• Real-time quantum dynamics, path integrals and the method of thimbles 

      Mou, Zonggang; Saffin, Paul M.; Tranberg, Anders; Woodward, Simon (Peer reviewed; Journal article, 2019)
      Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field ...
    • Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations 

      Kurkela, Aleksi; Wiedemann, Urs Achim; Wu, Bin (Peer reviewed; Journal article, 2019)
      To study the microscopic structure of quark–gluon plasma, data from hadronic collisions must be confronted with models that go beyond fluid dynamics. Here, we study a simple kinetic theory model that encompasses fluid ...
    • Chemical equilibration in weakly coupled QCD 

      Kurkela, Aleksi; Mazeliauskas, Aleksas (Peer reviewed; Journal article, 2019)
      We study thermalization, hydrodynamization, and chemical equilibration in out-of-equilibrium quark-gluon plasma starting from various initial conditions using QCD effective kinetic theory, valid at weak coupling. In ...
    • Chemical equilibration in hadronic collisions 

      Kurkela, Aleksi; Mazeliauskas, Aleksas (Peer reviewed; Journal article, 2019)
      We study chemical equilibration in out-of-equilibrium quark-gluon plasma using the first principles method of QCD effective kinetic theory, accurate at weak coupling. In longitudinally expanding systems—relevant for ...
    • A GIT construction of degenerations of Hilbert schemes of points 

      Gulbrandsen, Martin G; Halle, Lars H.; Hulek, Klaus (Peer reviewed; Journal article, 2019)
      We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu ...
    • Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks 

      Karpie, Joseph; Orginos, Kostas; Rothkopf, Alexander Karl; Zafeiropoulos, Savvas (Peer reviewed; Journal article, 2019)
      The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem. In this study, we present and evaluate the efficiency ...
    • Flavor structure of GUTs and uncertainties in proton lifetime estimates 

      Kolesova, Helena; Malinsky, Michal (Peer reviewed; Journal article, 2019)
      We study the flavor aspects of proton lifetime estimates in simple grand-unified models, paying particular attention to their inherent fragility due to the notorious lack of control of some of the key parameters governing ...
    • Spontaneous momentum dissipation and coexistence of phases in holographic Horndeski theory 

      Filios, Georgios; Gonzalez, P. A.; Kuang, Xiao-Mei; Papantonopoulos, Eleftherios; Vasquez, Yerko (Peer reviewed; Journal article, 2019)
      We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory. In the probe limit breaking the translational invariance, we study the conductivity and we find a nontrivial structure indicating a ...
    • Chiral soliton lattice in QCD-like theories 

      Brauner, Tomas; Filios, Georgios; Kolesova, Helena (Peer reviewed; Journal article, 2019)
      Recently, it has been shown that the ground state of quantum chromodynamics (QCD) in suffciently strong magnetic fields and at moderate baryon number chemical potential carries a crystalline condensate of neutral pions: ...
    • Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem 

      Brauner, Tomas; Filios, Georgios; Kolesova, Helena (Peer reviewed; Journal article, 2019)
      We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vectorlike gauge theories without the sign problem, thus disproving the long-standing conjecture that the absence of the sign problem ...
    • Spectral function for overoccupied gluodynamics from classical lattice simulations 

      Boguslavski, Kirill; Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko (Peer reviewed; Journal article, 2019)
      We study the spectral properties of an overoccupied gluonic system far from equilibrium. Using classical Yang–Mills simulations and linear response theory, we determine the statistical and spectral functions. We measure ...
    • Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations 

      Petreczky, Peter; Rothkopf, Alexander Karl; Weber, Johannes Heinrich (Peer reviewed; Journal article, 2019)
      We present our first results on a direct computation of the complex in-medium heavy quark potential from realistic lattice QCD simulations. Ensembles with Nτ = 12 from the HotQCD and TUMQCD collaboration offer unprecedented ...
    • Bottomonium suppression at RHIC and LHC 

      Krouppa, Brandon; Rothkopf, Alexander Karl; Strickland, Michael (Peer reviewed; Journal article, 2019-02)
      The strong suppression of heavy quarkonia is a good indicator that one has generated a quark-gluon plasma (QGP) in an ultrarelativistic heavy ion collision. Recent advancements in first principles calculations of the heavy ...
    • Quantum dynamical dissociation of quarkonia by wave function decoherence in quark-gluon plasma 

      Kajimoto, Shiori; Akamatsu, Yukinao; Asakawa, Masayuki; Rothkopf, Alexander Karl (Peer reviewed; Journal article, 2019-02)
      In this study, we investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in an improved QCD based stochastic potential model. This model describes the quarkonium dynamics in terms of a ...
    • Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory 

      Kurkela, Aleksi; Mazeliauskas, Aleksas; Paquet, Jean-Francois; Schlichting, Sören; Teaney, Derek (Peer reviewed; Journal article, 2019-03)
      High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in ...
    • A Class of Tests for Trend in Time Censored Recurrent Event Data 

      Kvaløy, Jan Terje; Lindqvist, Bo Henry (Journal article; Peer reviewed, 2019-04)
      Statistical tests for trend in recurrent event data not following a Poisson process are generally constructed for event censored data. However, time censored data are more frequently encountered in practice. In this paper ...
    • Quarkonium phenomenology from a generalised Gauss law 

      Lafferty, David; Rothkopf, Alexander Karl (Peer reviewed; Journal article, 2019-05)
      We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum ...
    • Lattice study of static quark-antiquark interactions in dense quark matter 

      Astrakhantsev, Nikita Yu.; Bornyakov, Vitaly G.; Braguta, Victor V.; Ilgenfritz, Ernst-Michael; Kotov, Andrey Yuryevich; Nikolaev, Alexander A.; Rothkopf, Alexander Karl (Peer reviewed; Journal article, 2019-05)
      In this paper we study the interactions among a static quark-antiquark pair in the presence of dense two-color quark matter with lattice simulation. To this end we compute Polyakov line correlation functions and determine ...
    • Quarkonium production in the QGP 

      Rothkopf, Alexander Karl (Peer reviewed; Journal article, 2019-05)
      We report on recent theory progress in understanding the production of heavy quarkonium in heavy-ion collisions based on the in-medium heavy-quark potential extracted from lattice QCD simulations. On the one hand, the ...
    • FCC-ee: The Lepton Collider: Future Circular Collider Conceptual Design Report Volume 2 

      Abbrescia, M; AbdusSalam, SS; Abdyukhanov, I; Abelleira Fernandez, J; Abramov, A; Aburaia, M; Acar, AO; Adzic, PR; Agrawal, P; Aguilar-Saavedra, JA; Aguilera-Verdugo, JJ; Aiba, M; Aichinger, I; Aielli, G; Akay, A; Akhundov, A; Aksakal, H; Albacete, JL; Albergo, S; Alekou, A; Aleksa, M; Aleksan, R; Alemany Fernandez, RM; Alexahin, Y; Alia, RG; Alioli, S; Alipour Tehrani, N; Allanach, BC; Allport, PP; Altınlı, M; Altmannshofer, W; Ambrosio, G; Amorim, D; Amstutz, O; Anderlini, L; Andreazza, A; Andreini, M; Andriatis, A; Andris, C; Andronic, A; Angelucci, M; Antinori, F; Antipov, SA; Antonelli, M; Antonello, M; Antonioli, P; Antusch, S; Anulli, F; Apolinario, L; Apollinari, G; Apollonio, A; Appelö, D; Appleby, RB; Apyan, A; Arbey, A; Arbuzov, A; Arduini, G; Arı, V; Arias, S; Armesto, N; Arnaldi, R; Arsenyev, SA; Arzeo, M; Asai, S; Aslanides, E; Aßmann, RW; Astapovych, D; Atanasov, M; Atieh, S; Attié, D; Auchmann, B; Audurier, A; Aull, S; Aumon, S; Aune, S; Avino, F; Avrillaud, G; Aydın, G; Azatov, A; Azuelos, G; Azzi, P; Azzolini, O; Azzurri, P; Bacchetta, N; Bacchiocchi, E; Bachacou, H; Baek, YW; Baglin, V; Bai, Y; Baird, S; Baker, MJ; Baldwin, MJ; Ball, AH; Ballarino, A; Banerjee, S; Barber, DP; Barducci, D; Barjhoux, P; Barna, D; Barnaföldi, GG; Barnes, MJ; Barr, A; Barranco Garcia, J; Barreiro Guimarães da Costa, J; Bartmann, W; Baryshevsky, V; Barzi, E; Bass, SA; Bastianin, A; Baudouy, B; Bauer, F; Bauer, M; Baumgartner, T; Bautista-Guzmán, I; Bayındır, C; Beaudette, F; Bedeschi, F; Béguin, M; Bellafont, I; Bellagamba, L; Bellegarde, N; Belli, E; Bellingeri, E; Bellini, F; Bellomo, G; Belomestnykh, S; Bencivenni, G; Benedikt, Michael; Bernardi, G; Bernardi, J; Bernet, C; Bernhardt, JM; Bernini, C; Berriaud, C; Bertarelli, A; Bertolucci, S; Besana, MI; Besançon, M; Beznosov, O; Bhat, P; Bhat, C; Biagini, ME; Biarrotte, JL; Bibet Chevalier, A; Bielert, ER; Biglietti, M; Bilei, GM; Bilki, B; Biscari, C; Bishara, F; Blanco-García, OR; Blánquez, FR; Blekman, F; Blondel, A; Blümlein, J; Boccali, T; Boels, R; Bogacz, SA; Bogomyagkov, A; Boine-Frankenheim, O; Boland, MJ; Bologna, S; Bolukbasi, O; Bomben, M; Bondarenko, S; Bonvini, M; Boos, E; Bordini, B; Bordry, F; Borghello, G; Borgonovi, L; Borowka, S; Bortoletto, D; Boscherini, D; Boscolo, M; Boselli, S; Bosley, RR; Bossu, F; Botta, C; Bottura, L; Boughezal, R; Boutin, D; Bovone, G; Božović Jelisavić, I; Bozbey, A; Bozzi, C; Bozzini, D; Braccini, V; Braibant-Giacomelli, S; Bramante, J; Braun-Munzinger, P; Briffa, JA; Britzger, D; Brodsky, SJ; Brooke, JJ; Bruce, R; Brückman De Renstrom, P; Bruna, E; Brüning, O; Brunner, O; Brunner, K; Bruzzone, P; Buffat, X; Bulyak, E; Burkart, F; Burkhardt, H; Burnet, JP; Butin, F; Buttazzo, D; Butterworth, A; Caccia, M; Cai, Y; Caiffi, B; Cairo, V; Cakir, O; Calaga, R; Calatroni, S; Calderini, G; Calderola, G; Caliskan, A; Calvet, D; Calviani, M; Camalich, JM; Camarri, P; Campanelli, M; Camporesi, T; Canbay, AC; Canepa, A; Cantergiani, E; Cantore-Cavalli, D; Capeans, M; Cardarelli, R; Cardella, U; Cardini, A; Carloni Calame, CM; Carra, F; Carra, S; Carvalho, A; Casalbuoni, S; Casas, J; Cascella, M; Castelnovo, P; Castorina, G; Catalano, G; Cavasinni, V; Cazzato, E; Cennini, E; Cerri, A; Cerutti, F; Cervantes, J; Chaikovska, I; Chakrabortty, J; Chala, M; Chamizo-Llatas, M; Chanal, H; Chanal, D; Chance, S; Chancé, A; Charitos, P; Charles, J; Charles, TK; Chattopadhyay, S; Chehab, R; Chekanov, SV; Chen, N; Chernoded, A; Chetvertkova, V; Chevalier, L; Chiarelli, G; Chiarello, G; Chiesa, M; Chiggiato, P; Childers, JT; Chmielińska, A; Cholakian, A; Chomaz, P; Chorowski, M; Chou, W; Chrzaszcz, M; Chyhyrynets, E; Cibinetto, G; Ciftci, AK; Ciftci, R; Cimino, R; Ciuchini, M; Clark, PJ; Coadou, Y; Cobal, M; Coccaro, A; Cogan, J; Cogneras, E; Collamati, F; Colldelram, C; Collier, P; Collot, J; Contino, R; Conventi, F; Cook, CTA; Cooley, L; Corcella, G; Cornell, AS; Corral, GH; Correia-Rodrigues, H; Costanza, F; Costa Pinto, P; Couderc, F; Coupard, J; Craig, N; Crespo Garrido, I; Crivellin, A; Croteau, JF; Crouch, M; Cruz Alaniz, E; Cure, B; Curti, J; Curtin, D; Czech, M; Dachauer, C; D'Agnolo, RT; Daibo, M; Dainese, A; Dalena, B; Daljevec, A; Dallapiazza, W; D'Aloia Schwartzentruber, L; Dam, M; D'Ambrosio, G; Das, SP; DasBakshi, S; da Silva, W; da Silveira, GG; D'Auria, V; D'Auria, S; David, A; Davidek, T; Deandrea, A; de Blas, J; Debono, CJ; De Curtis, S; De Filippis, N; de Florian, D; Deghaye, S; de Jong, SJ; Del Bo, C; Del Duca, V; Delikaris, D; Deliot, F; Dell'Acqua, A; Delle Rose, L; Delmastro, M; De Lucia, E; Demarteau, M; Denegri, D; Deniau, L; Denisov, D; Denizli, H; Denner, A; d'Enterria, D; de Rijk, G; De Roeck, A; Derue, F; Deschamps, O; Descotes-Genon, S; Dev, PSB; de Vivie de Régie, JB; Dewanjee, RK; Di Ciaccio, A; Di Cicco, A; Dillon, BM; Di Micco, B; Di Nezza, P; Di Vita, S; Doblhammer, A; Dominjon, A; D'Onofrio, M; Dordei, F; Drago, A; Draper, P; Drasal, Z; Drewes, M; Duarte, L; Dubovyk, I; Duda, P; Dudarev, A; Dudko, L; Duellmann, D; Dunser, M; du Pree, T; Durante, M; Duran Yildiz, H; Dutta, S; Duval, F; Duval, JM; Dydyshka, Y; Dziewit, B; Eisenhardt, S; Eisterer, M; Ekelof, T; El Khechen, D; Ellis, SA; Ellis, J; Ellison, JA; Elsener, K; Elsing, M; Enari, Y; Englert, C; Eriksson, H; Eskola, KJ; Esposito, LS; Etisken, O; Etzion, E; Fabbricatore, P; Falkowski, A; Falou, A; Faltova, J; Fan, J; Fanò, L; Farilla, A; Farinelli, R; Farinon, S; Faroughy, DA; Fartoukh, SD; Faus-Golfe, A; Fawcett, WJ; Felici, G; Felsberger, L; Ferdeghini, C; Fernandez Navarro, AM; Fernández-Téllez, A; Ferradas Troitino, J; Ferrara, G; Ferrari, R; Ferreira, L; Ferreira da Silva, P; Ferrera, G; Ferro, F; Fiascaris, M; Fiorendi, S; Fiorio, C; Fischer, O; Fischer, E; Flieger, W; Florio, M; Fonnesu, D; Fontanesi, E; Foppiani, N; Foraz, K; Forkel-Wirth, D; Forte, S; Fouaidy, M; Fournier, D; Fowler, T; Fox, J; Francavilla, P; Franceschini, R; Franchino, S; Franco, E; Freitas, A; Fuks, B; Furukawa, K; Furuseth, Sondre Vik; Gabrielli, E; Gaddi, A; Galanti, M; Gallo, E; Ganjour, S; Gao, J; Garcia Diaz, V; García Pérez, M; García Tabarés, L; Garion, C; Garzelli, MV; Garzia, I; Gascon-Shotkin, SM; Gaudio, G; Gay, P; Ge, SF; Gehrmann, T; Genest, MH; Gerard, R; Gerigk, F; Gerwig, H; Giacomelli, P; Giagu, S; Gianfelice-Wendt, E; Gianotti, F; Giffoni, F; Gilardoni, SS; Gil Costa, M; Giovannetti, M; Giovannozzi, M; Giubellino, P; Giudice, GF; Giunta, A; Gladilin, LK; Glukhov, S; Gluza, J; Gobbi, G; Goddard, B; Goertz, F; Golling, T; Goncalves, VP; Goncalves Netto, D; Gonçalo, R; Gonzalez Gomez, LA; Gorgi Zadeh, S; Gorine, G; Gorini, E; Gourlay, SA; Gouskos, L; Grancagnolo, F; Grassellino, A; Grau, A; Graverini, E; Gray, HM; Greco, M; Grenard, JL; Grimm, O; Grojean, C; Gromov, VA; Grosse-Oetringhaus, JF; Grudiev, A; Grzanka, K; Gu, J; Guadagnoli, D; Guidi, V; Guiducci, S; Guillermo Canton, G; Gunaydin, YO; Gupta, R; Gupta, RS; Gutierrez, J; Gutleber, J; Guyot, C; Guzey, V; Gwenlan, C; Haberstroh, C; Hacışahinoğlu, B; Haerer, B; Hahn, K; Hahn, T; Hammad, A; Han, C; Hance, M; Hannah, A; Harris, PC; Hati, C; Haug, S; Hauptman, J; Haurylavets, V; He, HJ; Hegglin, A; Hegner, B; Heinemann, K; Heinemeyer, S; Helsens, C; Henriques, A; Hernandez, P; Hernández-Pinto, RJ; Hernandez-Sanchez, J; Herzig, T; Hiekkanen, I; Hillert, W; Hoehn, T; Hofer, M; Höfle, W; Holdener, F; Holleis, S; Holzer, B; Hong, DK; Honorato, CG; Hopkins, SC; Hrdinka, J; Hug, F; Humann, B; Humer, H; Hurth, T; Hutton, A; Iacobucci, G; Ibarrola, N; Iconomidou-Fayard, L; Ilyina-Brunner, K; Incandela, J; Infantino, A; Ippolito, V; Ishino, M; Islam, R; Ita, H; Ivanovs, A; Iwamoto, S; Iyer, A; Izquierdo Bermudez, S; Jadach, S; Jamin, DO; Janot, P; Jarry, P; Jeff, A; Jenny, P; Jensen, E; Jensen, M; Jiang, X; Jimenez, JM; Jones, MA; Jones, OR; Jowett, JM; Jung, S; Kaabi, W; Kado, M; Kahle, K; Kalinovskaya, L; Kalinowski, J; Kamenik, JF; Kannike, K; Kara, SO; Karadeniz, H; Karaventzas, V; Karpov, I; Kartal, S; Karyukhin, A; Kashikhin, V; Katharina Behr, J; Kaya, U; Keintzel, J; Keinz, PA; Keppel, K; Kersevan, R; Kershaw, K; Khanpour, H; Khatibi, S; Khatiri Yanehsari, M; Khoze, VV; Kieseler, J; Kilic, A; Kilpinen, A; Kim, YK; Kim, DW; Klein, U; Klein, M; Kling, F; Klinkenberg, N; Klöppel, S; Klute, M; Klyukhin, VI; Knecht, M; Kniehl, B; Kocak, F; Koeberl, C; Kolano, AM; Kollegger, A; Kołodziej, K; Kolomiets, AA; Komppula, J; Koop, I; Koppenburg, P; Koratzinos, M; Kordiaczyńska, M; Korjik, M; Kortner, O; Kostka, P; Kotlarski, W; Kotnig, C; Köttig, T; Kotwal, AV; Kovalenko, AD; Kowalski, S; Kozaczuk, J; Kozlov, GA; Kozub, SS; Krainer, AM; Kramer, T; Krämer, M; Krammer, M; Krasnov, AA; Krauss, F; Kravalis, K; Kretzschmar, L; Kriske, RM; Kritscher, H; Krkotic, P; Kroha, H; Kucharczyk, M; Kuday, S; Kuendig, A; Kuhlmann, G; Kulesza, A; Kumar, M; Kusina, A; Kuttimalai, S; Kuze, M; Kwon, T; Lackner, F; Lackner, M; La Francesca, E; Laine, M; Lamanna, G; La Mendola, S; Lançon, E; Landsberg, G; Langacker, P; Lange, C; Langner, A; Lankford, AJ; Lansberg, JP; Lari, T; Laycock, PJ; Lebrun, P; Lechner, A; Lee, K; Lee, S; Lee, R; Lefevre, T; Le Guen, P; Lehtinen, T; Leith, SB; Lenzi, P; Leogrande, E; Leonidopoulos, C; Leon-Monzon, I; Lerner, G; Leroy, O; Lesiak, T; Lévai, P; Leveratto, A; Levichev, E; Li, G; Li, S; Li, R; Liberati, D; Liepe, M; Lissauer, DA; Liu, Z; Lobko, A; Locci, E; Logothetis Agaliotis, E; Lombardo, MP; Long, AJ; Lorin, C; Losito, R; Louzguiti, A; Low, I; Lucchesi, D; Lucchini, MT; Luciani, A; Lueckhof, M; Lunt, AJG; Luzum, M; Lyubimtsev, DA; Maggiora, M; Magnin, N; Mahmoud, MA; Mahmoudi, F; Maitre, J; Makarenko, V; Malagoli, A; Malcles, J; Malgeri, L; Mallon, PJ; Maltoni, F; Malvezzi, S; Malyshev, OB; Mancinelli, G; Mandrik, P; Manfrinetti, P; Mangano, M; Manil, P; Mannelli, M; Marchiori, G; Marhauser, F; Mariani, V; Marinozzi, V; Mariotto, S; Marquard, P; Marquet, C; Marriott-Dodington, T; Martin, R; Martin, O; Martin Camalich, J; Martinez, T; Martinez Bruzual, H; Martínez-Hernández, MI; Martins, DE; Marzani, S; Marzocca, D; Marzola, L; Masciocchi, S; Masina, I; Massimiliano, A; Massironi, A; Masubuchi, T; Matveev, VA; Mazzoni, MA; McCullough, M; McIntosh, PA; Meade, P; Medina, L; Meier, A; Meignan, J; Mele, B; Mendes Saraiva, JG; Menez, F; Mentink, M; Meoni, E; Meridiani, P; Merk, M; Mermod, P; Mertens, V; Mether, L; Métral, E; Migliorati, M; Milanese, A; Milardi, C; Milhano, G; Militsyn, BL; Millet, F; Minashvili, I; Minervini, JV; Miralles, LS; Mirarchi, D; Mishima, S; Missiaen, DP; Mitselmakher, G; Mitsuhashi, T; Mnich, J; Mohammadi Najafabadi, M; Mohapatra, RN; Mokhov, N; Molson, JG; Monge, R; Montag, C; Montagna, G; Monteil, S; Montenero, G; Montesinos, E; Moortgat, F; Morange, N; Morello, G; Moreno Llácer, M; Moretti, M; Moretti, S; Morley, AK; Moros, A; Morozov, I; Morretta, V; Morrone, M; Mostacci, A; Muanza, S; Muchnoi, N; Muhlegger, M; Mulder, M; Mulders, M; Müller, B; Müller, F; Müller, AS; Munilla, J; Murray, MJ; Muttoni, Y; Myers, S; Mylona, M; Nachtman, J; Nakamoto, T; Nardecchia, M; Nardini, Germano; Nason, P; Nergiz, Z; Nesterenko, AV; Nettstrater, A; 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Zivkovic, L; Zlobin, AV; Zobov, M; Zupan, J; Zurita, J (Journal article; Peer reviewed, 2019-06)
      In response to the 2013 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) study was launched, as an international collaboration hosted by CERN. This study covers a highest-luminosity ...