⚛️ high-energy experiments

A Bayesian approach to the long-baseline neutrino oscillation sensitivity of DUNE

This paper applies a Bayesian Markov Chain Monte Carlo approach to re-evaluate DUNE's long-baseline neutrino oscillation sensitivity using existing inputs, revealing enhanced octant sensitivity through post-hoc reactor constraints and presenting the first study of DUNE's sensitivity to the Jarlskog invariant.

Original authors: DUNE Collaboration, S. Abbaslu, F. Abd Alrahman, A. Abed Abud, R. Acciarri, M. A. Acero, M. R. Adames, G. Adamov, M. Adamowski, K. Adhikari, C. Adriano, K. Agudelo-Jaramillo, F. Akbar, F. Alemanno, N.DUNE Collaboration, S. Abbaslu, F. Abd Alrahman, A. Abed Abud, R. Acciarri, M. A. Acero, M. R. Adames, G. Adamov, M. Adamowski, K. Adhikari, C. Adriano, K. Agudelo-Jaramillo, F. Akbar, F. Alemanno, N. S. Alex, L. Aliaga Soplin, A. Alqaisi, O. Alterkait, A. Alton, R. Alvarez, T. Alves, A. Aman, H. Amar, R. M. Amarinei, P. Amedo, E. P. M. Amorim, D. A. Andrade, C. Andreopoulos, M. Andreotti, M. P. Andrews, M. Andriamirado, F. Andrianala, S. Andringa, S. Ansarifard, D. Antic, A. Antonakis, T. Araya-Santander, L. Arellano, E. Arrieta Diaz, M. A. Arroyave, M. Artero Pons, B. Aryal, J. Asaadi, M. Ascencio, A. Ashkenazi, L. Asquith, M. S. Athar, E. Atkin, A. Aurisano, V. Aushev, D. Autiero, M. B. Azam, F. Azfar, J. J. Back, Y. Bae, I. Bagaturia, L. Bagby, H. Bagdu, D. Baigarashev, S. Balasubramanian, A. Balboni, P. Baldi, W. Baldini, J. Baldonedo, B. Baller, B. Bambah, F. Barao, T. Barbera, D. Barbu, G. Barenboim, P. Barham Alzás, G. J. Barker, W. Barkhouse, E. Barlas Yucel, G. Barr, W. Barrett, D. Barrow, J. L. Barrow, A. Basharina-Freshville, A. Bashyal, V. Basque, M. Bassani, D. Basu, L. Bathe-Peters, J. B. R. Battat, F. Battisti, J. Bautista, F. Bay, J. L. L. Bazo Alba, J. F. Beacom, E. Bechetoille, A. Beever, B. Behera, E. Belchior, B. Bell, G. Bell, L. Bellantoni, G. Bellettini, V. Bellini, O. Beltramello, C. Benitez Montiel, D. Benjamin, A. Ben Porat, K. Benslama, F. Bento Neves, J. Berger, S. Berkman, J. Bernal, P. Bernardini, A. Bersani, E. Bertholet, E. Bertolini, S. Bertolucci, M. Betancourt, A. Betancur Rodríguez, Y. Bezawada, A. T. Bezerra, A. Bhat, V. Bhatnagar, M. Bhattacharjee, S. Bhattacharjee, M. Bhattacharya, S. Bhuller, B. Bhuyan, S. Biagi, J. Bian, K. Biery, B. Bilki, A. Binau, M. Bishai, A. Blake, A. Blanchet, F. D. 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Chalifour, A. Chappell, A. Chatterjee, B. Chauhan, C. Chavez Barajas, H. Chen, M. Chen, W. C. Chen, Y. Chen, Z. Chen, D. Cherdack, S. S. Chhibra, F. Chiapponi, R. Chirco, K. Cho, S. Choate, G. Choi, D. Chokheli, O. Chow, B. Chowdhury, D. Christian, E. Church, M. F. Cicala, M. Cicerchia, V. Cicero, P. Clarke, J. Cleeve, G. Cline, A. G. Cocco, J. Collazo, J. Collot, H. Combs, J. M. Conrad, L. Conti, T. Contreras, M. Convery, S. Copello, P. Cova, C. Cox, L. Cremonesi, J. I. Crespo-Anadón, M. Crisler, E. Cristaldo, J. Crnkovic, G. Crone, R. Cross, A. Cudd, C. Cuesta, Y. Cui, F. Curciarello, D. Cussans, O. Dalager, W. Dallaway, R. D'Amico, H. da Motta, Z. A. Dar, R. Darby, L. Da Silva Peres, Q. David, G. S. Davies, S. Davini, C. Davis, J. Dawson, M. P. Decowski, A. de Gouvêa, P. C. De Holanda, P. De Jong, P. Del Amo Sanchez, G. De Lauretis, A. Delbart, M. Delgado, A. Dell'Acqua, G. Delle Monache, N. Delmonte, G. De Matteis, J. R. T. de Mello Neto, A. P. A. De Mendonca, D. M. DeMuth, S. Dennis, C. Densham, P. Denton, G. W. Deptuch, V. De Romeri, J. P. Detje, K. Dhanmeher, R. Dharmapalan, M. Dias, A. Diaz, J. S. Díaz, F. Díaz, F. Di Capua, A. Di Domenico, S. Di Domizio, S. Di Falco, D. Di Ferdinando, L. Di Giulio, P. Ding, L. Di Noto, E. Diociaiuti, G. Di Sciascio, C. Distefano, R. Di Stefano, R. Diurba, M. Diwan, Z. Djurcic, S. Dolan, M. Dolce, M. J. Dolinski, D. Domenici, S. Donati, S. Doran, D. Douglas, F. Drielsma, D. J. Drobner, D. Duchesneau, K. Duffy, K. Dugas, P. Dunne, S. Durando, B. Dutta, D. A. Dwyer, A. S. Dyshkant, S. Dytman, M. Eads, S. Edayath, J. Eisch, S. Elias, J. Ellis, W. Emark, P. Englezos, A. Ereditato, D. T. Ergonul, T. Erjavec, C. O. Escobar, J. J. Evans, E. Ewart, A. C. Ezeribe, K. Fahey, A. Falcone, C. Fang, M. Fani', F. Fanomezana, D. Faragher, C. Farnese, Y. Farzan, J. Felix, Y. Feng, C. Ferrari, M. Ferreira da Silva, E. Fialova, L. Fields, P. Filip, A. Filkins, F. Filthaut, G. Fiorillo, M. Fiorini, N. F. Fiuza De Barros, A. Flather, S. Fogarty, W. Foreman, B. Fossing, J. Franc, K. Francis, D. Franco, J. Franklin, J. Freeman, A. Friedland, S. Fuess, I. K. Furic, K. Furman, A. P. Furmanski, R. Gaba, A. Gabrielli, A. M Gago, F. Galizzi, H. Gallagher, M. Galli, N. Gallice, V. Galymov, E. Gamberini, T. Gamble, R. Gan, R. Gandhi, S. Ganguly, F. Gao, S. Gao, A. Garcia, D. Garcia-Gamez, M. Á. García-Peris, V. Garcia Pol, F. Gardim, S. Gardiner, P. Gauzzi, S. Gent, A. C. Germer, A. Ghosh, A. Ghosh, T. Giammaria, D. Gibin, I. Gil-Botella, A. Gioiosa, S. Giovannella, A. K. Giri, D. Gnani, O. Gogota, S. Gollapinni, K. Gollwitzer, R. A. Gomes, L. S. Gomez Fajardo, C. Gonzalez, D. Gonzalez-Diaz, J. Gonzalez-Santome, M. C. Goodman, S. Goswami, C. Gotti, J. Goudeau, C. Grace, E. Gramellini, R. Gran, E. Granados, P. Granger, C. Grant, D. R. Gratieri, P. Green, S. Greenberg, W. C. Griffith, K. Grzelak, L. Gu, W. Gu, M. Guarise, R. Guenette, D. Guffanti, A. Guglielmi, F. Y. Guo, A. Gupta, V. Gupta, G. Gurung, D. Gutierrez, P. Guzowski, M. M. Guzzo, S. Gwon, A. Habig, R. Hafeji, L. Hagaman, A. Hahn, J. Hakenmüller, A. Hambardzumyan, T. Hamernik, P. Hamilton, M. Handley, F. Happacher, B. Harris, D. A. Harris, L. Harris, A. L. Hart, J. Hartnell, T. Hartnett, T. Hasegawa, C. M. Hasnip, K. Hassinin, R. Hatcher, S. Hawkins, J. Hays, M. He, A. Heavey, K. M. Heeger, A. Heindel, J. Heise, K. Heller, P. Hellmuth, L. Henderson, A. Hergenhan, J. Hernández, M. A. Hernandez Morquecho, K. Herner, V. Hewes, A. Higuera, K. Hildebrandt, A. Himmel, E. Hinkle, L. R. Hirsch, J. Ho, A. Holin, G. A. Horton-Smith, R. Hosokawa, T. Houdy, B. Howard, I. Hristova, M. S. Hronek, Y. Hua, J. Huang, R. G. Huang, X. Huang, Z. Hulcher, A. Hussain, N. Ilic, A. M. Iliescu, R. Illingworth, G. Ingratta, A. Ioannisian, M. Ismerio Oliveira, C. M. Jackson, A. Jacobi, V. Jain, C. James, E. James, R. James, S. Jana, W. Jang, B. Jargowsky, C. Jiang, J. Jiang, X. Jin, A. Jipa, J. H. Jo, A. M. Johnson, W. Johnson, C. Jollet, M. Joshi, N. 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Published 2026-08-06

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Original authors: DUNE Collaboration, S. Abbaslu, F. Abd Alrahman, A. Abed Abud, R. Acciarri, M. A. Acero, M. R. Adames, G. Adamov, M. Adamowski, K. Adhikari, C. Adriano, K. Agudelo-Jaramillo, F. Akbar, F. Alemanno, N. S. Alex, L. Aliaga Soplin, A. Alqaisi, O. Alterkait, A. Alton, R. Alvarez, T. Alves, A. Aman, H. Amar, R. M. Amarinei, P. Amedo, E. P. M. Amorim, D. A. Andrade, C. Andreopoulos, M. Andreotti, M. P. Andrews, M. Andriamirado, F. Andrianala, S. Andringa, S. Ansarifard, D. Antic, A. Antonakis, T. Araya-Santander, L. Arellano, E. Arrieta Diaz, M. A. Arroyave, M. Artero Pons, B. Aryal, J. Asaadi, M. Ascencio, A. Ashkenazi, L. Asquith, M. S. Athar, E. Atkin, A. Aurisano, V. Aushev, D. Autiero, M. B. Azam, F. Azfar, J. J. Back, Y. Bae, I. Bagaturia, L. Bagby, H. Bagdu, D. Baigarashev, S. Balasubramanian, A. Balboni, P. Baldi, W. Baldini, J. Baldonedo, B. Baller, B. Bambah, F. Barao, T. Barbera, D. Barbu, G. Barenboim, P. Barham Alzás, G. J. Barker, W. Barkhouse, E. Barlas Yucel, G. Barr, W. Barrett, D. Barrow, J. L. Barrow, A. Basharina-Freshville, A. Bashyal, V. Basque, M. Bassani, D. Basu, L. Bathe-Peters, J. B. R. Battat, F. Battisti, J. Bautista, F. Bay, J. L. L. Bazo Alba, J. F. Beacom, E. Bechetoille, A. Beever, B. Behera, E. Belchior, B. Bell, G. Bell, L. Bellantoni, G. Bellettini, V. Bellini, O. Beltramello, C. Benitez Montiel, D. Benjamin, A. Ben Porat, K. Benslama, F. Bento Neves, J. Berger, S. Berkman, J. Bernal, P. Bernardini, A. Bersani, E. Bertholet, E. Bertolini, S. Bertolucci, M. Betancourt, A. Betancur Rodríguez, Y. Bezawada, A. T. Bezerra, A. Bhat, V. Bhatnagar, M. Bhattacharjee, S. Bhattacharjee, M. Bhattacharya, S. Bhuller, B. Bhuyan, S. Biagi, J. Bian, K. Biery, B. Bilki, A. Binau, M. Bishai, A. Blake, A. Blanchet, F. D. Blaszczyk, G. C. Blazey, E. Blucher, A. Bodek, B. Bogart, J. Boissevain, T. Bolton, L. Bomben, M. Bonesini, C. Bonilla-Diaz, A. Booth, F. Boran, C. Borden, R. Borges Merlo, D. Borodulina, N. Bostan, G. Botogoske, B. Bottino, R. Bouet, J. Boza, B. Brahma, D. Brailsford, F. Bramati, A. Branca, A. Brandt, J. Bremer, S. J. Brice, S. Brickner, V. Brio, C. Brizzolari, C. Bromberg, J. Brooke, A. Bross, M. B. Brunetti, G. Buccino, N. Buchanan, H. Budd, J. Buergi, A. Bundock, D. Burgardt, S. Butchart, G. Caceres V., R. Calabrese, J. Calcutt, L. Calivers, S. Calvez, E. Calvo, A. Caminata, A. F. Camino, W. Campanelli, A. Campani, N. Canci, J. Capó, I. Caracas, D. Caratelli, G. Carini, M. F. Carneiro, P. Carniti, H. Carranza, N. Carrara, A. Carter, E. Casarejos, D. Casazza, J. F. Castaño Forero, F. A. Castaño, R. Castillo Fernandez, C. Castromonte, E. Catano-Mur, C. Cattadori, F. Cavalier, F. Cavanna, S. Centro, G. Cerati, C. Cerna, A. Cervelli, A. Cervera Villanueva, J. Chakrani, M. Chalifour, A. Chappell, A. Chatterjee, B. Chauhan, C. Chavez Barajas, H. Chen, M. Chen, W. C. Chen, Y. Chen, Z. Chen, D. Cherdack, S. S. Chhibra, F. Chiapponi, R. Chirco, K. Cho, S. Choate, G. Choi, D. Chokheli, O. Chow, B. Chowdhury, D. Christian, E. Church, M. F. Cicala, M. Cicerchia, V. Cicero, P. Clarke, J. Cleeve, G. Cline, A. G. Cocco, J. Collazo, J. Collot, H. Combs, J. M. Conrad, L. Conti, T. Contreras, M. Convery, S. Copello, P. Cova, C. Cox, L. Cremonesi, J. I. Crespo-Anadón, M. Crisler, E. Cristaldo, J. Crnkovic, G. Crone, R. Cross, A. Cudd, C. Cuesta, Y. Cui, F. Curciarello, D. Cussans, O. Dalager, W. Dallaway, R. D'Amico, H. da Motta, Z. A. Dar, R. Darby, L. Da Silva Peres, Q. David, G. S. Davies, S. Davini, C. Davis, J. Dawson, M. P. Decowski, A. de Gouvêa, P. C. De Holanda, P. De Jong, P. Del Amo Sanchez, G. De Lauretis, A. Delbart, M. Delgado, A. Dell'Acqua, G. Delle Monache, N. Delmonte, G. De Matteis, J. R. T. de Mello Neto, A. P. A. De Mendonca, D. M. DeMuth, S. Dennis, C. Densham, P. Denton, G. W. Deptuch, V. De Romeri, J. P. Detje, K. Dhanmeher, R. Dharmapalan, M. Dias, A. Diaz, J. S. Díaz, F. Díaz, F. Di Capua, A. Di Domenico, S. Di Domizio, S. Di Falco, D. Di Ferdinando, L. Di Giulio, P. Ding, L. Di Noto, E. Diociaiuti, G. Di Sciascio, C. Distefano, R. Di Stefano, R. Diurba, M. Diwan, Z. Djurcic, S. Dolan, M. Dolce, M. J. Dolinski, D. Domenici, S. Donati, S. Doran, D. Douglas, F. Drielsma, D. J. Drobner, D. Duchesneau, K. Duffy, K. Dugas, P. Dunne, S. Durando, B. Dutta, D. A. Dwyer, A. S. Dyshkant, S. Dytman, M. Eads, S. Edayath, J. Eisch, S. Elias, J. Ellis, W. Emark, P. Englezos, A. Ereditato, D. T. Ergonul, T. Erjavec, C. O. Escobar, J. J. Evans, E. Ewart, A. C. Ezeribe, K. Fahey, A. Falcone, C. Fang, M. Fani', F. Fanomezana, D. Faragher, C. Farnese, Y. Farzan, J. Felix, Y. Feng, C. Ferrari, M. Ferreira da Silva, E. Fialova, L. Fields, P. Filip, A. Filkins, F. Filthaut, G. Fiorillo, M. Fiorini, N. F. Fiuza De Barros, A. Flather, S. Fogarty, W. Foreman, B. Fossing, J. Franc, K. Francis, D. Franco, J. Franklin, J. Freeman, A. Friedland, S. Fuess, I. K. Furic, K. Furman, A. P. Furmanski, R. Gaba, A. Gabrielli, A. M Gago, F. Galizzi, H. Gallagher, M. Galli, N. Gallice, V. Galymov, E. Gamberini, T. Gamble, R. Gan, R. Gandhi, S. Ganguly, F. Gao, S. Gao, A. Garcia, D. Garcia-Gamez, M. Á. García-Peris, V. Garcia Pol, F. Gardim, S. Gardiner, P. Gauzzi, S. Gent, A. C. Germer, A. Ghosh, A. Ghosh, T. Giammaria, D. Gibin, I. Gil-Botella, A. Gioiosa, S. Giovannella, A. K. Giri, D. Gnani, O. Gogota, S. Gollapinni, K. Gollwitzer, R. A. Gomes, L. S. Gomez Fajardo, C. Gonzalez, D. Gonzalez-Diaz, J. Gonzalez-Santome, M. C. Goodman, S. Goswami, C. Gotti, J. Goudeau, C. Grace, E. Gramellini, R. Gran, E. Granados, P. Granger, C. Grant, D. R. Gratieri, P. Green, S. Greenberg, W. C. Griffith, K. Grzelak, L. Gu, W. Gu, M. Guarise, R. Guenette, D. Guffanti, A. Guglielmi, F. Y. Guo, A. Gupta, V. Gupta, G. Gurung, D. Gutierrez, P. Guzowski, M. M. Guzzo, S. Gwon, A. Habig, R. Hafeji, L. Hagaman, A. Hahn, J. Hakenmüller, A. Hambardzumyan, T. Hamernik, P. Hamilton, M. Handley, F. Happacher, B. Harris, D. A. Harris, L. Harris, A. L. Hart, J. 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Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Great Neutrino Hunt: A Cosmic Game of Hide-and-Seek

Imagine the universe is filled with invisible, ghostly messengers called neutrinos. These tiny particles are so shy that they can pass through a light-year of solid lead without bumping into a single atom. They zip through the Earth, through your body, and through the walls of your house trillions of times every second, completely undetected. For decades, scientists have been trying to catch these ghosts to understand a massive mystery: why does our universe exist at all?

The story begins with a strange trick these particles play. Neutrinos come in three "flavors"—electron, muon, and tau—but as they travel, they don't stay the same. They morph, or "oscillate," from one flavor into another. This shape-shifting is governed by a secret recipe called the "mixing angles" and a hidden clock called the "CP-violating phase." If these settings are just right, the universe might have created more matter than antimatter in the Big Bang, allowing stars, planets, and us to exist. If they are wrong, everything would have annihilated itself instantly. The Deep Underground Neutrino Experiment (DUNE) is a massive machine designed to catch these shape-shifters in action, measuring exactly how they change to solve the puzzle of our existence.

The Paper's Mission: A Bayesian Detective Story

This paper doesn't present new data from the DUNE experiment itself, because the experiment hasn't finished collecting its real-world clues yet. Instead, it acts like a master detective using a powerful new tool to simulate what will happen when the real data arrives. The authors used a statistical method called Bayesian inference (specifically a Markov Chain Monte Carlo, or MCMC, approach) to map out the "sensitivity" of DUNE. Think of this as running a million virtual simulations of the experiment to see how well it will be able to solve the mystery under different scenarios.

The paper's main finding is that this Bayesian approach is incredibly powerful for untangling the complex web of relationships between neutrino properties. In the past, scientists often looked at one variable at a time, like trying to solve a puzzle by looking at a single piece. This paper shows that by looking at the whole picture at once, they can see how the pieces fit together. For instance, they found a strong "dance" between two specific mixing angles, $\sin^2 \theta_{23}$ and $\sin^2 \theta_{13}$ . When you try to measure one, the other tries to hide, creating a confusing blur. The Bayesian method allows them to see the full, four-dimensional shape of this blur, showing exactly where the true values are likely to hide.

One of the most exciting discoveries in the paper is how much the experiment improves when it gets help from outside sources. The authors simulated what happens if DUNE combines its own data with precise measurements of $\theta_{13}$ from reactor experiments (short-baseline experiments that act like a "reference" for one part of the puzzle). They found that adding this external constraint is a game-changer. Without it, DUNE struggles to tell if a specific angle is in its "upper" or "lower" range (known as the octant). But with the reactor data, the simulation shows DUNE can reject the wrong answer with high confidence, potentially ruling out the incorrect octant at a significance level of $3\sigma$ (a very strong statistical signal) with a large amount of data (1000 kt-MW-yr).

The paper also introduces a brand-new way of looking at the data: the Jarlskog invariant ( $J$ ). While previous studies focused on the individual angles, $J$ is a single number that combines them all to measure the total amount of "CP violation" (the matter-antimatter asymmetry) in a way that doesn't depend on how you choose to label the angles. The authors simulated DUNE's ability to measure this and found that even with a moderate amount of data (200 kt-MW-yr), the experiment could likely rule out the idea that CP is conserved (where $J=0$ ) at the $3\sigma$ level if the true value of the phase is $-\pi/4$ . This means DUNE could prove that neutrinos are indeed the reason the universe has matter, rather than just antimatter.

The authors are careful to note that these are results from simulations, not final measurements. They used "Asimov datasets," which are perfect, idealized versions of the data the experiment hopes to collect, to test their methods. They explicitly rule out the idea that they have already solved the mystery; rather, they have built a robust, flexible map showing exactly how DUNE will solve it once the real data starts flowing. They also demonstrated that their method is flexible enough to easily add new constraints later, making it a superior tool for the long journey ahead. In short, this paper is a proof-of-concept that a new, more holistic way of thinking about the data will allow DUNE to see the neutrino's secrets with unprecedented clarity.

Technical Summary: A Bayesian Approach to the Long-Baseline Neutrino Oscillation Sensitivity of DUNE

Problem Statement
The Deep Underground Neutrino Experiment (DUNE) aims to perform a comprehensive study of neutrino mixing, specifically targeting the determination of the neutrino mass ordering, the measurement of charge-parity violation (CPV), and precision measurements of oscillation parameters ( $\delta_{CP}$ , $\theta_{13}$ , $\theta_{23}$ , $\Delta m^2_{32}$ ). While previous DUNE sensitivity studies utilized classical frequentist methods, these approaches can struggle with the complexity of high-dimensional parameter spaces, particularly regarding parameter correlations and degeneracies (e.g., between the $\theta_{23}$ octant and $\theta_{13}$ ). Furthermore, deriving sensitivity to derived, non-linear quantities like the Jarlskog invariant ( $J$ )—a parameterization-independent measure of CP violation—is computationally difficult within the frequentist framework. This paper addresses the need for a flexible statistical framework to evaluate DUNE's sensitivity, explore multidimensional correlations, and assess the impact of external constraints on posterior distributions.

Methodology
The authors employ a Bayesian statistical treatment using Markov Chain Monte Carlo (MCMC) sampling, specifically the Metropolis–Rosenbluth–Rosenbluth–Teller–Teller (MR2T2) algorithm, to extract posterior probability distributions for oscillation parameters.

Efficient Sampling: To address the computational cost of sampling complex, high-dimensional spaces, the authors utilize the Adaptive Metropolis (AM) algorithm. This method iteratively updates the proposal covariance matrix based on the steps taken in the chain. To further optimize efficiency, the tuning phase is performed on a 5% downsampled subset of Monte Carlo (MC) events, upweighted to match the predicted data rate, before reverting to the full sample for the final fit. This reduces computational costs by approximately 15x for tuning and 50x for sampling compared to manual covariance tuning.
Prior Reweighting: The framework allows for the post-hoc incorporation of external constraints (such as reactor measurements of $\theta_{13}$ ) without re-running the MCMC chains. This is achieved by reweighting existing samples by the ratio of the new prior to the old prior.
Analysis Framework: The study uses the MaCh3 framework to model the neutrino flux (G4LBNF), neutrino interactions (GENIE v2.12.10), and detector responses. Systematic uncertainties (flux, cross-section, detector) are implemented via binned response functions and covariance matrices. The analysis utilizes Asimov datasets generated from nominal MC predictions based on two distinct true parameter sets: the NuFIT 6.0 global fit (Normal Ordering, lower $\theta_{23}$ octant) and the T2K-NOvA joint analysis best-fit (Inverted Ordering, upper $\theta_{23}$ octant).
Exposures: Sensitivity is evaluated for two exposure benchmarks: 200 kt-MW-yr (representing 2 detector modules and a 1.2 MW beam) and 1000 kt-MW-yr (long-term reach).

Key Contributions

Four-Dimensional Posterior Distributions: The paper presents the first comprehensive 4D posterior probability distributions for DUNE, visualizing the full correlation structure between $\sin^2\theta_{23}$ , $\sin^2\theta_{13}$ , $\Delta m^2_{32}$ , and $\delta_{CP}$ . This highlights how marginalization effects in lower-dimensional projections can obscure the true parameter values.
Quantification of $\theta_{23}$ Octant Sensitivity: The study quantifies the sensitivity to the $\theta_{23}$ octant using Bayes factors. It demonstrates that applying an external Gaussian constraint on $\sin^2\theta_{13}$ (derived from reactor experiments) significantly suppresses the posterior probability of the "wrong" octant, particularly for the T2K-NOvA best-fit scenario.
First Study of Jarlskog Invariant Sensitivity: The paper presents the first sensitivity study of DUNE to the Jarlskog invariant ( $J$ ). By evaluating $J$ at each MCMC step, the authors derive posterior distributions for this parameterization-independent measure of CP violation without modifying the underlying fit.

Results

Parameter Correlations: At the 200 kt-MW-yr exposure, strong anti-correlations exist between $\sin^2\theta_{23}$ and $\sin^2\theta_{13}$ , and degeneracies prevent a definitive preference for the $\theta_{23}$ octant. The Highest Posterior Density (HPD) point in 1D projections for $\sin^2\theta_{13}$ does not align with the true value due to these marginalization effects, a discrepancy resolved only when viewing the full 2D posterior.
Exposure Impact: Increasing exposure to 1000 kt-MW-yr significantly lifts degeneracies across the 4D parameter space. The correlation between $\delta_{CP}$ and other parameters reduces, and the preference for the true octant strengthens, causing the HPD of the 1D $\sin^2\theta_{13}$ posterior to align with the true value.
Octant Sensitivity with Constraints: Without external constraints, the Bayes factor for the correct octant is low at 200 kt-MW-yr. However, applying the reactor $\theta_{13}$ constraint significantly increases the Bayes factor. For the T2K-NOvA best-fit scenario, this results in a rejection of the wrong octant at $>3\sigma$ significance at 1000 kt-MW-yr exposure.
Jarlskog Invariant ( $J$ ): For a true $\delta_{CP} = -\pi/4$ , the study finds that the region of CP conservation ( $J=0$ ) lies just outside the $3\sigma$ credible interval at 200 kt-MW-yr. At 1000 kt-MW-yr, the posterior width narrows significantly, and the distribution becomes insensitive to the choice of prior (uniform in $\delta_{CP}$ vs. $\sin\delta_{CP}$ ). The analysis reveals that DUNE primarily constrains the combined CP-violating amplitude rather than individual mixing angles in isolation.

Significance
The paper claims that the Bayesian framework offers a robust and flexible tool for characterizing the complete parameter space of neutrino oscillations, particularly in handling complex correlations and degeneracies that are difficult to visualize or quantify using frequentist methods. The ability to easily incorporate external constraints and derive posterior distributions for non-linear, derived quantities like the Jarlskog invariant represents a significant methodological advancement for the DUNE collaboration. The results underscore the critical role of external $\theta_{13}$ constraints in resolving the $\theta_{23}$ octant ambiguity and demonstrate DUNE's potential to provide a parameterization-independent measure of CP violation in the lepton sector.

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