $>$49 |  $>$25 |  $>$9
$\chi_{\rm vertex}^{2}$ | $<25$ | $<25$ | $<25$
$\mbox{$p_{T}$}^{\mu\mu}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] | $>1.5$ | - | -
Rate [Hz] | 70 | 75 | 35

Hlt2DiMuonDetached is the main trigger for low mass muon pairs.
Hlt2DiMuonDetachedHeavy is an analogous trigger line for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and higher mass muon pairs,
with relaxed lifetime selection criteria. Hlt2DiMuonDetachedJPsi enhances the
efficiency for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ by reducing the
flight distance requirement for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidates even further. Figure 8 compares the performance of two
representative HLT2DiMuon lines: Hlt2DiMuonJPsiHighPT and
Hlt2DiMuonDetachedJPsi in
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays.
Hlt2DiMuonJPsiHighPT avoids by design a bias in the proper lifetime, at the
price of losing efficiency at low
$\mbox{$p_{T}$}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$. The detached
lines allow the selection of decays with a significant flight distance with
high efficiency even at low
$\mbox{$p_{T}$}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$, but their
efficiency is reduced at small lifetimes.

Figure 8: Efficiencies $\epsilon^{\rm TOS}$ of Hlt2DiMuonJPsiHighPT and
Hlt2DiMuonDetachedJPsi for
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ as a
function of $p_{T}$ and $\tau$ of the $B^{+}$.

There are nine BBDT topological lines: Hlt2Topo$n$Body, Hlt2TopoMu$n$Body and
Hlt2TopoE$n$Body, where $n$=2,3,4 for the multiplicities considered. TopoMu
(TopoE) require at least one of the decay particles to have been identified as
a muon (electron). Each line returns an output of the BBDT between 0 and 1.
Hlt2Topo$n$Body lines accept events with a combined rate of 930 Hz with a cut
on the BBDT output at 0.4, 0.4 and 0.3 for the 2, 3 and 4 body lines
respectively. While the TopoMu and TopoE lines are based on the same BBDT, the
extra requirement of either a muon or electron allows the cut on the BBDT
output to be reduced to 0.1 for all six lines, which results in rates of 290
and 260 Hz for TopoMu and TopoE respectively.

The performance of the topological lines is given in Fig. 9 for fully hadronic
$B$-decays and Fig. 10 for
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decays.
Figure 10 also shows the complementarity of Hlt2Topo$n$Body and
Hlt2TopoMu$n$Body; the efficiency increases if either of these lines has
selected the signal event. The inclusive performance of the topological lines
is demonstrated in Fig. 10 by giving the performance of Hlt2Topo2Body alone.
This line requires only two of the three decay tracks of
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ to have
been reconstructed and selected. Adding Hlt2Topo3Body mainly recovers
efficiency at low $p_{T}$ compared to the Hlt2Topo2Body line alone.

Figure 9:  Efficiency $\epsilon^{\rm TOS}$ if at least one of the lines
Hlt2Topo$n$Body, with $n=2,3$, selected the event for $B^{-}\\!\rightarrow
D^{0}\pi^{-}$ and one of the lines with $n=2,3,4$ for $B^{0}\\!\rightarrow
D^{-}\pi^{+}$ as a function of $p_{T}$ and $\tau$ of the $B$-meson. The
efficiency is measured relative to events that are TOS in Hlt1TrackAllL0.

Figure 10:  Efficiency $\epsilon^{\rm TOS}$ if at least one of the lines
Hlt2Topo$n$Body or Hlt2TopoMu$n$Body, with $n=2,3$, selected events for
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, as a
function of $p_{T}$ and $\tau$ of the $B$-meson. Also shown is $\epsilon^{\rm
TOS}$ if the line Hlt2Topo$n$Body, with $n=2,3$, selected the events.
Hlt2Topo2Body shows the inclusive performance of the topological lines. The
efficiency is measured relative to events that are TOS in either
Hlt1TrackAllL0 or Hlt1TrackMuon.

Table 9 lists the cuts applied in the two HLT2 exclusive lines
Hlt2CharmHadD02HH$\\_$D02KPi and Hlt2CharmHadD2HHH. The off-line selections of
$D^{0}\rightarrow K^{-}\pi^{+}$ are only slightly tighter than the cuts
applied in HLT2, resulting in an almost maximum efficiency of the
Hlt2CharmHadD02HH$\\_$D02KPi line for this channel, as shown in Fig. 11. This
figure also shows the performance of Hlt2CharmHadD2HHH for $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$. Here HLT2 loses efficiency due to the necessity of first
having to apply hard cuts to two of the three decay products before allowing
an extra reconstruction step for low $p_{T}$ tracks, as described in Section
3.2.3.

Table 9: HLT2 selection cuts applied for the exclusive lines Hlt2CharmHadD02HH$\\_$D02KPi and Hlt2CharmHadD2HHH. The 2-track cuts refer to a candidate constructed of two tracks, and $m_{\rm corr}$ is defined in equation 2. The angle $\alpha$ is the angle between the momentum of the $D$ and the vector connecting the PV with the $D$ vertex. Some selections require that at least one or two tracks pass a cut, indicated with "$\geqq$".  Variable | Hlt2CharmHadD02HH$\\_$D02KPi | Hlt2CharmHadD2HHH
---|---|---
$\chi_{\rm track}^{2}/\rm ndf$ | $<3$ |  $<$3
Track $p_{T}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] |  $>$ 800 |  $>$250
Track $p$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | $>5000$ |  $>$2000
Track $\Sigma$$p_{T}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | - |  $>$ 2500
$\geqq 1$ track $p_{T}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | $>1500$ | -
2-track mass [${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ ] | - |  $<$ 2100
2-track $m_{\rm corr}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ ] | - |  $<$3500
2-track IP$\chi^{2}$ | - |  $>$40
$\geqq 2$ tracks $p_{T}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | - |  $>$500
$\geqq 2$ tracks $p$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | - |  $>$5000
Track IP$\chi^{2}$ | $>9$ | $>5$
$\geqq 2$ tracks IP$\chi^{2}$ | - | $>10$
2-track DOCA [mm] | - |  $<$0.1
$\chi_{\rm vertex}^{2}/\rm ndf$ | $<10$ | $<20$
FD$\chi^{2}$ | $>40$ |  $>$ 150
D IP$\chi^{2}$ | - |  $<$ 12
$D$ cos($\alpha$) | $>0.99985$ | -
$D$ $p_{T}$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ ] | $>2000$ |  $>$ 1000
$D$ mass interval [${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ ] | 1815-1915 | 1800-2040
Rate [Hz] | 260 | 390

Figure 11:  Efficiency $\epsilon^{\rm TOS}$ of the lines Hlt2CharmHadD2HHH and
Hlt2CharmHadD02HH$\\_$D02KPi for $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ and
$D^{0}\rightarrow K^{-}\pi^{+}$ respectively as a function of $p_{T}$ and
$\tau$ of the $D$-meson. The efficiency is measured relative to events that
are TOS in Hlt1TrackAllL0.

##  6 Summary

The LHCb trigger is designed to select charm and beauty hadrons in a large
range of decay modes, and permits the measurement of its efficiency directly
from data. In 2011 the trigger has been tuned to cope with $pp$ interactions
at $\sqrt{s}=7$ TeV, with 1296 colliding bunches in LHCb and an average number
of visible $pp$ interactions per bunch crossing of 1.4. This corresponds to a
bunch crossing rate with at least one visible $pp$ interaction of $\sim 11$
MHz.

L0 reduces this rate to 870 kHz by applying $p_{T}$ cuts on muons and $E_{T}$
cuts on clusters in the calorimeters. HLT1 performs a partial reconstruction
of tracks and performs muon identification. It employs a combination of cuts
on $p_{T}$, invariant mass and IP to reduce the rate to around 43 kHz. HLT2
reconstructs all tracks in the event with $p_{T}$ $>$500
${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. It selects candidates based on lepton
identification, lifetime information and invariant mass. Its output rate is 3
kHz, consisting of 50 $\%$ inclusive hadronic triggers, 25 $\%$ triggers on
leptons and the remaining rate from exclusive triggers, mainly on charmed
hadrons. The efficiencies for the major trigger lines are presented for
representative decay modes as a function of $p_{T}$ and lifetime of $c$ and
$b$-hadrons.

The successful exploitation of the LHC as a beauty factory relies crucially on
the ability to trigger on heavy flavour decays in a hadronic environment. To
achieve this, the trigger is designed to be able to determine the impact
parameter of tracks at a high rate, and to measure the momentum of those
tracks with sufficiently large impact parameter, or to identify them as muon
candidates. The trigger managed to adapt to the larger pile-up conditions
imposed by the machine delivering only 1296 instead of the planned 2622
colliding bunches in the LHC. The trigger performance and the fact that its
efficiency can be evaluated in a data-driven way, in combination with the
excellent performance of the sub-detectors, allowed LHCb to publish more than
40 papers based on the data collected in 2011.

LHCb is preparing to upgrade the detector [11] in 2018. It will feature a
fully software based trigger that will allow it to explore its physics goals
at even larger luminosities.

###### 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 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); ANCS/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on. A special acknowledgement goes to
all our LHCb collaborators who over the years have contributed to obtain the
results presented in this paper.

## References

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L. Breiman, _Bagging predictors_ , Machine Learning 24 (1996) 123.
H. Yang, B.P. Roe, J. Zhu., _Studies of Boosted Decision Trees for MiniBooNE
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Kevin Glocker1, Aaricia Herygers1, Munir Georges1,2

# Allophant: Cross-lingual Phoneme Recognition with Articulatory Attributes

###### Abstract

This paper proposes Allophant, a multilingual phoneme recognizer. It requires
only a phoneme inventory for cross-lingual transfer to a target language,
allowing for low-resource recognition. The architecture combines a
compositional phone embedding approach with individually supervised phonetic
attribute classifiers in a multi-task architecture. We also introduce
Allophoible, an extension of the PHOIBLE database. When combined with a
distance based mapping approach for grapheme-to-phoneme outputs, it allows us
to train on PHOIBLE inventories directly.

By training and evaluating on 34 languages, we found that the addition of
multi-task learning improves the model's capability of being applied to unseen
phonemes and phoneme inventories. On supervised languages we achieve phoneme
error rate improvements of 11 percentage points (pp.) compared to a baseline
without multi-task learning. Evaluation of zero-shot transfer on 84 languages
yielded a decrease in PER of 2.63 pp. over the baseline.

Index Terms: speech recognition, cross-lingual, zero-shot, phoneme recognition

##  1 Introduction

Speech technologies such as automatic speech recognition (ASR) have greatly
improved in recent years. However, despite the increase in research interest
[1, 2, 3, 4, 5, 6], for many low-resource languages these technologies are
still not available or perform poorly. Such languages may be endangered or
lack a ``stable orthography" [7]. Similarly, many models experience
difficulties in recognizing regional or non-native accented speech [8, 9, 10],
for which there is often little data available.

To reduce the amount of training data needed for these languages, various
techniques (e.g., probabilistic transcriptions [11]) and benchmarks [12] have
been proposed. To avoid the dependence on training data in the target
language, architectures have been introduced that allow zero-shot phoneme
recognition on unseen languages using only their phoneme inventories [13, 14].
Both architectures use allophone-to-phoneme mappings (i.e., variations of
phonemes that retain word meanings but are generally articulated in distinct
contexts [15]).

In the ASR2K architecture [16], multilingual acoustic and pronunciation models
are trained jointly without any supervision. They successfully use pre-trained
self-supervised learning (SSL) models, such as the multilingually pre-trained
XLS-R [17, 16]. Additionally, multi-task learning with articulatory attributes
has been shown to improve character error rates in Mandarin [18] and cross-
lingual phoneme error rates [19].

Following the examples set by Allosaurus [13], a ``multilingual allophone
system", and AlloVera [20], a ``multilingual allophone database", we thus
present our multilingual phoneme recognition architecture called ``Allophant"
and phoneme database called ``Allophoible". Allophant combines an allophone
layer and phonetic composition [21, 16] with multi-task learning for cross-
lingual phoneme recognition.

We describe the Allophant architecture in Section 2. In Section 3 we present
Allophoible, an extension of the PHOIBLE database [22] that includes
articulatory attributes for additional phoneme segments such as allophones. We
describe our experiments in Section 4 and present and discuss the results in
Section 5 before concluding in Section 6.

##  2 Allophant Architecture

AgStressAgSyllabic…AgClickCTCCTCCTCXLS-R Raw Audio ConcatenationAffine to
Embedding SizeAgDotPhone Embeddings$L_{N}$…$L_{2}$$L_{1}$CTCCTCCTCAllophone
LayerShared Phoneme LogitsCTCShared Layer Figure 1: Illustration of the
Allophant architecture, including an allophone layer [13], phone composition
[14] and hierarchical multi-task connections [19]. Multi-task models use the
dashed connections and hierarchical multi-task models also use the dotted
connections. ``Shared'' models use the shared layer while all other models use
the allophone layer instead.

The proposed Allophant architecture and its evaluated variants are illustrated
in Figure 1. As in previous work on zero-shot phoneme recognition [16, 23], we
finetune a model trained with an SSL objective. We choose the 300 million
parameter version of the cross-lingual speech representation model (XLS-R),
which was pre-trained on 128 languages [23]. XLS-R was found to outperform
other SSL models for this task [16].

As the phoneme classifier, we use the compositional architecture from [14] and
apply it to the PHOIBLE feature set [22] as motivated in Section 3. In this
architecture, phone embeddings are computed by summing the embeddings of their
attribute values. We designate an embedding to represent each possible value
of the 35 articulatory attributes in addition to a special ``blank''
attribute, which represents blanks for connectionist temporal classification
(CTC) training [24, 14].

Each attribute can have a value of ``+'' if it exists, ``-'' if it does not,
or ``0'' if it is impossible in combination with other attributes of a
phoneme. The only exception for this is the stress attribute, which is only
``-'' or ``0'' in PHOIBLE. Since we do not consider tonal languages (e.g.,
Mandarin) in this paper, the tone attribute was unused and therefore removed
from training and inference. Complex phoneme segments such as some diphthongs,
affricates, and multiple articulations contain attribute contours such as
``+,-,-'' instead of only a single value. For simplicity, we only use the
first attribute from complex contours for the composition.

Out of 107 attribute values, six are not used by any phonemes in the training
data and are replaced by zero vectors to not affect inference. The missing
attribute values are [+retractedTongueRoot], [+advancedTongueRoot],
[+epilaryngealSource], [+raisedLarynxEjective], [+loweredLarynxEjective], and
[+click]. We then compute phone logits with the scaled dot product [25, 14]
between the output hidden representation from the final XLS-R layer and the
composed phone or blank embeddings. At training time, phoneme probabilities
are computed by additionally passing the phone logits through an allophone
layer [13, 14, 16]. The resulting language-specific phoneme sequences are then
trained with CTC loss.

Following our previous work [19], we additionally explicitly supervise
articulatory attribute classifiers for all 35 attributes that are also used
for embedding composition. In this architecture, CTC loss is computed for each
attribute sequence individually and minimized together with the phoneme CTC
loss during training. In contrast to embedding composition, we use the full
complex contours in label sequences for attribute classifiers. As a result,
attribute sequences may differ in length.

To analyze the interactions between embedding composition, multi-task learning
and the allophone layer, we test five variations of the architecture. All
variants use phoneme composition. Two different architectures that are trained
only on phoneme recognition without multi-task learning are used as baselines.
Our first baseline is closest to the compositional model first introduced in
[14] and used as the acoustic model in [16]. We also consider a simplified
form of the proposed architecture without an allophone layer to better
understand the interaction of multi-task learning with phoneme composition on
its own. In variants using this ``Shared'' layer instead we compose embeddings
for the union of all phonemes that occur in the training languages instead of
all allophones during training and optimize it directly. This configuration is
comparable to shared phoneme models used in previous work [13], where a feed-
forward projection layer was used instead of embedding composition to compute
phoneme logits [23, 19].

In addition, we evaluate two more multi-task architectures to identify how the
attribute classifiers impact phoneme recognition. ``Multi-Task Shared'' is the
multi-task analogue to ``Baseline Shared'' for direct comparison without the
allophone layer. ``Multi-Task Hierarchy'' adds the hierarchical connection
between attribute classifiers and the phoneme classifier as in [19]. In this
architecture, probability distributions from attribute classifiers are
concatenated with the acoustic model outputs from XLS-R before passing the
resulting vector through the affine transformation to embedding size.

##  3 Allophoible: Allophone Inventory

Allophoible111https://github.com/Aariciah/allophoible/releases/tag/v1.0.0
(version 1.0) is an open-access inventory that builds upon PHOIBLE 2.0 [22],
which contains phoneme information for $\approx$2200 languages. We provided
phoneme attributes for diacritics and phonemes that were not included as
phonemes in PHOIBLE 2.0 but were included as allophones or in eSpeak NG [26]
(version 1.51). This allows us to use the compositional architecture from [14]
with PHOIBLE allophone mappings and compose phoneme embeddings for eSpeak NG
phonemes.

Table 1: Zero-shot transfer results on UCLA including average PERs, AERs and
the variances of PERs between languages.

Name | PER | PER $\sigma^{2}$ | AER
---|---|---|---
Baseline (15k steps) | 57.01% | 374.35 | –
Baseline Shared | 48.25% | 250.59 | –
Multi-Task Shared | 46.05% | 250.34 | 19.52%
Multi-Task | 45.62% | 229.06 | 19.44%
Multi-Task Hierarchy | 46.09% | 230.28 | 19.18%

Figure 2: Absolute changes in PER on UCLA (top) and CV (bottom) by language
family (Glottolog [27]) from ``Baseline Shared'' to ``Multi-Task'' learning in
percentage points.

##  4 Experiments

###  4.1 Datasets

We selected a subset of at most 800,000 utterances per language from 34
eSpeak-supported, non-tonal languages from the Mozilla Common Voice (CV)
corpus [28] (version 10.0). In total, our training set consisted of 4628h of
speech. For validation and testing we used the CV development and test sets
and filtered some utterances as described in Section 4.2.

Cross-lingual transfer was evaluated on the phonetically transcribed
utterances from the first release of the UCLA Phonetic Corpus [29]. It
contains 5,509 utterances from 95 low-resource languages, of which 11 occurred
in our training set. Since evaluation on these languages would not be zero-
shot, they were removed. Their ISO 639-3 codes are: ``ben'', ``ces'', ``dan'',
``ell'', ``eus'', ``fin'', ``hin'', ``hun'', ``lit'', ``mlt'', and ``nld''.

Furthermore, from the remaining 84 languages, 17 were included in the pre-
training data for XLS-R. While the model being aware of the acoustic
properties of these languages could benefit phoneme recognition after fine-
tuning, we did not find any significant effect (Welch's T-test:
$t(22.7)=0.64,p=0.528$ for ``Multi-Task"). Their ISO 639-3 language codes are:
``abk", ``afr", ``asm", ``guj", ``hau", ``haw", ``heb", ``hrv", ``hye",
``isl", ``kan", ``khm", ``lav", ``lug", ``mal", ``mya", ``yue". For testing,
we use the phoneme inventories specified in the corpus to compose phoneme
embeddings for each language.

###  4.2 Data and Processing

We used the allophone inventories available in PHOIBLE [22] to provide
allophone mappings for the architectures using an allophone layer. This is
applied to all languages in the training set. Since the phoneme inventories in
the database differ to varying degrees from the grapheme-to-phoneme output, we
mapped phonemes to their closest equivalents in each inventory.

All phonemes that are already in the target inventory were retained. Similarly
to previous work [23], we then mapped the remaining phonemes to the target
phonemes with the lowest attribute Hamming distance. For simplicity, we only
considered the first attribute in contours of complex segments for this
mapping. Finally, we prevented e.g., diphthongs being mapped to single vowels
by splitting complex segments whenever the number of segments between pairs of
matched phonemes differ. After splitting, each sub-segment was mapped
individually. Using this approach, we covered approximately 79% of PHOIBLE
inventories for each language compared to 17.5% without it.

To provide a phoneme transcription of the CV data we used eSpeak NG, which was
shown to outperform other grapheme-to-phoneme models [23]. Characters in
eSpeak NG that were not International Phonetic Alphabet characters were
manually replaced. For eSpeak NG, we constructed inventories from the union of
all phonemes that occur in the transcriptions of each language. In all three
CV subsets (i.e., train, validation, and test) we removed the segments with
mixed scripts (e.g., Latin character text in Tamil sentences) as eSpeak NG
treats them as being in a different language. This would lead to a mix in
phoneme inventories (e.g., English phonemes in the Tamil inventory). To ensure
that evaluation results are not skewed based on our mapping, we test on the
unmapped reference transcriptions. For this, we computed embeddings for all
phonemes that occur in the training and test set for all languages at test
time.

###  4.3 Training

Allophant was implemented in Python with PyTorch [30] and Torchaudio [31]. Our
implementation is open-source222https://github.com/kgnlp/allophant. We use the
pre-trained XLS-R model provided by Hugging Face with the transformers library
[32, 17]. We use a dropout rate of 0.2 after the final XLS-R output layer. The
attribute embedding size for composition is set to 640 as in previous work
[14]. We use dynamic batching where batches are constructed from as many raw
audio frame sequences as can fit in an at most 16,000,000 element matrix,
including padding.

Following [17], we use language upsampling with $\alpha=0.5$ for more diverse
multilingual training batches. We use transformer-style warmup [25] but we
keep the learning rate constant for 10,000 steps after linearly increasing it
for 2,500 before starting the decay. This change and step numbers are inspired
by the schedule from [23]. Also following their work, we keep the feature
encoder of XLS-R frozen. However, we finetune all other layers for the entire
training process. We finetuned our models for 30,000 updates on single NVIDIA
A100 instances with 40gb of memory. The average training duration was
$\approx$60 hours. Since not all utterances are seen after 30,000 updates, we
ensured that batches were sampled with the same random seed.

##  5 Results & Discussion

Figure 3: ``Baseline Shared" and ``Multi-Task" PERs for CV test languages with
corresponding hours of training data on a log scale.

Results for zero-shot transfer are presented in Section 5.1 and supervised
languages analyzed in Section 5.2. We use average attribute error rate (AER)
for evaluation. It is computed by calculating the average of individual
attribute error rates as in [19]. The ``Baseline'' model was evaluated after
15,000 (15k) steps instead of 30,000 to allow for a fairer comparison since it
started to overfit to the training data. PERs after 30,000 steps increased by
7.5 pp. and 3.3 pp. on UCLA and CV respectively.

###  5.1 Zero-Shot Transfer on the UCLA Phonetic Corpus

Table 2: CV test set results for languages in the training data.

Name | PER | PER $\sigma^{2}$ | AER
---|---|---|---
Baseline (15k steps) | 46.95% | 133.31 | –
Baseline Shared | 45.35% | 140.17 | –
Multi-Task Shared | 41.20% | 153.31 | 8.88%
Multi-Task | 34.34% | 149.25 | 8.36%
Multi-Task Hierarchy | 34.35% | 128.86 | 8.56%

Evaluation results of the zero-shot capabilities of our model on the UCLA
Phonetic Corpus are listed in Table 1. ``Baseline Shared" performs
substantially better than ``Baseline" by 8.76 percentage points (pp.) PER.
This suggests that the combination of composition and allophone layer does not
generalize as well.

An explanation for this potential overfitting is that the allophone layer
allows the model to maximize logits of allophones of a phoneme even if its
attributes do not represent the acoustic signal well enough. The small
difference between ``Baseline'' and ``Baseline Shared'' on the training data
presented in Section 5.2 supports this hypothesis. Potentially, the
initialization of the attribute embeddings lead to some allophones that have a
high feature Hamming distance to the corresponding phoneme to start with high
logits. Since only the most probable allophone is selected in the allophone
layer via max pooling [13], overfitting to initially high scoring allophones
is possible.

Both non-hierarchical ``Multi-Task'' models outperform our strongest baseline
model (``Baseline Shared''). The ``Multi-Task Shared'' model lowers the PER by
2.2 pp. and ``Multi-Task'' by 2.63 pp., showing the overall benefit of
explicitly supervising attribute classifiers to improve the generalization of
unseen languages. Compared to ``Baseline'', adding multi-task learning
decreases the PER substantially by 11.39 pp. without the overfitting issues.
We suspect that attribute level supervision signals indirectly help stabilize
the attribute embeddings in the composition layer. This might prevent them
from diverging too much from underlying attributes to maximize specific
allophones.

We did not encounter the same benefits of using hierarchical multi-task
learning as in our previous work [19]. With a PER difference of 0.47 pp. it
performs almost identically. This might be since in contrast to a projection
layer with independent weights for each phoneme, composed phone embeddings do
not suffer from the same sparsity and improvements of attribute embeddings for
one phoneme also benefits others. This sharing of attribute-level information
could only be achieved by the hierarchical connection in [19]. On the
attribute level, we found that AERs are within $\approx 0.3$ of each other
across architecture variations. While the hierarchical models reach the lowest
AERs, the difference is smaller than in our previous work [19] likely due to
the same effects we observe on a phoneme level.

In contrast to [19], where a feed-forward layer was used instead of embedding
composition and no correlation between PER and AER was found ($r^{2}=0.016$),
we find a moderate correlation for ``Multi-Task'' ($r^{2}=0.679$). This shows,
how acoustic representations that benefit attribute classification are more
likely to also directly improve phoneme recognition with the compositional
approach.

###  5.2 Common Voice

Results on the CV tests sets for languages in the training data are shown in
Table 2. We find overall very similar patterns in how models perform relative
to each other as on UCLA. When comparing the baselines, the difference between
the ``Baseline'' and ``Baseline Shared'' models of 1.6 PER is much smaller
than on UCLA. This provides further evidence for its tendency to overfit to
the training data and languages.

As in the zero-shot results, both multi-task models outperform the baselines.
Compared to the baselines, the impact of multi-task learning is larger on CV
than on unseen languages. ``Multi-Task Shared'' outperforms ``Baseline
Shared'' by 4.15 pp. PER. Our ``Multi-Task'' model lowers PER substantially by
11 pp. over ``Baseline Shared'' and is our best model overall. This shows that
multi-task learning benefits the embedding composition layers through improved
acoustic representations both cross-lingually and on supervised languages.

We find that ``Multi-Task Hierarchical'' yields almost identical PERs as
``Multi-Task'', with only a decrease in PER variance across languages. This
shows that the hierarchical connection does not benefit supervised languages
either, likely for the same reasons outlined in Section 5.1. For higher
resource languages, additional resources such as phoneme n-gram language
models [23] have been shown to decrease PERs further. Investigating this is
left for future work. Correlation between PER and AER is lower on CV than UCLA
for ``Multi-Task'' ($r^{2}=0.571$).

A more detailed comparison of error rates across languages between ``Baseline
Shared'' and ``Multi-Task'' model alongside hours of training data can be seen
in Figure 3. ``Multi-Task'' reduces PERs to varying degrees for every language
in CV. We improve recognition the most on Kyrgyz (ky, 38.8 pp.), English (en,
27.4 pp.), French (fr, 24.9 pp.), and Polish (pl, 21.9 pp.). To further
analyze the difference in recognition performance, the relative changes are
shown by language family in Figure 2. Recognition of the three Turkic
languages improved the most on average, mainly through Kyrgyz and Turkish. It
is followed by the 22 Indo-European languages, Basque, and Tamil. The latter
is the single Dravidian language in our training set.

In UCLA, Atlantic-Congo is the language family with the most improvements,
likely due to the PER improvements of 10 pp. in Swahili (sw). Afro-Asiatic
languages likely also benefit from the 3.6 pp. PER improvement of Maltese
(mt). Furthermore, PER improvements for Austroasiatic and Austronesian
languages can be explained by the improved modeling of the single languages
from these families in our CV training set. In some language families, PER
also increases after Multi-Task learning, which requires further investigation
in future work. In particular, for the single Salishan language in UCLA, PER
rises by almost 10 pp. over ``Baseline Shared''.

##  6 Conclusion

We proposed Allophant, a multilingual phoneme recognizer that can be applied
zero-shot to low-resource languages. Its architecture combines phonetic
embedding composition with multi-task articulatory attribute classifiers,
improving phoneme recognition across both unseen and supervised languages. We
also introduced Allophoible, an extension of the PHOIBLE database with
attributes for all of its allophones. Together with a mapping scheme of
phonemes from eSpeak NG to PHOIBLE inventories, this allowed us to train
models with a previously introduced attribute composition and allophone layer
on 34 languages.

Additionally, our multi-task learning model outperformed our strongest
baseline without it by 2.63 pp. PER on cross-lingual transfer to 84 languages
of the UCLA phonetic corpus. Furthermore, our multi-task model outperformed
the baseline by 11 pp. PER on the supervised languages from the CV corpus. We
showed that multi-task learning compliments the attribute embedding
composition architectures by improving their generalization to unseen
inventories and reducing overfitting.

A limitation of this work is that phoneme inventories with attributes must be
available for the target languages. Future work could expand on inferring
inventories for unseen languages [33]. More work is needed to investigate the
effects of the Allophant architecture on the recognition of tonal languages
and regional or non-native language variants.

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