Fundamental Physics with High-Energy Cosmic Neutrinos

TL;DR

High-energy cosmic neutrinos offer a unique window into fundamental physics, enabling tests of new particles and interactions at scales unreachable by current laboratories through detailed measurements of their properties.

Contribution

This white paper outlines the potential of high-energy cosmic neutrinos to address key particle physics questions and guides future experimental efforts.

Findings

Neutrino observations can probe physics beyond the Standard Model.

Energy spectrum and flavor measurements are crucial for new physics searches.

Cosmic neutrinos can test fundamental interactions at extreme energies.

Abstract

High-energy cosmic neutrinos can reveal new fundamental particles and interactions, probing energy and distance scales far exceeding those accessible in the laboratory. This white paper describes the outstanding particle physics questions that high-energy cosmic neutrinos can address in the coming decade. A companion white paper discusses how the observation of cosmic neutrinos can address open questions in astrophysics. Tests of fundamental physics using high-energy cosmic neutrinos will be enabled by detailed measurements of their energy spectrum, arrival directions, flavor composition, and timing.

Full text

See cover_fundamental_physics.pdf

Abstract

\justify

High-energy cosmic neutrinos can reveal new fundamental particles and interactions, probing energy and distance scales far exceeding those accessible in the laboratory. This white paper describes the outstanding particle physics questions that high-energy cosmic neutrinos can address in the coming decade. A companion white paper discusses how the observation of cosmic neutrinos can address open questions in astrophysics. Tests of fundamental physics using high-energy cosmic neutrinos will be enabled by detailed measurements of their energy spectrum, arrival directions, flavor composition, and timing.

Endorsers

Kevork N. Abazajian1, Sanjib Kumar Agarwalla2, Juan Antonio Aguilar Sánchez3, Marco Ajello4, Roberto Aloisio5 6, Jaime Álvarez-Muñiz7, Rafael Alves Batista8, Hongjun An9, Karen Andeen10, Shin’ichiro Ando11, Gisela Anton12, Ignatios Antoniadis13 14, Katsuaki Asano15, Katie Auchettl16, Jan Auffenberg17, Hugo Ayala18, Xinhua Bai19, Gabriela Barenboim20, Vernon Barger21, Imre Bartos22, Steve W. Barwick1, John Beacom23, James J. Beatty23, Nicole F. Bell24, José Bellido25, Segev BenZvi26, Douglas R. Bergman27, José Bernabéu20, Elisa Bernardini28 29, Mario Bertaina30, Gianfranco Bertone11, Peter F. Bertone31, Francesca Bisconti32, Jonathan Biteau33, Erik Blaufuss34, Summer Blot29, Julien Bolmont35, Zeljka Bosnjak36, Olga Botner37, Federica Bradascio29, Esra Bulbul38, Alexander Burgman37, Francesco Cafagna39, Regina Caputo40, M. Carmen Carmona-Benitez18, Rossella Caruso41, Marco Casolino5, Karem Peñaló Castillo42, Silvia Celli43,

Andrew Chen44, Yaocheng Chen45, Talai Mohamed Cherif46, Nafis Rezwan Khan Chowdhury20, Eugene M. Chudnovsky47, Brian A. Clark23, Pablo Correa48, Doug F. Cowen18, Paschal Coyle49, Linda Cremonesi50, Jane Lixin Dai51, Basudeb Dasgupta52, André de Gouvêa53, Sijbrand de Jong55 56, Simon De Kockere48, João R. T. de Mello Neto54, Luiz de Viveiros18, Krijn D. de Vries48,

Valentin Decoene57, Peter B. Denton58, Tyce DeYoung59, Rebecca Diesing60, Markus Dittmer61, Caterina Doglioni62, Klaus Dolag63, Michele Doro28, Michael A. DuVernois21, Toshikazu Ebisuzaki64,

John Ellis65,

Rikard Enberg37, Ralph Engel66, Johannes Eser67, Arman Esmaili68, Ke Fang69, Jonathan L. Feng1, Gustavo Figueiredo70, George Filippatos67, Chad Finley71, Derek Fox18, Anna Franckowiak29, Elizabeth Friedman34, Toshihiro Fujii72, Daniele Gaggero73, Alberto M. Gago74, Thomas Gaisser75, Shan Gao29, Carlos García Canal76, Daniel García-Fernández29, Simone Garrappa29, Maria Vittoria Garzelli77 78, Graciela B. Gelmini79, Christian Glaser1, Allan Hallgren37, Jordan C. Hanson80, Andreas Haungs66, John W. Hewitt81, Jannik Hofestädt12, Kara Hoffman34, Benjamin Hokanson-Fasig21, Dan Hooper82 60, Shunsaku Horiuchi83, Feifei Huang84, Patrick Huber83, Tim Huege66, Kaeli Hughes60, Naoya Inoue85, Susumu Inoue64, Fabio Iocco86, Kunihito Ioka72, Clancy W. James87, Eleanor Judd88, Daniel Kabat47,

Fumiyoshi Kajino89, Takaaki Kajita15, Marc Kamionkowski90, Alexander Kappes61, Dimitra Karabali47, Timo Karg29, Teppei Katori91, Uli F. Katz12,

Norita Kawanaka72,

Azadeh Keivani92, John L. Kelley21, Myoungchul Kim93, Shigeo S. Kimura18, Spencer Klein94, Stefan Klepser29, David Koke61, Hermann Kolanoski95, Lutz Köpke96, Joachim Kopp96 97, Claudio Kopper59, Jason Koskinen16,

V. Alan Kostelecký98,

Dmitriy Kostunin29, Antoine Kouchner99, Ilya Kravchenko100, John Krizmanic101, Naoko Kurahashi Neilson102, Michael Kuss103, Evgeny Kuznetsov104, Ranjan Laha97, Uzair Abdul Latif105, John G. Learned106, Jean-Philippe Lenain13, Rebecca K. Leane107, Shirley Weishi Li108, Lu Lu93, Francesco Longo109, Andrew Ludwig60, Cecilia Lunardini110, Paolo Lipari111, James Madsen112, Keiichi Mase93, Manuela Mallamaci113, Karl Mannheim114, Danny Marfatia106, Raffaella Margutti53, Cristian Jesús Lozano Mariscal61, Szabolcs Marka92, Olivier Martineau-Huynh35, Oscar Martínez-Bravo115, Manuel Masip116, Nikolaos E. Mavromatos65, Arthur B. McDonald117, Frank McNally118, Olga Mena20, Kevin-Druis Merenda67, Philipp Mertsch17, Peter Mészáros18,

Matthew Mewes119,

Hisakazu Minakata15, Nestor Mirabal40, Lino Miramonti120, Omar G. Miranda121, Razmik Mirzoyan122, John W. Mitchell40, Irina Mocioiu18, Teresa Montaruli123, Maria Elena Monzani108, Roger Moore124, Shigehiro Nagataki64, Masayuki Nakahata15, Jiwoo Nam45, Kenny C. Y. Ng125, Ryan Nichol50, Valentin Niess126, David F. Nitz127, Samaya Nissanke11, Eric Nuss128, Eric Oberla60, Stefan Ohm29, Kouji Ohta72, Foteini Oikonomou129, Roopesh Ojha101 40, Nepomuk Otte130, Timothy A. D. Paglione47, Sandip Pakvasa106, Andrea Palladino29, Sergio Palomares-Ruiz20, Vasiliki Pavlidou131, Carlos Pérez de los Heros37, Christopher Persichilli1, Piergiorgio Picozza5 132, Zbigniew Plebaniak133, Vlad Popa134, Steven Prohira23, Bindu Rani40, Brian Flint Rauch135, Soebur Razzaque136,

Mary Hall Reno137, Elisa Resconi138, Marco Ricci5, Jarred M. Roberts139, Nicholas L. Rodd88 94,

Werner Rodejohann43,

Juan Rojo140, Carsten Rott141, Iftach Sadeh29, Benjamin R. Safdi142, Naoto Sakaki64,

David Saltzberg79,

Jordi Salvadó144, Dorothea Samtleben143, Marcos Santander145, Fred Sarazin67, Konstancja Satalecka29, Michael Schimp146, Olaf Scholten147, Harm Schoorlemmer43,

Sergio J. Sciutto76, Valentina Scotti148, David Seckel75, Pasquale D. Serpico149, Shashank Shalgar16, Jerry Shiao45,

Kenji Shinozaki30, Ian M. Shoemaker83, Günter Sigl150, Lorenzo Sironi92, Tracy R. Slatyer107, Radomir Smida60, Alexei Yu Smirnov43, Jorge F. Soriano47, Daniel Southall60, Glenn Spiczak112, Anatoly Spitkovsky151, Maurizio Spurio152, Juliana Stachurska29, Krzysztof Z. Stanek23, Floyd Stecker40, Christian Stegmann29, Robert Stein29, Anna M. Suliga16, Greg Sullivan34, Jacek Szabelski133,

Ignacio Taboada130,

Yoshiyuki Takizawa64, Mauro Taiuti153 154, Irene Tamborra16, Xerxes Tata106, Todd A. Thompson23, Charles Timmermans55 56, Kirsten Tollefson59, Diego F. Torres155, Jorge Torres23, Simona Toscano3, Delia Tosi21, Matías Tueros76, Sara Turriziani64, Elisabeth Unger37, Michael Unger66, Martin Unland Elorrieta61, José Wagner Furtado Valle20, Lawrence Wiencke67, Nick van Eijndhoven48, Jakob van Santen29, Arjen van Vliet29, Justin Vandenbroucke21, Gary S. Varner106, Tonia Venters40, Matthias Vereecken48, Alex Vilenkin156, Francesco L. Villante157, Aaron Vincent117, Martin Vollmann138, Philip von Doetinchem106, Alan A. Watson158, Eli Waxman125, Thomas Weiler159, Christoph Welling29, Nathan Whitehorn79, Dawn R. Williams145, Walter Winter29, Hubing Xiao113, Donglian Xu160, Tokonatsu Yamamoto89, Lili Yang161, Gaurang Yodh1, Shigeru Yoshida93, Tianlu Yuan21, Danilo Zavrtanik162, Arnulfo Zepeda121, Bing Zhang163, Hao Zhou164, Anne Zilles57, Stephan Zimmer165, Juan de Dios Zornoza20, Renata Zukanovich Funchal8,  and Juan Zúñiga20

*1University of California, Irvine  2**Institute of Physics, Bhubaneswar  3**Université Libre de Bruxelles  4**Clemson University  5**Istituto Nazional di Fisica Nucleare (INFN)  6**Gran Sasso Science Institute (GSSI)  7**Universidade de Santiago de Compostela  8**Universidade de São Paulo  9**Chungbuk National University  10**Marquette University  11**Universiteit van Amsterdam  12**Friedrich-Alexander-Universität Erlangen-Nürnberg  13**Sorbonne Université  14**Université de Berne  15**University of Tokyo  16**Niels Bohr Institute, University of Copenhagen  17**Rheinisch-Westfälische Technische Hochschule Aachen  18**Pennsylvania State University  19**South Dakota School of Mines and Technology  20**Institut de Física Corpuscular, Universitat de València  21**University of Wisconsin, Madison  22**University of Florida  23**The Ohio State University  24**University of Melbourne  25**University of Adelaide  26**University of Rochester  27**University of Utah  28**Università degli Studi di Padova  29**Deutsches Elektronen-Synchrotron (DESY) Zeuthen  30**Università degli Studi di Torino  31**NASA Marshall Space Flight Center  32**Istituto Nazional di Fisica Nucleare (INFN), Sezione di Torino  33**Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Université Paris-Saclay  34**University of Maryland, College Park  35**Institut National de Physique Nucléaire et de Physique des Particules (IN2P3)  36**University of Zagreb  37**Uppsala Universitet  38**Center for Astrophysics, Harvard & Smithsonian  39**Istituto Nazional di Fisica Nucleare (INFN), Sezione di Bari  40**NASA Goddard Space Flight Center  41**Università degli Studi di Catania  42**Florida State University  43**Max-Planck-Institut für Kernphysik, Heidelberg  44**University of the Witwatersrand  45**National Taiwan University  46**Badji Mokhtar University of Annaba  47**City University of New York  48**Vrije Universiteit Brussels  49**Centre de Physique des Particules de Marseille (CPPM)  50**University College London  51**The University of Hong Kong  52**Tata Institute of Fundamental Research, Mumbai (TIFR)  53**Northwestern University  54**Universidade Federal do Rio de Janeiro  55**Radboud Universiteit Nijmegen  56**Nikhef  57**Institut d’Astrophysique de Paris  58**Brookhaven National Laboratory  59**Michigan State University  60**University of Chicago  61**Westfälische Wilhelms-Universität Münster  62**Lunds Universitet  63**Ludwig-Maximilians-Universität München  64**RIKEN  65**King’s College London  66**Karlsruher Institut für Technologie  67**Colorado School of Mines  68**Pontificia Universidade Catolicá do Rio de Janeiro  69**Stanford University  70**Oklahoma State University  71**Stockholm Universitet  72**Kyoto University  73**Instituto de Física Teórica UAM-CSIC  74**Pontificia Universidad Católica del Perú  75**Bartol Research Institute, University of Delaware  76**Universidad Nacional de La Plata  77**Eberhard Karls Universität Tübingen  78**Università degli Studi di Firenze  79**University of California, Los Angeles  80**Whittier College  81**University of North Florida  82**Fermi National Accelerator Laboratory  83**Virginia Polytechnic Institute and State University  84**Institut Pluridisciplinaire Hubert Curien (IPHC)  85**Saitama University  86**International Center for Theoretical Physics – South American Institute for Fundamental Research  87**International Centre for Radio Astronomy Research, Curtin University  88**University of California, Berkeley  89**Konan University  90**Johns Hopkins University  91**Queen Mary University of London  92**Columbia University  93**Chiba University  94**Lawrence Berkeley National Laboratory  95**Humboldt-Universität zu Berlin  96**Johannes Gutenberg-Universität Mainz  97**CERN  98**Indiana University  99**Laboratoire AstroParticule et Cosmologie  100**University of Nebraska-Lincoln  101**University of Maryland, Baltimore County  102**Drexel University  103**Istituto Nazional di Fisica Nucleare (INFN), Sezione di Pisa  104**University of Alabama in Huntsville  105**University of Kansas  106**University of Hawaii, Manoa  107**Massachusetts Institute of Technology  108**SLAC National Accelerator Lab  109**Università degli Studi di Trieste  110**Arizona State University  111**Sapienza – Università di Roma  112**University of Wisconsin-River Falls  113**Istituto Nazional di Fisica Nucleare (INFN), Sezione di Padova  114**Julius-Maximilians-Universität Würzburg  115**Benemérita Universidad Autónoma de Puebla  116**Universidad de Granada  117**Queen’s University  118**Mercer University  119**California Polytechnic State University  120**Università degli Studi di Milano  121**Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav)  122**Max-Planck-Institut fur Physik, München  123**Université de Genève  124**University of Alberta  125**Weizmann Institute of Science  126**Université Clermont Auvergne  127**Michigan Technological University  128**Université de Montpellier  129**European Southern Observatory  130**Georgia Institute of Technology  131**University of Crete  132**Università degli Studi di Roma Tor Vergata  133**Naradowe Centrum Badań Jądrowych  134Institutul de \cbStiin\cbte Spa\cbtiale *  *135Washington University in St. Louis  136**University of Johannesburg  137**University of Iowa  138**Technische Universität München  139**University of California, San Diego  140**Vrije Universiteit Amsterdam  141**Sungkyunkwan University (SKKU)  142**University of Michigan, Ann Arbor  143**Universiteit Leiden  144**Universitat de Barcelona  145**University of Alabama  146**Bergische Universität Wuppertal  147**Rijksuniversiteit Groningen  148**Università degli Studi di Napoli Federico II  149**Université Grenoble Alpes, Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh)  150**Universität Hamburg  151**Princeton University  152**Università degli Studi di Bologna  153**Università degli Studi di Genova  154**Istituto Nazional di Fisica Nucleare (INFN), Sezione di Genova  155**Institute of Space Sciences (IEEC-CSIC)  156**Tufts University  157**Università degli Studi dell’Aquila  158**University of Leeds  159**Vanderbilt University  160**Tsung-Dao Lee Institute  161**Sun Yet-sen University  162**Univerza v Novi Gorici  163**University of Nevada, Las Vegas  164**Los Alamos National Laboratory  165**Leopold-Franzens-Universität Innsbruck *

High-Energy Cosmic Neutrinos

What are the fundamental particles and interactions of Nature? High-energy cosmic neutrinos are uniquely poised to explore them in an uncharted and otherwise unreachable energy and distance regime. They allow us to explore the cosmic and energy frontiers of particle physics, complementing current and future colliders that will explore the energy and intensity frontiers.

Despite the spectacular success of the Standard Model (SM) of particle physics, we know that it must be extended to account for at least the existence of neutrino mass, dark matter, and dark energy. A common feature of many theories beyond the Standard Model (BSM) is that their effects are more clearly apparent the higher the energy of the process, where new particles, interactions, and symmetries, undetectable at lower energies, could make themselves evident. Yet, particle colliders have failed to find clear evidence of BSM physics up to TeV energies, the highest reachable in the lab. To access particle interactions beyond the TeV scale, we must use particle beams made by natural cosmic accelerators. They produce the most energetic neutrinos, photons, and charged particles known, with energies orders of magnitude higher than in man-made colliders.

Cosmic neutrinos are especially fitting probes of fundamental physics beyond the TeV scale, as shown in Fig. 1. First, cosmic neutrinos reach higher energies than neutrinos made in the Sun, supernovae, the atmosphere of Earth, particle accelerators, and nuclear reactors. Further, they reach Earth with energies higher than that of gamma rays and likely as high as ultra-high-energy (UHE) cosmic rays. Second, because most cosmic neutrinos come from extragalactic sources located at cosmological distances, even tiny BSM effects could accumulate up to observable levels as neutrinos travel to Earth, having crossed essentially the observable Universe. And, third, because the propagation of neutrinos from the sources to the detectors is well understood and predicted by the SM, BSM effects could be more easily spotted than in charged particles.

Tests of fundamental physics using cosmic neutrinos are possible in spite of astrophysical and cosmological uncertainties. Yet this endeavor is not without challenges: the neutrino detection cross section is tiny and cosmic neutrino fluxes are expected to fall rapidly with neutrino energy. Nevertheless, we show below that these obstacles are either surmountable or can be planned for.

Open Questions: What Can High-Energy Cosmic Neutrinos Test?

Figure 1 shows the wide breadth of important open questions in fundamental physics that cosmic neutrinos can address [1, 2, 3]. They complement questions tackled by neutrinos of lower energies.

Cosmic neutrinos span a wide range in energy. In the TeV–PeV range, astrophysical neutrinos are regularly detected by IceCube [4, 5, 6, 7, 8, 9] from what are likely mainly extragalactic sources [10, 11, 12, 13, 14, 15, 16]. At the EeV scale, cosmogenic neutrinos, produced by UHE cosmic rays interacting with photon backgrounds through the GZK effect [17, 18], are predicted but have not yet been observed [19, 20, 21]. See Ref. [22] for a discussion of astrophysics enabled by observations of cosmic neutrinos.

How do neutrino cross sections behave at high energies? The neutrino-nucleon cross section in the TeV–PeV range was measured for the first time using astrophysical and atmospheric neutrinos [23, 24, 25], extending [26, 27, 28, 29, 30] measurements that used GeV neutrinos from accelerators [31, 32, 33]. Fig. 3 shows that the measurements agree with high-precision SM predictions [34]. Future measurements in the EeV range would probe BSM modifications of the cross section at center-of-momentum energies of 100 TeV [35, 36, 37, 38, 39, 40, 41, 3, 42, 43] and test the structure of nucleons [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54] more deeply than colliders [55, 56].

How do flavors mix at high energies? Experiments with neutrinos of up to TeV energies have confirmed that the different neutrino flavors, $\nu_{e}$, $\nu_{\mu}$, and $\nu_{\tau}$, mix and oscillate into each other as they propagate [33]. Figure 3 shows that, if high-energy cosmic neutrinos en route to Earth oscillate as expected, the predicted allowed region of the ratios of each flavor to the total flux is small, even after accounting for uncertainties in the parameters that drive the oscillations and in the neutrino production process [57]. However, at these energies and over cosmological propagation baselines [58], mixing is untested; BSM effects could affect oscillations, vastly expanding the allowed region of flavor ratios and making them sensitive probes of BSM [59, 60, 61, 62, 63, 57, 64, 65, 66, 67, 68].

What are the fundamental symmetries of Nature? Beyond the TeV scale, the symmetries of the SM may break or new ones may appear. The effects of breaking lepton-number conservation, or CPT and Lorentz invariance [69], cornerstones of the SM, are expected to grow with neutrino energy and affect multiple neutrino observables [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81]. Currently, the strongest constraints in neutrinos come from high-energy atmospheric neutrinos [82]; cosmic neutrinos could provide unprecedented sensitivity [83, 71, 84, 85, 86, 62, 73, 87, 88, 76, 78, 89, 90]. Further, detection of ZeV neutrinos, well beyond astrophysical expectations, would probe Grand Unified Theories [91, 92, 93, 94, 43].

Are neutrinos stable? Neutrinos are essentially stable in the SM [95, 96, 97], but BSM physics could introduce new channels for the heavier neutrinos to decay into the lighter ones [98, 99, 100], with shorter lifetimes. During propagation over cosmological baselines, neutrino decay could leave imprints on the energy spectrum and flavor composition [101, 102, 65, 103, 104]. The associated sensitivity outperforms existing limits obtained using neutrinos with shorter baselines [103]. Comparable sensitivities are expected for similar BSM models, like pseudo-Dirac neutrinos [105, 106, 65].

What is dark matter? Cosmic neutrinos can probe the nature of dark matter. Dark matter may decay or self-annihilate into neutrinos [107, 108, 109, 110], leaving imprints on the neutrino energy spectrum, e.g., line-like features. Searches for these features have yielded strong constraints on dark matter in the Milky Way [111, 112, 113] and nearby galaxies [114]. High-energy cosmic neutrinos can probe superheavy dark matter with PeV masses [115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127] and light dark matter [117, 128, 129, 126, 130]. Multi-messenger constraints are crucial to assess dark matter explanations of the observed neutrino spectrum [10, 131, 122, 129, 132]. Further, anisotropies in the neutrino sky towards the Galactic Center can reveal dark matter decaying [133] or interacting with neutrinos [134].

Are there hidden interactions with cosmic backgrounds? High-energy cosmic neutrinos may interact with low-energy relic neutrino backgrounds via new interactions [135, 136, 137, 138, 65, 139, 140], with large-scale distributions of matter via new forces [141], or with dark backgrounds [142], including dark energy [143, 144]. These interactions may mimic the existence of neutrino mass, affect the neutrino flavor composition, and induce anisotropies in the high-energy neutrino sky.

Neutrino Observables: What Do We Use to Probe Fundamental Physics?

To probe fundamental physics, we look at four neutrino observables, individually or together [149].

Energy spectrum: The spectrum of neutrinos depends on their production processes, but BSM effects could introduce identifiable features, e.g., peaks, troughs, and cut-offs. Present neutrino telescopes reconstruct the energy $E$ of detected events to within 0.1 in $\log_{10}(E/{\rm GeV})$ [150]. For TeV–PeV astrophysical neutrinos, the spectrum is predicted to be a featureless power law. IceCube data are consistent with that, but also with a broken power law [151, 152, 153, 154, 155, 156]. For EeV cosmogenic neutrinos, the spectrum has a different but predictable shape [157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176], so BSM effects, e.g., modifications of neutrino-nucleon cross sections [35, 36, 37, 38, 39, 40, 41, 3, 42, 43], may also be apparent.

Arrival directions: If the diffuse flux of cosmic neutrinos comes from an isotropic distribution of sources, then it should be isotropic itself. However, interactions with cosmic backgrounds might induce anisotropies. For instance, they could create a neutrino horizon, whereby high-energy neutrinos could only reach us from a few nearby sources [136, 137, 177]. Similarly, neutrino interactions with dark matter could introduce an anisotropy towards the Galactic Center [134]. Presently, the pointing resolution at neutrino telescopes is sub-degree for events initiated by $\nu_{\mu}$ — tracks — and of a few degrees for events initiated mainly by $\nu_{e}$ and $\nu_{\tau}$ — showers [150].

Flavor composition: At the neutrino sources, high-energy cosmic neutrinos are believed to be produced in the decay of pions, i.e., $\pi^{+}\to\mu^{+}\nu_{\mu}$ followed by $\mu^{+}\to e^{+}\nu_{e}\bar{\nu}_{\mu}$. This results in an initial flavor composition of $\left(\nu_{e}:\nu_{\mu}:\nu_{\tau}\right)=\left(1:2:0\right)$, adding $\nu$ and $\bar{\nu}$. Upon reaching Earth, oscillations have transformed this into nearly $\left(1:1:1\right)_{\oplus}$ [178]. The detection of $\nu_{\tau}$ is minimally required for testing this standard oscillation scenario [179, 180]. While there are variations on this canonical expectation [181, 182, 183], the expected flavor ratios fall within a well-defined region [57]. However, numerous BSM models active during propagation may modify this [63, 67], including neutrino decay and Lorentz invariance violation, as shown in Fig. 3. A precise measurement of the flavor composition could distinguish between these two classes of models [57]. Presently, measuring flavor at neutrino telescopes is challenging, since the showers made by $\nu_{e}$ and $\nu_{\tau}$ look similar [184, 154], which makes the contours of allowed flavor composition in Fig. 3 wide.

Timing: A violation of Lorentz invariance would modify the energy-momentum relation of neutrinos and photons [185, 186, 187], causing them to have different speeds at different energies. This would manifest in neutrinos [188, 189], photons [190, 191, 192, 193], and gravitational waves [194] emitted at the same time from transient sources arriving at Earth at different times. Presently, electronics in neutrino telescopes can timestamp events to within a few nanoseconds [195].

Today, the strength of the tests performed using these observables is limited at PeV energies, where data is scant, but event statistics are growing and there are ongoing efforts to improve the reconstruction of neutrino properties. Once neutrinos of higher energies are detected, the same observables can be used to test fundamental physics in a new energy regime.

Observatory Requirements to Achieve the Science Goals

Answering fundamental physics questions requires improving the precision with which neutrino observables are measured, which is currently limited by the low numbers of events. The statistics in the TeV–PeV energy range will grow using existing neutrino detectors and their planned upgrades. This will be supplemented by improved techniques to reconstruct neutrino energy, direction, and flavor. At the EeV scale, our ability to address fundamental physics questions is contingent on the discovery of neutrinos at these energies. In addition to emphasizing the importance of improved statistics, we highlight two measurements that can be improved in the coming decade: the neutrino cross section and flavor composition.

Presently, the measurement of the TeV–PeV neutrino cross section in multiple energy bins is sorely statistics-limited [24]. In this energy range, where the measured cross section is compatible with SM expectations, large BSM deviations are unlikely. But smaller deviations are still possible, especially close to PeV energies. To extract the cross section, Ref. [24] used about 60 shower events collected by IceCube in six years across all energies. A detector that is five times larger [196] would collect 300 showers in the same time, reducing the statistical error in the extracted cross sections by a factor of $\sqrt{6}/6\approx 0.4$ [197]. At that point, the statistical and systematic errors would become comparable, with a size of about 0.2 in the logarithm of the cross section (in units of cm2).

At the EeV scale, measuring the cross section to within an order of magnitude could distinguish between SM predictions and BSM modifications; see Fig. 3. This target is achievable with tens of events in the PeV–EeV energy range. Detection will be challenging, since the flux is expected to decrease fast with energy and the cross section is expected to grow with energy, making the Earth opaque to neutrinos. Facing significant uncertainties in the predicted flux of cosmogenic neutrinos [167, 169, 172, 173, 176], we advocate for the construction of larger neutrino observatories to boost the chances of discovering and collecting a sufficiently large number of cosmogenic neutrinos.

Flavor composition must be measured with a precision better than 40% to match the theoretical SM uncertainty band and identify BSM deviations, as shown in Fig. 3. Reaching this target at TeV–PeV energies requires supplementing the larger event statistics with the detection of flavor-specific signals [198, 58, 199]. With 20% precision, we could distinguish between models similar to neutrino decay or to Lorentz invariance violation. Improved statistics will also permit searches for a potential energy dependence of mixing, which could point to the presence of BSM effects [63, 57].

In the EeV range, we advocate exploring new methods to measure flavor in existing and upcoming experiments (e.g., Ref. [200]). Some planned EeV detectors will be sensitive primarily [201] to $\nu_{\tau}$[202, 203, 204, 205, 206, 207], while others will be sensitive to all flavors [208, 209, 196, 210, 211, 212], but might not be able to distinguish between them easily. Thus, we should consider combining data from the two types of experiments in order to infer at least the $\nu_{\tau}$ fraction.

Further, with the available sub-degree pointing resolution, we can begin to probe anisotropies in the neutrino sky that may result, e.g., from Lorentz-invariance violation [213] or BSM matter interactions [134]. Additionally, we can cull a set of neutrino events that are truly extragalactic, by using only those that point away from the Galactic Center, which allows us to make robust searches for BSM effects that are enhanced over cosmological distances (e.g., Ref. [103]).

We advocate for a strategy for the coming decade that improves precision on flavor identification and improves statistics across a broad energy scale, from 10 TeV up to the EeV scale. While this strategy targets mainly cross section and flavor measurements, it will impact other neutrino observables and relentlessly test the predictions of the SM and of many BSM scenarios.