EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-EP-2022-165

December 22, 2022

Performance of the NA62 trigger system
The NA62 Collaboration

###### Abstract

The NA62 experiment at CERN targets the measurement of the ultra-rare
$K^{+}~{}\to~{}\pi^{+}\nu\bar{\nu}$ decay, and carries out a broad physics
programme that includes probes for symmetry violations and searches for exotic
particles. Data were collected in 2016–2018 using a multi-level trigger
system, which is described highlighting performance studies based on 2018
data.

Accepted for publication in JHEP

The NA62 Collaboration111Corresponding authors: A. Romano, C. Parkinson,
email<EMAIL_ADDRESS><EMAIL_ADDRESS>

E. Cortina Gil111Corresponding authors: A. Romano, C. Parkinson, email:
<EMAIL_ADDRESS><EMAIL_ADDRESS>A. Kleimenova111Corresponding
authors: A. Romano, C. Parkinson, email<EMAIL_ADDRESS>chris.parkinson@cern.ch,111Corresponding authors: A. Romano, C. Parkinson,
email<EMAIL_ADDRESS><EMAIL_ADDRESS>E.
Minucci111Corresponding authors: A. Romano, C. Parkinson, email:
<EMAIL_ADDRESS>chris.parkinson@cern.ch,222Deceased,33footnotemark: 3,
S. Padolski111Corresponding authors: A. Romano, C. Parkinson, email:
<EMAIL_ADDRESS>chris.parkinson@cern.ch,44footnotemark: 4, P.
Petrov111Corresponding authors: A. Romano, C. Parkinson, email:
<EMAIL_ADDRESS><EMAIL_ADDRESS>A. Shaikhiev111Corresponding
authors: A. Romano, C. Parkinson, email<EMAIL_ADDRESS>chris.parkinson@cern.ch,55footnotemark: 5, R. Volpe111Corresponding authors:
A. Romano, C. Parkinson, email<EMAIL_ADDRESS>chris.parkinson@cern.ch,66footnotemark: 6, T. Numao222Deceased, Y.
Petrov222Deceased, B. Velghe222Deceased, V.W.S. Wong222Deceased, D.
Bryman33footnotemark: 3,77footnotemark: 7, J. Fu33footnotemark: 3, T.
Husek44footnotemark: 4,88footnotemark: 8, J. Jerhot44footnotemark:
4,99footnotemark: 9, K. Kampf,44footnotemark: 4, M. Zamkovsky44footnotemark:
4,222Deceased, R. Aliberti55footnotemark: 5,1010footnotemark: 10, G.
Khoriauli55footnotemark: 5,1111footnotemark: 11, J. Kunze55footnotemark: 5, D.
Lomidze55footnotemark: 5,1212footnotemark: 12, L. Peruzzo55footnotemark: 5, M.
Vormstein55footnotemark: 5, R. Wanke55footnotemark: 5, P.
Dalpiaz66footnotemark: 6, M. Fiorini66footnotemark: 6, I. Neri66footnotemark:
6, A. Norton66footnotemark: 6,1313footnotemark: 13, F. Petrucci66footnotemark:
6, H. Wahl66footnotemark: 6,1414footnotemark: 14, A. Cotta
Ramusino77footnotemark: 7, A. Gianoli77footnotemark: 7, E.
Iacopini88footnotemark: 8, G. Latino88footnotemark: 8, M. Lenti88footnotemark:
8, A. Parenti88footnotemark: 8, A. Bizzeti99footnotemark: 9,1515footnotemark:
15, F. Bucci99footnotemark: 9, A. Antonelli1010footnotemark: 10, G.
Georgiev1010footnotemark: 10,1616footnotemark: 16, V.
Kozhuharov1010footnotemark: 10,1616footnotemark: 16, G.
Lanfranchi1010footnotemark: 10, S. Martellotti1010footnotemark: 10, M.
Moulson1010footnotemark: 10, T. Spadaro1010footnotemark: 10, G.
Tinti1010footnotemark: 10, F. Ambrosino1111footnotemark: 11, T.
Capussela1111footnotemark: 11, M. Corvino1111footnotemark: 11,222Deceased, D.
Di Filippo1111footnotemark: 11, R. Fiorenza1111footnotemark:
11,1717footnotemark: 17, P. Massarotti1111footnotemark: 11, M.
Mirra1111footnotemark: 11, M. Napolitano1111footnotemark: 11, G.
Saracino1111footnotemark: 11, G. Anzivino1212footnotemark: 12, F.
Brizioli1212footnotemark: 12,222Deceased, E. Imbergamo1212footnotemark: 12, R.
Lollini1212footnotemark: 12, R. Piandani1212footnotemark: 12,1818footnotemark:
18, C. Santoni1212footnotemark: 12, M. Barbanera1313footnotemark: 13, P.
Cenci1313footnotemark: 13, B. Checcucci1313footnotemark: 13, P.
Lubrano1313footnotemark: 13, M. Lupi1313footnotemark: 13,1919footnotemark: 19,
M. Pepe1313footnotemark: 13, M. Piccini1313footnotemark: 13, F.
Costantini1414footnotemark: 14, L. Di Lella1414footnotemark:
14,1414footnotemark: 14, N. Doble1414footnotemark: 14,1414footnotemark: 14, M.
Giorgi1414footnotemark: 14, S. Giudici1414footnotemark: 14, G.
Lamanna1414footnotemark: 14, E. Lari1414footnotemark: 14, E.
Pedreschi1414footnotemark: 14, M. Sozzi1414footnotemark: 14, C.
Cerri1515footnotemark: 15, R. Fantechi1515footnotemark: 15, L.
Pontisso1515footnotemark: 15,2020footnotemark: 20, F.
Spinella1515footnotemark: 15, I. Mannelli1616footnotemark: 16, G.
D’Agostini1717footnotemark: 17, M. Raggi1717footnotemark: 17, A.
Biagioni1818footnotemark: 18, P. Cretaro1818footnotemark: 18, O.
Frezza1818footnotemark: 18, E. Leonardi1818footnotemark: 18, A.
Lonardo1818footnotemark: 18, M. Turisini1818footnotemark: 18, P.
Valente1818footnotemark: 18, P. Vicini1818footnotemark: 18, R.
Ammendola1919footnotemark: 19, V. Bonaiuto1919footnotemark:
19,2121footnotemark: 21, A. Fucci1919footnotemark: 19, A.
Salamon1919footnotemark: 19, F. Sargeni1919footnotemark: 19,2222footnotemark:
22, R. Arcidiacono2020footnotemark: 20,2323footnotemark: 23, B. Bloch-
Devaux2020footnotemark: 20, M. Boretto2020footnotemark: 20,222Deceased, E.
Menichetti2020footnotemark: 20, E. Migliore2020footnotemark: 20, D.
Soldi2020footnotemark: 20, C. Biino2121footnotemark: 21, A.
Filippi2121footnotemark: 21, F. Marchetto2121footnotemark: 21, J.
Engelfried2222footnotemark: 22, N. Estrada-Tristan2222footnotemark:
22,2424footnotemark: 24, A.M. Bragadireanu2323footnotemark: 23, S.A.
Ghinescu2323footnotemark: 23, O.E. Hutanu2323footnotemark: 23, A.
Baeva2424footnotemark: 24, D. Baigarashev2424footnotemark:
24,2525footnotemark: 25, D. Emelyanov2424footnotemark: 24, T.
Enik2424footnotemark: 24, V. Falaleev2424footnotemark: 24,2626footnotemark:
26, V. Kekelidze2424footnotemark: 24, A. Korotkova2424footnotemark: 24, L.
Litov2424footnotemark: 24,1616footnotemark: 16, D. Madigozhin2424footnotemark:
24, M. Misheva2424footnotemark: 24,2727footnotemark: 27, N.
Molokanova2424footnotemark: 24, S. Movchan2424footnotemark: 24, I.
Polenkevich2424footnotemark: 24, Yu. Potrebenikov2424footnotemark: 24, S.
Shkarovskiy2424footnotemark: 24, A. Zinchenko2424footnotemark: 24,222Deceased,
S. Fedotov2525footnotemark: 25, E. Gushchin2525footnotemark: 25, A.
Khotyantsev2525footnotemark: 25, Y. Kudenko2525footnotemark:
25,2828footnotemark: 28, V. Kurochka2525footnotemark: 25, M.
Medvedeva2525footnotemark: 25, A. Mefodev 2525footnotemark: 25, S.
Kholodenko2626footnotemark: 26, V. Kurshetsov2626footnotemark: 26, V.
Obraztsov2626footnotemark: 26, A. Ostankov2626footnotemark: 26,222Deceased, V.
Semenov2626footnotemark: 26,222Deceased, V. Sugonyaev2626footnotemark: 26, O.
Yushchenko2626footnotemark: 26, L. Bician2727footnotemark:
27,2929footnotemark: 29, T. Blazek2727footnotemark: 27, V.
Cerny2727footnotemark: 27, Z. Kucerova2727footnotemark: 27, J.
Bernhard2828footnotemark: 28, A. Ceccucci2828footnotemark: 28, H.
Danielsson2828footnotemark: 28, N. De Simone2828footnotemark:
28,3030footnotemark: 30, F. Duval2828footnotemark: 28, B.
Döbrich2828footnotemark: 28, L. Federici2828footnotemark: 28, E.
Gamberini2828footnotemark: 28, L. Gatignon2828footnotemark:
28,3131footnotemark: 31, R. Guida2828footnotemark: 28, F.
Hahn2828footnotemark: 28,222Deceased, E.B. Holzer2828footnotemark: 28, B.
Jenninger2828footnotemark: 28, M. Koval2828footnotemark: 28,2929footnotemark:
29, P. Laycock2828footnotemark: 28,44footnotemark: 4, G. Lehmann
Miotto2828footnotemark: 28, P. Lichard2828footnotemark: 28, A.
Mapelli2828footnotemark: 28, R. Marchevski2828footnotemark:
28,3232footnotemark: 32, K. Massri2828footnotemark: 28, M.
Noy2828footnotemark: 28, V. Palladino2828footnotemark: 28, M. Perrin-
Terrin2828footnotemark: 28,3333footnotemark: 33,3434footnotemark: 34, J.
Pinzino2828footnotemark: 28,3535footnotemark: 35, V. Ryjov2828footnotemark:
28, S. Schuchmann2828footnotemark: 28, S. Venditti2828footnotemark: 28, T.
Bache2929footnotemark: 29, M.B. Brunetti2929footnotemark: 29,3636footnotemark:
36, V. Duk2929footnotemark: 29,66footnotemark: 6, V.
Fascianelli2929footnotemark: 29,3737footnotemark: 37, J. R.
Fry2929footnotemark: 29, F. Gonnella2929footnotemark: 29, E.
Goudzovski2929footnotemark: 29, J. Henshaw2929footnotemark: 29, L.
Iacobuzio2929footnotemark: 29, C. Lazzeroni2929footnotemark: 29, N.
Lurkin2929footnotemark: 29,99footnotemark: 9, F. Newson2929footnotemark: 29,
C. Parkinson2929footnotemark: 29,111Corresponding authors: A. Romano, C.
Parkinson, email<EMAIL_ADDRESS><EMAIL_ADDRESS>A.
Romano2929footnotemark: 29,111Corresponding authors: A. Romano, C. Parkinson,
email<EMAIL_ADDRESS><EMAIL_ADDRESS>A.
Sergi2929footnotemark: 29,3838footnotemark: 38, A. Sturgess2929footnotemark:
29, J. Swallow2929footnotemark: 29,222Deceased, A. Tomczak2929footnotemark:
29, H. Heath3030footnotemark: 30, R. Page3030footnotemark: 30, S.
Trilov3030footnotemark: 30, B. Angelucci3131footnotemark: 31, D.
Britton3131footnotemark: 31, C. Graham3131footnotemark: 31, D.
Protopopescu3131footnotemark: 31, J. Carmignani3232footnotemark:
32,3939footnotemark: 39, J.B. Dainton3232footnotemark: 32, R.W. L.
Jones3232footnotemark: 32, G. Ruggiero3232footnotemark: 32,4040footnotemark:
40, L. Fulton3333footnotemark: 33, D. Hutchcroft3333footnotemark: 33, E.
Maurice3333footnotemark: 33,4141footnotemark: 41, B. Wrona3333footnotemark:
33, A. Conovaloff3434footnotemark: 34, P. Cooper3434footnotemark: 34, D.
Coward3434footnotemark: 34,4242footnotemark: 42, P. Rubin3434footnotemark: 34

1 Université Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium

2 TRIUMF, Vancouver, British Columbia, V6T 2A3, Canada

3 University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada

4 Charles University, 116 36 Prague 1, Czech Republic

5 Institut für Physik and PRISMA Cluster of Excellence, Universität Mainz,
D-55099 Mainz, Germany

6 Dipartimento di Fisica e Scienze della Terra dell’Università e INFN, Sezione
di Ferrara, I-44122 Ferrara, Italy

7 INFN, Sezione di Ferrara, I-44122 Ferrara, Italy

8 Dipartimento di Fisica e Astronomia dell’Università e INFN, Sezione di
Firenze, I-50019 Sesto Fiorentino, Italy

9 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy

10 Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

11 Dipartimento di Fisica “Ettore Pancini” e INFN, Sezione di Napoli, I-80126
Napoli, Italy

12 Dipartimento di Fisica e Geologia dell’Università e INFN, Sezione di
Perugia, I-06100 Perugia, Italy

13 INFN, Sezione di Perugia, I-06100 Perugia, Italy

14 Dipartimento di Fisica dell’Università e INFN, Sezione di Pisa, I-56100
Pisa, Italy

15 INFN, Sezione di Pisa, I-56100 Pisa, Italy

16 Scuola Normale Superiore e INFN, Sezione di Pisa, I-56100 Pisa, Italy

17 Dipartimento di Fisica, Sapienza Università di Roma e INFN, Sezione di Roma
I, I-00185 Roma, Italy

18 INFN, Sezione di Roma I, I-00185 Roma, Italy

19 INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy

20 Dipartimento di Fisica dell’Università e INFN, Sezione di Torino, I-10125
Torino, Italy

21 INFN, Sezione di Torino, I-10125 Torino, Italy

22 Instituto de Física, Universidad Autónoma de San Luis Potosí, 78240 San
Luis Potosí, Mexico

23 Horia Hulubei National Institute for R&D in Physics and Nuclear
Engineering, 077125 Bucharest-Magurele, Romania

24 Joint Institute for Nuclear Research, 141980 Dubna (MO), Russia

25 Institute for Nuclear Research of the Russian Academy of Sciences, 117312
Moscow, Russia

26 Institute for High Energy Physics of the Russian Federation, State Research
Center “Kurchatov Institute”, 142281 Protvino (MO), Russia

27 Faculty of Mathematics, Physics and Informatics, Comenius University, 842
48, Bratislava, Slovakia

28 CERN, European Organization for Nuclear Research, CH-1211 Geneva 23,
Switzerland

29 School of Physics and Astronomy, University of Birmingham, Birmingham, B15
2TT, UK

30 School of Physics, University of Bristol, Bristol, BS8 1TH, UK

31 School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ,
UK

32 Faculty of Science and Technology, University of Lancaster, Lancaster, LA1
4YW, UK

33 School of Physical Sciences, University of Liverpool, Liverpool, L69 7ZE,
UK

34 Physics and Astronomy Department, George Mason University, Fairfax, VA
22030, USA

${}^{\alphalph{1}}$Present address: Faculty of Mathematics, Physics and
Informatics, Comenius University, 842 48, Bratislava, Slovakia
${}^{\alphalph{2}}$Present address: CERN, European Organization for Nuclear
Research, CH-1211 Geneva 23, Switzerland
${}^{\alphalph{3}}$Also at Laboratori Nazionali di Frascati, I-00044 Frascati,
Italy
${}^{\alphalph{4}}$Present address: Brookhaven National Laboratory, Upton, NY
11973, USA
${}^{\alphalph{5}}$Present address: School of Physics and Astronomy,
University of Birmingham, Birmingham, B15 2TT, UK
${}^{\alphalph{6}}$Present address: INFN, Sezione di Perugia, I-06100 Perugia,
Italy
${}^{\alphalph{7}}$Also at TRIUMF, Vancouver, British Columbia, V6T 2A3,
Canada
${}^{\alphalph{8}}$Present address: Department of Astronomy and Theoretical
Physics, Lund University, Lund, SE 223-62, Sweden
${}^{\alphalph{9}}$Present address: Université Catholique de Louvain, B-1348
Louvain-La-Neuve, Belgium
${}^{\alphalph{10}}$Present address: Institut für Kernphysik and Helmholtz
Institute Mainz, Universität Mainz, Mainz, D-55099, Germany
${}^{\alphalph{11}}$Present address: Universität Würzburg, D-97070 Würzburg,
Germany
${}^{\alphalph{12}}$Present address: European XFEL GmbH, D-22761 Hamburg,
Germany
${}^{\alphalph{13}}$Present address: University of Glasgow, Glasgow, G12 8QQ,
UK
${}^{\alphalph{14}}$Present address: Institut für Physik and PRISMA Cluster of
Excellence, Universität Mainz, D-55099 Mainz, Germany
${}^{\alphalph{15}}$Also at Dipartimento di Scienze Fisiche, Informatiche e
Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy
${}^{\alphalph{16}}$Also at Faculty of Physics, University of Sofia, BG-1164
Sofia, Bulgaria
${}^{\alphalph{17}}$Present address: Scuola Superiore Meridionale e INFN,
Sezione di Napoli, I-80138 Napoli, Italy
${}^{\alphalph{18}}$Present address: Instituto de Física, Universidad Autónoma
de San Luis Potosí, 78240 San Luis Potosí, Mexico
${}^{\alphalph{19}}$Present address: Institut am Fachbereich Informatik und
Mathematik, Goethe Universität, D-60323 Frankfurt am Main, Germany
${}^{\alphalph{20}}$Present address: INFN, Sezione di Roma I, I-00185 Roma,
Italy
${}^{\alphalph{21}}$Also at Department of Industrial Engineering, University
of Roma Tor Vergata, I-00173 Roma, Italy
${}^{\alphalph{22}}$Also at Department of Electronic Engineering, University
of Roma Tor Vergata, I-00173 Roma, Italy
${}^{\alphalph{23}}$Also at Università degli Studi del Piemonte Orientale,
I-13100 Vercelli, Italy
${}^{\alphalph{24}}$Also at Universidad de Guanajuato, 36000 Guanajuato,
Mexico
${}^{\alphalph{25}}$Also at L.N. Gumilyov Eurasian National University, 010000
Nur-Sultan, Kazakhstan
${}^{\alphalph{26}}$Also at Institute for Nuclear Research of the Russian
Academy of Sciences, 117312 Moscow, Russia
${}^{\alphalph{27}}$Present address: Institute of Nuclear Research and Nuclear
Energy of Bulgarian Academy of Science (INRNE-BAS), BG-1784 Sofia, Bulgaria
${}^{\alphalph{28}}$Also at National Research Nuclear University (MEPhI),
115409 Moscow and Moscow Institute of Physics and Technology, 141701 Moscow
region, Moscow, Russia
${}^{\alphalph{29}}$Present address: Charles University, 116 36 Prague 1,
Czech Republic
${}^{\alphalph{30}}$Present address: DESY, D-15738 Zeuthen, Germany
${}^{\alphalph{31}}$Present address: University of Lancaster, Lancaster, LA1
4YW, UK
${}^{\alphalph{32}}$Present address: Weizmann Institute, Rehovot, 76100,
Israel
${}^{\alphalph{33}}$Present address: Aix Marseille University, CNRS/IN2P3,
CPPM, F-13288, Marseille, France
${}^{\alphalph{34}}$Also at Université Catholique de Louvain, B-1348 Louvain-
La-Neuve, Belgium
${}^{\alphalph{35}}$Present address: INFN, Sezione di Pisa, I-56100 Pisa,
Italy
${}^{\alphalph{36}}$Present address: Department of Physics, University of
Warwick, Coventry, CV4 7AL, UK
${}^{\alphalph{37}}$Present address: Center for theoretical neuroscience,
Columbia University, New York, NY 10027, USA
${}^{\alphalph{38}}$Present address: Dipartimento di Fisica dell’Università e
INFN, Sezione di Genova, I-16146 Genova, Italy
${}^{\alphalph{39}}$Present address: University of Liverpool, Liverpool, L69
7ZE, UK
${}^{\alphalph{40}}$Present address: Dipartimento di Fisica e Astronomia
dell’Università e INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
${}^{\alphalph{41}}$Present address: Laboratoire Leprince Ringuet, F-91120
Palaiseau, France
${}^{\alphalph{42}}$Also at SLAC National Accelerator Laboratory, Stanford
University, Menlo Park, CA 94025, USA

###### Contents

  1. 1 Introduction
  2. 2 The NA62 experiment
  3. 3 The NA62 trigger system
    1. 3.1 The low-level trigger
    2. 3.2 The high-level trigger
  4. 4 The trigger performance
    1. 4.1 Trigger rates
    2. 4.2 Efficiency of the PNN trigger line
    3. 4.3 Efficiencies of the other $K^{+}$ trigger lines
    4. 4.4 Efficiencies of the beam-dump trigger lines
    5. 4.5 Simulation of the trigger response
  5. 5 Conclusions and outlook

##  1 Introduction

The NA62 experiment at CERN is devoted to precision tests of the Standard
Model (SM) with $K^{+}$ decays using a decay-in-flight technique. The main
goal of NA62 is the measurement of the branching ratio (BR) of the ultra-rare
decay $K^{+}\to\pi^{+}\nu\bar{\nu}$, which is both precisely predicted by the
SM and discriminating among possible SM extensions. The branching ratio is
predicted to be BR$(K^{+}\to\pi^{+}\nu\bar{\nu})=(8.4\pm 1.0)\times 10^{-11}$
in the SM [1]. The smallness of the expected BR and the presence of two
undetected neutrinos in the final state make this measurement challenging.

Data collected in 2016–2018 allowed significant progress in the study of the
$K^{+}\to\pi^{+}\nu\bar{\nu}$ decay. The analysis of 2016 data demonstrated
the feasibility of measuring BR($K^{+}\to\pi^{+}\nu\bar{\nu}$) using a decay-
in-flight technique [2]. With data collected in 2017, NA62 observed two SM
$K^{+}\to\pi^{+}\nu\bar{\nu}$ signal candidates with an expected background of
$1.5$ events, ensuring the robustness of the measurement strategy and
background suppression capabilities [3]. The result based on data collected in
2018 provided first evidence for the $K^{+}\to\pi^{+}\nu\bar{\nu}$ decay with
$17$ signal candidates and an expected background of $5.3$ events [4]. The
combined result

$\text{BR}(K^{+}\to\pi^{+}\nu\bar{\nu})=(10.6^{+4.0}_{-3.4}\big{|}_{\text{stat}}\pm
0.9_{\text{syst}})\times 10^{-11}$

gives evidence for this decay with a significance of 3.4 standard deviations.

A large dataset of $6\times 10^{12}$ $K^{+}$ decays allows several other
physics goals to be pursued, including searches for decays forbidden by SM
symmetries and searches for hidden-sector particles produced in $K^{+}$ decays
[5]. The NA62 experiment also operates in a beam-dump configuration, providing
the opportunity to seek decays of hidden-sector particles with masses above
the $K^{+}$ mass; the sensitivity to hidden-sector particles is reported in
[6]. A dataset corresponding to $3\text{\times}{10}^{16}$ protons on target
(POT) was collected in beam-dump configuration in 2016–2018.

The diverse physics programme demands a selective and flexible trigger system.
In the following, the structure and performance of the trigger system that
operated in 2018 are described.

##  2 The NA62 experiment

The NA62 experiment is sketched in Fig. 1 and is described in detail in [7]. A
beam of positively charged hadrons is formed by impinging
$400\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ protons
extracted from the CERN SPS onto a beryllium target in spills of
$3\text{\,}\mathrm{s}$ effective duration. The target defines the origin of
the NA62 reference system: the beam travels along the Z axis in the positive
direction (downstream), the Y axis points vertically up, and the X axis is
horizontal and directed to form a right-handed coordinate system. The beam has
a nominal momentum of
$75\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ and consists
of 70% $\pi^{+}$, 23% protons and 6% $K^{+}$.

NA48-CHOD

Figure 1: Schematic side view of the NA62 beamline and detector.

Particles in the hadron beam are characterised by a differential Cherenkov
counter (KTAG) and a three-station silicon-pixel beam spectrometer (GTK 1–3).
The beam passes through a vacuum tank which contains a $60\text{\,}\mathrm{m}$
long fiducial volume (FV). Charged products of $K^{+}$ decays inside the FV
travel downstream, and are detected by a straw-chamber spectrometer (STRAW), a
ring-imaging Cherenkov detector (RICH), and two plastic scintillator
hodoscopes: CHOD made of one plane of tiles; NA48-CHOD with two planes of
slabs. The RICH, filled with neon at atmospheric pressure, tags the charged
products with a timing precision of better than $100\text{\,}\mathrm{ps}$ and
provides particle identification. Further particle identification is provided
by an electromagnetic calorimeter (LKr), two hadronic calorimeters (MUV1,
MUV2), and a scintillator-tile hodoscope (MUV3) located behind a
$80\text{\,}\mathrm{cm}$ iron wall. Dedicated photon detectors (LAV, IRC, SAC)
are placed to form a hermetic photon-veto system. An argon ionisation chamber
(Argonion) located downstream of the SAC measures the number of particles in
the hadron beam in each spill [8].

The beam intensity is defined in terms of the particle rate exiting the GTK.
The nominal beam intensity is $750\text{\,}\mathrm{MHz}$, of which
$45\text{\,}\mathrm{MHz}$ is $K^{+}$. There are about
$10\text{\,}\mathrm{MHz}$ of $K^{+}$ decays within the
$150\text{\,}\mathrm{m}$ region between the exit of the GTK and the MUV3
detector, with $5\text{\,}\mathrm{MHz}$ occurring inside the FV. A muon halo
originating primarily from $K^{+}$ and $\pi^{+}$ decays upstream of the FV
accompanies the hadron beam, and introduces an additional particle rate of
several in the detectors downstream of the FV. To handle the high particle
rate, NA62 utilises timing measurements with sub-$100\text{\,}\mathrm{ps}$
precision in the RICH, KTAG, and GTK, and from $100\text{\,}\mathrm{ps}$ to
$1\text{\,}\mathrm{ns}$ in the other detectors.

The intensity of the hadron beam is estimated in two ways. The average beam
intensity during the spill is evaluated using the number of beam particles
observed by the Argonion detector. This information is available immediately
after the spill, with the nominal beam intensity corresponding to about
$2.0\times 10^{9}$ Argonion counts. The instantaneous beam intensity is
evaluated on an event-by-event basis by measuring the GTK signal rate. This
information is available after event reconstruction.

When operating in beam-dump configuration, the target is removed and the
proton beam is stopped in movable collimators that act as a beam dump, located
about $45\text{\,}\mathrm{m}$ upstream of the KTAG. In this configuration, the
particle rate in the detectors downstream of the FV is
$300\text{\,}\mathrm{kHz}$, dominated by muons produced in the beam dump.

##  3 The NA62 trigger system

The NA62 trigger system is arranged in two stages. The first stage is a low-
level hardware trigger (L0) that uses custom programmable electronics to
process data from a subset of detectors and form a L0 trigger decision. The
subsequent L1 trigger stage is a software trigger running on a dedicated data-
acquisition (DAQ) computing cluster (DAQ-farm). Each trigger stage is designed
to reduce the event rate by roughly a factor of 10, going from about
$10\text{\,}\mathrm{MHz}$ of events from $K^{+}$ decays occurring in the
detector to about $100\text{\,}\mathrm{kHz}$ written to permanent storage.

The data are collected through trigger lines. Each trigger line is a sequence
of L0 and L1 trigger conditions designed to select a specific category of
events. Each condition can either be required or forbidden (vetoed). Applying
trigger conditions in veto introduces random veto, whereby events are rejected
by the trigger due to unrelated activity in the detector. An event is stored
if it is accepted by at least one of the trigger lines.

Ten trigger lines are defined to serve the $K^{+}\to\pi^{+}\nu\bar{\nu}$
branching ratio measurement and cover the breadth of the $K^{+}$ physics
programme. The _PNN_ line collects data for the $K^{+}\to\pi^{+}\nu\bar{\nu}$
branching ratio measurement. The _non-muon_ (Non-$\mu$) line is used to
collect $K^{+}$ decays without muons in the final state. The _multi-track_
(MT) line collects samples of multi-track $K^{+}$ decays. The _di-muon multi-
track_ (2$\mu$MT), _electron multi-track_ ($e$MT), and _muon multi-track_
($\mu$MT) lines collect $K^{+}$ decays to multi-lepton final states. The
_displaced muon_ (DV-$\mu$) and _displaced di-muon_ (DV-2$\mu$) lines collect
events with a vertex in the FV displaced with respect to the nominal beam
axis. The _neutrino_ line collects $K^{+}\to\mu^{+}\nu$ events in which the
neutrino interacts with the LKr material, for a proof-of-concept study of
flavour-tagged neutrino interaction events. Finally, the _control_ line
collects minimum-bias events for calibration and data-quality monitoring, for
the normalization of the $K^{+}\to\pi^{+}\nu\bar{\nu}$ branching ratio
measurement, and for the measurement of detector and trigger efficiencies.
Three trigger lines are defined for use in beam-dump configuration – _neutral_
, _charged_ , and _control_ – which collect di-photon, multi-track and control
data samples, respectively.

###  3.1 The low-level trigger

The hardware implementation of the L0 trigger system is described in detail in
[9]. In total, five detectors are involved. The RICH, CHOD, NA48-CHOD and MUV3
participate via specialised firmware implemented in the readout hardware, with
access to information from each readout channel. The CHOD, NA48-CHOD, and MUV3
define four regions as quadrants, with the MUV3 excluding eight tiles close to
the detector centre from the quadrant definition (Fig. 2). The LKr
participates via a dedicated calorimeter L0 trigger system that uses
information from groups of channels provided by calorimeter readout modules
[10].

The data from each detector are processed to identify groups of coincident
signals in the detector. Each group is compared to a programmable set of up to
16 conditions per detector. The RICH conditions are based on the total signal
multiplicity, while the NA48-CHOD conditions are based on the number of
quadrants in which there are signals. The CHOD and MUV3 conditions are based
on the total signal multiplicity as well as the number and pattern of
quadrants in which there are signals. The LKr conditions are based on the
total energy deposited and the number of localised energy deposits (clusters).
The full list of L0 trigger conditions is given in Table 1. If at least one of
the conditions is satisfied in a given detector, a _trigger primitive_ is
produced. Each trigger primitive encodes which of the 16 conditions are
satisfied, and a timestamp at $100\text{\,}\mathrm{ps}$ precision.

Figure 2:  Layout of the tiles and quadrants of the CHOD detector (left), and the tiles, quadrants, and inner/outer regions of the MUV3 detector (right). The smaller, inner MUV3 tiles are shown in grey; quadrants only involve the large outer tiles shown in white. The hole in the centre of each detector allows the passage of the undecayed beam particles. Detector | Condition | Description
---|---|---
RICH | RICH | At least two signals in the detector
CHOD | Q1 | At least one signal in any quadrant
| Q2 | At least one signal in each of two different quadrants
| QX | At least one signal in each of two diagonally-opposite quadrants
| UTMC | Upper multiplicity condition: fewer than five signals in the detector
NA48-CHOD | NA48-CHOD | At least one signal in any quadrant
MUV3 | M1 | At least one signal in the detector
| MO1 | At least one signal in the outer tiles
| MO2 | At least two signals in the outer tiles
| MOQX | At least one signal in each of two diagonally-opposite quadrants
LKr | E10 |  At least $10\text{\,}\mathrm{GeV}$ deposited in the LKr
| E20 |  At least $20\text{\,}\mathrm{GeV}$ deposited in the LKr
| E30 |  At least $30\text{\,}\mathrm{GeV}$ deposited in the LKr
| C2E5 |  At least $5\text{\,}\mathrm{GeV}$ deposited in the LKr by at least two clusters
| LKr30 | Logical OR between E30 and C2E5
LKr | E1 |  At least $1\text{\,}\mathrm{GeV}$ deposited in the LKr
(beam dump) | E2 |  At least $2\text{\,}\mathrm{GeV}$ deposited in the LKr
| E4 |  At least $4\text{\,}\mathrm{GeV}$ deposited in the LKr
| C2E2 |  At least $2\text{\,}\mathrm{GeV}$ deposited in the LKr by at least two clusters
Table 1: List of L0 trigger conditions. The LKr conditions differ between
$K^{+}$ and beam-dump configuration.

The trigger primitives are sent to the L0 trigger processor (L0TP) [11]. The
L0TP produces triggers by combining primitives within
$6.25\text{\,}\mathrm{ns}$ of those from a specified reference detector. The
reference detector is either the RICH or NA48-CHOD in $K^{+}$ mode, and either
the CHOD or LKr in beam-dump configuration. The time of the primitive from the
reference detector defines the L0 trigger time. The time resolutions of the
primitives with respect to the RICH primitive are $0.7\text{\,}\mathrm{ns}$
for the CHOD and MUV3, and $2\text{\,}\mathrm{ns}$ for the NA48-CHOD and LKr.
These values are larger than those achieved offline, as precise time
calibrations are not available at trigger level.

The combinations of primitives are compared to up to 16 criteria, which define
the L0 part of each trigger line. A trigger is generated if at least one of
the criteria is satisfied. Each trigger line can be downscaled individually,
with a downscaling of $N$ indicating that one in $N$ generated triggers is
transmitted. The trigger lines and corresponding L0 trigger conditions for
$K^{+}$ mode are given in Table 2, and those for beam-dump configuration are
given in Table 3.

Trigger line | L0 trigger conditions | L1 trigger conditions
---|---|---
PNN | $\mathrm{RICH\cdot Q1\cdot UTMC\,\cdot\overline{QX}\,\cdot\,\overline{M1}\,\cdot\,\overline{LKr30}}$ | $\mathrm{KTAG\cdot\overline{LAV}\cdot STRAW}$
Non-$\mu$ | $\mathrm{RICH\cdot Q1\,\cdot\,\overline{M1}}$ | $\mathrm{KTAG\cdot\text{STRAW-1TRK}}$
MT | $\mathrm{RICH\cdot QX}$ | $\mathrm{KTAG\cdot\text{STRAW-Exo}}$
2$\mu$MT | $\mathrm{RICH\cdot QX\cdot MO2}$ | $\mathrm{KTAG\cdot\text{STRAW-Exo}}$
$e$MT | $\mathrm{RICH\cdot QX\cdot E20}$ | $\mathrm{KTAG\cdot\text{STRAW-Exo}}$
$\mu$MT | $\mathrm{RICH\cdot QX\cdot MO1\cdot E10}$ | $\mathrm{KTAG\cdot\overline{LAV}\cdot\text{STRAW-MT}}$
DV-$\mu$ | $\mathrm{RICH\cdot Q2\cdot MO1\cdot E10}$ | $\mathrm{\overline{KTAG}\cdot\text{STRAW-DV}}$
DV-$2\mu$ | $\mathrm{RICH\cdot Q2\cdot MO2\,\cdot\,\overline{E10}}$ | STRAW-DV
Neutrino | $\mathrm{RICH\cdot Q1\cdot MOQX\,\cdot\,\overline{Q2}}$ | $\mathrm{KTAG\cdot\overline{LAV}\cdot\text{STRAW-1TRK}}$
Control | NA48-CHOD | None
Table 2: $K^{+}$ trigger lines and the corresponding L0 and L1 trigger conditions. An overline indicates that the condition is used in veto.  Trigger line | L0 trigger conditions
---|---
Neutral | $\mathrm{C2E2}$
Charged | $\mathrm{Q2}$
Control | $\mathrm{Q1}$
Table 3: Beam-dump trigger lines and the corresponding L0 trigger conditions.
No L1 conditions are applied in beam-dump configuration.

###  3.2 The high-level trigger

The online framework consists of the DAQ software and the high-level trigger
(HLT) software. The framework is deployed on the DAQ-farm, a cluster of 30
computers, with each computer independently executing both parts of the
software on a subset of the L0-triggered events.

The data from all detectors except the GTK and calorimeters (LKr, MUV1, MUV2,
IRC, SAC) are transmitted to the DAQ-farm following a positive L0 trigger
decision. The DAQ software collects and combines event fragments sent by the
detectors to produce a L1 event [12]. The HLT software executes the L1 trigger
algorithms on the L1 event after applying detector-specific decoding and
reconstruction. If an event satisfies the L1 trigger requirements, the HLT
software requests data from the GTK and calorimeters, which are then merged
with the L1 event to produce a complete event with an average size of
$20\text{\,}\mathrm{kB}$.

The HLT software imposes sets of conditions from different algorithms in a
specified order. These conditions define the L1 part of each trigger line. An
HLT processor routine evaluates the trigger lines and executes the conditions
in the defined order. If an event does not fulfil a condition of a trigger
line, the event is discarded without checking the following conditions. A
fraction (1%) of the processed events are accepted by the HLT processor
regardless of whether any trigger condition is satisfied. The resulting
_autopass_ events are used to measure the L1 trigger efficiencies.

Three L1 algorithms – KTAG, LAV and STRAW – define the L1 trigger conditions.
Each algorithm is configurable, as discussed below, and the configuration can
be different for each trigger line. The list of $K^{+}$ trigger lines and
corresponding L1 trigger conditions is given in Table 2. No L1 trigger
conditions are applied in beam-dump configuration.

#### The L1 KTAG trigger

The L1 KTAG trigger requires a $K^{+}$ in time with the L0 trigger, which
rejects events triggered at L0 by halo muons and scattered beam pions. The
KTAG detects Cherenkov light produced by the $K^{+}$ in 8 azimuthal sectors,
each consisting of an array of 48 photomultipliers with a single-photon time
resolution of $280\text{\,}\mathrm{ps}$. As the average number of photons
detected per $K^{+}$ is 18, the KTAG measures the $K^{+}$ time with a
precision of $70\text{\,}\mathrm{ps}$ after offline corrections have been
applied [13]. The L1 KTAG trigger requires that more than four KTAG sectors
have at least one detected Cherenkov photon within $5\text{\,}\mathrm{ns}$ of
the L0 trigger time. The time window includes a safety margin to accommodate
time drifts in the KTAG readout system.

#### The L1 LAV trigger

The L1 LAV trigger identifies whether there is activity in the LAV detector in
time with the L0 trigger, with the primary aim of vetoing
$K^{+}\to\pi^{+}\pi^{0}$ decays. The LAV comprises 12 stations of ring-shaped
electromagnetic calorimeters made of lead-glass blocks located inside and
downstream of the vacuum tank, which detect photons with
$1.01.5\text{\,}\mathrm{ns}$ resolution. The L1 LAV trigger requires at least
three signals in stations 2–11 within $6\text{\,}\mathrm{ns}$ of the L0
trigger time. Stations 1 and 12 are not considered to avoid vetoing events
with inelastic interactions in the GTK and RICH detectors, respectively.

#### The L1 STRAW trigger

The L1 STRAW trigger reconstructs the tracks of charged particles that
traverse the STRAW detector in time with the L0 trigger. The STRAW detector
comprises four straw-chambers, two at either side of a dipole magnet, and
measures the trajectories and momenta of charged particles. The L1 STRAW
algorithm reconstructs tracks and performs a momentum computation by making a
two-dimensional Hough transform of signals in the four straw chambers [14].
The relative momentum resolution of the L1 STRAW algorithm is $\Delta p/p\sim$
1%, about constant in the
$1545\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ momentum
range of interest. This resolution is larger than 0.3% achieved offline due to
the simpler and faster reconstruction used at L1. A preliminary sample of
tracks is selected by requiring the track momentum to be at least
$3\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ and the track
direction to satisfy the conditions $|dX/dZ|<0.02$ and $|dY/dZ|<0.02$. To
reduce the number of fake tracks, quality conditions are applied on the signal
and track times.

The main L1 STRAW trigger condition is optimised for
$K^{+}\to\pi^{+}\nu\bar{\nu}$ decays. It aims to reject multi-track events and
one-track events with tracks originating outside the FV or with a momentum
outside the range used for $K^{+}\to\pi^{+}\nu\bar{\nu}$ event selection. The
track selection requires: positive charge; momentum below
$50\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$; closest
distance of approach (CDA) of the track to the nominal beam axis below
$200\text{\,}\mathrm{mm}$; and Z position at the CDA upstream of the first
straw chamber. Multi-track events are identified by the presence of a pair of
tracks with CDA between the two tracks below $30\text{\,}\mathrm{mm}$, which
is consistent with the two tracks originating from the same $K^{+}$ decay. An
event is accepted if it contains at least one track satisfying the track
selection, and is not identified as a multi-track event.

Several other L1 STRAW conditions share the same pattern recognition and track
reconstruction, only differing in the requirements on the reconstructed
tracks: L1 STRAW-1TRK is a less restrictive version of the L1 STRAW condition
that selects final states with at least one positively-charged track
originating in the FV with momentum below
$65\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$; multi-track
final states are collected by L1 STRAW-Exo, which requires at least one
negatively-charged track, and L1 STRAW-MT, which identifies events with at
least three tracks originating in the FV; and L1 STRAW-DV collects pairs of
tracks originating from a displaced vertex (DV) with CDA position at least
$100\text{\,}\mathrm{mm}$ from the nominal beam axis, indicating the decay of
a secondary long-lived particle.

##  4 The trigger performance

Throughout 2016–2018, fluctuations in the instantaneous beam intensity during
the spill caused the L0 trigger rate to rise above the
$1\text{\,}\mathrm{MHz}$ limit of the L0TP. To avoid this, the beam intensity
was set at 60% of the nominal value, corresponding to a mean instantaneous
intensity of $450\text{\,}\mathrm{MHz}$, or $1.2\times 10^{9}$ Argonion
counts. Late in 2018, a _choke_ system was developed that enables each readout
system and the L0TP to temporarily suppress L0 triggers if the trigger rate is
too high. The choke system allowed operation at 80% of the nominal beam
intensity towards the end of 2018.

###  4.1 Trigger rates

The number of L0 primitives produced by each detector is expected to rise
linearly with the average beam intensity. The number of L0 primitives received
by the L0TP is shown as a function of the average beam intensity in the left
panel of Fig. 3. At $1.2\text{\times}{10}^{9}$ Argonion counts, the CHOD
(NA48-CHOD) produces $3.7\text{\times}{10}^{7}$ ($3.8\text{\times}{10}^{7}$)
primitives per spill. The MUV3, despite only being traversed by muons, also
produces $3.8\text{\times}{10}^{7}$ primitives per spill; this is explained by
additional muons from $\pi^{+}\to\mu^{+}\nu$ decays of pions in the beam,
which do not enter the other detectors. The RICH is insensitive to particles
below the Cherenkov threshold, and produces $3.4\text{\times}{10}^{7}$
primitives per spill. The LKr is insensitive to minimum ionising particles,
and produces $9\text{\times}{10}^{6}$ primitives per spill.

Figure 3: Number of primitives (left) and L0 triggers before downscaling
(right) per spill as a function of the average beam intensity. Local
variations in the data distributions are within statistical uncertainties.

The number of L0 triggers generated by each L0 trigger line per spill is shown
as a function of the average beam intensity in the right panel of Fig. 3. The
number of generated triggers increases linearly with average beam intensity
below $1.2\times 10^{9}$ Argonion counts, and saturates above this value. The
saturation is caused by the rate of primitives temporarily exceeding the
maximum $17.3\text{\,}\mathrm{MHz}$ input rate of the L0TP due to fluctuations
in the instantaneous beam intensity; this has no significant effect on the
data acquisition. For each trigger line, the downscaling factor and typical
number of triggers per spill after downscaling are shown in Table 4. The total
number of L0 triggers per spill is $2.2\text{\times}{10}^{6}$, lower than the
sum of the entries in Table 4 as the same event can be triggered by more than
one line. The number of L1 triggers generated by each trigger line per spill
is shown in Table 4. The total number of L1 triggers per spill is $2.5\times
10^{5}$, with the majority of events collected by the PNN and control trigger
lines.

Trigger line | Downscaling | L0 triggers [$10^{3}$] | L1 triggers [$10^{3}$]
---|---|---|---
PNN | 1 | 1540 | 74
Non-$\mu$ | 200 | 30 | 12
MT | 100 | 39 | 4
2$\mu$MT | 2 | 150 | 30
$e$MT | 8 | 193 | 22
$\mu$MT | 5 | 99 | 10
DV-$\mu$ | 5 | 140 | 0.3
DV-$2\mu$ | 3 | 160 | 5
Neutrino | 15 | 10 | 3
Control | 400 | 94 | 94
Table 4: List of $K^{+}$ trigger lines, L0 downscaling factors, and numbers of L0 triggers after downscaling and L1 triggers produced per spill at a beam intensity of $1.2\text{\times}{10}^{9}$ Argonion counts. No L1 conditions are applied to the control trigger line.  Trigger line | Downscaling | L0 triggers [$10^{3}$]
---|---|---
Charged | 1 | 1
Neutral | 1 | 30
Control | 5 | 180
Table 5: List of beam-dump trigger lines, L0 downscaling factors, and numbers
of L0 triggers produced per spill at a beam rate of $10^{12}$ POT/s.

In beam-dump configuration only the L0 trigger is utilised. The downscaling
factors and numbers of L0 triggers per spill are shown in Table 5. About
$2.1\times 10^{5}$ events are collected per spill, with the majority collected
by the control trigger line.

###  4.2 Efficiency of the PNN trigger line

In the context of the $K^{+}\to\pi^{+}\nu\bar{\nu}$ analysis, the combined
efficiency of the L0 trigger conditions for RICH, CHOD, and MUV3 (Table 2) is
measured using a sample of $K^{+}\to\pi^{+}\pi^{0}$ events selected from
minimum-bias data using criteria based on the $K^{+}\to\pi^{+}\nu\bar{\nu}$
event selection [3]. The efficiency is 98% at the mean instantaneous beam
intensity of $450\text{\,}\mathrm{MHz}$, and varies with instantaneous beam
intensity (left panel of Fig. 4). The inefficiency, which arises because the
time window considered at L0 is larger than the offline one, is mainly due to
accidental activity in the MUV3 detector used in a veto condition. The
efficiency of the L0 trigger condition of the LKr is measured with a sample of
$K^{+}\to\pi^{+}\pi^{0}$ decays with the two photons from the
$\pi^{0}\to\gamma\gamma$ detected in the LAV, using $\pi^{+}$ from
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays to determine the relationship between
$\pi^{+}$ momentum and the energy deposited in the LKr [3]. The efficiency
decreases from 96.5% to 86% over the
$1545\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ $\pi^{+}$
momentum range relevant to the $K^{+}\to\pi^{+}\nu\bar{\nu}$ analysis (right
panel of Fig. 4). The main part of the inefficiency stems from the requirement
that the total energy deposited in the LKr is less than
$30\text{\,}\mathrm{GeV}$. The overall L0 trigger efficiency is computed as
the product of the two independent efficiencies discussed above. The
efficiency varies with instantaneous beam intensity and $\pi^{+}$ momentum
(Fig. 5).

Figure 4: Efficiency of the combined RICH, CHOD, and MUV3 conditions of the
PNN trigger line evaluated using $K^{+}\to\pi^{+}\pi^{0}$ events as a function
of instantaneous beam intensity (left), and efficiency of the LKr condition of
the PNN trigger line evaluated using $K^{+}\to\pi^{+}\pi^{0}$ events as a
function of the $\pi^{+}$ momentum (right). Figure 5:  Efficiency of the PNN
L0 trigger conditions as a function of the instantaneous beam intensity in
bins of $\pi^{+}$ momentum.

Figure 6: Efficiency of the L1 LAV trigger evaluated using
$K^{+}\to\mu^{+}\nu$ events as a function of the average beam intensity
(left), and efficiency of the L1 STRAW trigger condition evaluated using
$K^{+}\to\mu^{+}\nu$ events as a function of the track momentum (right).

The efficiencies of the L1 KTAG, LAV, and STRAW trigger conditions are
measured using a sample of $K^{+}\to\mu^{+}\nu$ events selected from minimum-
bias data using the same criteria for the KTAG, LAV, and STRAW as in the
$K^{+}\to\pi^{+}\nu\bar{\nu}$ selection. The L1 KTAG efficiency is 99.9%. The
L1 LAV efficiency ranges from 99.5% to 99.0% depending on the average beam
intensity (left panel of Fig. 6); the inefficiency is due to random veto, as
the time window used at L1 is larger than in the event selection. The
efficiency of L1 STRAW varies between 99.6% and 94.6% as a function of the
track momentum (right panel of Fig. 6). Non-gaussian tails in the online
momentum resolution reduce the efficiency in the
40–$45\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$ region.
The total L1 trigger efficiency is computed as the product of the individual
L1 KTAG, LAV, and STRAW efficiencies, and is 98% (94%) for $\pi^{+}$ momentum
in the 15–$40\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$
(40–$45\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{ $c$ }}$) range.

The overall trigger efficiency is computed as the product of the L0 and L1
trigger efficiencies and is found to be 90%, varying by 5% both as a function
of instantaneous beam intensity and $\pi^{+}$ momentum.

###  4.3 Efficiencies of the other $K^{+}$ trigger lines

The efficiencies of the L0 and L1 trigger conditions used in the other $K^{+}$
trigger lines (Table 2) are measured using a sample of
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays collected via the MT and control
trigger lines. This event sample also allows the study of trigger conditions
involving muons from $\pi^{\pm}~{}\to~{}\mu^{\pm}~{}\nu$ decays upstream of
the LKr. The efficiencies of a subset of the L0 conditions are shown as a
function of the instantaneous beam intensity in Fig. 7. At the mean
instantaneous beam intensity of $450\text{\,}\mathrm{MHz}$, the RICH,
NA48-CHOD, Q1, M1, and MO1 conditions have efficiencies above 99.7%, while the
Q2, QX, MO2 and MOQX conditions have efficiencies above 99%. The efficiencies
all decrease with increasing instantaneous beam intensity.

The efficiencies of the LKr conditions E10 and E20 are measured using
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ events in which each reconstructed cluster is
associated with one of the tracks and is within $6\text{\,}\mathrm{ns}$ of the
L0 trigger time. This requirement ensures that the energy reconstructed
offline is assigned to a single LKr primitive. Both conditions have
efficiencies above 99.5% in the plateau region of the turn-on curve (Fig. 8).

Figure 7: Efficiencies of the L0 trigger conditions measured as a function of
the instantaneous beam intensity using a sample of
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays. The hatched areas indicate the
statistical uncertainties of the measurements. Figure 8:  Efficiencies of the
E10 and E20 trigger conditions as a function of LKr energy deposit, measured
with a sample of $K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays.

The efficiencies of the L1 KTAG and STRAW-Exo conditions are evaluated using
autopass events as a function of the instantaneous beam intensity and the
$\pi^{-}$ momentum (Fig. 9). The efficiency of L1 KTAG is 99.9%, with no
dependence on either variable, while L1 STRAW-Exo is 95% efficient with a
dependence on both. The inefficiency of L1 STRAW-Exo is due to differences in
the track reconstructions used at L1 and offline.

Figure 9: L1 KTAG and STRAW-Exo efficiencies measured with a sample of
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays as functions of instantaneous beam
intensity (left) and $\pi^{-}$ momentum (right). The hatched areas indicate
the statistical uncertainties of the measurements.

###  4.4 Efficiencies of the beam-dump trigger lines

The efficiencies of the L0 trigger conditions Q2 and C2E2 are measured using
data collected via the control trigger line (Table 3), using a sample of
events with two oppositely-charged tracks that form a vertex in the FV. The
two tracks are required to extrapolate within the acceptance of the CHOD,
NA48-CHOD, and LKr. When determining the efficiency of the Q2 trigger
condition, the two tracks are required to extrapolate into different CHOD
quadrants. When determining the efficiency of the C2E2 condition, at least
$1\text{\,}\mathrm{GeV}$ in the LKr is required to be associated with each
track, with no other LKr energy deposit. The efficiency of the Q2 condition
evaluated as a function of the total momentum of the two tracks (total vertex
momentum) is larger than 99% and does not vary as a function of the total
vertex momentum (left panel of Fig. 10). As the Q1 and Q2 conditions are
correlated – both are produced by the CHOD – the efficiency is cross-checked
using data collected via the neutral trigger line (right panel of Fig. 10).
The efficiency is consistent between the two samples.

Figure 10: Efficiency of the Q2 trigger condition in beam-dump data, measured
as a function of the total vertex momentum using events collected via the
control trigger (left) or the neutral trigger (right) lines reported in Table.
3. The hatched areas indicate the statistical uncertainties of the
measurements.

The efficiency of the C2E2 condition is evaluated as a function of the smaller
energy deposit of the two tracks using a data sample collected via the charged
trigger line (Table 3). The efficiency rises to 95% at
$3\text{\,}\mathrm{GeV}$, and is close to 100% at $10\text{\,}\mathrm{GeV}$
(Fig. 11).

Figure 11: Efficiency of the C2E2 condition in beam-dump data, as a function
of the smaller LKr energy deposit of the two tracks. The hatched areas
indicate the statistical uncertainties of the measurements.

###  4.5 Simulation of the trigger response

To simulate the L0 trigger response offline, a software emulation reproduces
the firmware algorithms incorporated in the L0 trigger. The L0 emulator output
is compared to the measured trigger efficiency using a sample of
$K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ decays obtained via the control trigger line.
The QX efficiency, and its variation with instantaneous beam intensity, is
reproduced to within 0.2% (left panel of Fig. 12). The LKr30 efficiency is
also reproduced to within 0.2% for an energy deposit above
$20\text{\,}\mathrm{GeV}$ (right panel of Fig. 12). For an energy deposit
below $20\text{\,}\mathrm{GeV}$, the LKr30 efficiency is highly sensitive to
the emulation of the cluster reconstruction, leading to a larger discrepancy
between the emulated and measured efficiencies. For the L1 trigger, part of
the HLT software is integrated with the offline software, and as the libraries
and algorithms are shared between the HLT and offline software, the L1 trigger
response is reproduced exactly.

Figure 12: Efficiencies of the L0 trigger conditions QX (left) and LKr30
(right) measured using $K^{+}\to\pi^{+}\pi^{+}\pi^{-}$ events collected via
the control trigger line, and simulated using the trigger emulator on the same
data. The hatched areas indicate the statistical uncertainties of the
measurements.

##  5 Conclusions and outlook

The NA62 trigger system was successfully operated during the 2016–2018 data-
taking period, exhibiting good performance and reliability. The flexibility of
the system allowed its evolution during the data-taking, and several rate
limitations have been identified and removed.

Two major developments are anticipated for the L0 trigger. The first
development is an upgraded version of the L0TP, installed for testing in 2021,
that exploits newer hardware to handle a higher primitive rate and offer more
flexibility in the conditions used to generate triggers. The second
development is a ring-finding algorithm for the RICH detector implemented on
commercially-available Graphics Processing Units (GPU) [15]. The
$1\text{\,}\mathrm{ms}$ latency of the L0 trigger is sufficiently large for
such a system to operate.

Improvements to the HLT software exploit advances in the
$K^{+}\to\pi^{+}\nu\bar{\nu}$ analysis to refine the trigger selection used to
collect both the signal and the sample of ancillary data required for
background estimation and systematic checks. Several improvements have already
been implemented, namely in the L1 STRAW algorithm to recover the efficiency
loss at high $\pi^{+}$ momentum, and in the L1 LAV algorithm to reduce the
inefficiency caused by random veto. Further exploitation of the available
detector information can preserve specific categories of events that would be
rejected by simpler algorithms, allowing a broader physics programme without
impacting the $K^{+}\to\pi^{+}\nu\bar{\nu}$ trigger line. One major
improvement is to implement particle identification at L1 by matching tracks
in the STRAW with Cherenkov rings in the RICH or energy deposits in the LKr.
The latter is possible due to new hardware that transmits data from the
calorimeter L0 trigger to the L1 trigger. An additional L2 trigger stage can
also be used after the L1 to further reduce the data volume. Trigger
algorithms implemented at L2 will have the advantage of being executed on
complete events with information from all detectors.

## Acknowledgements

It is a pleasure to express our appreciation to the staff of the CERN
laboratory and the technical staff of the participating laboratories and
universities for their efforts in the operation of the experiment and data
processing.

The cost of the experiment and its auxiliary systems was supported by the
funding agencies of the Collaboration Institutes. We are particularly indebted
to: F.R.S.-FNRS (Fonds de la Recherche Scientifique - FNRS), under Grants No.
4.4512.10, 1.B.258.20, Belgium; CECI (Consortium des Equipements de Calcul
Intensif), funded by the Fonds de la Recherche Scientifique de Belgique
(F.R.S.-FNRS) under Grant No. 2.5020.11 and by the Walloon Region, Belgium;
NSERC (Natural Sciences and Engineering Research Council), funding
SAPPJ-2018-0017, Canada; MEYS (Ministry of Education, Youth and Sports)
funding LM 2018104, Czech Republic; BMBF (Bundesministerium für Bildung und
Forschung) contracts 05H12UM5, 05H15UMCNA and 05H18UMCNA, Germany; INFN
(Istituto Nazionale di Fisica Nucleare), Italy; MIUR (Ministero
dell’Istruzione, dell’Università e della Ricerca), Italy; CONACyT (Consejo
Nacional de Ciencia y Tecnología), Mexico; IFA (Institute of Atomic Physics)
Romanian CERN-RO No. 1/16.03.2016 and Nucleus Programme PN 19 06 01 04,
Romania; INR-RAS (Institute for Nuclear Research of the Russian Academy of
Sciences), Moscow, Russia; JINR (Joint Institute for Nuclear Research), Dubna,
Russia; NRC (National Research Center) “Kurchatov Institute” and MESRF
(Ministry of Education and Science of the Russian Federation), Russia; MESRS
(Ministry of Education, Science, Research and Sport), Slovakia; CERN (European
Organization for Nuclear Research), Switzerland; STFC (Science and Technology
Facilities Council), United Kingdom; NSF (National Science Foundation) Award
Numbers 1506088 and 1806430, U.S.A.; ERC (European Research Council)
“UniversaLepto” advanced grant 268062, “KaonLepton” starting grant 336581,
Europe.

Individuals have received support from: Charles University Research Center
(UNCE/SCI/ 013), Czech Republic; Ministero dell’Istruzione, dell’Università e
della Ricerca (MIUR “Futuro in ricerca 2012” grant RBFR12JF2Z, Project GAP),
Italy; Russian Science Foundation (RSF 19-72-10096), Russia; the Royal Society
(grants UF100308, UF0758946), United Kingdom; STFC (Rutherford fellowships
ST/J00412X/1, ST/M005798/1), United Kingdom; ERC (grants 268062, 336581 and
starting grant 802836 “AxScale”); EU Horizon 2020 (Marie Skłodowska-Curie
grants 701386, 754496, 842407, 893101, 101023808).

The data used in this paper were collected before February 2022.

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