Euclid preparation

LXXVIII. Full-shape modelling of two-point and three-point correlation functions in real space

¹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
² INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
⁴ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁵ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁶ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁸ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁹ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
¹⁰ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
¹¹ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
¹³ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
¹⁴ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
¹⁵ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
¹⁶ Technion Israel Institute of Technology, Israel
¹⁷ Aix-Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France
¹⁸ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
¹⁹ INFN Gruppo Collegato di Parma, Viale delle Scienze 7/A, 43124 Parma, Italy
²⁰ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
²¹ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
²² Laboratoire d’Annecy-le-Vieux de Physique Theorique, CNRS & Universite Savoie Mont Blanc, 9 Chemin de Bellevue, BP 110 Annecy-le-Vieux, 74941 ANNECY Cedex, France
²³ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2 Bologna, Italy
²⁴ INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, 23807 Merate, Italy
²⁵ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
²⁶ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
²⁷ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
²⁸ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²⁹ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
³⁰ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
³¹ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
³² INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
³³ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
³⁴ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
³⁵ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
³⁶ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
³⁷ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
³⁸ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
³⁹ INFN-Sezione di Roma, Piazzale Aldo Moro 2 – c/o Dipartimento di Fisica Edificio G. Marconi, 00185 Roma, Italy
⁴⁰ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁴¹ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
⁴² INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴³ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive Honolulu, HI 96822, USA
⁴⁴ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁵ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁴⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill Edinburgh EH9 3HJ, UK
⁴⁷ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁴⁸ ESAC/ESA, Camino Bajo del Castillo, s/n. Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁴⁹ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁵⁰ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁵¹ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁵² UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁵³ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8 Campo Grande, PT1749-016 Lisboa, Portugal
⁵⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁵⁵ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁵⁶ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
⁵⁷ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵⁸ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00100 Roma, Italy
⁵⁹ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁶⁰ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁶¹ School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue Bristol BS8 1TL, UK
⁶² INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁶³ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁶⁴ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁶⁵ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
⁶⁶ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive Pasadena, CA 91109, USA
⁶⁷ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁶⁸ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁶⁹ Cosmic Dawn Center (DAWN), Denmark
⁷⁰ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁷¹ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁷² Department of Physics and Astronomy, University College London, Gower Street London WC1E 6BT, UK
⁷³ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁷⁴ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁷⁵ Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
⁷⁶ Helsinki Institute of Physics, Gustaf Hällströmin katu 2 University of Helsinki Helsinki, Finland
⁷⁷ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁷⁸ SKA Observatory, Jodrell Bank Lower Withington Macclesfield, Cheshire SK11 9FT, UK
⁷⁹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁸⁰ University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
⁸¹ Department of Physics, Institute for Computational Cosmology, Durham University, South Road Durham DH1 3LE, UK
⁸² Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁸³ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
⁸⁴ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁸⁵ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸⁶ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁸⁷ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸⁸ Telespazio UK S.L. for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692 Madrid, Spain
⁸⁹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁹⁰ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁹¹ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁹² Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁹³ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁹⁴ Institute of Space Science, Str. Atomistilor nr. 409 Măgurele Ilfov 077125, Romania
⁹⁵ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006 Madrid, Spain
⁹⁶ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
⁹⁷ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁸ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁹⁹ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
¹⁰⁰ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008 Santiago, Chile
¹⁰¹ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
¹⁰² Satlantis, University Science Park, Sede Bld 48940 Leioa-Bilbao, Spain
¹⁰³ Department of Physics, Royal Holloway, University of London, TW20 0EX, UK
¹⁰⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹⁰⁵ Cosmic Dawn Center (DAWN)
¹⁰⁶ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁰⁷ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰⁸ Centre for Information Technology, University of Groningen, P.O. Box 11044, 9700 CA, Groningen, The Netherlands
¹⁰⁹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
¹¹⁰ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹¹¹ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹² Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹³ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹¹⁴ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
¹¹⁵ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire CS 34229, 06304 Nice cedex 4, France
¹¹⁶ Department of Physics, Oxford University, Keble Road Oxford, OX1 3RH, UK
¹¹⁷ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692 Madrid, Spain
¹¹⁸ Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
¹¹⁹ Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano CP-I93, 73100 Lecce, Italy
¹²⁰ INFN, Sezione di Lecce, Via per Arnesano CP-193, 73100 Lecce, Italy
¹²¹ INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica Via per Arnesano, 73100 Lecce, Italy
¹²² INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, and INFN-Sezione di Genova Via Dodecaneso 33, 16146 Genova, Italy
¹²³ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹²⁴ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹²⁵ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue Cleveland, OH 44106, USA
¹²⁶ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany
¹²⁷ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
¹²⁸ Departamento de Física Fundamental. Universidad de Salamanca, Plaza de la Merced s/n., 37008 Salamanca, Spain
¹²⁹ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹³⁰ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹³¹ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹³² Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹³³ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹³⁴ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹³⁵ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road Manchester, M13 9PL, UK
¹³⁶ California Institute of Technology, 1200 E California Blvd Pasadena, CA 91125, USA
¹³⁷ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹³⁸ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹³⁹ Instituto de Física de Cantabria, Edificio Juan Jordá Avenida de los Castros, 39005 Santander, Spain
¹⁴⁰ Observatorio Nacional, Rua General Jose Cristino 77-Bairro Imperial de Sao Cristovao Rio de Janeiro, 20921-400, Brazil
¹⁴¹ CEA Saclay, DFR/IRFU, Service d’Astrophysique Bat. 709, 91191 Gif-sur-Yvette, France
¹⁴² Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK
¹⁴³ Department of Computer Science, Aalto University, PO Box 15400 Espoo, FI-00 076, Finland
¹⁴⁴ Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna 38200, Spain. Departamento de Astrofísica de la Universidad de La Laguna Avda. Francisco Sanchez La Laguna, 38200, Spain
¹⁴⁵ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹⁴⁶ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹⁴⁷ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴⁸ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹⁴⁹ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹⁵⁰ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa
¹⁵¹ DAMTP, Centre for Mathematical Sciences, Wilberforce Road Cambridge, CB3 0WA, UK
¹⁵² Kavli Institute for Cosmology Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁵³ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁵⁴ Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road Durham, DH1 3LE, UK
¹⁵⁵ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
¹⁵⁶ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁵⁷ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm, SE-106 91, Sweden
¹⁵⁸ Astrophysics Group, Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK
¹⁵⁹ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53 Avenue des Martyrs, 38000 Grenoble, France
¹⁶⁰ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁶¹ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁶² Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁶³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
¹⁶⁴ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692 Madrid, Spain
¹⁶⁵ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 37 Uppsala, Sweden
¹⁶⁶ Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA, Leiden, The Netherlands
¹⁶⁷ Institute of Astronomy, University of Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁶⁸ Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, 59000 Lille, France
¹⁶⁹ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁷⁰ Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, FI-90014 Oulu, Finland
¹⁷¹ Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁷² Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

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Received: 30 June 2025
Accepted: 21 October 2025

Abstract

We investigated the accuracy and range of validity of the perturbative model for the two-point (2PCF) and three-point (3PCF) correlation functions in real space in view of the forthcoming analysis of the Euclid mission spectroscopic sample. We took advantage of clustering measurements from four snapshots of the Flagship I N-body simulations at z = {0.9,1.2,1.5,1.8}, which mimic the expected galaxy population in the ideal case, i.e. in the absence of observational effects such as purity and completeness. For the 3PCF we considered all available triangular configurations given a minimal separation (r_min). We first assessed the model performance by fixing the cosmological parameters and evaluating the goodness of fit provided by the perturbative bias expansion in the joint analysis of the two statistics, finding an overall agreement with the data down to separations of 20 h⁻¹ Mpc. Subsequently, we built on the state-of-the-art analysis and extended it to include the dependence on three cosmological parameters: the amplitude of scalar perturbations (A_s), the matter density (ω_cdm), and the Hubble parameter (h). To achieve this goal, we developed an emulator capable of generating fast and robust modelling predictions for the two summary statistics, which thus enables an efficient sampling of the joint likelihood function. We therefore present the first joint full-shape analysis of the real-space 2PCF and 3PCF, testing the consistency and constraining power of the perturbative model across both probes and assessing its performance in a combined likelihood framework. We explored possible systematic uncertainties induced by the perturbative model at small scales, finding an optimal scale cut of r_min = 30 h⁻¹ Mpc for the 3PCF when imposing an additional limitation on the nearly isosceles triangular configurations included in the data vector. This work is part of a series of papers in which we validate theoretical models for galaxy clustering measurements in preparation for the Euclid mission.