###### Abstract

The Compact Linear Collider (CLIC) is a TeV-scale high-luminosity linear
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider under development at CERN. Following the CLIC conceptual design
published in $2012$, this report provides an overview of the CLIC project, its
current status, and future developments. It presents the CLIC physics
potential and reports on design, technology, and implementation aspects of the
accelerator and the detector. For an optimal exploitation of its physics
potential, CLIC is foreseen to be built and operated in stages, at centre-of-
mass energies of , and , respectively, for a site length ranging from
$11\text{\,}\km$ to $50\text{\,}\km$. CLIC uses a two-beam acceleration
scheme, in which normal-conducting high-gradient $12\text{\,}\GHz$
accelerating structures are powered via a high-current drive beam. For the
first stage, an alternative with X-band klystron powering is also considered.
CLIC accelerator optimisation, technical developments and system tests have
resulted in significant progress in recent years. Moreover, this has led to an
increased energy efficiency (power around $170\text{\,}\mathrm{MW}$) for the
stage, together with a reduced cost estimate at the level of $6$ billion
$\mathrm{C}\mathrm{H}\mathrm{F}$. The detector concept, which matches the
physics performance requirements and the CLIC experimental conditions, has
been refined using improved software tools for simulation and reconstruction.
Significant progress has been made on detector technology developments for the
tracking and calorimetry systems. A wide range of CLIC physics studies has
been conducted, both through full detector simulations with overlay of beam-
induced backgrounds, and through parametric studies, together providing a
broad overview of the CLIC physics potential. Each of the three energy stages
adds cornerstones of the full CLIC physics programme, such as Higgs width and
couplings, top-quark properties, Higgs self-coupling, direct searches, and
many precision electroweak measurements. The interpretation of the combined
results gives crucial and accurate insight into new physics, largely
complementary to LHC and HL-LHC. The construction of the first CLIC energy
stage could start by $2026$. First beams would be available by $2035$, marking
the beginning of a broad CLIC physics programme spanning
$2530\text{\,}\mathrm{years}$.

CERN-2018-005-M14 December 2018The Compact Linear Collider (CLIC)2018 Summary
ReportGENEVA2018

CERN Yellow Reports: Monographs

Published by CERN, CH-1211 Geneva 23, Switzerland

ISBN | 978–92–9083–506–6 (paperback)
---|---
ISBN | 978–92–9083–507–3 (PDF)
ISSN | 2519-8068 (Print)
ISSN | 2519-8076 (Online)
DOI | https://doi.org/10.23731/CYRM-2018-002

Accepted for publication by the CERN Report Editorial Board (CREB) on 10
December 2018

Available online at http://publishing.cern.ch/ and http://cds.cern.ch/

Copyright © CERN, 2018

Creative Commons Attribution 4.0

Knowledge transfer is an integral part of CERN’s mission.

CERN publishes this volume Open Access under the Creative Commons Attribution
4.0 license

(http://creativecommons.org/licenses/by/4.0/) in order to permit its wide
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The submission of a contribution to a CERN Yellow Report series shall be
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necessary for this purpose.

This volume is indexed in: CERN Document Server (CDS), INSPIRE.

This volume should be cited as:

The Compact Linear Collider (CLIC) – 2018 Summary Report, edited by P.N.
Burrows, N. Catalan Lasheras, L. Linssen, M. Petrič, A. Robson, D. Schulte, E.
Sicking, S. Stapnes, CERN Yellow Reports: Monographs, Vol. 2/2018,
CERN-2018-005-M (CERN, Geneva, 2018). https//doi.org/10.23731/CYRM-2018-002

Abstract

> Corresponding editors

Philip N. Burrows (University of Oxford), Nuria Catalan Lasheras (CERN),

Lucie Linssen (CERN), Marko Petrič (CERN),

Aidan Robson (University of Glasgow), Daniel Schulte (CERN),

Eva Sicking (CERN), Steinar Stapnes (CERN)

The CLIC and CLICdp collaborations

T.K. Charles, P.J. Giansiracusa, T.G. Lucas, R.P. Rassool, M. Volpi1
_University of Melbourne, Melbourne, Australia_

C. Balazs
_Monash University, Melbourne, Australia_

K. Afanaciev, V. Makarenko
_Belarusian State University, Minsk, Belarus_

A. Patapenka, I. Zhuk
_Joint Institute for Power and Nuclear Research - Sosny, Minsk, Belarus_

C. Collette
_Université libre de Bruxelles, Brussels, Belgium_

M.J. Boland
_University of Saskatchewan, Saskatoon, Canada_

A.C. Abusleme Hoffman, M.A. Diaz, F. Garay
_Pontificia Universidad Católica de Chile, Santiago, Chile_

Y. Chi, X. He, G. Pei, S. Pei, G. Shu, X. Wang, J. Zhang, F. Zhao, Z. Zhou
_Institute of High Energy Physics, Beijing, China_

H. Chen, Y. Gao, W. Huang, Y.P. Kuang, B. Li, Y. Li, X. Meng, J. Shao, J. Shi,
C. Tang, P. Wang, X. Wu, H. Zha
_Tsinghua University, Beijing, China_

L. Ma, Y. Han
_Shandong University, Jinan, China_

W. Fang, Q. Gu, D. Huang, X. Huang, J. Tan, Z. Wang, Z. Zhao
_Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai,
China_

U.I. Uggerhøj, T.N. Wistisen
_Aarhus University, Aarhus, Denmark_

A. Aabloo, R. Aare, K. Kuppart, S. Vigonski, V. Zadin
_University of Tartu, Tartu, Estonia_

M. Aicheler, E. Baibuz, E. Brücken, F. Djurabekova2, P. Eerola2, F. Garcia, E.
Haeggström2, K. Huitu2, V. Jansson2, I. Kassamakov2, J. Kimari2, A.
Kyritsakis, S. Lehti, A. Meriläinen2, R. Montonen2, K. Nordlund2, K.
Österberg2, A. Saressalo, J. Väinölä, M. Veske
_Helsinki Institute of Physics, University of Helsinki, Helsinki, Finland_

W. Farabolini, A. Mollard, F. Peauger3, J. Plouin
_CEA, Gif-sur-Yvette, France_

P. Bambade, I. Chaikovska, R. Chehab, N. Delerue, M. Davier, A. Faus-Golfe, A.
Irles, W. Kaabi, F. LeDiberder, R. Pöschl, D. Zerwas
_Laboratoire de l’Accélérateur Linéaire, Université de Paris-Sud XI,
IN2P3/CNRS, Orsay, France_

B. Aimard, G. Balik, J.-J. Blaising, L. Brunetti, M. Chefdeville, A. Dominjon,
C. Drancourt, N. Geoffroy, J. Jacquemier, A. Jeremie, Y. Karyotakis, J.M.
Nappa, M. Serluca, S. Vilalte, G. Vouters
_LAPP, Université de Savoie, IN2P3/CNRS, Annecy, France_

A. Bernhard, E. Bründermann, S. Casalbuoni, S. Hillenbrand, J. Gethmann, A.
Grau, E. Huttel, A.-S. Müller, P. Peiffer4, I. Perić, D. Saez de Jauregui
_Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany_

L. Emberger, C. Graf, F. Simon, M. Szalay, N. van der Kolk5
_Max-Planck-Institut für Physik, Munich, Germany_

S. Brass, W. Kilian
_Department of Physics, University of Siegen, Siegen, Germany_

T. Alexopoulos, T. Apostolopoulos6, E.N. Gazis, N. Gazis, V. Kostopoulos7, S.
Kourkoulis
_National Technical University of Athens, Athens, Greece_

B. Heilig
_Department of Basic Geophysical Research, Mining and Geological Survey of
Hungary, Tihany, Hungary_

J. Lichtenberger
_Space Research Laboratory, Eötvös Loránd University, Budapest, Hungary_

P. Shrivastava
_Raja Ramanna Centre for Advanced Technology, Department of Atomic Energy,
Indore, India_

M.K. Dayyani, H. Ghasem1, S.S. Hajari, H. Shaker1
_The School of Particles and Accelerators, Institute for Research in
Fundamental Sciences, Tehran, Iran_

Y. Ashkenazy, I. Popov, E. Engelberg, A. Yashar
_Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem,
Israel_

H. Abramowicz, Y. Benhammou, O. Borysov, M. Borysova, A. Levy, I. Levy
_Raymond & Beverly Sackler School of Physics & Astronomy, Tel Aviv University,
Tel Aviv, Israel_

D. Alesini, M. Bellaveglia, B. Buonomo, A. Cardelli, M. Diomede, M. Ferrario,
A. Gallo, A. Ghigo, A. Giribono, L. Piersanti, A. Stella, C. Vaccarezza
_INFN e Laboratori Nazionali di Frascati, Frascati, Italy_

J. de Blas
_Università di Padova and INFN, Padova, Italy_

R. Franceschini
_Università degli Studi Roma Tre and INFN, Roma, Italy_

G. D’Auria, S. Di Mitri
_Elettra Sincrotrone Trieste, Trieste, Italy_

T. Abe, A. Aryshev, M. Fukuda, K. Furukawa, H. Hayano, Y. Higashi, T. Higo, K.
Kubo, S. Kuroda, S. Matsumoto, S. Michizono, T. Naito, T. Okugi, T. Shidara,
T. Tauchi, N. Terunuma, J. Urakawa, A. Yamamoto1
_High Energy Accelerator Research Organization, KEK, Tsukuba, Japan_

R. Raboanary
_University of Antananarivo, Antananarivo, Madagascar_

O.J. Luiten, X.F.D. Stragier
_Eindhoven University of Technology, Eindhoven, Netherlands_

R. Hart, H. van der Graaf
_Nikhef, Amsterdam, Netherlands_

G. Eigen
_Department of Physics and Technology, University of Bergen, Bergen, Norway_

E. Adli1, C.A. Lindstrøm, R. Lillestøl, L. Malina1, J. Pfingstner, K.N.
Sjobak1
_University of Oslo, Oslo, Norway_

A. Ahmad, H. Hoorani, W.A. Khan
_National Centre for Physics, Islamabad, Pakistan_

S. Bugiel, R. Bugiel, M. Firlej, T.A. Fiutowski, M. Idzik, J. Moroń, K.P.
Świentek
_AGH University of Science and Technology, Krakow, Poland_

P. Brückman de Renstrom, B. Krupa, M. Kucharczyk, T. Lesiak, B. Pawlik, P.
Sopicki, B. Turbiarz, T. Wojtoń, L.K. Zawiejski
_Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland_

J. Kalinowski, K. Nowak, A.F. Żarnecki
_Faculty of Physics, University of Warsaw, Warsaw, Poland_

E. Firu, V. Ghenescu, A.T. Neagu, T. Preda, I.S. Zgura
_Institute of Space Science, Bucharest, Romania_

A. Aloev, N. Azaryan, I. Boyko, J. Budagov, M. Chizhov, M. Filippova, V.
Glagolev, A. Gongadze, S. Grigoryan, D. Gudkov, V. Karjavine, M. Lyablin, Yu.
Nefedov, A. Olyunin1, A. Rymbekova, A. Samochkine, A. Sapronov, G. Shelkov, G.
Shirkov, V. Soldatov, E. Solodko1, G. Trubnikov, I. Tyapkin, V. Uzhinsky, A.
Vorozhtov, A. Zhemchugov
_Joint Institute for Nuclear Research, Dubna, Russia_

E. Levichev, N. Mezentsev, P. Piminov, D. Shatilov, P. Vobly, K. Zolotarev
_Budker Institute of Nuclear Physics, Novosibirsk, Russia_

I. Božović Jelisavčić, G. Kačarević, G. Milutinović Dumbelović, M. Pandurović,
M. Radulović, J. Stevanović, N. Vukasinović
_Vinča Institute of Nuclear Sciences, University of Belgrade, Belgrade,
Serbia_

D.-H. Lee
_School of Space Research, Kyung Hee University, Yongin, Gyeonggi, South
Korea_

N. Ayala, G. Benedetti, T. Guenzel, U. Iriso, Z. Marti, F. Perez, M. Pont
_CELLS-ALBA, Barcelona, Spain_

J. Trenado
_University of Barcelona, Barcelona, Spain_

A. Ruiz-Jimeno, I. Vila
_IFCA, CSIC-Universidad de Cantabria, Santander, Spain_

J. Calero, M. Dominguez, L. Garcia-Tabares, D. Gavela, D. Lopez, F. Toral
_Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain_

C. Blanch Gutierrez, M. Boronat, D. Esperante1, E. Fullana, J. Fuster, I.
García, B. Gimeno, P. Gomis Lopez, D. González, M. Perelló, E. Ros, M.A.
Villarejo, A. Vnuchenko, M. Vos
_Instituto de Física Corpuscular (CSIC-UV), Valencia, Spain_

Ch. Borgmann, R. Brenner, T. Ekelöf, M. Jacewicz, M. Olvegård, R. Ruber, V.
Ziemann
_Uppsala University, Uppsala, Sweden_

D. Aguglia, J. Alabau Gonzalvo, M. Alcaide Leon, N. Alipour Tehrani, M.
Anastasopoulos, A. Andersson, F. Andrianala8, F. Antoniou, A. Apyan, D.
Arominski9, K. Artoos, S. Assly, S. Atieh, C. Baccigalupi, R. Ballabriga Sune,
D. Banon Caballero, M.J. Barnes, J. Barranco Garcia, A. Bartalesi, J. Bauche,
C. Bayar, C. Belver-Aguilar, A. Benot Morell10, M. Bernardini, D.R. Bett, S.
Bettoni11, M. Bettencourt, B. Bielawski, O. Blanco Garcia, N. Blaskovic
Kraljevic, B. Bolzon12, X.A. Bonnin, D. Bozzini, E. Branger, E. Brondolin, O.
Brunner, M. Buckland13, H. Bursali, H. Burkhardt, D. Caiazza, S. Calatroni, M.
Campbell, N. Catalan Lasheras∗, B. Cassany, E. Castro, R.H. Cavaleiro Soares,
M. Cerqueira Bastos, A. Cherif, E. Chevallay, V. Cilento14, R. Corsini, R.
Costa15, B. Cure, S. Curt, A. Dal Gobbo, D. Dannheim, E. Daskalaki, L. Deacon,
A. Degiovanni, G. De Michele, L. De Oliveira, V. Del Pozo Romano, J.P.
Delahaye, D. Delikaris, P.G. Dias de Almeida16, T. Dobers, S. Doebert, I.
Doytchinov, M. Draper, F. Duarte Ramos, M. Duquenne, N. Egidos Plaja, K.
Elsener, J. Esberg, M. Esposito, L. Evans, V. Fedosseev, P. Ferracin, A.
Fiergolski, K. Foraz, A. Fowler, F. Friebel, J-F. Fuchs, A. Gaddi, D. Gamba,
L. Garcia Fajardo17, H. Garcia Morales, C. Garion, M. Gasior, L. Gatignon,
J-C. Gayde, A. Gerbershagen, H. Gerwig, G. Giambelli, A. Gilardi, A.N.
Goldblatt, S. Gonzalez Anton, C. Grefe18, A. Grudiev, H. Guerin, F.G. Guillot-
Vignot, M.L. Gutt-Mostowy, M. Hein Lutz, C. Hessler, J.K. Holma, E.B. Holzer,
M. Hourican, D. Hynds19, E. Ikarios, Y. Inntjore Levinsen, S. Janssens, A.
Jeff, E. Jensen, M. Jonker, S.W. Kamugasa, M. Kastriotou, J.M.K. Kemppinen, V.
Khan, R.B. Kieffer, W. Klempt, N. Kokkinis, I. Kossyvakis, Z. Kostka, A.
Korsback, E. Koukovini Platia, J.W. Kovermann, C-I. Kozsar, I. Kremastiotis20,
J. Kröger21, S. Kulis, A. Latina, F. Leaux, P. Lebrun, T. Lefevre, E.
Leogrande, L. Linssen∗, X. Liu, X. Llopart Cudie, S. Magnoni, C. Maidana, A.A.
Maier, H. Mainaud Durand, S. Mallows, E. Manosperti, C. Marelli, E. Marin
Lacoma, S. Marsh, R. Martin, I. Martini, M. Martyanov, S. Mazzoni, G.
Mcmonagle, L.M. Mether, C. Meynier, M. Modena, A. Moilanen, R. Mondello, P.B.
Moniz Cabral, N. Mouriz Irazabal, M. Munker, T. Muranaka, J. Nadenau, J.G.
Navarro, J.L. Navarro Quirante, E. Nebo Del Busto, N. Nikiforou22, P. Ninin,
M. Nonis, D. Nisbet, F.X. Nuiry, A. Nürnberg23, J. Ögren, J. Osborne, A.C.
Ouniche, R. Pan24, S. Papadopoulou, Y. Papaphilippou, G. Paraskaki, A.
Pastushenko10, A. Passarelli, M. Patecki, L. Pazdera, D. Pellegrini, K.
Pepitone, E. Perez Codina, A. Perez Fontenla, T.H.B. Persson, M. Petrič25∗, S.
Pitman, F. Pitters26, S. Pittet, F. Plassard, D. Popescu, T. Quast27, R.
Rajamak, S. Redford11, L. Remandet, Y. Renier24, S.F. Rey, O. Rey Orozco, G.
Riddone, E. Rodriguez Castro, P. Roloff, C. Rossi, F. Rossi, V. Rude, I.
Ruehl, G. Rumolo, A. Sailer, J. Sandomierski, E. Santin, C. Sanz, J. Sauza
Bedolla, U. Schnoor, H. Schmickler, D. Schulte∗, E. Senes, C. Serpico, G.
Severino, N. Shipman, E. Sicking∗, R. Simoniello28, P.K. Skowronski, P.
Sobrino Mompean, L. Soby, P. Sollander, A. Solodko, M.P. Sosin, S. Spannagel,
S. Sroka, S. Stapnes∗, G. Sterbini, G. Stern, R. Ström, M.J. Stuart, I.
Syratchev, K. Szypula, F. Tecker, P.A. Thonet, P. Thrane, L. Timeo, M.
Tiirakari, R. Tomas Garcia, C.I. Tomoiaga, P. Valerio29, T. Vaňát, A.L.
Vamvakas, J. Van Hoorne, O. Viazlo, M. Vicente Barreto Pinto30, N. Vitoratou,
V. Vlachakis, M.A. Weber, R. Wegner, M. Wendt, M. Widorski, O.E. Williams, M.
Williams31, B. Woolley, W. Wuensch, A. Wulzer, J. Uythoven, A. Xydou, R. Yang,
A. Zelios, Y. Zhao32, P. Zisopoulos
_CERN, Geneva, Switzerland_

M. Benoit, D M S Sultan
_Département de Physique Nucléaire et Corpusculaire (DPNC), Université de
Genève, Genève, Switzerland_

F. Riva1
_Département de Physique Théorique, Université de Genève, Genève, Switzerland_

M. Bopp, H.H. Braun, P. Craievich, M. Dehler, T. Garvey, M. Pedrozzi, J.Y.
Raguin, L. Rivkin33, R. Zennaro
_Paul Scherrer Institut, Villigen, Switzerland_

S. Guillaume, M. Rothacher
_ETH Zurich, Institute of Geodesy and Photogrammetry, Zurich, Switzerland_

A. Aksoy, Z. Nergiz34, Ö. Yavas
_Ankara University, Ankara, Turkey_

H. Denizli, U. Keskin, K. Y. Oyulmaz, A. Senol
_Department of Physics, Abant İzzet Baysal University, Bolu, Turkey_

A.K. Ciftci
_Izmir University of Economics, Izmir, Turkey_

V. Baturin, O. Karpenko, R. Kholodov, O. Lebed, S. Lebedynskyi, S. Mordyk, I.
Musienko, Ia. Profatilova, V. Storizhko
_Institute of Applied Physics, National Academy of Sciences of Ukraine, Sumy,
Ukraine_

R.R. Bosley, T. Price, M.F. Watson, N.K. Watson, A.G. Winter
_University of Birmingham, Birmingham, United Kingdom_

J. Goldstein
_University of Bristol, Bristol, United Kingdom_

S. Green, J.S. Marshall35, M.A. Thomson, B. Xu, T. You36
_Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom_

W.A. Gillespie
_University of Dundee, Dundee, United Kingdom_

M. Spannowsky
_Department of Physics, Durham University, Durham, United Kingdom_

C. Beggan
_British Geological Survey, Edinburgh, United Kingdom_

V. Martin, Y. Zhang
_University of Edinburgh, Edinburgh, United Kingdom_

D. Protopopescu, A. Robson1∗
_University of Glasgow, Glasgow, United Kingdom_

R.J. Apsimon37, I. Bailey38, G.C. Burt37, A.C. Dexter37, A.V. Edwards37, V.
Hill38, S. Jamison, W.L. Millar37, K. Papke37
_Lancaster University, Lancaster, United Kingdom_

G. Casse, J. Vossebeld
_University of Liverpool, Liverpool, United Kingdom_

T. Aumeyr, M. Bergamaschi1, L. Bobb38, A. Bosco, S. Boogert, G. Boorman, F.
Cullinan, S. Gibson, P. Karataev, K. Kruchinin, K. Lekomtsev, A. Lyapin, L.
Nevay, W. Shields, J. Snuverink, J. Towler, E. Yamakawa
_The John Adams Institute for Accelerator Science, Royal Holloway, University
of London, Egham, United Kingdom_

V. Boisvert, S. West
_Royal Holloway, University of London, Egham, United Kingdom_

R. Jones, N. Joshi
_University of Manchester, Manchester, United Kingdom_

D. Bett, R.M. Bodenstein1, T. Bromwich, P.N. Burrows1∗, G.B. Christian38, C.
Gohil1, P. Korysko1, J. Paszkiewicz1, C. Perry, R. Ramjiawan, J. Roberts
_John Adams Institute, Department of Physics, University of Oxford, Oxford,
United Kingdom_

T. Coates, F. Salvatore
_University of Sussex, Brighton, United Kingdom_

A. Bainbridge37, J.A. Clarke37, N. Krumpa B.J.A. Shepherd37, D. Walsh3
_STFC Daresbury Laboratory, Warrington, United Kingdom_

S. Chekanov, M. Demarteau, W. Gai, W. Liu, J. Metcalfe, J. Power, J. Repond,
H. Weerts, L. Xia, J. Zhang
_Argonne National Laboratory, Argonne, USA_

J. Zupan
_Department of Physics, University of Cincinnati, Cincinnati, OH, USA_

J.D. Wells, Z. Zhang
_Physics Department, University of Michigan, Ann Arbor, MI, USA_

C. Adolphsen, T. Barklow, V. Dolgashev, M. Franzi, N. Graf, J. Hewett, M.
Kemp, O. Kononenko, T. Markiewicz, K. Moffeit, J. Neilson, Y. Nosochkov, M.
Oriunno, N. Phinney, T. Rizzo, S. Tantawi, J. Wang, B. Weatherford, G. White,
M. Woodley
_SLAC National Accelerator Laboratory, Menlo Park, USA_

1Also at CERN, Geneva, Switzerland

2Also at Department of Physics, University of Helsinki, Helsinki, Finland

3Now at CERN, Geneva, Switzerland

4Now at Johannes-Gutenberg University, Mainz, Germany

5Now at Nikhef / Utrecht University, Amsterdam / Utrecht, The Netherlands

6Also at Department of Informatics, Athens University of Business and
Economics, Athens, Greece

7Also at University of Patras, Patras, Greece

8Also at University of Antananarivo, Antananarivo, Madagascar

9Also at Warsaw University of Technology, Warsaw, Poland

10Also at IFIC, Valencia, Spain

11Now at Paul Scherrer Institute, Villigen, Switzerland

12Now at CEA, Gif-sur-Yvette, France

13Also at University of Liverpool, United Kingdom

14Also at LAL, Orsay, France

15Also at Uppsala University, Uppsala, Sweden

16Also at IFCA, CSIC-Universidad de Cantabria, Santander, Spain

17Now at LBNL, Berkeley CA, USA

18Now at University of Bonn, Bonn, Germany

19Now at Nikhef, Amsterdam, The Netherlands

20Also at KIT, Karlsruhe, Germany

21Also at Ruprecht-Karls-Universität Heidelberg, Germany

22Now at University of Texas, Austin, USA

23Now at Karlsruhe Institute of Technology, Karlsruhe, Germany

24Now at DESY, Zeuthen, Germany

25Also at J. Stefan Institute, Ljubljana, Slovenia

26Also at Vienna University of Technology, Vienna, Austria

27Also at RWTH Aachen University, Aachen, Germany

28Now at Johannes Gutenberg Universität, Mainz, Germany

29Now at Département de Physique Nucléaire et Corpusculaire (DPNC), Université
de Genève, Geneva, Switzerland

30Also at Département de Physique Nucléaire et Corpusculaire (DPNC),
Université de Genève, Geneva, Switzerland

31Also at University of Glasgow, Glasgow, United Kingdom

32Also at Shandong University, Jinan, China

33Also at EPFL, Lausanne, Switzerland

34Also at Omer Halis Demir University, Nigde, Turkey

35Now at University of Warwick, Coventry, United Kingdom

36Also at DAMTP, University of Cambridge, Cambridge, United Kingdom

37Also at The Cockcroft Institute, Daresbury, United Kingdom

38Now at Diamond Light Source, Harwell, United Kingdom

∗Editors<EMAIL_ADDRESS>
###### Contents

  1. 1 Introduction
  2. 2 CLIC physics overview
    1. 2.1 CLIC physics exploration at three energy stages
    2. 2.2 Higgs physics potential
    3. 2.3 Top-quark physics potential
    4. 2.4 Direct and indirect searches for BSM physics
    5. 2.5 Overall CLIC physics reach
  3. 3 CLIC accelerator design, technologies and performance
    1. 3.1 Introduction
    2. 3.2 CLIC design and performance at $380\text{\,}\mathrm{GeV}$
      1. 3.2.1 Design overview
      2. 3.2.2 Main-beam design considerations and choices
      3. 3.2.3 Performance of the drive-beam concept
      4. 3.2.4 Luminosity performance
      5. 3.2.5 Operation and availability
      6. 3.2.6 Energy flexibility
      7. 3.2.7 Beam experiments
    3. 3.3 A klystron-based CLIC at $380\text{\,}\mathrm{GeV}$
      1. 3.3.1 Design choice
      2. 3.3.2 Design implications
    4. 3.4 Extension to higher energy stages
      1. 3.4.1 Baseline design upgrade
      2. 3.4.2 Upgrade from the klystron-based option
    5. 3.5 Accelerator technologies
      1. 3.5.1 Main linac accelerating structures
      2. 3.5.2 RF power generation and distribution
      3. 3.5.3 Alignment and stabilisation
      4. 3.5.4 Beam instrumentation
      5. 3.5.5 Vacuum system
      6. 3.5.6 Magnets
      7. 3.5.7 Klystron-based main linac RF unit and module design
  4. 4 CLIC detector design, technologies and performance
    1. 4.1 Experimental conditions at CLIC
    2. 4.2 Physics-driven detector requirements
    3. 4.3 CLIC detector concept
    4. 4.4 Detector technologies
      1. 4.4.1 Vertex and tracking technologies
      2. 4.4.2 Electromagnetic and hadronic calorimeters
      3. 4.4.3 Very forward calorimeters
    5. 4.5 Detector performance
  5. 5 CLIC project implementation
    1. 5.1 The CLIC stages and construction
      1. 5.1.1 Civil engineering and infrastructure
      2. 5.1.2 Annual and integrated luminosities
    2. 5.2 Construction and operation schedules
      1. 5.2.1 380 GeV drive-beam schedule
      2. 5.2.2 380 GeV klystron-driven schedule
      3. 5.2.3 Schedules for the stages at higher energies and the complete project
      4. 5.2.4 Concluding remarks on the schedule
    3. 5.3 Cost estimate
      1. 5.3.1 Scope and method
      2. 5.3.2 Value estimates and cost drivers
      3. 5.3.3 Labour estimates
      4. 5.3.4 Value estimate and cost drivers of the CLIC detector
      5. 5.3.5 Operation costs
    4. 5.4 Power and energy consumption
      1. 5.4.1 Energy consumption
      2. 5.4.2 Power reduction studies and future prospects
  6. 6 Future opportunities
    1. 6.1 Physics motivation
    2. 6.2 Opportunities for extension based on future technologies
      1. 6.2.1 General concept
      2. 6.2.2 Dielectric accelerating structures
      3. 6.2.3 Plasma-based acceleration
      4. 6.2.4 Luminosity enabling technologies
  7. 7 CLIC objectives for the period 2020–2025
    1. 7.1 Accelerator complex
      1. 7.1.1 Accelerator programme overview
      2. 7.1.2 Programme implementation, technology demonstrators and collaboration
    2. 7.2 Detector and physics
  8. 8 Summary

##  1 Introduction

The Compact Linear Collider (CLIC) is a multi-$\mathrm{TeV}$ high-luminosity
linear
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider under development by the CLIC accelerator collaboration [1]. CLIC
uses a novel two-beam acceleration technique, with normal-conducting
accelerating structures operating in the range of
$70100\text{\,}\mathrm{M}\mathrm{V}\mathrm{/}\mathrm{m}$. Detailed studies of
the CLIC physics potential, design of a detector for CLIC, and R&D on detector
technologies are performed by the CLIC detector and physics (CLICdp)
collaboration [1]. The CLIC Conceptual Design Report (CDR) was published in
$2012$ [2, 3, 4]. The main focus of the CDR was to demonstrate the feasibility
of the CLIC accelerator at high energy ($3\text{\,}\mathrm{TeV}$) and to
confirm that high-precision physics measurements can be performed, despite the
luminosity spectrum and the presence of particles from beam-induced
background.

Following the completion of the CDR, detailed studies on Higgs and top-quark
physics, with particular focus on the first energy stage of CLIC, concluded
that the optimal centre-of-mass energy for the first stage is
$380\text{\,}\mathrm{GeV}$. As a result, a comprehensive optimisation study of
the CLIC accelerator complex was performed, by scanning the full parameter
space for the accelerating structures, and by using the CLIC performance, cost
and energy consumption as a gauge for operation at $380\text{\,}\mathrm{GeV}$
and $3\text{\,}\mathrm{TeV}$. The results led to optimised accelerator design
parameters for the proposed CLIC staging scenario, with operation at
$380\text{\,}\mathrm{GeV}$, $1.5\text{\,}\mathrm{TeV}$ and
$3\text{\,}\mathrm{TeV}$, as reported in [5].

This report summarises progress and results of the CLIC studies at the time of
submitting input to the update of the European Strategy for Particle Physics,
in December $2018$. The report describes recent achievements in accelerator
design, technology development, system tests and beam tests. Large-scale CLIC-
specific beam tests have taken place, for example, at the CLIC Test Facility
CTF3 at CERN [6], at the Accelerator Test Facility ATF2 at KEK [7, 8], at the
FACET facility at SLAC [9] and at the FERMI facility in Trieste [10]. Crucial
experience also emanates from the expanding field of Free Electron Laser (FEL)
linacs and recent-generation light sources. Together they provide the
demonstration that all implications of the CLIC design parameters are well
understood and reproduced in beam tests. Therefore the CLIC performance goals
are realistic. An alternative CLIC scenario for the first stage, where the
accelerating structures are powered by X-band klystrons, is also under study.
The implementation of CLIC near CERN has been investigated. Principally
focusing on the $380\text{\,}\mathrm{GeV}$ stage, this includes civil
engineering aspects, electrical networks, cooling and ventilation,
installation scheduling, transport, and safety aspects. All CLIC studies have
put emphasis on optimising cost and energy efficiency, and the resulting power
and cost estimates are reported.

Since the completion of the CDR, the CLIC detector was further optimised
through a broad range of simulation studies, resulting in the CLICdet detector
design [11, 12]. In order to enlarge the angular acceptance of the detector,
the final focusing quadrupoles are now placed outside the detector in the
accelerator tunnel. The software suite for simulation and event reconstruction
was modernised and tuned for use with CLICdet. Detector technology
developments have focused on the most challenging aspects of the experiment,
namely the light-weight silicon vertex and tracker system and the highly-
granular calorimeters. The detector R&D activities have resulted in technology
demonstrators, showing that the required performance is already achievable or
will be achieved in the next phase, compatible with the CLIC timescale [13].

The physics potential at the three CLIC energy stages has been explored in
much detail. The first stage of CLIC provides collisions at
$\sqrt{s}=$380\text{\,}\mathrm{GeV}$$. This gives access to Higgs boson
measurements through Higgsstrahlung and WW-fusion [14], thereby providing
accurate model-independent measurements of the Higgs couplings and the Higgs
width. Precision top-quark physics [15] is also addressed at this energy, and
a fraction of the running time will be devoted to a threshold scan of top-
quark pair production around $350\text{\,}\mathrm{GeV}$.

The second stage, with collisions foreseen at $1.5\text{\,}\mathrm{TeV}$,
opens the energy frontier, allowing for the discovery of new physics phenomena
[4, 16]. The double Higgsstrahlung process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$
can be observed and additional Higgs and top-quark properties are within
reach, such as the Higgs self-coupling and rare Higgs branching ratios. The
third stage at $3\text{\,}\mathrm{TeV}$ further enlarges the CLIC physics
potential, e.g. allowing discovery of new electroweak particles or dark matter
candidates, which may be more easily observed at CLIC than at the HL-LHC. The
$3\text{\,}\mathrm{TeV}$ stage also provides the best sensitivity to new
physics processes at much higher energy scales, via indirect searches.

Section 2 of this report gives an overview of physics measurements at CLIC,
demonstrating how they improve our knowledge of the Standard Model and how
CLIC results have an impact on understanding the nature and scale of new
physics Beyond the Standard Model (BSM). Section 3 provides an overview of the
CLIC accelerator design and performance at $380\text{\,}\mathrm{GeV}$ for both
the two-beam baseline design and the klystron-based option. This section also
describes the path to the higher energies, $1.5\text{\,}\mathrm{TeV}$ and
$3\text{\,}\mathrm{TeV}$, and gives an overview of the key CLIC technology
developments. Referring to beam experiments and hardware tests, Section 3 also
describes key achievements providing evidence that the CLIC performance goals
can be met.

In Section 4 the CLIC detector and its performance results through simulation
and event reconstruction are described. The progress made and the status of
the detector technology developments are summarised. Section 5 describes the
present plans for the implementation of CLIC, with emphasis on the 380 GeV
stage. It reports on civil engineering and schedule aspects, and provides
estimates of the energy consumption and of the cost for construction and
operation. Physics motivation and options to expand the energy reach of CLIC
using future technologies are discussed in Section 6. The CLIC objectives for
the period $20202025$ are outlined in Section 7. Section 8 provides a short
summary of this report.

##  2 CLIC physics overview

###  2.1 CLIC physics exploration at three energy stages

CLIC’s physics programme will substantially improve our knowledge and probe
the open questions arising from the LHC and other particle physics facilities,
and from related astronomical observations. As CLIC gives access to a very
wide range of energies, it can reach unprecedented precision in the properties
and interactions of the Higgs boson, top quark, and electroweak gauge bosons.
It has the potential to make discoveries of new states that are inaccessible
at other facilities, including the possible discovery of dark matter, and
could potentially give some experimental insight to cosmological questions
such as the stability or instability of the vacuum and the origin of the
baryon asymmetry. The science program ranges from the ‘guaranteed physics’ of
precision studies of the Standard Model (SM), which through effective field
theory interpretations give access beyond the capacity of other facilities to
new physics at high scales, to ‘prospect physics’ of directly producing new
states or observing new interactions.

##### Detector and experimental environment

A single optimised CLIC detector, CLICdet [11], has been refined from the two
CLIC detector concepts CLIC_SiD and CLIC_ILD that were adapted from the
International Linear Collider (ILC) concepts as described in the CLIC CDR [3].
All three detector designs are compatible with the experimental conditions at
CLIC and satisfy the performance requirements driven by the physics
objectives, which are described in Sections 4.1 and 4.3. Common software tools
for CLIC_SiD and CLIC_ILD perform full simulation [17, 18], digitisation and
reconstruction [19, 20], particle flow reconstruction [21, 22, 23, 24], and
vertexing and heavy flavour tagging [25]. The corresponding, and partially
overlapping, software tools for CLICdet are described in Section 4.5. Full
simulations of the CLIC_ILD and CLIC_SiD detector concepts have been used for
the physics projections in the areas of Higgs and top-quark physics reported
in this section. Physics background processes, as well as the CLIC
experimental conditions and luminosity spectrum have systematically been taken
into account. The dark matter search using the mono-photon signature (see
Section 2.4) is the first full simulation study using CLICdet. Recent
phenomenological studies to explore the BSM potential of CLIC often use
parameterised detector performance derived from full simulations, for example
through the fast simulation package Delphes [26, 27].

##### Staging and polarisation

The total integrated luminosities for each energy stage are summarised in
Table 1. Each stage takes seven or eight years and stages are separated by
around two years, resulting in a total programme of
$2530\text{\,}\mathrm{years}$.

Table 1: Baseline CLIC energy stages and integrated luminosities for each stage in the updated scenario [28].  Stage |  $\sqrt{s}$ [$\mathrm{TeV}$] |  $\mathcal{L}_{\textrm{int}}$ [${\mathrm{ab}}^{-1}$]
---|---|---
$1$ |  $0.38$ (and 0.35) | $1.0$
$2$ | $1.5$ | $2.5$
$3$ | $3.0$ | $5.0$

The staged approach allows optimal exploitation of the CLIC physics
capabilities. For the initial stage, a centre-of-mass energy of
$\sqrt{s}=$380\text{\,}\mathrm{GeV}$$ gives access to SM Higgs physics and
top-quark physics, and provides direct and indirect sensitivity to BSM
effects. A top-quark pair-production threshold scan around
$350\text{\,}\mathrm{GeV}$ is also foreseen. The second stage at
$1.5\text{\,}\mathrm{TeV}$ opens more Higgs production channels including
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$, double-
Higgs production, and rare decays, and allows further direct sensitivity to
many BSM models. The ultimate stage at $3\text{\,}\mathrm{TeV}$ gives the best
sensitivity to many new physics scenarios and to the Higgs self-coupling. The
energies of the second and third stages are benchmarks, and can be optimised
in light of new physics information. For many of the studies reported here, an
earlier energy staging baseline of $\sqrt{s}=$350\text{\,}\mathrm{GeV}$$,
$1.4\text{\,}\mathrm{TeV}$, and $3\text{\,}\mathrm{TeV}$ was assumed; it was
as a consequence of these and other studies that the present initial stage
energy of $\sqrt{s}=380\,\text{GeV}$ was adopted in order to optimise the
physics reach of CLIC.

The CLIC baseline specifies $\pm 80\text{\,}\mathrm{\%}$ electron
polarisation, and no positron polarisation. At the initial energy stage, equal
amounts of $-80\text{\,}\mathrm{\%}$ and $+80\text{\,}\mathrm{\%}$
polarisation running are foreseen. For the two higher-energy stages, a
compromise is required between the strong enhancement in single and double-
Higgs production through $\mathup{{{W}}}\mathup{{{W}}}$-fusion that comes by
running with $-80\text{\,}\mathrm{\%}$ electron polarisation, and the full
reach to BSM effects, which requires some running with
$+80\text{\,}\mathrm{\%}$ electron polarisation. The baseline is to share the
running time for $-80\text{\,}\mathrm{\%}$ and $+80\text{\,}\mathrm{\%}$
electron polarisation in the ratio 80:20.

The following sections discuss the Higgs physics, top-quark physics, and BSM
physics reach of CLIC across the three energy stages.

###  2.2 Higgs physics potential

A detailed understanding of the Higgs sector is one of the highest priorities
in particle physics. While the discovery of a Higgs boson confirms the
electroweak symmetry breaking mechanism, the nature of the particle is still
to be determined: whether it is the fundamental scalar of the SM, or a more
complex object, or part of an extended Higgs sector. The Higgs interactions
could provide access to BSM physics that couples to the SM only through the
Higgs boson.

Around $160\,000$ Higgs bosons will be produced at the initial CLIC energy
stage, and millions will be produced at $\sqrt{s}=$3\text{\,}\mathrm{TeV}$$.
All collider events will be read out, without online event filters, and high
acceptance and event selection efficiencies will result in very large datasets
available for analysis. The large datasets and the large energy range will
allow a comprehensive Higgs programme with unique reach. The staging of the
collider is crucial to the Higgs physics programme, with some measurements
accessible only at the initial energy, while other measurements are enabled or
improved by the high-energy running.

Different BSM scenarios result in different patterns of modifications to the
Higgs couplings from their SM values; for new physics at the $\mathrm{TeV}$
scale this is typically at the percent level and so measurement of the
couplings with similar or better precision is necessary. The CLIC Higgs reach
has been comprehensively investigated using full simulation studies [14]. Some
updated studies and the sensitivities resulting from the updated luminosity
staging scenario are summarised in this section. BSM Higgs scenarios are
further explored in Section 2.4.

##### Higgs production

Cross sections for the main Higgs production processes are shown in Figure 1.
At the initial CLIC energy stage the dominant Higgs production mechanism is
the Higgsstrahlung process,
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$.
These events can be selected based only on the decay products of the
$\mathup{{{Z}}}$ boson, enabling measurements of the total production cross
section and hence the Higgs branching ratios and width. This allows a model-
independent determination of the Higgs couplings, without any assumptions
about BSM invisible decays of the Higgs boson; a feature that is unique to
lepton colliders. Higgs production at the initial energy stage also has a
significant contribution from the $\mathup{{{W}}}\mathup{{{W}}}$-fusion
process,
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$,
and the combined study of the Higgsstrahlung and
$\mathup{{{W}}}\mathup{{{W}}}$-fusion processes improves the precision of the
Higgs couplings and width measurements. Around
$\sqrt{s}=$1.5\text{\,}\mathrm{TeV}$$ and at
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$ Higgs production is dominated by
$\mathup{{{W}}}\mathup{{{W}}}$-fusion; at these energies also the
$\mathup{{{Z}}}\mathup{{{Z}}}$-fusion process,
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$,
becomes significant, and
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$ and
direct double-Higgs production become accessible.

Figure 1: Production cross section as a function of centre-of-mass energy for
the main Higgs production processes at an
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider. The values shown correspond to unpolarised beams with initial-state
radiation and do not include the effect of beamstrahlung. (image credit:
CLICdp)

##### Invisible Higgs decays

The recoil mass distribution from
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$
events can be used to search for BSM decay modes of the Higgs boson into
‘invisible’ final states [29]. For $1\text{\,}{\mathrm{ab}}^{-1}$ at
$\sqrt{s}=$350\text{\,}\mathrm{GeV}$$ the upper limit on the invisible Higgs
branching ratio, obtained from Higgsstrahlung events with hadronic
$\mathup{{{Z}}}$ boson decays, is
$\text{BR}({\mathup{{{H}}}\to\mathrm{invis.}})<$0.69\text{\,}\mathrm{\%}$$ at
$90\text{\,}\mathrm{\%}$ C.L.

##### Higgs couplings

Measurements of Higgs production cross sections times branching fractions to
many final states can be combined to extract the Higgs couplings and widths.
Precisions extracted from a model-independent global fit, described in [14],
are given in Figures 2 and 2. The fit assumes the current baseline scenario of
operation with $-80\text{\,}\mathrm{\%}$ ($+80\text{\,}\mathrm{\%}$) electron
beam polarisation for $80\text{\,}\mathrm{\%}$ ($20\text{\,}\mathrm{\%}$) of
the collected luminosity at the second and third energy stages. Each energy
stage contributes significantly to the Higgs programme; the initial stage
provides $\sigma_{\mathup{{{H}}}\mathup{{{Z}}}}$ and couplings to most
fermions and bosons, while the higher-energy stages improve them and add the
top-quark and muon couplings. The initial stage is required, to allow the
model-independent coupling fits to be performed at all energy stages.
Precisions extracted from a model-dependent global fit, also described in
[14], where it is assumed that there are no non-Standard-Model Higgs decays,
are given in Figures 3 and 3. This fit also assumes the current beam
polarisation scenario. Already after the initial energy stage, in many cases
the CLIC precision is significantly better than for the HL-LHC [30], and
improves further with the higher-energy running.

Parameter | Relative precision
---|---
| $350\text{\,}\mathrm{GeV}$ | \+ $1.4\text{\,}\mathrm{TeV}$ | \+ $3\text{\,}\mathrm{TeV}$
| $1\text{\,}{\mathrm{ab}}^{-1}$ | \+ $2.5\text{\,}{\mathrm{ab}}^{-1}$ | \+ $5\text{\,}{\mathrm{ab}}^{-1}$
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ |  $0.6$$\mathrm{\%}$ |  $0.6$$\mathrm{\%}$ |  $0.6$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$ |  $1.0$$\mathrm{\%}$ |  $0.6$$\mathrm{\%}$ |  $0.6$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$ |  $2.1$$\mathrm{\%}$ |  $0.7$$\mathrm{\%}$ |  $0.7$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$ |  $4.4$$\mathrm{\%}$ |  $1.9$$\mathrm{\%}$ |  $1.4$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$ |  $3.1$$\mathrm{\%}$ |  $1.4$$\mathrm{\%}$ |  $1.0$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ |  $12.1$$\mathrm{\%}$ |  $5.7$$\mathrm{\%}$
$g_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$ | $-$ |  $3.0$$\mathrm{\%}$ |  $3.0$$\mathrm{\%}$
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$ |  $2.6$$\mathrm{\%}$ |  $1.4$$\mathrm{\%}$ |  $1.0$$\mathrm{\%}$
$g^{\dagger}_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ |  $4.8$$\mathrm{\%}$ |  $2.3$$\mathrm{\%}$
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ | $-$ |  $13.3$$\mathrm{\%}$ |  $6.7$$\mathrm{\%}$
$\Gamma_{\mathup{{{H}}}}$ |  $4.7$$\mathrm{\%}$ |  $2.6$$\mathrm{\%}$ |  $2.5$$\mathrm{\%}$
Table 2:

Figure 2:

CLIC results of the model-independent fit to the Higgs couplings. For
$g_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$, the $3\text{\,}\mathrm{TeV}$
case has not yet been studied. The three effective couplings
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$,
$g^{\dagger}_{\mathup{{{H}}}\mathup{}\mathup{}}$ and
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ are also included in the
fit. Operation with $-80\text{\,}\mathrm{\%}$ ($+80\text{\,}\mathrm{\%}$)
electron beam polarisation is assumed for $80\text{\,}\mathrm{\%}$
($20\text{\,}\mathrm{\%}$) of the collected luminosity above
$1\text{\,}\mathrm{TeV}$, corresponding to the baseline scenario. (image
credit: CLICdp)

Parameter | Relative precision
---|---
| $350\text{\,}\mathrm{GeV}$ | \+ $1.4\text{\,}\mathrm{TeV}$ | \+ $3\text{\,}\mathrm{TeV}$
| $1\text{\,}{\mathrm{ab}}^{-1}$ | \+ $2.5\text{\,}{\mathrm{ab}}^{-1}$ | \+ $5\text{\,}{\mathrm{ab}}^{-1}$
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ |  $0.4$$\mathrm{\%}$ |  $0.3$$\mathrm{\%}$ |  $0.2$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$ |  $0.8$$\mathrm{\%}$ |  $0.2$$\mathrm{\%}$ |  $0.1$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$ |  $1.3$$\mathrm{\%}$ |  $0.3$$\mathrm{\%}$ |  $0.2$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$ |  $4.1$$\mathrm{\%}$ |  $1.8$$\mathrm{\%}$ |  $1.3$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ |  $2.7$$\mathrm{\%}$ |  $1.2$$\mathrm{\%}$ |  $0.9$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ |  $12.1$$\mathrm{\%}$ |  $5.6$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$ | $-$ |  $2.9$$\mathrm{\%}$ |  $2.9$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$ |  $2.1$$\mathrm{\%}$ |  $1.2$$\mathrm{\%}$ |  $0.9$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ |  $4.8$$\mathrm{\%}$ |  $2.3$$\mathrm{\%}$
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ | $-$ |  $13.3$$\mathrm{\%}$ |  $6.6$$\mathrm{\%}$
Table 3:  Figure 3:

CLIC results of the model-dependent fit to the Higgs coupling, without
theoretical uncertainties. For
$\kappa_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$, the
$3\text{\,}\mathrm{TeV}$ case has not yet been studied. Operation with
$-80\text{\,}\mathrm{\%}$ ($+80\text{\,}\mathrm{\%}$) electron beam
polarisation is assumed for $80\text{\,}\mathrm{\%}$
($20\text{\,}\mathrm{\%}$) of the collected luminosity above
$1\text{\,}\mathrm{TeV}$, corresponding to the baseline scenario. (image
credit: CLICdp)

##### Higgs self-coupling

Centre-of-mass energies of $1.4\text{\,}\mathrm{TeV}$ or
$1.5\text{\,}\mathrm{TeV}$ and $3\text{\,}\mathrm{TeV}$ give access to double-
Higgs production processes, which are sensitive to the trilinear Higgs
coupling $\lambda$ at tree level. The second energy stage allows a
5$\sigma$-observation of the double Higgsstrahlung process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$
and provides evidence for the $\mathup{{{W}}}$ boson fusion process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
with a significance of $3.6\sigma$ assuming the SM value of $\lambda$. At
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$ the vector-boson fusion process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
is the leading double-Higgs production process and its cross section can be
measured with a precision $\Delta\sigma/\sigma=$7.4\text{\,}\mathrm{\%}$$ at
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$. The cross section dependence on $\lambda$
is not monotonic, so that using only the cross section information to extract
$\lambda$, or equivalently the variation $\Delta\kappa_{\lambda}$ from the
Standard Model value $\kappa_{\lambda}=1$, leads to an ambiguity as shown in
the Figure 4(a). This can be resolved by adding the differential information
including the invariant mass $M(\mathup{{{H}}}\mathup{{{H}}})$ in
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
at $\sqrt{s}=$3\text{\,}\mathrm{TeV}$$, and the cross section measurement of
the double Higgsstrahlung process $\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$
at $\sqrt{s}=$1.4\text{\,}\mathrm{TeV}$$. This removes the ambiguity and
increases the sensitivity as shown in Figure 4(b). The
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
process also contains the quartic vertex
$\mathup{{{H}}}\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}$.

The final sensitivity that can be reached on the trilinear self-coupling
$\lambda$ is $[$-7\text{\,}\mathrm{\%}$,$+11\text{\,}\mathrm{\%}$]$ [31].

The analysis can also be used to set two-dimensional constraints on $\lambda$
and $\kappa_{\mathup{{{H}}}\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$.

(a)

(b)

Figure 4: Nominal $\Delta\chi^{2}$ distributions from template fitting with
different values of the Higgs self-coupling $\lambda$, shown for the variation
$\Delta\kappa_{\lambda}$ from the SM value of $\kappa_{\lambda}=1$ and using
(a) only cross section information for the
$\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
process at $3\text{\,}\mathrm{TeV}$; (b) additionally using the differential
distribution $M(\mathup{{{H}}}\mathup{{{H}}})$ in
$\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
at $3\text{\,}\mathrm{TeV}$ and the cross section measurement of
$\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$ at $1.4\text{\,}\mathrm{TeV}$. In
this case the ambiguity is removed and the sensitivity is increased. (image
credit: CLICdp)

##### Composite Higgs

Constraints from the CLIC Higgs measurements, along with measurements of
Drell-Yan production
($\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to
f\bar{f}$) and $\mathup{{{W}}}\mathup{{{W}}}$ production, can be interpreted
in concrete classes of BSM scenarios; for example, scenarios where the known
particles are in fact composite bound states. Composite Higgs frameworks could
address the electroweak naturalness problem. In these frameworks the Higgs
boson is a pseudo-Nambu-Goldstone boson of an underlying strongly-interacting
composite sector. The 5$\sigma$ discovery reach in the plane of the mass scale
$m_{*}$ and coupling strength parameter $g_{*}$ that characterise the Higgs
composite sector is shown in Figure 5 [16]. CLIC will discover Higgs
compositeness if the compositeness scale is below $8\text{\,}\mathrm{TeV}$.
Scales up to $40\text{\,}\mathrm{TeV}$ can be discovered, in particularly
favourable conditions, for large composite sector couplings $g_{*}\simeq 8$.
For comparison, the model-independent projected HL-LHC exclusion reach is only
around $3\text{\,}\mathrm{TeV}$, and for $g_{*}\simeq 8$ the maximum HL-LHC
reach is around $7\text{\,}\mathrm{TeV}$ [16].

Figure 5: Higgs compositeness: ‘Optimistic’ (light colour) and ‘pessimistic’
(dark colour) $5\sigma$ discovery regions for Higgs compositeness derived from
a combined fit to Higgs and $\mathup{{{W}}}\mathup{{{W}}}$ production (green)
and Drell-Yan processes (orange); and the HL-LHC 95% C.L. exclusion reach.
From [16].

###  2.3 Top-quark physics potential

The top quark is the heaviest known fundamental particle and occupies an
important role in many BSM theories; it therefore provides unique
opportunities to test the SM and probe signatures of BSM effects. So far, top
quarks have been produced only in hadron collisions, whereas studying their
properties in electron-positron collisions will provide a new set of
complementary and improved-precision measurements. Cross sections for the main
top-quark pair production processes are shown in Figure 6. Each stage of CLIC
provides sensitivity to different aspects of top-quark production and
properties: at the initial stage this includes top-quark mass measurements and
cross section and asymmetry measurements, while higher-energy stages
additionally allow studies including direct access to the top Yukawa coupling
and CP properties in the $\mathup{{{t}}}\mathup{{{t}}}\mathup{{{H}}}$
coupling. The $3\text{\,}\mathrm{TeV}$ stage is most favourable for study of
top-quark pair production via vector boson fusion. A broad set of measurements
has been investigated for CLIC [15]; they are summarised in the following
sections.

Figure 6: Production cross section as a function of centre-of-mass energy for
the main top-quark pair production processes at an
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider. Leading-order values for unpolarised beams with initial-state
radiation are shown, not including the effect of beamstrahlung. (image credit:
CLICdp)

##### Top-quark mass

Several complementary methods allow precise determinations of the top-quark
mass at CLIC: a threshold scan; measurements of the cross section for
radiative events; and direct reconstruction. Direct reconstruction of the top-
quark decay products yields a statistical precision of around
$30\text{\,}\mathrm{MeV}$; a systematic accuracy that matches the statistical
accuracy would require control of the jet energy scale at the level of
$0.02\text{\,}\mathrm{\%}$, and the theoretical interpretation of the
measurement introduces a large systematic uncertainty. Fitting templates to
cross sections as a function of centre-of-mass energy has the advantage that
the extracted mass is well defined theoretically, which significantly reduces
the overall uncertainty. This can be done for radiative events above
threshold, as a function of the effective
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ centre-of-mass energy
$\sqrt{s^{\prime}}$ after radiation of an energetic initial state photon from
the incoming electron or positron beam,
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{}$.
This method leads to a total uncertainty on the top-quark mass of around
$140\text{\,}\mathrm{MeV}$ with an integrated luminosity of
$1\text{\,}{\mathrm{ab}}^{-1}$. However, the most precise top-quark mass
determination comes from an energy scan around the top-quark pair-production
threshold. The study assumes a scan collecting $10\text{\,}{\mathrm{fb}}^{-1}$
at each of ten points in $\sqrt{s}$, separated by $1\text{\,}\mathrm{GeV}$. A
highly pure sample of top-quark events can be selected and used to measure the
cross section at each point. The top-quark mass is extracted using a template
fit to the measured cross sections as a function of $\sqrt{s}$ as shown in
Figure 7. The flexibility of the CLIC accelerator design is illustrated by
potential optimisation of the luminosity spectrum for the threshold scan as
described in Section 3.2.6, and shown by the two bunch charge options in
Figure 7. The cross section and the position and shape of the turn-on curve
are strongly dependent on the precise value of the top-quark mass and width,
Yukawa coupling, and strong coupling $\alpha_{s}$. The template line shapes
can be computed at NNNLO QCD, taking into account NLO Higgs and electroweak
effects. The statistical uncertainty is $20\text{\,}\mathrm{MeV}$ for the
reduced bunch charge option and $22\text{\,}\mathrm{MeV}$ for the nominal
luminosity spectrum. The small theoretical uncertainty of around
$10\text{\,}\mathrm{MeV}$ associated with converting the measured quantity to
the $\overline{\mathrm{M}S}$ (modified minimal subtraction) mass scheme means
that a total uncertainty of around $50\text{\,}\mathrm{MeV}$ is thus feasible.

(a)

(b)

Figure 7: Illustration of a top-quark threshold scan at CLIC with a total
integrated luminosity of $100\text{\,}{\mathrm{fb}}^{-1}$, for two scenarios
for the luminosity spectrum (LS): (a) nominal, and (b) ‘reduced charge’. The
bands around the central cross section curve show the dependence of the cross
section on the top-quark mass and width, illustrating the sensitivity of the
threshold scan. The error bars on the simulated data points show the
statistical uncertainties of the cross section measurement, taking into
account signal efficiencies and background levels. From [15].

##### Top-quark pair-production properties

Top-quark pair production at all three energy stages contributes to the
determination of electroweak couplings.

At the initial stage, semi-leptonic events, where the $\mathup{{{W}}}$ boson
from one top-quark decay decays hadronically and the other leptonically, are
reconstructed by clustering into four jets, identifying a reconstructed lepton
and jets that originate from $\mathup{{{b}}}$-quarks, and performing a
kinematic fit. The efficient $\mathup{{{b}}}$-tagging of two jets allows
suppression of most of the backgrounds. Measurements of the cross section can
be made with a statistical accuracy below $1\text{\,}\mathrm{\%}$ for each
electron beam polarisation, and the measured top-quark angular distribution in
semi-leptonic events gives the forward-backward asymmetry with a statistical
uncertainty of around $34\text{\,}\mathrm{\%}$.

At the higher energy stages the top quarks are produced with significant
boosts. Jet substructure techniques [32] have been successfully applied to
reconstructing boosted semi-leptonic events and measuring the forward-backward
asymmetry. The total cross section and forward-backward asymmetries are
extracted with precisions of
$\Delta\sigma/\sigma=$1.1\text{\,}\mathrm{\%}$\;($2.3\text{\,}\mathrm{\%}$)$
and $\Delta
A_{FB}/A_{FB}=$1.5\text{\,}\mathrm{\%}$\;($2.0\text{\,}\mathrm{\%}$)$ at
$1.4\text{\,}\mathrm{TeV}$ ($3\text{\,}\mathrm{TeV}$) for an electron beam
polarisation of $-80\text{\,}\mathrm{\%}$. All of these measurements, along
with a set of ten statistically optimised observables defined for each centre-
of-mass energy and electron beam polarisation on the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\to\mathup{{{b}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{\overline{{\mathup{{{b}}}}}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}$
differential distribution [33, 34, 35, 36], are used in global fits to
constrain possible BSM effects induced by heavy new physics, as described in
Section 2.4.

##### Top-quark Yukawa coupling and CP properties

Associated
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
production is accessible at the second CLIC stage. Studies of
$\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$ with
fully-hadronic and semi-leptonic
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ decays give an expected
precision on the cross section at $1.4\text{\,}\mathrm{TeV}$ with
$2.5\text{\,}{\mathrm{ab}}^{-1}$ of $5.7\text{\,}\mathrm{\%}$. The cross
section is sensitive to the strength of the Yukawa coupling and its
measurement can be translated into a determination of the Yukawa coupling with
a precision of $2.9\text{\,}\mathrm{\%}$. As an extra probe of the CP
structure of the Standard Model, to search for sources of CP violation that
could give insight into the matter-antimatter asymmetry in the universe, the
CP structure of the $\mathup{{{t}}}\mathup{{{t}}}\mathup{{{H}}}$ coupling can
be investigated. A CP-odd admixture to the coupling can be parameterised with
a mixing angle $\phi$ as
$-ig_{\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}}(\cos\phi+i\sin\phi\gamma_{5}$);
this alters the cross section, which can therefore be used to set limits on
the admixture. Further sensitivity can be obtained from differential
distributions, for example the up-down asymmetry of the anti-top quark with
respect to the plane defined by the incoming electron and the top quark [37].
The sensitivity is $\Delta\sin^{2}\phi<0.07\;(0.04)$ for the range
$0<\sin^{2}\phi<1$ ($0.3<\sin^{2}\phi<1$).

##### Compositeness interpretation

Constraints from the global fit of optimised observables from
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production and from
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
production can also be interpreted in compositeness scenarios. Top-quark
compositeness emerges naturally in the composite Higgs frameworks discussed at
the end of section Section 2.2. The
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ and
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
sensitivities have been interpreted for the discovery reach of top-quark
compositeness scenarios at $\sqrt{s}=$3\text{\,}\mathrm{TeV}$$. The 5$\sigma$
discovery reach in the plane of the mass scale $m_{*}$ and coupling strength
parameter $g_{*}$ that characterise the composite sector is shown in Figure 8
[38, 15, 16], for optimistic and pessimistic values of coefficients of the
top-philic operators. In this framework the top-quark compositeness is
characterised by couplings $y_{L}$ and $y_{R}$ that control the strength of
the mixing of the $\mathup{{{q}}}_{L}$ doublet and the $\mathup{{{t}}}_{R}$
singlet with the composite sector. The two benchmark scenarios considered are
partial compositeness, where $y_{L}=y_{R}=\sqrt{y_{L}g_{*}}$; and total
$\mathup{{{t}}}_{R}$ compositeness, where $y_{L}=y_{\mathup{{{t}}}}$ and
$y_{R}=g_{*}$. The strong sensitivity of the observables to effects that grow
with centre-of-mass energy results in a discovery reach for top compositeness
beyond $7\text{\,}\mathrm{TeV}$, and more than $20\text{\,}\mathrm{TeV}$ in
favourable conditions, at CLIC. These values are higher than could be excluded
at HL-LHC.

(a)

(b)

Figure 8: Top compositeness: ‘Optimistic’ (light colour) and ‘pessimistic’
(dark colour) $5\sigma$ discovery regions for (a) the partial compositeness,
and (b) the total $t_{R}$ compositeness scenarios. The orange contours are
derived from the $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ global
fit, while the green contours are derived from the top Yukawa analysis. From
[15].

##### Vector-boson fusion production of top-quark pairs

The high-energy stages of CLIC allow the production of top-quark pairs through
vector boson fusion, which could reveal large BSM effects. An important role
is played by longitudinally-polarised vector bosons, which at high energy are
equivalent to the Higgs field. In several new physics scenarios that address
the naturalness problem, Higgs boson and top-quark interactions receive large
modifications, and a process like
$\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$
is directly sensitive to this, for example through the modification of the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ scattering angle in the
centre-of-mass frame. The process
$\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$
and its backgrounds have been studied at parton level at
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$. In
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collisions at CLIC, the backgrounds to this process (including
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production) can be
suppressed to a negligible level. The vector-boson fusion process has been
used to constrain possible BSM effects as described in Section 2.4, and in
particular the high $M(\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}})$
region is sensitive to BSM effects that grow with energy.

###  2.4 Direct and indirect searches for BSM physics

The exploration of physics beyond the Standard Model is well motivated by
problems that the Standard Model cannot address, such as the origin of the
weak scale, the nature of dark matter, and the origin of the asymmetry between
baryons and anti-baryons in the universe. Typically, at
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
colliders new particles can be observed almost up to the kinematic limit, e.g.
$m\lesssim\sqrt{s}/2$, and the flexibility to adjust beam energies and
polarisations at a linear collider potentially allows accurate determination
of their quantum numbers. Earlier CLIC studies emphasised the capabilities for
characterising BSM particles expected to be discovered at the LHC or CLIC, and
unveiling the underlying BSM theory [39, 3, 4]. While this is still important,
recent work has focused on the prospects for discoveries at CLIC, in the event
of no new physics being observed at the LHC. The goal is to go beyond
attempting to quantify the performance in terms of a few benchmark models or
scenarios, and to explore the landscape of fundamental physics as broadly as
possible, showing the reach for broad classes of theories. With this in mind,
many new physics models and scenarios have been investigated and are gathered
together in a dedicated report [16].

Potential new physics can be probed directly by searching for new states, and
indirectly through interpretation of precision measurements. The latter
approach can be investigated through the Standard Model Effective Field Theory
(SM-EFT), which allows the systematic parameterisation of BSM effects and
their modification of SM processes. Direct searches are explored in the
context of general scenarios: for example, extended Higgs sectors, which can
be connected with models of electroweak baryogenesis; and general dark matter
models, such as Higgsinos and minimal dark matter. CLIC can discover the
Higgsino for a mass of $1\text{\,}\mathrm{TeV}$, which is the mass that it
would need to have to be responsible for the observed relic dark matter
density. CLIC can also be conclusive on other relevant and less standard dark
matter scenarios. In the remainder of this section, these and other highlights
from the recent studies are discussed further in order to illustrate the range
and reach of CLIC.

##### Global EW EFT analysis

CLIC precision measurements can be sensitive to different BSM contributions
that arise from heavy BSM dynamics, associated with a mass scale beyond CLIC’s
direct energy reach. CLIC sensitivities to Higgs couplings, top-quark
observables, $\mathup{{{W}}}\mathup{{{W}}}$ production, and two-fermion
scattering processes
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to
f\overline{f}$ where
$f=\mathup{{{c}}},\mathup{{{b}}},\mathup{{{e}}},\mathup{}$, have all been put
together in a global fit using the SM-EFT. The purpose of the global fit is to
probe many classes of BSM theory at once, in a model-independent fashion. The
SM-EFT extends the dimension-four SM Lagrangian to include interaction
operators of higher dimension $d>4$. Here, BSM particles are implicit and must
be light enough and strongly-enough coupled to the SM to generate large enough
operators to give visible effects, while being heavy enough not to be produced
directly. The leading effects can be captured by dimension-6 operators:

$\mathcal{L}_{\mathrm{e}ff}=\mathcal{L}_{\mathrm{S}M}+\frac{1}{\Lambda^{2}}\sum_{i}c_{i}\mathcal{O}_{i}+\cdots$

for dimensionless coefficients $c_{i}$ and a common suppression scale
$\Lambda$. Through the global fit, limits are placed on the coefficients for
operators or combinations of operators, which can be translated into
constraints on particular BSM models.

The CLIC sensitivity to the operator coefficients $c_{i}/\Lambda^{2}$ for one
operator basis set is shown in Figure 9. Sensitivity to smaller values
corresponds to probing higher mass scales. Sensitivities for the three CLIC
energy stages are shown, along with preliminary HL-LHC sensitivities for
comparison. The HL-LHC sensitivities are shown for two scenarios of systematic
uncertainties: ‘S1’, where LHC Run 2 systematics are kept constant with
integrated luminosity; and ‘S2’, where Run 2 theoretical uncertainties are
halved and experimental uncertainties are scaled down with the square root of
integrated luminosity until they reach a defined minimum [30, 40]. CLIC’s
measurements in the Higgs, top, and EW sectors at all three energy stages are
found to be highly synergistic. Figure 9 shows that the initial stage of CLIC
is already very complementary to the HL-LHC for many of the operators. The
high-energy stages, which are unique to CLIC among all proposed
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
colliders, are found to be crucial for the precision programme. For example,
the operators $c_{3\mathup{{{W}}}},c_{2\mathup{{{W}}}}$, and
$c_{2\mathup{{{B}}}}$ have effects that grow with energy. Hence, they can be
probed better by observable measurements at high energy with even moderate
accuracy, than they can by very accurate Higgs measurements. The operator
$c_{6}$ relates to the Higgs self-coupling, and benefits from the direct
double-Higgs production available at high energies. The overall result is to
probe the SM-EFT much more precisely than is possible at the HL-LHC, to mass
scales well beyond the centre-of-mass energy of the collider.

In the following sections, the direct and indirect sensitivities to some
general models are discussed.

Figure 9: Summary of the sensitivity to SM-EFT operators $c_{i}/\Lambda^{2}$
from a global analysis of CLIC’s sensitivities to Higgs couplings, top-quark
observables, $\mathup{{{W}}}\mathup{{{W}}}$ production, and two-fermion
scattering processes
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to
f\overline{f}$, for three energy stages. Smaller values correspond to a higher
scale probed. Preliminary projections for HL-LHC are shown for comparison,
under two systematic uncertainty scenarios (described in text). Blue markers
correspond to single-operator sensitivies, and yellow markers correspond to
results from dedicated individual analyses (for example, the Higgs self-
coupling analysis). From [16].

##### Extended Higgs sectors

In many extensions of the Standard Model the scalar sector is extended by new
states that are not charged under the Standard Model gauge group. These
states, referred to as ‘singlet’ states, do not interact with Standard Model
gauge bosons and fermions at tree level, but may acquire such interactions at
loop level or through mixing with the Higgs boson radial mode. Through the
couplings that the singlets ‘inherit’, their production and decay can be like
Higgs bosons. Experimentally, therefore, they may be searched for directly as
resonances, or indirectly through their modifications to the Higgs couplings.

In this example a singlet-like state that is heavier than twice the
$125\text{\,}\mathrm{GeV}$ SM-like Higgs boson, decays to two SM-like Higgs
bosons. Owing to the large branching fraction
$\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$, the
most promising final state comes from the decay to four
$\mathup{{{b}}}$-quarks, which can be well identified at CLIC:
$\mathup{}\to\mathup{{{H}}}\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$.
This has been analysed using a fast simulation of the CLIC detector, including
background processes.

The phenomenology of the model is determined by $\sin\gamma$, where $\gamma$
describes the mixing between the interaction eigenstates $\mathup{{{h}}}_{0}$
(a pure doublet of the weak interaction) and $S$ (a real scalar singlet) to
give the mass basis $\mathup{{{H}}}($125\text{\,}\mathrm{GeV}$)$ and :

$\mathup{{{H}}}=\mathup{{{h}}}_{0}\cos\gamma+\text{S}\sin\gamma,\;\;\;\;\;\;\mathup{}=\text{S}\cos\gamma-\mathup{{{h}}}_{0}\sin\gamma.$

The parameter space of the mass of the heavy state , $m$, and the mixing
$\sin^{2}\gamma$ can be explored, and the projected cross section bounds for
the resonant final states translated into $95\text{\,}\mathrm{\%}$ C.L. limits
as shown in Figure 10 [41, 16].

The CLIC Higgs coupling sensitivities also give an indirect constraint on
$\sin^{2}\gamma$, because the Higgs signal strengths are reduced universally
by a factor $(1-\sin^{2}\gamma)$ from their SM values. This constraint is
complementary to the direct search constraint, and is also shown as a
horizontal line in Figure 10.

It is seen that the CLIC limits extend significantly beyond those projected
for the HL-LHC, to much lower values of the mixing: for
$m<$1\text{\,}\mathrm{TeV}$$, the mixing $\sin^{2}\gamma$ must be lower than
around 0.0013.

Figure 10: Constraints on singlet-like states at $95\text{\,}\mathrm{\%}$ C.L.
in the plane $(m,\sin^{2}\gamma)$. The reach from the direct search for
$\mathup{}\to\mathup{{{H}}}\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$,
for the second (green) and third (blue) CLIC stages are compared with the
projections for LHC with a luminosity of $300\text{\,}{\mathrm{fb}}^{-1}$
(solid red) and $3\text{\,}{\mathrm{ab}}^{-1}$ (dashed red). Branching ratios
of the have been fixed as
$\text{BR}({\mathup{}\to\mathup{{{h}}}\mathup{{{h}}}})=\text{BR}({\mathup{}\to\mathup{{{Z}}}\mathup{{{Z}}}})=$25\text{\,}\mathrm{\%}$$.
The horizontal line shows the indirect constraint from the CLIC Higgs
couplings measurements (stat. only). The shaded regions are the present
constraints from LHC direct searches for
$\mathup{}\to\mathup{{{Z}}}\mathup{{{Z}}}$ (red) and Higgs couplings
measurements (pink). From [41, 16].

Model interpretations Many BSM models contain extra singlets of the kind
generically described above, and so the same experimental measurements can be
interpreted in different model frameworks. The next-to-minimal supersymmetric
Standard Model, NMSSM, is the MSSM augmented by a single chiral super-field,
and contains a scalar singlet. The above results have been translated into the
NMSSM parameter space of $m$ and $\tan\beta$; in this framework the
$\sqrt{s}=$1.5\text{\,}\mathrm{TeV}$$ stage of CLIC is already more sensitive
than the HL-LHC over the whole parameter space, and the
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$ stage significantly extends the reach.
Similarly for Twin Higgs models, the $\sqrt{s}=$3\text{\,}\mathrm{TeV}$$ CLIC
stage significantly surpasses the HL-LHC reach [41, 16].

Relaxions The examples above discuss heavy singlets. The case of light
singlets can also be examined. One example comes from the relaxion mechanism,
which stabilises the Higgs mass dynamically and is interesting for addressing
the hierarchy problem. Similarly to the heavy singlets, the relaxion mixes
with the Higgs and inherits its couplings to SM fields. The possible relaxion
mass range spans from sub-$\mathrm{eV}$ to tens of $\mathrm{GeV}$. For masses
in the $\mathrm{GeV}$ range the relaxion is short-lived and decays inside the
detector. At CLIC, three approaches have been considered: searching for the
exotic decay $\mathup{{{H}}}\to\mathup{}\mathup{}$ directly via the decay
$\mathup{}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$
(extrapolated from ILC studies), constraining the decay
$\mathup{{{H}}}\to\mathup{}\mathup{}$ indirectly via Higgs ‘untagged’ decays
that, while not invisible, consist of soft particles that are not
reconstructed as Higgs decays and appear as an extra invisible contribution to
the Higgs width; and directly searching via the recoil mass in the process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{}\mathup{{{Z}}}$.
CLIC will have the potential to exclude masses down to
$20\text{\,}\mathrm{GeV}$ with indirect searches and further down to
$12\text{\,}\mathrm{GeV}$ with direct searches [42, 16], significantly
reducing the available model parameter space beyond the reach of the HL-LHC in
regions that are challenging for hadron colliders.

##### Dark matter

The Higgsino is a compelling target of searches for supersymmetric extensions
of the Standard Model: it is strongly connected to the naturalness of the weak
scale, is important for gauge coupling unification, and is an ideal WIMP dark
matter candidate. Naturalness considerations motivate Higgsinos in the range
$m\lesssim$\mathrm{TeV}$$, while the observed dark matter relic abundance
singles out $m\simeq$1.1\text{\,}\mathrm{TeV}$$ for thermal Higgsino dark
matter. High centre-of-mass lepton colliders such as CLIC provide one of the
best avenues for probing Higgsinos across this mass range. A Higgsino that is
not the lightest supersymmetric particle can decay into a SM boson and missing
energy, and these cases have been examined in previous studies [3]. Here, two
complementary approaches to searches for Higgsinos in challenging scenarios
are discussed: searches for mono-photon signatures, and searches for
disappearing stub track signatures.

Mono-photon signature In the search for dark matter candidates using ISR
photons,
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{}\mathup{}\mathup{}$,
the experimental signature is a single photon reconstructed in the detector,
while the particles escape undetected. A full simulation study at
$\sqrt{s}=$380\text{\,}\mathrm{GeV}$$ has been carried out, including the main
SM background processes, for different values of $m$. The
$95\text{\,}\mathrm{\%}$ upper cross section limit for the process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{}\mathup{}\mathup{}$
is shown as a function of $m$ in Figure 11(a) [16]. It can be seen that CLIC
at $\sqrt{s}=$380\text{\,}\mathrm{GeV}$$ would be sensitive to the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{}\mathup{}\mathup{}$
process down to cross sections of $510\text{\,}\mathrm{fb}$ in the mass range
from the LEP limit of around $100\text{\,}\mathrm{GeV}$ up to almost
$180\text{\,}\mathrm{GeV}$, depending on the systematic error assumption, and
Higgsino pair production with an ISR photon would be excluded across the
entire mass range. The mono-photon-based search at an
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider is complementary to mono-jet searches at hadron colliders as the
different production mechanism allows the coupling to leptons to be probed.
Also, once a signal is established, the photon energy distribution could be
used to measure the mass of the dark matter candidate in a way that would be
very difficult at a hadron collider. For a $120\text{\,}\mathrm{GeV}$ Higgsino
particle, a precision on its mass of about $2\text{\,}\mathrm{GeV}$ is
expected using the endpoint of the photon energy distribution.

(a)

(b)

Figure 11: (a): $95\text{\,}\mathrm{\%}$ C.L. upper limit on the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{}\mathup{}\mathup{}$
cross section at $\sqrt{s}=$380\text{\,}\mathrm{GeV}$$ as a function of $m$.
The limit without including systematic uncertainties (blue) is compared to two
different assumptions on the systematic uncertainty for the two main
background processes (red). In addition, the cross section for Higgsino pair
production with an ISR photon is shown (magenta). (b):
$95\text{\,}\mathrm{\%}$ C.L. exclusion contours in lifetime–mass for $N=3$
(solid) and $N=30$ (dashed) Higgsino events in the detector acceptance at the
three stages of CLIC. The black dashed line indicates the lifetime of the pure
Higgsino state of a given mass, and the pure Higgsino thermal relic dark
matter mass of $1.1\text{\,}\mathrm{TeV}$ is indicated by a vertical line.
From [16].

Disappearing track signature A very different experimental signature for dark
matter production could be ‘disappearing tracks’, for example caused by a
heavy charged particle passing through the detector before decaying to a
neutral particle that escapes detection. Generically, ‘long-lived particles’
could produce this signature. A particular example is the charged particle in
a Higgsino multiplet, ±, which can be only slightly heavier than the neutral
components $\mathup{}^{0}_{1,2}$. In this case the ± travels a macroscopic
distance, of order 1 cm, before decaying into an invisible 0 and SM states
that are too soft to reconstruct:
$\mathup{}^{\pm}\to\mathup{{}^{\scriptstyle{\pm}}}\mathup{}^{0}$. The charged
Higgsino lifetime makes it particularly challenging for LHC searches, as the
‘charged stub’ left by the Higgsino is short and is challenging to reconstruct
among the large number of hits from pile-up.

CLIC prospects for probing the pure Higgsino via the production of charged
Higgsino pairs and the ensuing disappearing track signature have been
assessed. The study does not use full simulation, but takes into account the
CLIC detector geometry by requiring that the track stub traverses enough of
the CLIC tracker to leave at least four hits. The most sensitive analysis
comes from requiring a signature of only one charged stub; for which the
$95\text{\,}\mathrm{\%}$ C.L. exclusion limits are shown in Figure 11(b) [16].
Possible variations in the Higgsino lifetime, which may arise if the Higgsino
is not exactly a pure state, are also given. It is seen that for
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$, the 1-stub strategy yields around 30
events in the acceptance up to the thermal dark matter target of
$m\simeq$1.1\text{\,}\mathrm{TeV}$$. A handful of events are produced in
acceptance even if an ISR photon with $p_{T}>$100\text{\,}\mathrm{GeV}$$ is
required. CLIC should therefore be able to probe the thermal relic Higgsino
dark matter even with some level of background. The large tracker volume,
compact vertex detector geometry and low background conditions compared to
those at hadron colliders give CLIC better sensitivity for this type of
signature than the HL-LHC.

##### Electroweak precision tests

The process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to
f\bar{f}$, where $f$ is a SM fermion, can be studied in depth at CLIC, for
example through the differential cross section with respect to polar angle,
$d\sigma/d\cos\theta$, and related asymmetries. Precision measurements of
differential distributions and asymmetries are sensitive to corrections
induced by any new state that has SM charges, which can modify the EW gauge
boson propagators. This has been investigated by adding form factors to the
effective Lagrangian and establishing $95\text{\,}\mathrm{\%}$ C.L. limits
that could be set through a combination of the
$\mathup{{{e}}},\mathup{},\mathup{{{b}}}$, and $\mathup{{{c}}}$ channels on
the masses of different states . These limits are shown in Figure 12 [43, 16],
for the second and third stages of CLIC. The exclusions assume polarisation
fractions
$P(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}})=$-80\text{\,}\mathrm{\%}$$
and $P(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}})=0$. Limits are given for
different states $\mathup{}\sim(1,n,Y)$, where the entries denote the
$\mathrm{SU}(3)_{c}\times\mathrm{SU}(2)_{L}\times\mathrm{U}(1)_{Y}$
representation; and for different Lorentz representations: complex scalar
(CS), Majorana fermion (MF), and Dirac fermion (DF). For example, the $n=2$
Dirac fermion corresponds to the Higgsino and the $n=3$ Majorana fermion to
the wino. The limits show that CLIC at $\sqrt{s}=$3\text{\,}\mathrm{TeV}$$
excludes the $n=3$ Dirac fermion for $m<$0.8\text{\,}\mathrm{TeV}$$ and
$$1\text{\,}\mathrm{TeV}$<m<$2\text{\,}\mathrm{TeV}$$; and in addition the
intermediate region $$0.8\text{\,}\mathrm{TeV}$<m<$1\text{\,}\mathrm{TeV}$$ is
covered by CLIC at $\sqrt{s}=$1.5\text{\,}\mathrm{TeV}$$. For the $n=3$ Dirac
fermion, a mass of $m=$2\text{\,}\mathrm{TeV}$$ is needed to saturate the dark
matter relic abundance [16, 43], and so CLIC covers the whole relevant
parameter space and fully tests that dark matter hypothesis.

Figure 12: $95\text{\,}\mathrm{\%}$ C.L. exclusion ranges on the mass of new
SM-charged states from
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to
f\bar{f}$ precision measurements for
$P_{\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}}=$-80\text{\,}\mathrm{\%}$$
data at $\sqrt{s}=$1.5\text{\,}\mathrm{TeV}$$ (blue) and
$3\text{\,}\mathrm{TeV}$ (beige). Green regions would be excluded by data from
both centre-of-mass energies. Exclusion regions are obtained by combining the
$\mathup{{{e}}},\mathup{},\mathup{{{b}}}$, and $\mathup{{{c}}}$ channels with
$0.3\text{\,}\mathrm{\%}$ systematic error. $(1,n,Y)$ denotes the
$\mathrm{SU}(3)_{c}\times\mathrm{SU}(2)_{L}\times\mathrm{U}(1)_{Y}$
representation of the state, and the mass exclusions are given for different
Lorentz representations: complex scalar (CS), Majorana fermion (MF), and Dirac
fermion (DF). $\epsilon$ denotes a milli-charge which has no bearing on
collider physics, but ensures stability. From [43, 16].

##### Electroweak phase transition

The SM plus singlet scenario discussed previously can be used to probe the
nature of the electroweak phase transition in the early universe. As the
universe expanded it cooled, and electroweak symmetry breaking occurred when
it became energetically favourable for the Higgs field to acquire a non-zero
vacuum expectation value. If there is a potential barrier separating the
symmetric vacuum from the broken one, the electroweak phase transition could
be first order. The addition of a singlet can result in such a first-order
electroweak phase transition. A strong first-order phase transition is a
necessary condition for electroweak baryogenesis, so the shape of the Higgs
potential and the nature of the electroweak phase transition is a critical
open question that could shed light on the stability or instability of the
vacuum, and potentially on the origin of the baryon asymmetry.

CLIC can search for resonant double-Higgs production arising from a singlet,
as well as looking for deviations from SM predictions for the Higgsstrahlung
cross section and the Higgs self-coupling. These measurements can set limits
on the parameter space for general scenarios that lead to a strong first-order
phase transition. Examples are shown in Figure 13 [44, 16]. The parameter
space has been scanned for various fixed values of the singlet mass and
singlet mixing; shown here is the singlet mass
$m_{2}=$500\text{\,}\mathrm{GeV}$$ and two values of the mixing:
$\sin\,\theta=0.05$, and $0.1$. Values of $\sin\,\theta$ higher than around
0.2 will be excluded by HL-LHC. The parameter space is that of coefficients
$a_{2}$, $b_{3}$, and $b_{4}$ of additional $T^{2}$ terms in a temperature-
dependent effective potential that is added to the Higgs potential and
modifies the behaviour as the early universe expands and cools. Points in the
parameter space compatible with unitary, perturbativity, and absolute
stability of the EW vacuum have been identified (red circles), and among them
the points yielding a strong first-order phase transition have been identified
(green circles). Constraints are provided by a fit to an overall rescaling of
the Higgs couplings $\Delta\kappa$ (grey regions), the Higgs self-coupling
(black lines), and by searches for resonant double-Higgs production in the
4$\mathup{{{b}}}$ final state at $\sqrt{s}=$1.4\text{\,}\mathrm{TeV}$$ and
$3\text{\,}\mathrm{TeV}$ (orange and blue lines). The excluded regions are the
regions outside the pairs of lines, for higher absolute values of $a_{2}$.

The three complementary methods are all competitive in the interesting region
and in the examples in Figure 13 are able to exclude all of the interesting
parameter space. CLIC therefore provides a direct avenue to probe the nature
of the EW phase transition for non-minimal scalar sectors, and the possible
origin of the cosmic matter-antimatter asymmetry via electroweak baryogenesis.

(a)

(b)

Figure 13: Region of parameter space in ($a_{2}$, $b_{3}/v$) for singlet mass
$m_{2}=$500\text{\,}\mathrm{GeV}$$ and singlet mixing (a)
${\mathrm{s}in}\,\theta=0.05$ and (b) ${\mathrm{s}in}\,\theta=0.1$ within the
$95\text{\,}\mathrm{\%}$ C.L. sensitivity reach of resonant double-Higgs
production searches at CLIC. Limits are given for
$\sqrt{s}=$1.4\text{\,}\mathrm{TeV}$$ (orange) and
$\sqrt{s}=$3\text{\,}\mathrm{TeV}$$ (blue) for a $b$-tagging efficiency of
$70\text{\,}\mathrm{\%}$ (solid) and $90\text{\,}\mathrm{\%}$ (dashed): the
CLIC sensitivity is the region not contained within each pair of sensitivity
lines. The red circles indicate the region compatible with the requirements of
unitary, perturbativity and absolute stability of the EW vacuum. The parameter
$b_{4}$ has been scanned over. Overlaid is the region yielding a strongly
first order EW phase transition (green points). The dashed black lines are
$95\text{\,}\mathrm{\%}$ C.L. lines corresponding to the
$68\text{\,}\mathrm{\%}$ C.L. CLIC sensitivity
$[$-7\text{\,}\mathrm{\%}$,$+11\text{\,}\mathrm{\%}$]$ on the Higgs self-
coupling. The yellow band (only for $\sin\theta=0.1$) corresponds to the
projected sensitivity of
$\mathup{{{p}}}\mathup{{{p}}}\to\mathup{{{h}}}_{2}\to\mathup{{{Z}}}\mathup{{{Z}}}$
searches at HL-LHC. The region within reach of a measurement of an overall
scaling of Higgs couplings $\Delta\kappa$ from the first, second, and third
CLIC stages is shown in dark, middle, and light grey, respectively. From [44,
16].

###  2.5 Overall CLIC physics reach

This section has presented a selection of recent studies to illustrate the
overall CLIC physics reach.

In Higgs physics, the initial CLIC energy stage already provides coupling
measurements that are in many cases significantly more precise than for the
HL-LHC. The higher CLIC energy stages improve upon these, and give access to
further couplings. Measured in
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collisions, the couplings can be determined in a model-independent way; at
CLIC they can reach precisions at the percent level, while the model-dependent
precisions reach the per-mille level. The Higgs self-coupling can be
determined at the level of
$[$-7\text{\,}\mathrm{\%}$,$+11\text{\,}\mathrm{\%}$]$. CLIC can measure the
top-quark mass at the level of $50\text{\,}\mathrm{MeV}$, including current
theory systematics. Measurements of top-quark production and decay properties
at all three energy stages can be used to probe the top-quark couplings, and
give sensitivity to potential new physics scenarios such as top compositeness
or CP violation in the $\mathup{{{t}}}\mathup{{{t}}}\mathup{{{H}}}$ coupling.

All of these SM probes, together with measurements of diboson and Drell-Yan
production, can be combined and interpreted in the SM-EFT framework. In this
way the precision studies at CLIC allow sensitivity to physics beyond the SM
that originates from scales at tens of TeV, well above the centre-of-mass
energy of the collider. The high energy stages of CLIC, and the electron
polarisation afforded by the linear collider, gives sensitivity beyond that
achievable at other colliders.

General examples have been given to show that through direct searches, CLIC is
sensitive to new particles produced in a wide range of new physics scenarios,
including those that are challenging experimentally. These scenarios include
extended Higgs sectors and a variety of dark matter candidates. Combining the
direct and indirect searches provides a direct avenue to probe the nature of
the EW phase transition for non-minimal scalar sectors, and the possible
origin of the cosmic matter-antimatter asymmetry via electroweak baryogenesis.

Previous studies have demonstrated that if particles are discovered at CLIC or
the LHC, CLIC has the ability to measure their masses and couplings at the
percent level or better: typically much more precisely than is possible at a
hadron collider [3].

A summary of these and further studies showing the overall reach for many
aspects of potential new physics is given in Table 4. For example, new
particles can be discovered directly over the whole CLIC kinematic reach,
under many new physics scenarios, and the sensitivity to high energy scales
from EFT fitting is complemented by limits on new physics scales in particular
sectors arising from dedicated searches, such as those for lepton flavour
violation.

Overall, the stand-alone discovery and precision capacity of CLIC,
complementary to that of the HL-LHC, makes it an ideal facility for extending
the search for physics beyond the SM.

Table 4: CLIC reach for new physics. Sensitivities are given for the full CLIC
programme covering the three centre-of-mass energy stages at
$\sqrt{s}=$380\text{\,}\mathrm{GeV}$$, $1.5\text{\,}\mathrm{TeV}$ and
$3\text{\,}\mathrm{TeV}$ with integrated luminosities of
$1\text{\,}{\mathrm{ab}}^{-1}$, $2.5\text{\,}{\mathrm{ab}}^{-1}$ and
$5\text{\,}{\mathrm{ab}}^{-1}$, respectively. At $380\text{\,}\mathrm{GeV}$,
equal amounts of $-80\text{\,}\mathrm{\%}$ and $+80\text{\,}\mathrm{\%}$
polarisation running are assumed. Above $1\text{\,}\mathrm{TeV}$ a sharing in
the ratio 80:20 is assumed between $-80\text{\,}\mathrm{\%}$ and
$+80\text{\,}\mathrm{\%}$ electron polarisation. All limits are at 95% C.L.
unless stated otherwise.

Process HL-LHC CLIC Heavy Higgs scalar mixing angle $\sin^{2}\gamma$
$<$4\text{\,}\mathrm{\%}$$ $<$0.24\text{\,}\mathrm{\%}$$ Higgs self-coupling
$\Delta\lambda$ $\sim 50\%$ at $68\text{\,}\mathrm{\%}$ C.L.
$[$-7\text{\,}\mathrm{\%}$,$+11\text{\,}\mathrm{\%}$]$ at
$68\text{\,}\mathrm{\%}$ C.L.
$\text{BR}({\mathup{{{H}}}\to\mathrm{invisible}})$
$<$0.69\text{\,}\mathrm{\%}$$ at $90\text{\,}\mathrm{\%}$ C.L. Higgs
compositeness scale $m_{*}$ $m_{*}>$3\text{\,}\mathrm{TeV}$$ Discovery up to
$m_{*}$ = $10\text{\,}\mathrm{TeV}$ ($>$7\text{\,}\mathrm{TeV}$$ for
$g_{*}\simeq 8$) ($40\text{\,}\mathrm{TeV}$ for $g_{*}\simeq 8$) Top
compositeness scale $m_{*}$ Discovery up to $m_{*}$ = $8\text{\,}\mathrm{TeV}$
($20\text{\,}\mathrm{TeV}$ for small coupling $g_{*}$) Higgsino mass
(disappearing track search) $>$250\text{\,}\mathrm{GeV}$$
$>$1.2\text{\,}\mathrm{TeV}$$ Slepton mass Discovery up to $\sim 1.5$ TeV RPV
wino mass $>$1.5\text{\,}\mathrm{TeV}$$
($$0.03\text{\,}\mathrm{m}$<c\tau<$30\text{\,}\mathrm{m}$$)
$\mathup{{{Z}}}^{\prime}$ (SM couplings) mass Discovery up to 7 TeV Discovery
up to 20 TeV NMSSM scalar singlet mass $>$650\text{\,}\mathrm{GeV}$$
($\tan\beta=4$) $>$1.5\text{\,}\mathrm{TeV}$$ ($\tan\beta=4$) Twin Higgs
scalar singlet mass $m_{\sigma}=f>1$ TeV $m_{\sigma}=f>4.5$ TeV Relaxion mass
$<$24\text{\,}\mathrm{GeV}$$ $<$12\text{\,}\mathrm{GeV}$$ (all for vanishing
$\sin\theta$) Relaxion mixing angle $\sin^{2}\theta$
$\leq$2.3\text{\,}\mathrm{\%}$$ Neutrino Type-2 see-saw triplet
$>$1.5\text{\,}\mathrm{TeV}$$ (for any triplet VEV)
$>$10\text{\,}\mathrm{TeV}$$ (for triplet Yukawa coupling $\simeq 0.1$)
Inverse see-saw RH neutrino $>$10\text{\,}\mathrm{TeV}$$ (for Yukawa coupling
$\simeq 1$) Scale $V_{LL}^{-1/2}$ for LFV
$(\bar{\mathup{{{e}}}}\mathup{{{e}}})(\bar{\mathup{{{e}}}}\mathup{})$
$>$42\text{\,}\mathrm{TeV}$$

##  3 CLIC accelerator design, technologies and performance

###  3.1 Introduction

The aim of the studies for CLIC has been to develop the designs and the
technologies to enable the building of a multi-$\mathrm{TeV}$
electron–positron collider. The feasibility of the concept and the
technologies has been documented in the CLIC CDR [2]. As reported in Section
2, the new staged approach to the project optimally addresses the physics
needs. The accelerator design, technologies and implementation have recently
been optimised for the first energy stage at $380\text{\,}\mathrm{GeV}$, while
fully taking upgrades to $1.5\text{\,}\mathrm{TeV}$ and
$3\text{\,}\mathrm{TeV}$ into account. The following will summarise the CLIC
design and parameters for the first energy stage, present a klystron-based
alternative, and show the staging to higher energies.

###  3.2 CLIC design and performance at $380\text{\,}\mathrm{GeV}$

####  3.2.1 Design overview

The schematic layout of the baseline CLIC complex for
$380\text{\,}\mathrm{GeV}$ operation is shown in Figure 14 and the key
parameters for all three energy stages are listed in Table 5.

Figure 14: Schematic layout of the CLIC complex at $380\text{\,}\mathrm{GeV}$.
(image credit: CLIC)

The main electron beam is produced in a conventional radio-frequency (RF)
source and accelerated to $2.86\text{\,}\mathrm{GeV}$. The beam emittance is
then reduced in a damping ring. To produce the positron beam, an electron beam
is accelerated to $5\text{\,}\mathrm{GeV}$ and sent into a crystal to produce
energetic photons, which hit a second target and produce electron–positron
pairs. The positrons are captured and accelerated to
$2.86\text{\,}\mathrm{GeV}$. Their beam emittance is reduced first in a pre-
damping ring and then in a damping ring. The ring to main linac system (RTML)
accelerates the beams to $9\text{\,}\mathrm{GeV}$ and compresses their bunch
length. The main linacs accelerate the beams to the beam energy at collision
of $190\text{\,}\mathrm{GeV}$. The beam delivery system removes transverse
tails and off-energy particles with collimators and compresses the beam to the
small sizes required at the collision point. After the collision the beams are
transported by the post collision lines to the respective beam dumps.

The RF power for each main linac is provided by a high current, low-energy
drive beam that runs parallel to the colliding beam through a sequence of
power extraction and transfer structures (PETS). The drive beam generates RF
power in the PETS that is then transferred to the accelerating structures by
waveguides.

The drive beam is generated in a central complex with a fundamental frequency
of $1\text{\,}\mathrm{GHz}$. A $48\text{\,}\mathrm{\SIUnitSymbolMicro s}$ long
beam pulse is produced in the injector and fills every other bucket, i.e. with
a bunch spacing of $0.6\text{\,}\mathrm{m}$. Every $244\text{\,}\mathrm{ns}$,
the injector switches from filling even buckets to filling odd buckets and
vice versa, creating $244\text{\,}\mathrm{ns}$ long sub-pulses. The beam is
accelerated in the drive-beam linac to $1.91\text{\,}\mathrm{GeV}$. A
$0.5\text{\,}\mathrm{GHz}$ resonant RF deflector sends half of the sub-pulses
through a delay loop such that its bunches can be interleaved with those of
the following sub-pulse that is not delayed. This generates a sequence of
$244\text{\,}\mathrm{ns}$ trains in which every bucket is filled, followed by
gaps of the same $244\text{\,}\mathrm{ns}$ length. In a similar fashion three
of the new sub-pulses are merged in the first combiner ring. Groups of four of
the new sub-pulses, now with $0.1\text{\,}\mathrm{m}$ bunch distance, are then
merged in the second combiner ring. The final pulses are thus
$244\text{\,}\mathrm{ns}$ long and have a bunch spacing of
$2.5\text{\,}\mathrm{cm}$, i.e. providing $24$ times the initial beam current.
The distance between the pulses has increased to
$24\text{\times}244\text{\,}\mathrm{ns}$, which corresponds to twice the
length of a $878\text{\,}\mathrm{m}$ decelerator. The first four sub-pulses
are transported through a delay line before they are used to power one of the
linacs while the next four sub-pulses are used to power the other linac
directly. The first sub-pulse feeds the first drive-beam decelerator, which
runs in parallel to the colliding beam. When the sub-pulse reaches the
decelerator end, the second sub-pulse has reached the beginning of the second
drive-beam decelerator and will feed it, while the colliding beam has
meanwhile reached the same location along the linac.

Table 5: Key parameters of the CLIC energy stages. Parameter | Symbol | Unit | Stage 1 | Stage 2 | Stage 3
---|---|---|---|---|---
Centre-of-mass energy | $\sqrt{s}$ | $\mathrm{GeV}$ | 380 | 1500 | 3000
Repetition frequency | $f_{\text{rep}}$ | $\mathrm{Hz}$ | 50 | 50 | 50
Number of bunches per train | $n_{b}$ |  | 352 | 312 | 312
Bunch separation | $\Delta\,t$ | $\mathrm{ns}$ | 0.5 | 0.5 | 0.5
Pulse length | $\tau_{\text{RF}}$ | $\mathrm{ns}$ | 244 | 244 | 244
Accelerating gradient | $G$ | $\mathrm{M}\mathrm{V}\mathrm{/}\mathrm{m}$ | 72 | 72/100 | 72/100
Total luminosity | $\mathcal{L}$ | ${10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ | 1.5 | 3.7 | 5.9
Luminosity above $99\text{\,}\mathrm{\%}$ of $\sqrt{s}$ | $\mathcal{L}_{0.01}$ | ${10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ | 0.9 | 1.4 | 2
Total integrated luminosity per year | $\mathcal{L}_{\mathrm{i}nt}$ | ${\mathrm{fb}}^{-1}$ | 180 | 444 | 708
Main linac tunnel length |  | $\mathrm{km}$ | 11.4 | 29.0 | 50.1
Number of particles per bunch | $N$ | ${10}^{9}$ | 5.2 | 3.7 | 3.7
Bunch length | $\sigma_{z}$ | $\mathrm{\SIUnitSymbolMicro m}$ | 70 | 44 | 44
IP beam size | $\sigma_{x}/\sigma_{y}$ | $\mathrm{nm}$ | 149/2.9 |  $\sim$ 60/1.5 |  $\sim$ 40/1
Normalised emittance (end of linac) | $\epsilon_{x}/\epsilon_{y}$ | $\mathrm{nm}$ | 900/20 | 660/20 | 660/20
Final RMS energy spread |  | $\mathrm{\%}$ | 0.35 | 0.35 | 0.35
Crossing angle (at IP) |  | $\mathrm{mrad}$ | 16.5 | 20 | 20

####  3.2.2 Main-beam design considerations and choices

The CLIC target luminosity at $380\text{\,}\mathrm{GeV}$ is
$\mathcal{L}=$1.5\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$.
The nominal beam parameters at the interaction point are given in Table 5.
Reaching the energy goal requires achieving the target gradient in the
accelerating structures. This in turn requires that the structures can sustain
the gradient and that the drive beam provides enough power. In addition, to
reach the luminosity goal, the colliding beam needs to have a high current and
an excellent quality. Thorough studies established a feasible concept for the
$380\text{\,}\mathrm{GeV}$ stage [2]. Based on this the first stage has been
designed. The key considerations are:

  * •

The choice of bunch charge and length ensures stable transport of the beam.
The main limitation arises from short-range wakefields in the Main Linac.

  * •

The spacing between subsequent bunches ensures that the long-range wakefields
in the Main Linac can be sufficiently damped to avoid beam break-up
instabilities.

  * •

The horizontal beam size at the collision point ensures that the beamstrahlung
caused by the high beam brightness is kept to an acceptable level for the
given bunch charge. This ensures a luminosity spectrum consistent with the
requirements of the physics experiments.

  * •

The horizontal emittance is dominated by single particle and collective
effects in the Damping Rings and includes some additional contributions from
the Ring To Main Linac.

  * •

The vertical emittance is given mainly by the Damping Ring and additional
contributions from imperfections of the machine implementation. The target
parameters take into account budgets for detrimental effects from static and
dynamic imperfections such as component misalignments and jitter.

  * •

The vertical beta-function is the optimum choice in terms of luminosity. The
horizontal beta-function is determined by the combination of required beam
size and horizontal emittance.

In summary, the parameters are largely determined by fundamental beam physics
and machine design with the exception of the vertical emittance that is
determined by imperfections. Without them a luminosity of
$\mathcal{L}=$4.3\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$
would be achieved.

####  3.2.3 Performance of the drive-beam concept

The successful technology demonstration of the CLIC accelerating gradient is
discussed in Section 3.5. The main performance limitation arises from vacuum
discharge, i.e. breakdowns; a rate of less than
$3\text{\times}{10}^{-7}\text{\,}{\mathrm{m}}^{-1}$ is required for the target
gradient of $72\text{\,}\mathrm{M}\mathrm{V}\mathrm{/}\mathrm{m}$. The key
parameters for the accelerating structure and the beam have been optimised
together. In particular, structures with smaller iris apertures achieve higher
gradients for the same breakdown rate, but they reduce the maximum bunch
charge for stable beam transport because they produce stronger wakefields.

To test the drive-beam concept, the third CLIC Test Facility (CTF3) [6] was
constructed and operated by an international collaboration. It has addressed
the key points of the concept:

  * •

The stable acceleration of the initial high-current drive beam in the
accelerator.

  * •

The high transfer efficiency from the RF to the drive beam.

  * •

The generation of the final drive-beam structure using the delay loop and a
combiner ring.

  * •

The quality of the final drive beam. In particular, feedback has been used to
stabilise the drive-beam current and phase to ensure correct main-beam
acceleration. CTF3 achieved the drive-beam phase stability that is required
for CLIC [45, 46, 47].

  * •

The use of the drive beam to accelerate the main beam and the performance of
the associated hardware. The main beam has been accelerated with a maximum
gradient of $145\text{\,}\mathrm{M}\mathrm{V}\mathrm{/}\mathrm{m}$.

CTF3 established the feasibility of the drive-beam concept and the ability to
use this scheme to accelerate the main beam. Figure 15 shows the corresponding
two-beam acceleration test stand in the CTF3 facility.

Figure 15: The two-beam acceleration test stand in the CTF3 facility. The
drive beam enters from the middle-right, while the probe (main) beam enters
from the bottom-right. (image credit: CLIC)

It has also been instrumental in developing all the different hardware
components that are essential for the scheme – among them the drive-beam gun,
the bunch compressor, the drive-beam accelerating structures, RF deflectors,
the PETS including a mechanism to switch them off individually, the power
distribution waveguide system, fast-feedback systems, drive-beam current and
phase monitors, as well as other instrumentation. CTF3 stopped operation after
successfully completing its experimental programme in December $2016$ and a
new facility, CLEAR, has started to operate. It is re-uses the CTF3 main-beam
installations and additional hardware to address further beam dynamics with
the focus on the main beam.

####  3.2.4 Luminosity performance

For static imperfections, the vertical emittance growth budgets are the same
at $380\text{\,}\mathrm{GeV}$ and $3\text{\,}\mathrm{TeV}$ and they correspond
to the values described in the CDR [2]. It is required that each system, i.e.
RTML, Main Linac and BDS, remains within its emittance budget with a
likelihood of more than $90\text{\,}\mathrm{\%}$ without further intervention.
The key static imperfection is the misalignment of the beamline components
with respect to the design. A sophisticated system has been developed and
tested that provides a spacial reference frame with unprecedented accuracy,
see Section 3.5. The Main Linac and BDS components are mounted on movable
supports and can be remotely aligned with respect to the reference system. In
addition, the main linac accelerating structures are equipped with wakefield
monitors that allow the measurement and correction of their offset with
respect to the beam. Dispersion-free steering, which has been successfully
tested at the SLAC Facility for Advanced Accelerator Experimental Tests
(FACET), will further reduce the emittance growth using high-resolution Beam
Position Monitors (BPM). In the BDS, additional tuning is required using
optical knobs that move several multi-pole magnets simultaneously to correct
the optics properties.

The performance specifications for the alignment systems and instrumentation
are kept the same at $380\text{\,}\mathrm{GeV}$ and $3\text{\,}\mathrm{TeV}$
and correspond to the CDR description. They are sufficient to achieve the
required performance at $3\text{\,}\mathrm{TeV}$ and most of them could be
relaxed for the first energy stage, typically by about a factor of two, to
meet the same emittance budget. However, the original, better performances are
required for the upgrade to the higher energy stages. No substantial cost
saving has been identified by relaxing the specifications for the first stage.
Therefore, it has been decided to ensure that the system is consistent with
the final energy from the very beginning, thus avoiding the need for upgrades
of the already existing hardware. This also provides additional margin for
achieving the required luminosity.

The tuning procedures for the RTML and the BDS have been improved compared to
the CDR. Studies of the static imperfections in the RTML [48], the Main Linac
[49] and the BDS [50] show that the target budgets can be met in each system
with a margin; in the BDS, the tuning is now also much faster. Combining these
effects, one can expect an average luminosity of
$\mathcal{L}=$3\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$,
about twice the luminosity target at $380\text{\,}\mathrm{GeV}$ [50].

Also, for the dynamic imperfections the vertical emittance budgets are the
same for $380\text{\,}\mathrm{GeV}$ and $3\text{\,}\mathrm{TeV}$. Key
imperfections are the movement of components due to ground motion or technical
noise, phase and amplitude jitter of the drive beam, and potentially dynamic
magnetic fields.

The level of ground motion is site dependent; measurements in the LEP tunnel
showed very small motion [51] while measurements in the CMS detector hall
showed much larger motion [52]. With the new design of the final focus system,
all relevant accelerator components are mounted in the tunnel of the collider,
so one can expect ground motion levels similar to the LEP tunnel. However, for
the ground motion studies the level of the CMS detector hall has been used in
order to evaluate the robustness of the solutions. The ground motion is
mitigated by the design of the magnets, a mechanical feedback that decouples
them from the ground, and by beam-based feedback on trajectories. Prototypes
of the mechanical feedback have been tested successfully. In the CDR, detailed
studies of the $3\text{\,}\mathrm{TeV}$ stage showed that the performance goal
can be met with margin. Studies of the $380\text{\,}\mathrm{GeV}$ case [46]
confirm that ground motion will only use about $10\text{\,}\mathrm{\%}$ of the
budget allocated to dynamic imperfections.

Dynamic magnetic stray fields deflect the colliding beams, leading to
trajectory jitter and emittance growth, thus reducing luminosity. Their impact
is particularly large in the RTML and the BDS. In the latter they are more
important at $380\text{\,}\mathrm{GeV}$ than at $3\text{\,}\mathrm{TeV}$ due
to the lower beam energy. A study in collaboration with experts from the
Hungarian Geophysics Institute has commenced to investigate these fields and
define the mitigation technologies. The magnetic fields can originate from
different sources: natural sources, such as geomagnetic storms; environmental
sources, such as railway trains and power lines and technical sources, i.e.
from the collider itself. A survey of natural sources showed that they should
not affect the luminosity [53] and a measurement station has been established
in the Jura mountains near CERN to collect long-term regional data. The study
of the environmental and technical sources has started but is not yet
complete. Preliminary estimates have been performed using the magnetic field
variations that were measured in the LHC tunnel. They concluded that a thin
mu-metal shield of the drifts in the RTML and BDS can bring the fields down to
a level that does not impact luminosity [46].

Further development of the foreseen technical and beam-based imperfection
mitigation systems should allow for a reduction in the emittance budgets and
an increase in the luminosity target. Also, new systems could be devised to
this end. As an example, the addition of a few klystron-powered, higher-
frequency accelerating structures could allow to reduce the energy spread of
the colliding beams, which can improve the luminosity and also the luminosity
spectrum for specific measurements such as the top-quark threshold scan.

####  3.2.5 Operation and availability

The machine protection and operational considerations and strategies at
$380\text{\,}\mathrm{GeV}$ are similar to those at $3\text{\,}\mathrm{TeV}$
and are described in the CDR [2]. Machine protection relies on passive
protection and the processing of the diagnostics data between two beam pulses
to generate a beam permit signal.

The tentative plan for the operation of CLIC includes a yearly shutdown of
$120\text{\,}\mathrm{days}$. In addition $30\text{\,}\mathrm{days}$ are
foreseen for the machine commissioning, $20\text{\,}\mathrm{days}$ for machine
development and $10\text{\,}\mathrm{days}$ for planned technical stops. This
leaves $185\text{\,}\mathrm{days}$ of operation for the experiments. The
target availability for the experiments during this period is
$75\text{\,}\mathrm{\%}$. Hence the integrated luminosity per year corresponds
to operation at full luminosity for
$1.2\text{\times}{10}^{7}\text{\,}\mathrm{s}$ [54]. An optimisation of the
schedule has started which will also refine the trade-off between planned
short stops and availability to reach the integrated luminosity goal.

Different events can impact both operation and availability and can be roughly
categorised as:

  * •

Events that do not require an intervention in the machine and are handled by
the control system. These include RF breakdowns in the accelerating
structures, which will lead to a small energy error and potentially slight
transverse deflection of the beam. Typically this will happen only every $100$
beam pulses and will be corrected by the feedback systems.

  * •

Events that require a short stop on the machine but no intervention, such as a
false trigger of the machine protection system – e.g. caused by a single event
upset. In this case, the machine can be brought back to full intensity in a
few seconds.

  * •

Failures of machine components that might compromise the performance but do
not require stopping the beam. This includes failures of klystrons or
instrumentation. These are mitigated by providing sufficient reserve.

  * •

Failures that require to stop the beam and repair the machine. This is the
case for failures of power converters.

Based on an assessment of the complexity of the different systems, an
availability goal has been defined for each of them. This allows investigation
of individual systems and focus on the key issues.

A number of key failures has been studied in detail, in particular of magnet
power converters and RF power systems. In the drive-beam accelerator, a
reserve of $5\text{\,}\mathrm{\%}$ RF units are installed and klystrons
operate below their maximum power. If one fails, the power of the others is
increased accordingly. Similarly, BPMs and orbit corrector failures in the
main linac compromise the correction of ground motion. However, if
$10\text{\,}\mathrm{\%}$ of them fail, the effect of ground motion is only
increased by $14\text{\,}\mathrm{\%}$. During the technical stops failed
klystrons and instrumentation can be replaced. The CLIC lattice design has
been optimised to minimise the impact of power converter failures. In
particular in the drive beam, the many quadrupoles are powered in groups to
minimise the number of power converters and small trims adjust their strength
as needed. Compared to individual powering, this strongly increases the mean
time between failures, since failures of trims can be mitigated to a large
extent. A similar strategy is used for the main-beam quadrupoles.

Detailed studies will be required during the technical design phase covering
all components to ensure that the availability goal can be met. Currently,
considering key failures, no obstacle has been identified to reaching the
target availability.

####  3.2.6 Energy flexibility

The beam parameters can be adjusted to different physics requirements. In
particular, the collision energy can be adjusted to the requirements by
lowering the gradient in the main linacs accordingly. For a significantly
reduced gradient, the bunch charge will have to be reduced in proportion the
energy to ensure beam stability. However, at this moment the only operation
energy different from $380\text{\,}\mathrm{GeV}$ that is required is around
$350\text{\,}\mathrm{GeV}$ to scan the top-quark pair-production threshold. In
this case, the bunch charge can remain constant. The RF phases of the
accelerating structures are slightly modified compared to the
$380\text{\,}\mathrm{GeV}$ case in order to achieve an RMS beam energy spread
of only $0.3\text{\,}\mathrm{\%}$. This allows reaching a luminosity of
$\mathcal{L}=$1.5\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$,
similar to the $380\text{\,}\mathrm{GeV}$ goal.

Also the beam energy can be reduced at the cost of some reduction in
luminosity. For example, at the top-quark threshold, one can reduce the bunch
charge by $10\text{\,}\mathrm{\%}$ and increase its length by
$10\text{\,}\mathrm{\%}$. This would keep the wakefield effects in the main
linac constant. This configuration slightly reduces the luminosity to
$\mathcal{L}=$1.18\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$,
but reduces the beam energy spread to $0.2\text{\,}\mathrm{\%}$. Similarly, it
is possible to reduce the beamstrahlung by increasing the horizontal beam
size, if the reduced luminosity is out-weighted by the improved luminosity
spectrum.

Operation at much lower energies can also be considered. At the Z-pole,
between $2.5\text{\,}{\mathrm{fb}}^{-1}$ and $45\text{\,}{\mathrm{fb}}^{-1}$
can be achieved per year for an unmodified and a modified collider,
respectively.

####  3.2.7 Beam experiments

Beam experiments and hardware tests provide the evidence that the CLIC
performance goals can be met. Some key cases are discussed in the following:

  * •

The novel drive-beam scheme has been demonstrated in CTF3, as discussed in
Section 3.2.3.

  * •

The Stanford Linear Collider (SLC) [55], the only linear collider so far, is a
proof of principle for the linear collider concept and contributed important
physics data at the Z-pole. The SLC achieved collision beam sizes smaller than
nominal, but did not reach the nominal bunch charge [56]. Two collective
effects led to the charge limitations. They have been fully understood and are
not present in the CLIC design.

  * •

The electron polarisation that has been achieved at collision in SLC is
similar to the CLIC goal.

  * •

The strong beam–beam effect increases the luminosity in CLIC. This effect has
been observed at the SLC, in agreement with the theoretical predictions [57].

  * •

Modern light sources achieve CLIC-level vertical emittances, in particular the
Swiss Light Source and the Australian Light Source [58, 59, 60].

  * •

CLIC parameters require strong focusing at the IP. This focusing has been
demonstrated at two test facilities, FFTB [61] at SLAC and the Accelerator
Test Facility ATF2 [7, 8] at KEK. The achieved vertical beam sizes were
$40\text{\,}\mathrm{\%}$ and $10\text{\,}\mathrm{\%}$ above the respective
design values for these test facilities. In the super B-factory at KEK the
beams will perform many turns through the final focus system, still one aims
at beta-functions that are only a factor three larger than in CLIC, and even
smaller beta-functions similar to the CLIC values are being discussed [62].

  * •

The use of beam-based alignment, i.e. dispersion free steering [63, 64] to
maintain small emittances in a linac has successfully been tested in FACET [9]
and FERMI [10].

  * •

The effective suppression of harmful long-range wakefields has been tested
with beam in the CLIC accelerating structures [65].

  * •

The novel precision pre-alignment system of CLIC and sophisticated beam-based
alignment and tuning ensure the preservation of the beam quality during
transport. The alignment system is based on a concept developed for the LHC
interaction regions, but with improved performance. Prototypes have been built
and successfully tested, see Section 3.5.3.

  * •

Quadrupole jitter has been an important source of beam jitter in the SLC. For
CLIC this has been addressed by designing the magnet supports to avoid
resonances at low frequencies and by developing an active stabilisation system
for the magnets, which demonstrated a reduction of the jitter to the sub-
nanometre regime, see Section 3.5.3.

  * •

CLIC requires excellent relative timing at the $50\text{\,}\mathrm{fs}$ level
over the collider complex. CTF3 has demonstrated the phase monitor and
correction with fast feed-forward. Modern Free Electron Lasers (FEL) have
developed the technology to provide the timing reference over large distances.

  * •

High availability is key to achieve the luminosity goal. The very reliable
routine operation of light sources, FELs, the B-factories and the LHC provide
concepts to address this issue.

In conclusion, the CLIC parameters are ambitious but are supported by
simulation studies, measured hardware performances and beam tests. This gives
confidence that the goals can be met. More details on the performance
benchmarks can be found in the Project Implementation Plan [66].

###  3.3 A klystron-based CLIC at $380\text{\,}\mathrm{GeV}$

An alternative design for the $380\text{\,}\mathrm{GeV}$ stage of CLIC is
based on the use of X-band klystrons to produce the RF power for the main
linac. On the one hand, this solution increases the cost of the main linac
because the klystrons and modulators are more expensive than the drive-beam
decelerator and also because a larger tunnel is needed to house the additional
equipment. On the other hand, it avoids the substantial cost of the
construction of the drive-beam complex and makes the linac more modular. One
can therefore expect a competitive cost at low energies while the drive-beam
solution leads to lower cost at high energies. The upgrade of the complex is
cheaper with a drive-beam based design, since the additional cost to upgrade
the drive-beam complex to feed a longer linac is relatively modest. However,
an important advantage of the klystron-based design is that the main linac
modules can easily be fully tested for performance when they are received. In
contrast, the drive-beam option requires the construction of a substantial
complex that can produce a $100\text{\,}\mathrm{A}$ drive beam before modules
can be fully tested. The klystron-based option could therefore be implemented
more rapidly than the drive-beam based solution.

####  3.3.1 Design choice

The klystron-powered design is based on a study [5] that uses the same
optimisation tools as for the drive-beam based option. The main linac model
has been replaced with one that consists of a sequence of RF units, each
powered by klystrons, see Section 3.5.7, and the drive-beam complex has been
removed. A cost model for the klystrons and modulators is included. Based on
the conclusions of the study, a tentative accelerating structure and a
parameter set have been chosen for this design. The optimum structure differs
from the drive-beam based design. It is slightly shorter and has a smaller
aperture. If one were to use the same accelerating structure as for the drive-
beam based design, the expected cost would be about
$330\text{\,}\mathrm{M}\mathrm{C}\mathrm{H}\mathrm{F}$ higher.

As can be seen in Table 6, the beam emittance, energy spread and charge of the
klystron-based design are very similar to the $380\text{\,}\mathrm{GeV}$
parameters, while the bunch is somewhat longer. The vertical emittance is also
the same as for the drive-beam based design, while the horizontal emittance is
smaller and proportional to the bunch charge. The number of bunches per train
is significantly higher in order to produce the required luminosity.

The evolution of the vertical emittance along the collider is similar to the
drive-beam based design, while the horizontal emittance corresponds to the
$380\text{\,}\mathrm{GeV}$ design. The horizontal and vertical emittances
remain below $500\text{\,}\mathrm{nm}$ and $5\text{\,}\mathrm{nm}$ at
extraction from the damping ring, below $600\text{\,}\mathrm{nm}$ and
$10\text{\,}\mathrm{nm}$ at injection into the main linac and below
$630\text{\,}\mathrm{nm}$ and $20\text{\,}\mathrm{nm}$ at the end of the main
linac. At the interaction point they will be below $660\text{\,}\mathrm{nm}$
and $30\text{\,}\mathrm{nm}$, respectively.

Table 6: Key beam parameters of the klystron-based alternative at the collision point. Parameter | Symbol | Unit | Stage 1
---|---|---|---
Centre-of-mass energy | $\sqrt{s}$ | $\mathrm{GeV}$ | 380
Repetition frequency | $f_{\text{rep}}$ | $\mathrm{Hz}$ | 50
Number of bunches per train | $n_{b}$ |  | 485
Bunch separation | $\Delta\,t$ | $\mathrm{ns}$ | 0.5
Total luminosity | $\mathcal{L}$ | ${10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ | 1.5
Luminosity above $99\text{\,}\mathrm{\%}$ of $\sqrt{s}$ | $\mathcal{L}_{0.01}$ | ${10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ | 0.9
Total integrated luminosity per year | $\mathcal{L}_{\mathrm{i}nt}$ | ${\mathrm{fb}}^{-1}$ | 180
Number of particles per bunch | $N$ | ${10}^{9}$ | 3.87
Bunch length | $\sigma_{z}$ | $\mathrm{\SIUnitSymbolMicro m}$ | 60
IP beam size | $\sigma_{x}/\sigma_{y}$ | $\mathrm{nm}$ | 119/2.9
Normalised emittance (end of linac) | $\epsilon_{x}/\epsilon_{y}$ | $\mathrm{nm}$ | $\leq 630/\leq 20$
Final RMS energy spread |  | $\mathrm{\%}$ | 0.35
Crossing angle (at IP) |  | $\mathrm{mrad}$ | 16.5

####  3.3.2 Design implications

For the klystron-based alternative, the main linac has been redesigned to
evaluate the cost and verify the beam dynamics. No design optimisation has
been performed for the other systems. It is expected that these have only
minor impact on cost and system performance, as detailed below.

The RF design of the klystron-based injector has to differ from the drive-beam
based case in order to accommodate the longer bunch train. However, the total
charge per pulse is the same in both cases. Hence, to first order the same
amount of installed RF is required. However, the choice of accelerating
structure and pulse compressor in the injection system would be slightly
different to obtain optimum efficiency.

The single bunch parameters at the entrance of the linac are very similar to
the drive-beam based design. The main difference is the lower bunch charge,
which helps the emittance preservation, and the smaller horizontal emittance,
which needs to be achieved. Both parameters are very similar to the
$380\text{\,}\mathrm{GeV}$ design and can thus be achieved with the
corresponding design. The bunch length at the start of the main linac and
afterwards is larger in the klystron-based design, which requires less
compression in the RTML and eases the system requirements.

An optimised layout of the main linac has been developed and beam dynamics
studies have been performed. They confirmed the expected results that the
performance is the same as for the drive-beam case.

The beam delivery system design is the same for the baseline option and the
klystron-based alternative, since the beta-functions at the collision point
are the same.

###  3.4 Extension to higher energy stages

The CLIC $380\text{\,}\mathrm{GeV}$ energy stage can be efficiently upgraded
to higher energies, like the proposed $1.5\text{\,}\mathrm{TeV}$ and
$3\text{\,}\mathrm{TeV}$ stages. This flexibility has been an integral part of
the design choices for the first energy stage. The highest energy stage