text:
\section{L0 Hardware Trigger}
\label{sec:l0}

The bunch crossing frequency of the LHC is 40\ensuremath{{\rm \,MHz}}\xspace. This rate is
reduced by the L0 trigger to a rate of 1\ensuremath{{\rm \,MHz}}\xspace, at which the full
detector is read out. The L0 trigger is implemented in custom
hardware and has a latency of 4\,$\mu$s. It triggers on high
transverse momentum (\mbox{$p_T$}\xspace) muons and on large transverse energy (\mbox{$E_T$}\xspace)
deposition in the calorimeter. A relative momentum resolution of about
20\% can be reached in the L0 muon reconstruction. The thresholds
applied in L0 are given in Tab.~\ref{l0cuts}.

\begin{center}
\begin{table}[h]
\caption{\label{l0cuts}L0 thresholds in 2011 and 2012.}
\vspace{1mm}
\centering
\begin{tabular}{l@{\hspace{5mm}}*{7}{c}{c}}
\hline
&\hspace{8mm} 2011 \hspace{14mm}&\hspace{8mm} 2012 \hspace{14mm}\\
\hline
single muon&1.48\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace&1.76\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace\\
dimuon $\mbox{$p_T$}\xspace_1 \times \mbox{$p_T$}\xspace_2$ &$(1.296\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace)^2$&$(1.6\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace)^2$\\
hadron &3.5\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace&3.7\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace\\
electron&2.5\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace&3\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace\\
photon&2.5\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace&3\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace\\
\hline
\end{tabular}
\end{table}
\end{center}

The trigger efficiencies are measured on offline selected events,
using the techniques described in Section~\ref{sec:tistos}. For L0
muon decisions, evaluated on \ensuremath{B^+\to J/\psi K^+}\xspace events, they are shown in
Fig.~\ref{fig:l0mu}. The single muon trigger contributes the dominant
part to the efficiency. The largest inefficiency originates in 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 integrated efficiency for both L0 muon triggers combined is
evaluated to be 89\%.

\begin{figure}[b]
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig1_L0MuonEff_PT.pdf}
\caption{\label{fig:l0mu} L0 muon trigger performance: TOS trigger
  efficiency for selected \ensuremath{B^+\to J/\psi K^+}\xspace candidates.}
\end{minipage}\hspace{2pc}%
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig21_L0Hadron_PT.pdf}
\caption{\label{fig:l0h}
L0 hadron trigger performance: TOS trigger efficiency for different
beauty and charm decay modes.}
\end{minipage}
\end{figure}

The L0 hadron efficiency is shown in Fig.~\ref{fig:l0h} for the two
and three prong beauty decays \ensuremath{\Bd\to K^+\pi^-}\xspace and \ensuremath{\Bd\to D^0\pi^-}\xspace and the two, three and
four prong charm decays \ensuremath{\D^0\to K^-\pi^+}\xspace, \ensuremath{\Dp\to K^-\pi^+\pi^+}\xspace and \ensuremath{D^{*+}\to D^0\pi^+}\xspace. The two prong
beauty decay is most efficiently triggered by the L0 hadron \mbox{$E_T$}\xspace
criterion (\ensuremath{\epsilon^{TOS}}\xspace = 40\%) and the four prong charm decay \ensuremath{D^{*+}\to D^0\pi^+}\xspace
is selected with the lowest efficiency (\ensuremath{\epsilon^{TOS}}\xspace = 22\%).  The other modes
lie in between, see Fig.~\ref{fig:l0h}.
Allowing also TIS triggers, the integrated efficiencies increases
significantly, (e.g. to \ensuremath{\epsilon^{TRIG}}\xspace=53\% for \ensuremath{\Bd\to K^+\pi^-}\xspace).

The total output rate of the L0 trigger is limited to 1\ensuremath{{\rm \,MHz}}\xspace, the
maximum rate at which the LHCb detector can be read out. This output
rate is composed of approximately 400\ensuremath{{\rm \,kHz}}\xspace of muon triggers (\texttt{L0Muon}
and \texttt{L0DiMuon}), 490\ensuremath{{\rm \,kHz}}\xspace \texttt{L0Hadron} triggers and 150\ensuremath{{\rm \,kHz}}\xspace
\texttt{L0Photon} and \texttt{L0Electron} triggers.

\section{Deferred trigger}

The LHC machine delivers stable beams only for about 30\% of the time. In
order to use the idle time of the Event Filter Farm, the local hard
discs of the Event Filter Farm nodes are used. In this approach, called deferred
triggering, about 20\% of the L0 accepted events are temporarily
saved. They are analysed at a later time during the inter-fill
gaps. The scheme of deferred triggering is discussed in more detail in
Ref.~\cite{mFrank}. This more optimal usage of CPU resources allowed
to improve the track reconstruction in HLT2 in two ways:
\begin{itemize}
\item
it allowed to decrease the \mbox{$p_T$}\xspace requirement inside the forward tracking
algorithm from 500\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace to 300\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace, and
\item
allowed the implementation of a specialised track reconstruction for
long lived particles (e.g. \KS), which reconstructs tracks also if no
hits are found in the Velo detector.
\end{itemize}
These modifications of the trigger configuration enhanced the
performance to select charm decays significantly.

\section{Future developments beyond LS1

The restart of the LHC accelerator after long shutdown 1 is
planned for 2015. The HLT1 and HLT2 will then be decoupled from each
other and  the deferral of events will occur after they are accepted
by HLT1. This deferral at a reduced rate allows to buffer the data
significantly longer and thus allows to perform an online calibration
of the detector.
The most important part here is the run-by-run calibration of the
refractive index and the mirror alignment of the RICH detectors.
This will allow PID selections in HLT2 which are very close in
performance to the currently used offline selections.
This enables to specifically select Cabibbo suppressed charm decays
and suppress the dominant Cabibbo favoured decays with pre-scales.
Details of the planned splitting between HLT1 and HLT2 are
given in Ref.~\cite{sebastian}.
In addition, LHCb will be able to profit
from a larger trigger farm. Increased computing resources available in
2015 will allow to record about 12.5\ensuremath{{\rm \,kHz}}\xspace of events to disk.
\vskip 2mm

\begin{figure}[h]
\centering
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/upgrade.pdf}
\caption{\label{fig:upgrade} Expected increase in signal yield per
  unit luminosity dependent on the LLT output rate for three benchmark
channels.}
\end{minipage}\hspace{2pc}%
\end{figure}
The upgraded LHCb detector following long shutdown 2 will
allow a detector readout at the full bunch crossing rate of 40\ensuremath{{\rm \,MHz}}\xspace.
A Low Level Trigger (LLT) with variable output rate between 1 and 40\ensuremath{{\rm \,MHz}}\xspace
will initially reduce the HLT input rate until the full DAQ network
and CPU farm are installed.
Fig.~\ref{fig:upgrade} shows the factor in signal yield for hadronic
channels that can be gained if the 1\ensuremath{{\rm \,MHz}}\xspace L0 trigger bottleneck is
removed by a  a flexible LLT. From LLT rates of 10\ensuremath{{\rm \,MHz}}\xspace onwards,
factors between 10 and 20 can be gained, depending on the particular
decay channel.

\section{High Level Trigger}
\label{sec:hlt}

The High Level Trigger consists of two stages, HLT1 and HLT2. The
first stage, HLT1, performs a partial event reconstruction and an
inclusive selection of signal candidates. At the reduced rate of
80\ensuremath{{\rm \,kHz}}\xspace, HLT2 performs a full event reconstruction with only minor
adjustments to the offline reconstruction sequence. After this
reconstruction, a set of inclusive and exclusive selections reduces
the trigger rate to 5\ensuremath{{\rm \,kHz}}\xspace, which are saved for later offline analysis.
The rates discussed above are average rates from the 2012 run of the
LHC, in 2011 the HLT1 output rate was approximately 40\ensuremath{{\rm \,kHz}}\xspace and the
HLT2 output rate was 3\ensuremath{{\rm \,kHz}}\xspace.

\subsection{First level software trigger}

The partial reconstruction in HLT1 starts by reconstructing track
segments in the vertex detector (VELO). High IP track segments and
track segments that can be matched with hits in the muon chambers are
then extrapolated into the main tracker. This extrapolation is done
using the identical forward tracking algorithm~\cite{Callot:1033584} as used in
offline processing, however, with reduced search window sizes
corresponding to  a minimum \mbox{$p_T$}\xspace requirement.

The inclusive beauty and charm trigger line \texttt{Hlt1TrackAllL0}
selects good quality track candidates based on their \mbox{$p_T$}\xspace ($\mbox{$p_T$}\xspace>1.6
\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$) and displacement from the primary vertex. This trigger line gets the dominant part
of the HLT1 bandwidth allocated, about 58\ensuremath{{\rm \,kHz}}\xspace. It is the dominant
trigger line for most physics channels that do not contain leptons in
the final state. The performance of HLT1 for hadronic signatures is
shown in Fig.~\ref{fig:hlt1h_pt} as a function of resonance \mbox{$p_T$}\xspace.

\vskip 2mm

A similar line exists if the track is matched with hits in the muon
chambers~\cite{Aaij:1384386}, \texttt{Hlt1TrackMuon}. This single muon trigger line
selects good quality muon candidates with a $\mbox{$p_T$}\xspace>1\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$ that are not
coming from the primary vertex.
Single muon candidates which satisfy a \mbox{$p_T$}\xspace requirement of
$\mbox{$p_T$}\xspace>4.8\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$ are selected by the line \texttt{Hlt1SingleMuonHighPT}
without any vertex separation requirements.

Dimuon candidates are either selected based on their mass
($m_{\mu\mu}>2.5\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$) without any kind of displacement requirement
(\texttt{Hlt1DiMuonHighMass}), or based on the distance between
primary and secondary
vertex, but without the mass restriction (\texttt{Hlt1DiMuonLowMass}). The dominant inefficiency for
these lines originates in the online muon identification algorithms.
The performance of HLT1 at selecting muonic signatures is shown in
Fig.~\ref{fig:hlt1mu_pt} as a function of \mbox{$p_T$}\xspace of the \ensuremath{B^+}\xspace
candidate. The integrated efficiency is summarised in Tab.~\ref{tab:HLT1}.

\begin{figure}[b]
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig5_Hlt1TrackAllL0_PT.pdf}
\caption{\label{fig:hlt1h_pt} \texttt{Hlt1TrackAllL0} per\-for\-mance: TOS
  efficiency for various channels as a
  function of \ensuremath{\PB}\xspace or \ensuremath{D^0}\xspace \mbox{$p_T$}\xspace.}
\end{minipage}\hspace{2pc}%
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig3_Hlt1MuonEff_PT.pdf}
\caption{\label{fig:hlt1mu_pt} HLT1 muon trigger performance: TOS
  efficiency for \ensuremath{B^+\to J/\psi K^+}\xspace candidates as function of \ensuremath{B^+}\xspace \mbox{$p_T$}\xspace.}
\end{minipage}%
\end{figure}

\begin{center}
\begin{table}[h]
\caption{\label{tab:HLT1} Integrated efficiencies of the HLT1
  triggers, normalised to events that are offline selected (see
  Sec.\ref{sec:tistos}) and have passed the previous trigger level.}
\vspace{1mm}
\centering
\begin{tabular}{c|c|c
\hline
channel & trigger line & \ensuremath{\epsilon^{TOS}}\xspace\\
\hline
\ensuremath{B^+\to J/\psi K^+}\xspace&single muon (dimuon)&90\% (69\%)\\
\ensuremath{\Bd\to K^+\pi^-}\xspace&1Track&86\%\\
\ensuremath{\Bd\to D^0\pi^-}\xspace&1Track&89\%\\
\ensuremath{\D^0\to K^-\pi^+}\xspace&1Track&67\%\\
\ensuremath{\Dp\to K^-\pi^+\pi^+}\xspace&1Track&59\%\\
\ensuremath{D^{*+}\to D^0\pi^+}\xspace&1Track&60\%\\
\hline
\end{tabular}
\end{table}
\end{center}

The trigger efficiency for events that are triggered by the
\texttt{L0Photon} or \texttt{L0Electron} triggers are enhanced by the
\texttt{Hlt1TrackPhoton} trigger line, which has relaxed track quality
and \mbox{$p_T$}\xspace requirements with respect to \texttt{Hlt1TrackAllL0}.

Additionally to the trigger lines discussed above, special lines are
implemented to enhance the trigger performance for events containing
candidates for high \mbox{$p_T$}\xspace electrons, di-protons, displaced vertices or
high \mbox{$E_T$}\xspace jets. A set of technical lines including selections for
luminosity and beam gas measurements complete the list of HLT1
triggers.

\subsection{Second level software trigger}

The second software trigger level, HLT2, performs a full event
reconstruction for all tracks with a minimum \mbox{$p_T$}\xspace of 300\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace. It
reduces the event rate to 5\ensuremath{{\rm \,kHz}}\xspace, which is written
to permanent storage.
Several exclusive and inclusive selections are performed in this
trigger level, the most important ones are discussed in this section.

\vskip 2mm
\noindent\textbf{Generic beauty trigger}\\
A multivariate selection is used to trigger \ensuremath{\PB}\xspace decays into charged
hadrons in an inclusive selection based on two- three- and four-prong
vertices~\cite{Gligorov:1384380}. These trigger lines, named \texttt{Hlt2Topo(N)Body}, are
based on a BDT classifier that uses discretized input
variables~\cite{bonsaiTree} which ensures a fast and robust implementation. A
crucial input to the BDT is the corrected mass, defined as
\begin{equation}
m_{corr}=\sqrt{m^2+|p_{T}^{miss}|^2}+p_{T}^{miss}\, ,
\end{equation}
where $p_{T}^{miss}$ denotes the missing momentum transverse to the
direction of flight. This allows the topological trigger to select
heavy flavour decays even in case not all final state particles are
reconstructed. Fig.~\ref{fig:mcorr} shows the reconstructed 2-body
mass for \decay{\Bd}{\Kstarz\mup\mun}\xspace events, and superimposed, the corrected
mass. Fig.~\ref{fig:topo} shows the efficiency for the topological
trigger lines for \ensuremath{\Bd\to K^+\pi^-}\xspace and \ensuremath{\Bd\to D^0\pi^-}\xspace events as well as the additional
efficiency that can be gained by an exclusive selection for \ensuremath{\Bd\to K^+\pi^-}\xspace in
the low \mbox{$p_T$}\xspace regime. The output rate of the topological trigger is
2\ensuremath{{\rm \,kHz}}\xspace.
\begin{figure}[h]
\begin{minipage}{18pc}

\includegraphics[width=16pc, height=13pc]{figs/CorrectedMass.pdf}
\caption{\label{fig:mcorr} Simulated \decay{\Bd}{\Kstarz\mup\mun}\xspace events: reconstructed
  2-body mass in red and corrected mass (see text for definition) in black.}
\end{minipage}\hspace{2pc}%
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig7_Hlt2TopoN_PT.pdf}
\caption{\label{fig:topo} HLT2 inclusive beauty trigger performance as
a function of \ensuremath{\PB}\xspace \mbox{$p_T$}\xspace. The efficiency for the exclusive \ensuremath{\Bd\to K^+\pi^-}\xspace trigger
line is also given.}
\end{minipage}%
\end{figure}
\begin{figure}[h]
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig9_Hlt2MuonEff_PT.pdf}
\caption{\label{fig:hlt2mu} HLT2 muon trigger performance for the
  \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace trigger lines.}
\end{minipage}\hspace{2pc}%
\begin{minipage}{18pc}
\includegraphics[width=18pc]{figs/Fig11_Hlt2CharmHad_PT.pdf}
\caption{\label{fig:hlt2c} HLT2 charm trigger performance for
  inclusive and exclusive selections.}
\end{minipage}%
\end{figure}

\vskip 2mm
\noindent\textbf{Muon triggers}\\
Several trigger lines select events with one or two identified
muons. The muon identification procedure in HLT2 is identical to the
one used in offline analysis~\cite{LHCbnote:muonid}. Single muon
candidate events are selected if the muon passes a tight \mbox{$p_T$}\xspace requirement
($\mbox{$p_T$}\xspace>10\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$) or if candidates not consistent with the primary vertex
as their origin and pass moderate \mbox{$p_T$}\xspace ($\mbox{$p_T$}\xspace>1.3\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace$) and tight
track quality requirements. Additionally, the latter line is pre-scaled
by a 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 consistent with a \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace resonance mass, three trigger
selection are applied
\begin{itemize}
\item \texttt{Hlt2DiMuonJPsi}: All candidates in a mass range of
  100\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace ($\approx 8\sigma$) around the \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace mass are accepted. In
  a part of the dataset, this prompt \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace trigger was pre-scaled.
\item \texttt{Hlt2DiMuonJPsiHighPT}: If the \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace resonance \mbox{$p_T$}\xspace is
  above 2\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace, the event is selected.
\item \texttt{Hlt2DiMuonDetachedJPsi}: If the \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace candidate vertex
  is separated from the primary vertex, the event is triggered.
\end{itemize}
This set of lines is optimised to fully exploit the large physics
potential in both prompt \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace and $\ensuremath{\PB}\xspace \ensuremath{\rightarrow}\xspace \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace X$
decays. Fig.~\ref{fig:hlt2mu} shows the performance of the \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace
triggers. The effective pre-scale of about a factor two on the prompt
\ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace line \texttt{Hlt2DiMuonJPsi} is visible, as well as the \mbox{$p_T$}\xspace turn
on of the \texttt{Hlt2DiMuonJPsiHighPT} line.
The total output rate of all single and dimuon trigger lines is about 1\ensuremath{{\rm \,kHz}}\xspace.

\vskip 2mm
\noindent\textbf{Charm triggers}\\
In the 2012 running, about 600\ensuremath{{\rm \,kHz}}\xspace of $c\bar{c}$-events are produced
in the acceptance of the LHCb spectrometer. This high rate implies
tight cuts on the invariant mass in exclusive trigger selections. Only
the decay chain \ensuremath{D^{*+}\to D^0\pi^+}\xspace can be selected inclusively, i.e. only
reconstructing two charged tracks from the \ensuremath{\D^0}\xspace decay matched to a slow
pion from the \ensuremath{D^{*+}}\xspace decay.
The mass difference between the \ensuremath{D^{*+}}\xspace and \ensuremath{\D^0}\xspace candidates remains a good
discriminating variable because of the small q-value of the decay,
enabling the rate to be sufficiently reduced.
The \ensuremath{\D^0}\xspace is partially reconstructed in all
different combinations of $\pi^\pm$, $K^\pm$, $p$, $\mu^\pm$, \KS or $\Lambda^0$
allowing both rare decay and CP violation measurements.
The dominant exclusive selections for prompt
charm are the hadronic two body selection \texttt{Hlt2CharmHadD02HH}
and three body selection \texttt{Hlt2CharmHadD2HHH}. The efficiency of
these trigger lines is summarised in Fig.~\ref{fig:hlt2c}.
Further selections for hadronic, leptonic and semi-leptonic \ensuremath{D^0}\xspace and \ensuremath{\L_c}\xspace
decays are implemented.
The total output rate of all charm selections is about 2\ensuremath{{\rm \,kHz}}\xspace.

\section{Introduction}

The LHCb detector, discussed in detail in Ref.~\cite{Alves:2008zz}, is
a single arm forward spectrometer that covers a pseudo-rapidity range
of $2<\eta<5$, with the primary purpose of performing precision measurements at
the LHC. The trigger system of the LHCb experiment consists of two
levels: the first level, implemented in hardware (L0), and the High
Level Trigger (HLT), implemented in a CPU farm of about 29\,000
logical cores. The LHCb trigger system and its performance during 2011
data taking has
been described in detail in Ref.~\cite{LHCb-DP-2012-004}. This paper
describes the adjustments of the system for 2012 running and evaluates
the performance on 2012 data.

The detector includes a high-precision tracking system consisting of a
silicon-strip vertex detector surrounding the pp interaction region, a
large-area silicon-strip detector located upstream of a dipole magnet
with a bending power of about 4\,Tm, and three stations of silicon-strip
detectors and straw drift tubes placed downstream.
Different types of charged hadrons are distinguished by information
from two ring-imaging Cherenkov detectors. Photon, electron and hadron
candidates are identified by a calorimeter system consisting of
scintillating-pad and pre-shower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a
system composed of alternating layers of iron and multiwire
proportional chambers.
The LHCb detector was originally designed for an instantaneous
luminosity of ${\cal L} = 2 \cdot 10^{32}\,{\rm cm}^{-2}{\rm s}^{-1}$. During the
running period of 2012, this design luminosity was doubled to ${\cal
  L} = 4 \cdot 10^{32}\,{\rm cm}^{-2}{\rm s}^{-1}$, which was possible thanks to
the excellent performance of both the detector hardware and the
trigger system. In these conditions, the average number of visible
interactions per bunch crossing is $\mu = 1.6$.

The LHCb trigger system and its performance during the 2012 run will
be discussed first. Afterwards, future developments of the
trigger system for the time after LS1 and the LHCb upgrade are
presented.

\section{List of all symbols}
\subsection{Experiments}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash lhcb} & LHCb\xspace & \texttt{\textbackslash atlas} & ATLAS\xspace & \texttt{\textbackslash cms} & CMS\xspace \\
\texttt{\textbackslash babar} & BABAR\xspace & \texttt{\textbackslash belle} & BELLE\xspace & \texttt{\textbackslash lhc} & LHC\xspace \\
\end{tabular*}

\subsection{Leptons}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash electron} & \ensuremath{\Pe}\xspace & \texttt{\textbackslash en} & \en & \texttt{\textbackslash ep} & \ensuremath{\Pe^+}\xspace \\
\texttt{\textbackslash epm} & \epm & \texttt{\textbackslash epem} & \ensuremath{\Pe^+\Pe^-}\xspace & \texttt{\textbackslash ee} & \ensuremath{\Pe^-\Pe^-}\xspace \\
\texttt{\textbackslash mmu} & \ensuremath{\Pmu}\xspace & \texttt{\textbackslash mup} & \ensuremath{\Pmu^+}\xspace & \texttt{\textbackslash mun} & \mun \\
\texttt{\textbackslash mumu} & \ensuremath{\Pmu^+\Pmu^-}\xspace & \texttt{\textbackslash mtau} & \ensuremath{\Ptau}\xspace & \texttt{\textbackslash taup} & \ensuremath{\Ptau^+}\xspace \\
\texttt{\textbackslash taum} & \ensuremath{\Ptau^-}\xspace & \texttt{\textbackslash tautau} & \ensuremath{\Ptau^+\Ptau^-}\xspace & \texttt{\textbackslash ellm} & \ensuremath{\ell^-}\xspace \\
\texttt{\textbackslash ellp} & \ensuremath{\ell^+}\xspace & \texttt{\textbackslash ellell} & \ensuremath{\ell^+ \ell^-}\xspace & \texttt{\textbackslash neu} & \ensuremath{\Pnu}\xspace \\
\texttt{\textbackslash neub} & \ensuremath{\overline{\Pnu}}\xspace & \texttt{\textbackslash nuenueb} & \ensuremath{\neu\neub}\xspace & \texttt{\textbackslash neue} & \ensuremath{\neu_e}\xspace \\
\texttt{\textbackslash neueb} & \ensuremath{\neub_e}\xspace & \texttt{\textbackslash neueneueb} & \ensuremath{\neue\neueb}\xspace & \texttt{\textbackslash neum} & \ensuremath{\neu_\mu}\xspace \\
\texttt{\textbackslash neumb} & \ensuremath{\neub_\mu}\xspace & \texttt{\textbackslash neumneumb} & \ensuremath{\neum\neumb}\xspace & \texttt{\textbackslash neut} & \ensuremath{\neu_\tau}\xspace \\
\texttt{\textbackslash neutb} & \ensuremath{\neub_\tau}\xspace & \texttt{\textbackslash neutneutb} & \ensuremath{\neut\neutb}\xspace & \texttt{\textbackslash neul} & \ensuremath{\neu_\ell}\xspace \\
\texttt{\textbackslash neulb} & \ensuremath{\neub_\ell}\xspace & \texttt{\textbackslash neulneulb} & \ensuremath{\neul\neulb}\xspace &  \\
\end{tabular*}

\subsection{Gauge bosons and scalars}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash g} & \ensuremath{\Pgamma}\xspace & \texttt{\textbackslash H} & \ensuremath{\PH^0}\xspace & \texttt{\textbackslash Hp} & \ensuremath{\PH^+}\xspace \\
\texttt{\textbackslash Hm} & \ensuremath{\PH^-}\xspace & \texttt{\textbackslash Hpm} & \ensuremath{\PH^\pm}\xspace & \texttt{\textbackslash W} & \ensuremath{\PW}\xspace \\
\texttt{\textbackslash Wp} & \ensuremath{\PW^+}\xspace & \texttt{\textbackslash Wm} & \ensuremath{\PW^-}\xspace & \texttt{\textbackslash Wpm} & \ensuremath{\PW^\pm}\xspace \\
\texttt{\textbackslash Z} & \ensuremath{\PZ^0}\xspace &  \\
\end{tabular*}

\subsection{Quarks}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash q} & \ensuremath{\Pq}\xspace & \texttt{\textbackslash qbar} & \ensuremath{\overline \q}\xspace & \texttt{\textbackslash qqbar} & \ensuremath{\q\qbar}\xspace \\
\texttt{\textbackslash u} & \ensuremath{\Pu}\xspace & \texttt{\textbackslash ubar} & \ensuremath{\overline \u}\xspace & \texttt{\textbackslash uubar} & \ensuremath{\u\ubar}\xspace \\
\texttt{\textbackslash d} & \ensuremath{\Pd}\xspace & \texttt{\textbackslash dbar} & \ensuremath{\overline \d}\xspace & \texttt{\textbackslash ddbar} & \ensuremath{\d\dbar}\xspace \\
\texttt{\textbackslash s} & \ensuremath{\Ps}\xspace & \texttt{\textbackslash sbar} & \ensuremath{\overline \s}\xspace & \texttt{\textbackslash ssbar} & \ensuremath{\s\sbar}\xspace \\
\texttt{\textbackslash c} & \ensuremath{\Pc}\xspace & \texttt{\textbackslash cbar} & \ensuremath{\overline \c}\xspace & \texttt{\textbackslash ccbar} & \ensuremath{\c\cbar}\xspace \\
\texttt{\textbackslash b} & \ensuremath{\Pb}\xspace & \texttt{\textbackslash bbar} & \ensuremath{\overline \b}\xspace & \texttt{\textbackslash bbbar} & \ensuremath{\b\bbar}\xspace \\
\texttt{\textbackslash t} & \ensuremath{\Pt}\xspace & \texttt{\textbackslash tbar} & \ensuremath{\overline \t}\xspace & \texttt{\textbackslash ttbar} & \ensuremath{\t\tbar}\xspace \\
\end{tabular*}

\subsection{Light mesons}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash pion} & \ensuremath{\Ppi}\xspace & \texttt{\textbackslash piz} & \ensuremath{\pion^0}\xspace & \texttt{\textbackslash pizs} & \ensuremath{\pion^0\mbox\,\rm{s}}\xspace \\
\texttt{\textbackslash ppz} & \ensuremath{\pion^0\pion^0}\xspace & \texttt{\textbackslash pip} & \ensuremath{\pion^+}\xspace & \texttt{\textbackslash pim} & \ensuremath{\pion^-}\xspace \\
\texttt{\textbackslash pipi} & \ensuremath{\pion^+\pion^-}\xspace & \texttt{\textbackslash pipm} & \ensuremath{\pion^\pm}\xspace & \texttt{\textbackslash pimp} & \ensuremath{\pion^\mp}\xspace \\
\texttt{\textbackslash kaon} & \ensuremath{\PK}\xspace & \texttt{\textbackslash Kb} & \ensuremath{\Kbar}\xspace & \texttt{\textbackslash Kz} & \ensuremath{\kaon^0}\xspace \\
\texttt{\textbackslash Kzb} & \ensuremath{\Kbar^0}\xspace & \texttt{\textbackslash KzKzb} & \ensuremath{\Kz \kern -0.16em \Kzb}\xspace & \texttt{\textbackslash Kp} & \ensuremath{\kaon^+}\xspace \\
\texttt{\textbackslash Km} & \ensuremath{\kaon^-}\xspace & \texttt{\textbackslash Kpm} & \ensuremath{\kaon^\pm}\xspace & \texttt{\textbackslash Kmp} & \ensuremath{\kaon^\mp}\xspace \\
\texttt{\textbackslash KpKm} & \ensuremath{\Kp \kern -0.16em \Km}\xspace & \texttt{\textbackslash KS} & \KS & \texttt{\textbackslash KL} & \KL \\
\texttt{\textbackslash Kstarz} & \ensuremath{\kaon^{*0}}\xspace & \texttt{\textbackslash Kstarzb} & \ensuremath{\Kbar^{*0}}\xspace & \texttt{\textbackslash Kstar} & \ensuremath{\kaon^*}\xspace \\
\texttt{\textbackslash Kstarb} & \ensuremath{\Kbar^*}\xspace & \texttt{\textbackslash Kstarp} & \ensuremath{\kaon^{*+}}\xspace & \texttt{\textbackslash Kstarm} & \ensuremath{\kaon^{*-}}\xspace \\
\texttt{\textbackslash Kstarpm} & \ensuremath{\kaon^{*\pm}}\xspace & \texttt{\textbackslash Kstarmp} & \ensuremath{\kaon^{*\mp}}\xspace & \texttt{\textbackslash etapr} & \ensuremath{\Peta^{\prime}}\xspace \\
\end{tabular*}

\subsection{Heavy mesons}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash D} & \ensuremath{D^0}\xspace & \texttt{\textbackslash Db} & \ensuremath{\Dbar}\xspace & \texttt{\textbackslash Dz} & \ensuremath{\D^0}\xspace \\
\texttt{\textbackslash Dzb} & \ensuremath{\Dbar^0}\xspace & \texttt{\textbackslash DzDzb} & \ensuremath{\Dz {\kern -0.16em \Dzb}}\xspace & \texttt{\textbackslash Dp} & \ensuremath{\D^+}\xspace \\
\texttt{\textbackslash Dm} & \ensuremath{\D^-}\xspace & \texttt{\textbackslash Dpm} & \ensuremath{\D^\pm}\xspace & \texttt{\textbackslash Dmp} & \ensuremath{\D^\mp}\xspace \\
\texttt{\textbackslash DpDm} & \ensuremath{\Dp {\kern -0.16em \Dm}}\xspace & \texttt{\textbackslash Dstar} & \ensuremath{\D^*}\xspace & \texttt{\textbackslash Dstarb} & \ensuremath{\Dbar^*}\xspace \\
\texttt{\textbackslash Dstarz} & \ensuremath{\D^{*0}}\xspace & \texttt{\textbackslash Dstarzb} & \ensuremath{\Dbar^{*0}}\xspace & \texttt{\textbackslash Dstarp} & \ensuremath{\D^{*+}}\xspace \\
\texttt{\textbackslash Dstarm} & \ensuremath{\D^{*-}}\xspace & \texttt{\textbackslash Dstarpm} & \ensuremath{\D^{*\pm}}\xspace & \texttt{\textbackslash Dstarmp} & \ensuremath{\D^{*\mp}}\xspace \\
\texttt{\textbackslash Ds} & \ensuremath{\D^+_s}\xspace & \texttt{\textbackslash Dsb} & \ensuremath{\Dbar^+_s}\xspace & \texttt{\textbackslash Dss} & \ensuremath{\D^{*+}_s}\xspace \\
\texttt{\textbackslash Dspm} & \ensuremath{\D^{\pm}_s}\xspace & \texttt{\textbackslash B} & \ensuremath{\PB}\xspace & \texttt{\textbackslash Bb} & \ensuremath{\Bbar}\xspace \\
\texttt{\textbackslash BBbar} & \BBbar & \texttt{\textbackslash Bz} & \ensuremath{\B^0}\xspace & \texttt{\textbackslash Bzb} & \ensuremath{\Bbar^0}\xspace \\
\texttt{\textbackslash Bu} & \ensuremath{B^+}\xspace & \texttt{\textbackslash Bub} & \ensuremath{\B^-}\xspace & \texttt{\textbackslash Bp} & \ensuremath{\Bu}\xspace \\
\texttt{\textbackslash Bm} & \ensuremath{\Bub}\xspace & \texttt{\textbackslash Bpm} & \ensuremath{\B^\pm}\xspace & \texttt{\textbackslash Bmp} & \ensuremath{\B^\mp}\xspace \\
\texttt{\textbackslash Bd} & \ensuremath{B^0_d}\xspace & \texttt{\textbackslash Bs} & \ensuremath{B^0_s}\xspace & \texttt{\textbackslash Bsb} & \ensuremath{\Bbar^0_s}\xspace \\
\texttt{\textbackslash Bdb} & \ensuremath{\Bbar^0}\xspace & \texttt{\textbackslash Bc} & \ensuremath{\B_c^+}\xspace & \texttt{\textbackslash Bcb} & \ensuremath{\B_c^-}\xspace \\
\end{tabular*}

\subsection{Onia}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash jpsi} & \ensuremath{{\PJ\mskip -3mu/\mskip -2mu\Ppsi\mskip 2mu}}\xspace & \texttt{\textbackslash psitwos} & \ensuremath{\Ppsi{(2S)}}\xspace & \texttt{\textbackslash psiprpr} & \ensuremath{\Ppsi(3770)}\xspace \\
\texttt{\textbackslash etac} & \ensuremath{\Peta_c}\xspace & \texttt{\textbackslash chiczero} & \ensuremath{\Pchi_{c0}}\xspace & \texttt{\textbackslash chicone} & \ensuremath{\Pchi_{c1}}\xspace \\
\texttt{\textbackslash chictwo} & \ensuremath{\Pchi_{c2}}\xspace & \texttt{\textbackslash OneS} & \Y1S & \texttt{\textbackslash TwoS} & \Y2S \\
\texttt{\textbackslash ThreeS} & \Y3S & \texttt{\textbackslash FourS} & \Y4S & \texttt{\textbackslash FiveS} & \Y5S \\
\texttt{\textbackslash chic} & \ensuremath{\Pchi_{c}}\xspace &  \\
\end{tabular*}

\subsection{Baryons}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash proton} & \ensuremath{\Pp}\xspace & \texttt{\textbackslash antiproton} & \ensuremath{\overline \proton}\xspace & \texttt{\textbackslash neutron} & \ensuremath{\Pn}\xspace \\
\texttt{\textbackslash antineutron} & \ensuremath{\overline \neutron}\xspace & \texttt{\textbackslash Deltares} & \ensuremath{\PDelta}\xspace & \texttt{\textbackslash Deltaresbar} & \ensuremath{\overline \Deltares}\xspace \\
\texttt{\textbackslash Xires} & \ensuremath{\PXi}\xspace & \texttt{\textbackslash Xiresbar} & \ensuremath{\overline \Xires}\xspace & \texttt{\textbackslash L} & \ensuremath{\PLambda}\xspace \\
\texttt{\textbackslash Lbar} & \kern 0.2em\overline{\kern -0.2em\Lambda\kern 0.05em}\kern-0.05em{}\xspace & \texttt{\textbackslash Lambdares} & \ensuremath{\PLambda}\xspace & \texttt{\textbackslash Lambdaresbar} & \ensuremath{\overline \Lambdares}\xspace \\
\texttt{\textbackslash Sigmares} & \ensuremath{\PSigma}\xspace & \texttt{\textbackslash Sigmaresbar} & \ensuremath{\overline \Sigmares}\xspace & \texttt{\textbackslash Omegares} & \ensuremath{\POmega}\xspace \\
\texttt{\textbackslash Omegaresbar} & \ensuremath{\overline \Omegares}\xspace & \texttt{\textbackslash Lb} & \ensuremath{\L_b}\xspace & \texttt{\textbackslash Lbbar} & \ensuremath{\Lbar_b}\xspace \\
\texttt{\textbackslash Lc} & \ensuremath{\L_c}\xspace & \texttt{\textbackslash Lcbar} & \ensuremath{\Lbar_c}\xspace &  \\
\end{tabular*}

\subsection{Physics symbols}
\subsubsection{Lifetimes}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash tauBs} & \ensuremath{\tau_{\ensuremath{B^0_s}\xspace}}\xspace & \texttt{\textbackslash tauBd} & \ensuremath{\tau_{\ensuremath{\PB}\xspace}}\xspace & \texttt{\textbackslash tauBz} & \ensuremath{\tau_{\ensuremath{\PB}\xspace}}\xspace \\
\texttt{\textbackslash tauBu} & \ensuremath{\tau_{\ensuremath{\Bu}\xspace}}\xspace & \texttt{\textbackslash tauDp} & \ensuremath{\tau_{\ensuremath{\D^+}\xspace}}\xspace & \texttt{\textbackslash tauDz} & \ensuremath{\tau_{\ensuremath{\D^0}\xspace}}\xspace \\
\texttt{\textbackslash tauL} & \ensuremath{\tau_{\rm L}}\xspace & \texttt{\textbackslash tauH} & \ensuremath{\tau_{\rm H}}\xspace &  \\
\end{tabular*}

\subsubsection{Masses}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash mBd} & \ensuremath{m_{\ensuremath{B^0_d}\xspace}}\xspace & \texttt{\textbackslash mBp} & \ensuremath{m_{\ensuremath{\Bu}\xspace}}\xspace & \texttt{\textbackslash mBs} & \ensuremath{m_{\ensuremath{B^0_s}\xspace}}\xspace \\
\texttt{\textbackslash mBc} & \ensuremath{m_{\ensuremath{\B_c^+}\xspace}}\xspace & \texttt{\textbackslash mLb} & \ensuremath{m_{\ensuremath{\L_b}\xspace}}\xspace &  \\
\end{tabular*}

\subsection{Units}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash unit[1] \textbackslash unit\{kg\}} & \unit{kg} &  \\
\end{tabular*}

\subsubsection{Energy and momentum}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash tev} & \ensuremath{\mathrm{\,Te\kern -0.1em V}}\xspace & \texttt{\textbackslash gev} & \ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace & \texttt{\textbackslash mev} & \ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace \\
\texttt{\textbackslash kev} & \ensuremath{\mathrm{\,ke\kern -0.1em V}}\xspace & \texttt{\textbackslash ev} & \ensuremath{\mathrm{\,e\kern -0.1em V}}\xspace & \texttt{\textbackslash gevc} & \ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c}}\xspace \\
\texttt{\textbackslash mevc} & \ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c}}\xspace & \texttt{\textbackslash gevcc} & \ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace & \texttt{\textbackslash gevgevcccc} & \ensuremath{{\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}}\xspace \\
\texttt{\textbackslash mevcc} & \ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace &  \\
\end{tabular*}

\subsubsection{Distance and area}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash km} & \ensuremath{\rm \,km}\xspace & \texttt{\textbackslash m} & \ensuremath{\rm \,m}\xspace & \texttt{\textbackslash cm} & \ensuremath{\rm \,cm}\xspace \\
\texttt{\textbackslash cma} & \ensuremath{{\rm \,cm}^2}\xspace & \texttt{\textbackslash mm} & \ensuremath{\rm \,mm}\xspace & \texttt{\textbackslash mma} & \ensuremath{{\rm \,mm}^2}\xspace \\
\texttt{\textbackslash mum} & \ensuremath{\,\upmu\rm m}\xspace & \texttt{\textbackslash muma} & \ensuremath{\,\upmu\rm m^2}\xspace & \texttt{\textbackslash nm} & \ensuremath{\rm \,nm}\xspace \\
\texttt{\textbackslash fm} & \ensuremath{\rm \,fm}\xspace & \texttt{\textbackslash nm} & \ensuremath{\rm \,nm}\xspace & \texttt{\textbackslash barn} & \ensuremath{\rm \,b}\xspace \\
\texttt{\textbackslash barnhyph} & \ensuremath{\rm -b}\xspace & \texttt{\textbackslash mbarn} & \ensuremath{\rm \,mb}\xspace & \texttt{\textbackslash mub} & \ensuremath{\rm \,\upmu b}\xspace \\
\texttt{\textbackslash mbarnhyph} & \ensuremath{\rm -mb}\xspace & \texttt{\textbackslash pb} & \ensuremath{\rm \,pb}\xspace & \texttt{\textbackslash invpb} & \ensuremath{\,{\rm pb}^{-1}}\xspace \\
\texttt{\textbackslash fb} & \ensuremath{\mbox{\,fb}}\xspace & \texttt{\textbackslash invfb} & \ensuremath{\,{\rm fb}^{-1}}\xspace &  \\
\end{tabular*}

\subsubsection{Time and mass}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash sec} & \ensuremath{\rm {\,s}}\xspace & \texttt{\textbackslash ms} & \ensuremath{{\rm \,ms}}\xspace & \texttt{\textbackslash mus} & \ensuremath{\,\upmu{\rm s}}\xspace \\
\texttt{\textbackslash ns} & \ensuremath{{\rm \,ns}}\xspace & \texttt{\textbackslash ps} & \ensuremath{{\rm \,ps}}\xspace & \texttt{\textbackslash fs} & \ensuremath{\rm \,fs}\xspace \\
\texttt{\textbackslash mhz} & \ensuremath{{\rm \,MHz}}\xspace & \texttt{\textbackslash khz} & \ensuremath{{\rm \,kHz}}\xspace & \texttt{\textbackslash hz} & \ensuremath{{\rm \,Hz}}\xspace \\
\texttt{\textbackslash invps} & \ensuremath{{\rm \,ps^{-1}}}\xspace &  \\
\end{tabular*}

\subsubsection{Decays}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash BR} & {\ensuremath{\cal B}\xspace} & \texttt{\textbackslash BRvis} & {\ensuremath{\BR_{\rm{vis}}}} & \texttt{\textbackslash decay[2] \textbackslash decay\{\Pa\}\{\Pb \Pc\}} & \decay{\Pa}{\Pb \Pc} \\
\texttt{\textbackslash ra} & \ensuremath{\rightarrow}\xspace & \texttt{\textbackslash to} & \ensuremath{\rightarrow}\xspace &  \\
\end{tabular*}

\subsubsection{Kinematics}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash ptot} & \mbox{$p$}\xspace & \texttt{\textbackslash pt} & \mbox{$p_T$}\xspace & \texttt{\textbackslash et} & \mbox{$E_T$}\xspace \\
\end{tabular*}

\subsubsection{Geometry}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash mphi} & \mbox{$\phi$}\xspace & \texttt{\textbackslash mtheta} & \mbox{$\theta$}\xspace & \texttt{\textbackslash ctheta} & \mbox{$\cos\theta$}\xspace \\
\end{tabular*}

\subsection{QCD parameters}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash as} & \ensuremath{\alpha_{\scriptscriptstyle S}}\xspace & \texttt{\textbackslash MSb} & \ensuremath{\overline{\mathrm{MS}}}\xspace & \texttt{\textbackslash lqcd} & \ensuremath{\Lambda_{\mathrm{QCD}}}\xspace \\
\end{tabular*}

\subsection{CKM, CP violation}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash eps} & \ensuremath{\varepsilon}\xspace & \texttt{\textbackslash epsK} & \ensuremath{\varepsilon_K}\xspace & \texttt{\textbackslash epsB} & \ensuremath{\varepsilon_B}\xspace \\
\texttt{\textbackslash epsp} & \ensuremath{\varepsilon^\prime_K}\xspace & \texttt{\textbackslash CP} & \ensuremath{C\!P}\xspace & \texttt{\textbackslash CPT} & \ensuremath{C\!PT}\xspace \\
\texttt{\textbackslash rhobar} & \ensuremath{\overline \rho}\xspace & \texttt{\textbackslash etabar} & \ensuremath{\overline \eta}\xspace & \texttt{\textbackslash Vud} & \ensuremath{|V_{ud}|}\xspace \\
\texttt{\textbackslash Vcd} & \ensuremath{|V_{cd}|}\xspace & \texttt{\textbackslash Vtd} & \ensuremath{|V_{td}|}\xspace & \texttt{\textbackslash Vus} & \ensuremath{|V_{us}|}\xspace \\
\texttt{\textbackslash Vcs} & \ensuremath{|V_{cs}|}\xspace & \texttt{\textbackslash Vts} & \ensuremath{|V_{ts}|}\xspace & \texttt{\textbackslash Vub} & \ensuremath{|V_{ub}|}\xspace \\
\texttt{\textbackslash Vcb} & \ensuremath{|V_{cb}|}\xspace & \texttt{\textbackslash Vtb} & \ensuremath{|V_{tb}|}\xspace &  \\
\end{tabular*}

\subsection{QM}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash bra[1] \textbackslash bra\{a\}} & \bra{a} & \texttt{\textbackslash ket[1] \textbackslash ket\{b\}} & \ket{b} & \texttt{\textbackslash braket[2] \textbackslash braket\{a\}\{b\}} & \braket{a}{b} \\
\end{tabular*}

\subsubsection{Miscellaneous}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash Xrad} & \ensuremath{X_0}\xspace & \texttt{\textbackslash NIL} & \ensuremath{\lambda_{int}}\xspace & \texttt{\textbackslash krad} & \ensuremath{\rm \,krad}\xspace \\
\texttt{\textbackslash yr} & \ensuremath{\rm \,yr}\xspace & \texttt{\textbackslash hr} & \ensuremath{\rm \,hr}\xspace & \texttt{\textbackslash degc} & \ensuremath{^\circ}{C}\xspace \\
\texttt{\textbackslash degk} & \ensuremath {\rm K}\xspace & \texttt{\textbackslash degrees} & \ensuremath{^{\circ}}\xspace & \texttt{\textbackslash mrad} & \ensuremath{\rm \,mrad}\xspace \\
\texttt{\textbackslash rad} & \ensuremath{\rm \,rad}\xspace & \texttt{\textbackslash sx} & \sx & \texttt{\textbackslash sy} & \sy \\
\texttt{\textbackslash sz} & \sz & \texttt{\textbackslash order} & {\ensuremath{\cal O}}\xspace & \texttt{\textbackslash stat} & \ensuremath{\mathrm{(stat)}}\xspace \\
\texttt{\textbackslash syst} & \ensuremath{\mathrm{(syst)}}\xspace & \texttt{\textbackslash dedx} & \ensuremath{\mathrm{d}\hspace{-0.1em}E/\mathrm{d}x}\xspace & \texttt{\textbackslash chisq} & \ensuremath{\chi^2}\xspace \\
\texttt{\textbackslash lum} & \lum & \texttt{\textbackslash deriv} & \ensuremath{\mathrm{d}} & \texttt{\textbackslash gsim} & \gsim \\
\texttt{\textbackslash lsim} & \lsim &  \\
\end{tabular*}

\subsection{Software}
\subsubsection{Programs}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash evtgen} & \mbox{\textsc{EvtGen}}\xspace & \texttt{\textbackslash pythia} & \mbox{\textsc{Pythia}}\xspace & \texttt{\textbackslash fluka} & \mbox{\textsc{Fluka}}\xspace \\
\texttt{\textbackslash geant} & \mbox{\textsc{GEANT}}\xspace & \texttt{\textbackslash root} & \mbox{\textsc{Root}}\xspace & \texttt{\textbackslash hepmc} & \mbox{\textsc{HepMC}}\xspace \\
\texttt{\textbackslash gauss} & \mbox{\textsc{Gauss}}\xspace & \texttt{\textbackslash gaudi} & \mbox{\textsc{Gaudi}}\xspace & \texttt{\textbackslash brunel} & \mbox{\textsc{Brunel}}\xspace \\
\texttt{\textbackslash davinci} & \mbox{\textsc{DaVinci}}\xspace & \texttt{\textbackslash ganga} & \mbox{\textsc{Ganga}}\xspace & \texttt{\textbackslash dirac} & \mbox{\textsc{DIRAC}}\xspace \\
\texttt{\textbackslash root} & \mbox{\textsc{Root}}\xspace & \texttt{\textbackslash roofit} & \mbox{\textsc{RooFit}}\xspace & \texttt{\textbackslash pyroot} & \mbox{\textsc{PyROOT}}\xspace \\
\end{tabular*}

\subsubsection{Languages}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash cpp} & \mbox{\textsc{C\raisebox{0.1em}{{\footnotesize{++}}}}}\xspace & \texttt{\textbackslash python} & \mbox{\textsc{Python}}\xspace & \texttt{\textbackslash ruby} & \mbox{\textsc{Ruby}}\xspace \\
\texttt{\textbackslash fortran} & \mbox{\textsc{FORTRAN}}\xspace &  \\
\end{tabular*}

\subsubsection{Data processing}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash kbytes} & \ensuremath{{\rm \,kbytes}}\xspace & \texttt{\textbackslash kbsps} & \ensuremath{{\rm \,kbits/s}}\xspace & \texttt{\textbackslash kbits} & \ensuremath{{\rm \,kbits}}\xspace \\
\texttt{\textbackslash kbsps} & \ensuremath{{\rm \,kbits/s}}\xspace & \texttt{\textbackslash mbsps} & \ensuremath{{\rm \,Mbytes/s}}\xspace & \texttt{\textbackslash mbytes} & \ensuremath{{\rm \,Mbytes}}\xspace \\
\texttt{\textbackslash mbps} & \ensuremath{{\rm \,Mbyte/s}}\xspace & \texttt{\textbackslash mbsps} & \ensuremath{{\rm \,Mbytes/s}}\xspace & \texttt{\textbackslash gbsps} & \ensuremath{{\rm \,Gbytes/s}}\xspace \\
\texttt{\textbackslash gbytes} & \ensuremath{{\rm \,Gbytes}}\xspace & \texttt{\textbackslash gbsps} & \ensuremath{{\rm \,Gbytes/s}}\xspace & \texttt{\textbackslash tbytes} & \ensuremath{{\rm \,Tbytes}}\xspace \\
\texttt{\textbackslash tbpy} & \ensuremath{{\rm \,Tbytes/yr}}\xspace &  \\
\end{tabular*}

\subsection{Key channels}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash BdToKstmm} & \decay{\Bd}{\Kstarz\mup\mun}\xspace & \texttt{\textbackslash BdbToKstmm} & \decay{\Bdb}{\Kstarzb\mup\mun}\xspace & \texttt{\textbackslash BsToJPsiPhi} & \decay{\Bs}{\jpsi\phi}\xspace \\
\texttt{\textbackslash BdToJPsiKst} & \decay{\Bd}{\jpsi\Kstarz}\xspace & \texttt{\textbackslash BdbToJPsiKst} & \decay{\Bdb}{\jpsi\Kstarzb}\xspace & \texttt{\textbackslash BsPhiGam} & \decay{\Bd}{\phi \g}\xspace \\
\texttt{\textbackslash BdKstGam} & \decay{\Bd}{\Kstarz \g}\xspace & \texttt{\textbackslash BTohh} & \decay{\B}{\Ph^+ \Ph^-}\xspace & \texttt{\textbackslash BdTopipi} & \decay{\Bd}{\pip\pim}\xspace \\
\texttt{\textbackslash BdToKpi} & \decay{\Bd}{\Kp\pim}\xspace & \texttt{\textbackslash BsToKK} & \decay{\Bs}{\Kp\Km}\xspace & \texttt{\textbackslash BsTopiK} & \decay{\Bs}{\pip\Km}\xspace \\
\end{tabular*}

\subsection{Rare Decays}
\subsubsection{Kinematics}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash qsq} & \ensuremath{q^2}\xspace & \texttt{\textbackslash ctl} & \ensuremath{\cos{\theta_l}}\xspace & \texttt{\textbackslash ctk} & \ensuremath{\cos{\theta_K}}\xspace \\
\end{tabular*}

\subsubsection{Decays}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash BdKstee} & \decay{\Bd}{\Kstarz\epem}\xspace & \texttt{\textbackslash BdbKstee} & \decay{\Bdb}{\Kstarzb\epem}\xspace & \texttt{\textbackslash bsll} & \decay{\b}{\s \ell^+ \ell^-}\xspace \\
\texttt{\textbackslash AFB} & \ensuremath{A_{\mathrm{FB}}}\xspace & \texttt{\textbackslash AT\#1 \textbackslash AT2} & \AT2 & \texttt{\textbackslash btosgam} & \decay{\b}{\s \g}\xspace \\
\texttt{\textbackslash btodgam} & \decay{\b}{\d \g}\xspace & \texttt{\textbackslash Bsmm} & \decay{\Bs}{\mup\mun}\xspace & \texttt{\textbackslash Bdmm} & \decay{\Bd}{\mup\mun}\xspace \\
\end{tabular*}

\subsubsection{Wilson coefficients and operators}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash C\#1 \textbackslash C9} & \C9 & \texttt{\textbackslash Cp\#1 \textbackslash Cp7} & \Cp7 & \texttt{\textbackslash Ceff\#1 \textbackslash Ceff9  } & \Ceff9   \\
\texttt{\textbackslash Cpeff\#1 \textbackslash Cpeff7} & \Cpeff7 & \texttt{\textbackslash Ope\#1 \textbackslash Ope2} & \Ope2 & \texttt{\textbackslash Opep\#1 \textbackslash Opep7} & \Opep7 \\
\end{tabular*}

\subsection{B oscillations}
\subsubsection{Decays}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash dm} & \ensuremath{\Delta m} & \texttt{\textbackslash dms} & \ensuremath{\Delta m_{\ensuremath{\Ps}\xspace}} & \texttt{\textbackslash dmd} & \ensuremath{\Delta m_{\ensuremath{\Pd}\xspace}} \\
\texttt{\textbackslash DG} & \ensuremath{\Delta\Gamma} & \texttt{\textbackslash DGs} & \ensuremath{\Delta\Gamma_{\ensuremath{\Ps}\xspace}} & \texttt{\textbackslash DGd} & \ensuremath{\Delta\Gamma_{\ensuremath{\Pd}\xspace}} \\
\texttt{\textbackslash Gs} & \ensuremath{\Gamma_{\ensuremath{\Ps}\xspace}} & \texttt{\textbackslash Gd} & \ensuremath{\Gamma_{\ensuremath{\Pd}\xspace}} & \texttt{\textbackslash MBq} & \ensuremath{M_{\ensuremath{\PB}\xspace_\ensuremath{\Pq}\xspace}} \\
\texttt{\textbackslash DGq} & \ensuremath{\Delta\Gamma_{\ensuremath{\Pq}\xspace}} & \texttt{\textbackslash Gq} & \ensuremath{\Gamma_{\ensuremath{\Pq}\xspace}} & \texttt{\textbackslash dmq} & \ensuremath{\Delta m_{\ensuremath{\Pq}\xspace}} \\
\texttt{\textbackslash GL} & \ensuremath{\Gamma_{\rm L}} & \texttt{\textbackslash GH} & \ensuremath{\Gamma_{\rm H}} & \texttt{\textbackslash DGsGs} & \ensuremath{\Delta\Gamma_{\ensuremath{\Ps}\xspace}/\Gamma_{\ensuremath{\Ps}\xspace}} \\
\texttt{\textbackslash Delm} & \mbox{$\Delta m $} & \texttt{\textbackslash ACP} & \ensuremath{{\cal A}^{\rm CP}} & \texttt{\textbackslash Adir} & \ensuremath{{\cal A}^{\rm dir}} \\
\texttt{\textbackslash Amix} & \ensuremath{{\cal A}^{\rm mix}} & \texttt{\textbackslash ADelta} & \ensuremath{{\cal A}^\Delta} & \texttt{\textbackslash phid} & \ensuremath{\phi_{\ensuremath{\Pd}\xspace}} \\
\texttt{\textbackslash sinphid} & \ensuremath{\sin\!\phid} & \texttt{\textbackslash phis} & \ensuremath{\phi_{\ensuremath{\Ps}\xspace}} & \texttt{\textbackslash betas} & \ensuremath{\beta_{\ensuremath{\Ps}\xspace}} \\
\texttt{\textbackslash sbetas} & \ensuremath{\sigma(\beta_{\ensuremath{\Ps}\xspace})} & \texttt{\textbackslash stbetas} & \ensuremath{\sigma(2\beta_{\ensuremath{\Ps}\xspace})} & \texttt{\textbackslash stphis} & \ensuremath{\sigma(\phi_{\ensuremath{\Ps}\xspace})} \\
\texttt{\textbackslash sinphis} & \ensuremath{\sin\!\phis} &  \\
\end{tabular*}

\subsubsection{Tagging}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l@{\extracolsep{\fill}}l@{\extracolsep{0.5cm}}l}
\texttt{\textbackslash edet} & {\ensuremath{\varepsilon_{\rm det}}} & \texttt{\textbackslash erec} & {\ensuremath{\varepsilon_{\rm rec/det}}} & \texttt{\textbackslash esel} & {\ensuremath{\varepsilon_{\rm sel/rec}}} \\
\texttt{\textbackslash etrg} & \ensuremath{\epsilon^{TRIG}\xspace} & \texttt{\textbackslash etot} & {\ensuremath{\varepsilon_{\rm tot}}} & \texttt{\textbackslash mistag} & \ensuremath{\omega} \\
\texttt{\textbackslash wcomb} & \ensuremath{\omega^{\rm comb}} & \texttt{\textbackslash etag} & {\ensuremath{\varepsilon_{\rm tag}}} & \texttt{\textbackslash etagcomb} & {\ensuremath{\varepsilon_{\rm tag}^{\rm comb}}} \\
\texttt{\textbackslash effeff} & \ensuremath{\varepsilon_{\rm eff}} & \texttt{\textbackslash effeffcomb} & \ensuremath{\varepsilon_{\rm eff}^{\rm comb}} & \texttt{\textbackslash efftag} & {\ensuremath{\etag(1-2\omega)^2}} \\
\texttt{\textbackslash effD} & {\ensuremath{\etag D^2}} & \texttt{\textbackslash etagprompt} & {\ensuremath{\varepsilon_{\rm tag}^{\rm Pr}}} & \texttt{\textbackslash etagLL} & {\ensuremath{\varepsilon_{\rm tag}^{\rm LL}}} \\
\end{tabular*}

\section{Summary}
The LHCb trigger system has been performing extraordinarily well in the
first running phase of the LHC.
It is designed to select charm and beauty hadrons in a large range of decay
modes and permits the measurement of its efficiency directly on data.
The flexible design of  the HLT, fully
deployed in software, allows to quickly adjust to changes in running
conditions and physics goals. Inclusive selections in the full trigger
chain allow an efficient trigger for basically any beauty decay to
charged tracks.
Several innovative concepts have enabled this performance: the
deferred triggering allows to optimise the trigger usage for mean
instead of peak usage of the available computing
resources. Multivariate selections allow the inclusive selection of
beauty decays into charged tracks with high efficiency.

For the future, several improvements of the trigger system are
planned: the two software trigger levels will be decoupled which
allows calibrations between them and thus a performance much closer to
the one achieved offline.
LHCb is preparing to upgrade the detector in 2018. It will feature a
fully software based trigger system that will allow to explore the
physics goals of the experiment at significantly increased
luminosities.

\section*{References}
\addcontentsline{toc}{section}{References}
\setboolean{inbibliography}{true}
\bibliographystyle{LHCb}

\section{Data-driven performance evaluation}
\label{sec:tistos}

The trigger efficiency is evaluated using events that are reconstructed
using the full offline software and selected with the final analysis
selection for the respective channel. Thus, the trigger efficiency
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 are chosen
to show the performance of the trigger:
\begin{itemize}
\item \ensuremath{B^+\to J/\psi K^+}\xspace, where the $\ensuremath{J/\psi}\xspace \ensuremath{\rightarrow}\xspace \ensuremath{\Pmu^+\Pmu^-}\xspace$ channel is selected. This
  decay allows the evaluation of the muon trigger efficiency and
  serves as excellent proxy for the CP violation and rare decay
  channels containing a dimuon final state.
\item \ensuremath{\Bd\to K^+\pi^-}\xspace as a typical two-body beauty decay.
\item \ensuremath{\Bd\to D^0\pi^-}\xspace, followed by the decay \ensuremath{\D^0\to K^-\pi^+}\xspace as a typical three-body beauty decay.
\item \ensuremath{\D^0\to K^-\pi^+}\xspace as a two-body charm decay.
\item \ensuremath{\Dp\to K^-\pi^+\pi^+}\xspace as a three-body charm decay.
\item \ensuremath{D^{*+}\to D^0\pi^+}\xspace, followed by the four body charm decay $D^{0} \ensuremath{\rightarrow}\xspace K^{-}
  \pi^{+} \pi^{-} \pi^{+}$.
\end{itemize}
These channels and their selections are representative for those used
in most analyses.
The selected charm modes cover the topologies most sensitive to CP
violating effects.
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 measurements 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:
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.
A number of events can be classified as TIS and TOS simultaneously
($N^{TIS\&TOS}$), 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,
\ensuremath{\epsilon^{TIS}}\xspace, is given by \linebreak \ensuremath{\epsilon^{TIS}}\xspace = $N^{TIS\&TOS}/N^{TOS}$, where $N^{TOS}$ is the number of events classified as TOS.
The efficiency to trigger an event on the signal alone, \ensuremath{\epsilon^{TOS}}\xspace, is given by \ensuremath{\epsilon^{TOS}}\xspace = $N^{TIS\&TOS}/N^{TIS}$,
where $N^{TIS}$ is the number of events classified as TIS.


text:
\section{WAVE FUNCTIONS}
We have been using wave functions reconstructed from lattice Monte Carlo
simulations of QCD to calculate the masses of orbital excitations.
We have also been trying to use wave functions as a tool for hadronic
phenomenology. Our work has been presented in a series of papers
\cite{ALLTDMH}. We present a synopsis of it here.
We will also comment on issues relevant to excited state spectroscopy which
came up during discussions during the conference.

\section{SPECTROSCOPY OF ORBITAL EXCITATIONS}

Lattice QCD is unique among the subfields of physics in focussing
only on  ground state spectroscopy.
 Some P-wave states' masses are regularly measured in
staggered simulations because they are the odd parity partners of
``ordinary'' states: the $a_1$ and $\rho$ are examples of such pairs.
In  nonrelativistic
QCD, Lepage and Thacker\cite{LEPAGET} have computed the masses of $\chi_C$
and $\chi_B$ states (without including spin effects).
The APE collaboration\cite{APE}  measured masses of
 some P-wave mesons in quenched simulations at $6/g^2 =\beta=5.7$, but
 had difficulty in continuing their program to higher
 $\beta$ \cite{APETWO}.
 Recently, the Fermilab group has presented a calculation
of the 1P-1S splitting in
charmonium, which they use to fix the strong coupling constant \cite{FNAL}.

We construct orbitally excited states by using
interpolating fields which couple only to a specific angular momentum
eigenstate, which are projected onto zero momentum and which
 are of large spatial extent to maximize overlap with the state.

At the $t \neq 0$ end
of the correlation function
we use an operator which depends on the relative separation of the
quarks, a ``wave function''\cite{ALLWF}.
The  wave function $\psi_G(r)$ of a hadron H in a gauge G
 is defined as
\begin{equation}
\psi_G(r) =
\sum_{\vec x} \langle H | q(\vec x)
{\bar q}(\vec x + \vec r) | 0 \rangle
\end{equation}
where $q(\vec x)$ and
${\bar q}(\vec y)$ are quantum mechanical operators
which create a quark and an antiquark at locations
$\vec x$ and $\vec y$. (We have suppressed Dirac and color indices.)
Our correlation function is  constructed from
 convolutions of quark and antiquark propagators
$G(x,y)$
\begin{eqnarray}
C(\vec r,t)  & = & \sum_{\vec x}\Psi(\vec y_1, \vec y_2)
G_q(\vec y_1,0;\vec x,t)\nonumber \\
 &  & G_{\bar q}(\vec y_2,0;\vec x + \vec r,t)
\label{eq:convol}
\end{eqnarray}
where $\Psi(\vec y_1, \vec y_2)$ is the $t=0$ operator.
At large $t$ if the mass of the hadron is $m_H$, then
\begin{equation}
C(\vec r,t ) \simeq \exp (-m_H t) \psi_G(\vec r)
\end{equation}
and so by plotting $C(\vec r, t)$ as a function of $\vec r$ we can reconstruct
the wave function up to an overall constant.
We measure the mass of a state by convoluting $C(\vec r,t)$ with some
  test function which further projects out the desired
state:
\begin{equation}
C(t) = \sum_{\vec r} \psi^*_{test}(\vec r) C(\vec r,t).
\label{eq:integ}
\end{equation}

At $t=0$ we take an operator which is separable in the coordinates
of the quarks. For a meson we use
\begin{equation}
\Psi(x_1,x_2) = \phi_1(x_1) \phi_2(x_2).
 \end{equation}
In order to couple to orbital excitations we take $\phi_1$
to be  an S-wave and $\phi_2$ to be some orbitally excited state
with angular momentum $l$,
 centered around some
specified coordinate.
 This state is a
linear superposition of a $\vec p = 0$ $L=l$ orbital excitation and a state
whose center of mass momentum is nonzero.
 (This is the familiar ``translation mode'' of a shell model state.)
Convoluting quark propagators as
in Eqn. \ref{eq:convol} removes the $\vec p \neq 0$ state and gives us
the wave function of the $\vec p = 0$ $L=l$ state.

Our trial states $\phi(x)$ were chosen to be Gaussians times an appropriate
spherical harmonic. We used Coulomb gauge.
We discussed with D. Richards whether P-wave spectroscopy could be done with
other sources and concluded that one could use Wuppertal sources
(see Ref. \cite{WUPP}): the S-wave $\phi$ could be the inverse of
$D^2 + m^2$ and the P-wave $\phi$ could be $\phi_P = D_i \Phi_S$.
This would eliminate any need to gauge fix or perform convolutions.
We have to say, however, that we prefer the possibility of reconstructing
the sink wave function at the end of the calculations; we have seen too
many QCD simulations where one discovered at the end of a lot of
data collection that one's
operators were not as effective at producing the desired state as one
would have wished.

There were several things that we should have done differently, which
should be part of a second generation simulation.  First, we only
recorded wave function information on a small number of time slices.
We took a trial function $\psi_{trial}(r)$ and recorded
the $C(t)$ resulting from Eqn. \ref{eq:integ}.
Had we possessed wave function information on all sites, we could have
reconstructed the wave function from the large $t$ $C(r,t)$ and used it
as the $\psi_{trial}(r)$ in Eqn. \ref{eq:integ}. This might have given a
better signal. Second, we used sources which were angular momentum eigenstates
only for the ${}^3P_2$, ${}^1P_1$, ${}^3D_3$, and ${}^1D_2$ mesons,
and the highest angular momentum baryons. The other states are merely
eigenstates of $m_J$.
This was done to limit the number of propagators constructed.
 We could have fully reconstructed the sink
angular momentum wave function, obtaining correlators which were eigenfunctions
of $j$ and $m_J$. We used nonrelativistic source and sink wave
functions (upper Dirac components in Bjorken-Drell basis). This is probably
good enough for heavier masses but might not be the optimal choice for
very light quarks. Finally, in excited state baryon spectroscopy
one must deal with the fact that many states with the same quantum numbers
are present in a multiplet. For example, there are two $j=1/2$ nucleons
in the $L=1$ [70] of SU(6). Separating these states presents a technical
challenge.

Our simulations used Wilson fermions on
$16^4$ lattices at a coupling $\beta=6.0$, in quenched approximation,
with 80 lattices for P waves and 50 for D waves.
They were performed at the Pittsburgh Supercomputing Center.

We present a picture of a D-wave hadron in Fig. \ref{fig:blah};
 a slice through
a ${}^3D_3$ meson. The light regions are where the wave function
is large and positive; in the dark regions it is large and negative. The
characteristic quadrupole lobes are obvious. The orbitally excited
mesons and baryons are much larger than the S-wave states.
\begin{figure}[htb]
\framebox[55mm]{\rule[-21mm]{0mm}{43mm}}
\caption{Portrait of a ${}^3D_3$ meson.}
\label{fig:blah}
\end{figure}

We were able to see a hint of P wave
fine structure splitting at our heaviest
quark mass. It is shown in Fig.  \ref{fig:finestructure}.
 With a nominal lattice spacing of
$1/a = 2$ GeV there is a remarkable similarity to charmonium, where the
${}^3P_0$ state is at 3415 MeV and the other states are at about 3500 MeV.
\begin{figure}[htb]
\framebox[55mm]{\rule[-21mm]{0mm}{43mm}}
\caption{Fine structure splitting at $\kappa=.1300$.}
\label{fig:finestructure}
\end{figure}

As a global way of presenting our results we show the ``Wilson fermion
wallet card'' in Fig. \ref{fig:walletcard}.
 We show S-wave mesons and baryons along with
the ${}^3P_2$, $N(5/2)$, ${}^3D_3$, and $N(7/2)$ excited states
(labelled ``p'', ``P'', ``d'', and ``D''.)
\begin{figure}[htb]
\framebox[55mm]{\rule[-21mm]{0mm}{43mm}}
\caption{Wilson spectroscopy vs. $\kappa$.}
\label{fig:walletcard}
\end{figure}

We extracted a lattice spacing by  lattice determinations
of the ${}^3P_2$ and ${}^3S_1$ states at $\kappa=0.130$, 0.145, and
0.152 and extrapolating their masses linearly in $\kappa$.
(We used the data of Ref. \cite{DL} for the $\kappa=.1300$ vector meson).
We determined the lattice spacing by fitting the extrapolated masses
to the  $\psi(3095)$ and $\chi(3555)$ masses.  This gave
a charm hopping parameter of $\kappa=.1224$ and an inverse lattice spacing
of $1/a=1790$ MeV. (Determining the lattice spacing from
our proton mass  would give $1/a=1710$ MeV; from the rho,
$1/a=2264$ MeV.)
The extrapolated common D-meson mass is then
3.99(16) MeV, where the error is only from the extrapolation.
The ${}^3D_1$ $c \bar c$ state is at 3.77 GeV but its mass
is influenced by the nearby $D \bar D$ threshold.
 Model calculations\cite{DWAVE}
 of D-wave states (some of which are narrow since their
decays to $D \bar D$ are forbidden) give masses of 3.81 to 3.84 GeV.
At this value of the lattice spacing our ${}^3P_2-{}^3P_0$ mass splitting
at $\kappa=.1300$ is 63 MeV; in charmonium the corresponding
number is 145 MeV.

This is a little different from the Fermilab procedure of extracting
a lattice spacing from the ${}^1P_1$ splitting from the center of gravity
of the S-wave mesons. We made our choice because we have a better signal
in the ${}^3P_2$ channel; anyway, the most robust experimental
 P-wave spectroscopy
pretty much across the board is in the  ${}^3P_2$ channel.

\section{PHENOMENOLOGY}
While wave functions in a smooth gauge have clearly demonstrated their worth as
interpolating fields for spectroscopy, it is still not clear if they have
any real physical significance.  We compared charge radii computed using
wave functions with form factor data. The calculation is simple:
for mesons one computes
\begin{equation}
\langle r^2 \rangle = \sum_i e_i \int d^3 r |\psi(r)|^2  (r/2)^2
\label{eq:char}
\end{equation}
and there is an analogous equation for baryons. We found that
$\langle r^2 \rangle$ computed from Eqn. \ref{eq:char}
 was about a factor of four
to six smaller than the observed pion or nucleon charge radius.
However, at the same time, we saw that the ratio of neutron to
proton charge radii was negative and about the same size as the
experimental ratio. Apparently this negative neutron charge radius
arises because the two $d$ quarks have a larger relative separation than
the $u$ quark does from either of the $d$'s. This effect is easy
to explain as being due to the color hyperfine interaction (compare Ref.
\cite{ELLIS}).
We show an example of this ratio in Fig. \ref{fig:radius}.
\begin{figure}[htb]
\framebox[55mm]{\rule[-21mm]{0mm}{43mm}}
\caption{Neutron/proton charge radius ratio.}
\label{fig:radius}
\end{figure}
\section{CONCLUSIONS}
The methods we describe here can and should be used for a large scale
calculation of the spectroscopy of orbital excitations.
We believe our signal for P-wave states is only limited by
statistics. However, the physical meaning
of the wave function remains obscure.

\section{ACKNOWLEDGEMENTS}
This work was supported by the U. S. Department of Energy. Simulations
were performed at the Pittsburgh Supercomputing Center. T. D. would like
to thank
A. El-Khadra,
D. Richards,
and
H. Thacker
for interesting conversations about wave functions during Lattice 92.

redpajama_set_name: RedPajamaArXiv