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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

MicroBooNE BNB Inclusive Overlay Sample (No Wire Info)

MicroBooNE samples are provided for collaborative development in two different formats: HDF5, targeting the broadest audience, and artroot, targeting users that are familiar with the software infrastructure of Fermilab neutrino experiments and more in general of HEP experiments. The HDF5 files are stored on Zenodo, together with a list of artroot files accessible with xrootd.This sample includes simulated interactions of neutrinos from the Booster Neutrino Beam (BNB), overlaid on top of cosmic ray data. The sample is inclusive, i.e. it includes all types of neutrinos and interactions, with relative abundance matching our nominal flux and cross section models. Interactions are simulated in in the whole cryostat volume.The HDF5 files in this sample do not include the information at the wire waveform level ("NoWire" label), allowing for larger number of events to be included in the data set.More documentation, including detailed description of content, recipes, and example usage, at https://github.com/uboone/OpenSamples.Suggested text for acknowledgment is the following:We acknowledge the MicroBooNE Collaboration for making publicly available the data sets [data set DOIs] employed in this work. These data sets consist of simulated neutrino interactions from the Booster Neutrino Beamline overlaid on top of cosmic data collected with the MicroBooNE detector [2017 JINST 12 P02017].In addition, we request that software products resulting from the usage of the datasets are also made publicly available.

Abratenko, Polina↗
DOE OSTI2022

MicroBooNE BNB Electron Neutrino Overlay Sample (With Wire Info)

MicroBooNE samples are provided for collaborative development in two different formats: HDF5, targeting the broadest audience, and artroot, targeting users that are familiar with the software infrastructure of Fermilab neutrino experiments and more in general of HEP experiments. The HDF5 files are stored on Zenodo, together with a list of artroot files accessible with xrootd.This sample includes simulated interactions of neutrinos from the Booster Neutrino Beam (BNB), overlaid on top of cosmic ray data. The sample is restricted to charged-current electron neutrino interactions within the argon active volume of the time projection chamber.The HDF5 files in this sample include the information at the wire waveform level (after deconvolution and finding of regions of interest). As this information significantly increases the file size, this sample contains about 20% of the events of the corresponding sample without wire information.More documentation, including detailed description of content, recipes, and example usage, at https://github.com/uboone/OpenSamples.Suggested text for acknowledgment is the following:We acknowledge the MicroBooNE Collaboration for making publicly available the data sets [data set DOIs] employed in this work. These data sets consist of simulated neutrino interactions from the Booster Neutrino Beamline overlaid on top of cosmic data collected with the MicroBooNE detector [2017 JINST 12 P02017].In addition, we request that software products resulting from the usage of the datasets are also made publicly available.

Abratenko, Polina↗
DOE OSTI2022

Searching for Clues for a Matter Dominated Universe in Liquid Argon Time Projection Chambers

Liquid Argon Time Projection Chambers (LArTPCs) represent one of the most widely utilized neutrino detection techniques in neutrino experiments, for instance, in the Short Baseline Neutrino (SBN) program and the future large-scale LArTPC: Deep Underground Neutrino Experiment (DUNE). The high-end technique, facilitating excellent spatial and calorimetric reconstruction resolution, also enables testing exotic Beyond Standard Model (BSM) theories, such as baryon number violation (BNV) processes (e.g., proton-decay, neutron-antineutron oscillation). At the same time, Machine Learning (ML) techniques have demonstrated their ubiquitous use in recent decades; ML techniques have also become some of the most powerful tools in high-energy physics (HEP) analyses. Furthermore, the development of algorithms to cater to the needs of problems in HEP (i.e., triggering, reconstruction, improving sensitivity, etc.) has also become an active area of research. By developing a combined approach using Convolutional Neural Network (CNN) and Boosted Decision Tree (BDT) techniques, the sensitivity of neutron-antineutron oscillation in DUNE is evaluated for a projected exposure of 400kton·years. Additionally, to meet the triggering requirement to select such rare events in DUNE, such a search is only supported with highly efficient self-triggering algorithms. An ML-based self-triggering scheme for large-scale LArTPCs, such as DUNE, is also developed with the intention of implementation on field-programmable gate arrays (FPGAs). The ML-based approach for searching for neutron-antineutron oscillation can be demonstrated and validated on the current LArTPC MicroBooNE. The analysis in MicroBooNE represents the first-ever search for neutron-antineutron oscillation in a LArTPC. DUNE's projected 90% C.L. sensitivity to the neutron antineutron oscillation lifetime is 6.45×10³² years, assuming 1.327×10³⁵ neutron·years, equivalent to 10 years of DUNE far detector exposure (400kton·years). For MicroBooNE, assuming 372 seconds of exposure (equivalent to 3.13×10³⁶ neutron·years), the 90% C.L. lifetime sensitivity is found at 3.07×10²⁵ yrs, after accounting for Monte-Carlo statistical uncertainty and systematic uncertainty from detector effects.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

MicroBooNE BNB Inclusive Overlay Sample (With Wire Info)

MicroBooNE samples are provided for collaborative development in two different formats: HDF5, targeting the broadest audience, and artroot, targeting users that are familiar with the software infrastructure of Fermilab neutrino experiments and more in general of HEP experiments. The HDF5 files are stored on Zenodo, together with a list of artroot files accessible with xrootd.This sample includes simulated interactions of neutrinos from the Booster Neutrino Beam (BNB), overlaid on top of cosmic ray data. The sample is inclusive, i.e. it includes all types of neutrinos and interactions, with relative abundance matching our nominal flux and cross section models. Interactions are simulated in in the whole cryostat volume.The HDF5 files in this sample include the information at the wire waveform level (after deconvolution and finding of regions of interest). As this information significantly increases the file size, this sample contains about 17% of the events of the corresponding sample without wire information.More documentation, including detailed description of content, recipes, and example usage, at https://github.com/uboone/OpenSamples.Suggested text for acknowledgment is the following:We acknowledge the MicroBooNE Collaboration for making publicly available the data sets [data set DOIs] employed in this work. These data sets consist of simulated neutrino interactions from the Booster Neutrino Beamline overlaid on top of cosmic data collected with the MicroBooNE detector [2017 JINST 12 P02017].In addition, we request that software products resulting from the usage of the datasets are also made publicly available.

Abratenko, Polina↗
DOE OSTI2025

FM4NPP: A Scaling Foundation Model for Nuclear and Particle Physics

Large language models have revolutionized artificial intelligence by enabling large, generalizable models trained through self-supervision. This paradigm has inspired the development of scientific foundation models (FMs). However, applying this capability to experimental particle physics is challenging due to the sparse, spatially distributed nature of detector data, which differs dramatically from natural language. This work addresses if an FM for particle physics can scale and generalize across diverse tasks. We introduce a new dataset with more than 11 million particle collision events and a suite of downstream tasks and labeled data for evaluation. We propose a novel self-supervised training method for detector data and demonstrate its neural scalability with models that feature up to 188 million parameters. With frozen weights and task-specific adapters, this FM consistently outperforms baseline models across all downstream tasks. The performance also exhibits robust data-efficient adaptation. Further analysis reveals that the representations extracted by the FM are task-agnostic but can be specialized via a single linear mapping for different downstream tasks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A Continuous Galactic Line Source of Axions: The Remarkable Case of 23 Na

Here, we argue that $^{23}$Na is a potentially significant source of galactic axions. For temperatures $\gtrsim 7 \times 10^8$K -- characteristic of carbon burning in the massive progenitors of supernovae and ONeMg white dwarfs -- the 440 keV first excited state of $^{23}$Na is thermally populated, with its repeated decays pumping stellar energy into escaping axions. Odd-A nuclear abundances are typically very low in high-temperature stellar environments (or absent entirely due to burn-up). $^{23}$Na is an exception: $\approx 0.1 M_\odot$ of the isotope is synthesized during carbon burning then maintained at $\approx 10^9$K for times ranging up to $6 \times 10^4$y. Using MESA simulations, a galactic model, and sampling over progenitor masses, locations, and evolutionary stages, we find a continuous flux at earth of $\langle ϕ_a \rangle \approx 22$/cm$^2$s for $g^\mathrm{eff}_{aNN} = 10^{-9}$. Some fraction of these axions convert to photons as they propagate through the galactic magnetic field, producing a distinctive 440 keV line $γ$ ray detectable by all-sky detectors like the Compton Spectrometer and Imager (COSI). Assuming a 1$μ$G galactic magnetic field and a sufficiently light axion mass, we find that COSI will be able to probe $| g_{aNN}^\mathrm{eff} g_{a γγ} | \gtrsim1.8 \times 10^{-22}$ GeV$^{-1}$ at $3σ$ after two years of surveying.

Dark matter↗
DOE OSTI2024

Discovering Elusive Dynamics Across Frontiers (Final Technical Report)

Profound puzzles, such as the nature of dark matter, the origins of the electroweak scale, the mechanism behind the small neutrino mass, and the strong CP problem, suggested new physics beyond the Standard Model and drove the particle physics program in search of the associated new particles. Despite extensive searches, conventional realizations of new physics have not yet provided conclusive evidence. This raised the serious possibility that new dynamics might be more elusive, perhaps due to a richer gauge and matter structure than previously considered. Notably, the existence of dark matter and advancements in understanding the naturalness problem urged exploration into sectors with complex gauge and matter structures. Through experiments like the LHC, DUNE, and small-scale experiments, the robust US HEP program played a critical role in pursuing these well-motivated but under-explored scenarios for new physics. I explored these physics opportunities in depth, focusing on novel searches and significant improvements in parameter space coverage. The elusive dynamics revealed rich information about the underlying theory and were essential in identifying observable opportunities. Understanding the observable consequences required a deep comprehension of the theory, which I also developed. The proposal included essential components aimed at coherently increasing our knowledge in well-motivated elusive dynamics models. Through research on high-quality axions, composite neutrinos, the Higgs boson as a portal to hidden strong dynamics, and new scalar potentials to generate alternative electroweak phase transitions, I focused on identifying new signatures and parameter regions in plausible elusive dynamics models. The exploration emphasized generic possibilities motivated by broad classes of elusive dynamics models. These signatures were not effectively probed previously due to various challenges such as triggering, background suppression, or experimental design. My research involved close interaction with experimental colleagues to overcome these difficulties, leveraging new theoretical and experimental possibilities. These efforts included identifying new observables such as timing information and substructure in calorimetries, new multiple-hit techniques, new scattering events, and new resonance searches in liquid argon detectors. This work created a positive feedback loop: theory and experimental work inspired each other, revealing new exciting opportunities that supported both programs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Atmospheric pion, kaon, and muon fluxes for sub-orbital experiments

Cosmic rays interacting with the Earth's atmosphere generate extensive air showers, which produce Cherenkov, fluorescence and radio emissions. These emissions are key signatures for detection by ground-based, sub-orbital, and satellite-based telescopes aiming to study high energy cosmic ray and neutrino events. However, detectors operating at ground and balloon altitudes are also exposed to a background of atmospheric charged particles, primarily pions, kaons, and muons, that can mimic or obscure the signals from astrophysical sources. In this work, we use coupled cascade equations to calculate the atmospheric pion, kaon and muon fluxes reaching detectors at various altitudes. Our analysis focuses on energies above 10 GeV, where the influence of the Earth's magnetic field on particle trajectories is minimal. We provide angular and energy-resolved flux estimates and discuss their relevance as background for extensive air shower detection. Furthermore, our results are potentially relevant for interpreting data from current and future balloon-borne experiments such as EUSO-SPB2 and for refining trigger and veto strategies in Cherenkov and fluorescence telescopes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Modeling of surface-state induced inter-electrode isolation of n -on- p devices in mixed-field and γ -irradiation environments

Position sensitive n-on-p silicon sensors will be utilized in the tracker and in the High Granularity Calorimeter (HGCAL) of the Compact Muon Solenoid (CMS) experiment at High Luminosity Large Hadron Collider (HL-LHC). The detrimental effect of the radiation-induced accumulation of positive net oxide charge on position resolution in n-on-p sensors has typically been countered by the application of isolation implants like p-stop or p-spray between n + -electrodes. In addition to the positively charged layer inside the oxide and close to the Si/SiO 2 -interface, surface damage introduced by ionizing radiation in SiO 2 -passivated silicon particle detectors includes the accumulation of trapped-oxide-charge and interface traps. A previous study of either n/γ (mixed field)- or γ-irradiated Metal-Oxide-Semiconductor (MOS) capacitors showed evidence of substantially higher introduction rates of acceptor- and donor-type deep interface traps (N it,acc/don ) in mixed-field environment. Here, in this work, an inter-pad and -strip resistance (or resistivity (ρ int )) simulation study of n-on-p sensors with and without p-stop isolation implants was conducted for both irradiation types. Higher levels of ρint showed correlation to higher densities of deep N it,acc/don , with the inter-pad isolation performance of the mixed-field irradiated sensors becoming independent of the presence of p-stop implant between the n + - electrodes up to about 100 kGy. The low introduction rates of deep N it,acc/don in γ-irradiated sensors resulted in high sensitivity of ρ int to the presence and peak doping of p-stop above the lowest dose of about 7 kGy in the study. As a consequence of the advantageous influence of radiation-induced accumulation of deep N it on the inter-electrode isolation, position sensitive n-on-p sensors without isolation implants may be considered for future HEP-experiments where the radiation is largely due to hadrons.

Akchurin, N. [Texas Tech Univ., Lubbock, TX (Unite↗
DOE OSTI2024

A method to observe field-region oxide charge and inter-electrode isolation from CV-characteristics of n-on-p devices

Abstract N-on-psilicon sensors will be utilized in the Compact Muon Solenoid (CMS) detector's tracker and High Granularity Calorimeter (HGCAL) in the High Luminosity upgrade of the Large Hadron Collider (HL-LHC). Among their several advantages in terms of radiation hardness over the traditionalp-on-nsensors in the extreme radiation environment of the HL-LHC are electron collection instead of holes and overlapping maxima of weighting and electric fields at the charge-collecting electrodes. The disadvantage of the multi-channel SiO 2 -passivatedn-on-psensors is the generation of an inversion layer under the Si/SiO 2 -interface by a positive interface-oxide-charge (N ox ) that at high densities can compromise the position resolution by creating a conduction channel between the electrodes. This issue is typically addressed by including additional isolnts (p-stp,p-spray) between n + -electrodes. Focusing on the guard-ring regions ofn-on-psensors where no isolation implants are applied between the electrodes, a capacitance-voltage (CV) characterization study of both 6-inch wafer test diodes and 8-inch HGCAL prototype and pre-series sensors showed a distinct threshold voltage (V th,iso ) in theCV-characteristics of a biased n + -electrode when its enclosing guard-ring was left floating. When reproduced by simulations, the measuredV th,iso was found to contain information on the field-regionN ox and indicate the threshold where the two electrodes become electrically isolated by the influence of the reverse bias voltage. Together with previous studies on the inter-electrode isolation of irradiatedn-on-psensors, the results indicate that position sensitiven-on-psensors without isolation implants may be feasible in future HEP experiments.

Instruments & Instrumentation↗
DOE OSTI2025

Measurement of the azimuthal anisotropy of charged particles in $\sqrt{s_{\mathrm{NN}}}=5.36$ TeV $^{16}$O$+^{16}$O and $^{20}$Ne$+^{20}$Ne collisions with the ATLAS detector

This paper presents the first measurements of the azimuthal anisotropy coefficients $v_{n}$, which quantify the $n^{\mathrm{th}}$-order Fourier modulation of charged-particle azimuthal distributions, for $n=2$-4 in $\sqrt{s_{\mathrm{NN}}}=5.36$ TeV $\mathrm{^{16}O}+\mathrm{^{16}O}$ and $\mathrm{^{20}Ne}+\mathrm{^{20}Ne}$ collisions recorded with the ATLAS detector at the Large Hadron Collider in 2025. The $v_{n}$ coefficients are measured as a function of transverse momentum ($p_{\mathrm{T}}$), collision centrality, and event multiplicity. They are extracted using two complementary methods: two-particle correlations with a template-fit subtraction of short-range non-flow contributions, and four-particle subevent cumulants, which intrinsically suppress non-flow effects and provide sensitivity to flow fluctuations. The results show a clear hierarchy $v_{2} > v_{3} > v_{4}$ and a non-monotonic dependence on $p_{\mathrm{T}}$, reaching a maximum around 2 GeV, consistent with trends observed in heavy-ion collisions. Detailed comparisons between the two collision systems reveal an enhanced $v_{2}$ in central $\mathrm{^{20}Ne}+\mathrm{^{20}Ne}$ collisions, consistent with theory expectations based on the predicted prolate deformation of neon nuclei, in contrast to the slightly tetrahedral structure predicted for oxygen. The four-particle cumulant results highlight strong event-by-event fluctuations and provide the greatest sensitivity to nuclear shape effects. These measurements can place new constraints on the initial geometry and the hydrodynamic response in light-ion collisions, offering valuable input for models of nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Hot QCD White Paper

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document.

FOS: Physical sciences↗
DOE OSTI2020

Liquid helium fluid dynamics studies. Final Technical Report

Future high energy physics accelerators depend on a number of advanced technologies to open the many doors of scientific discovery. Among these advanced technologies, superconducting magnets and superconducting radio frequency (SRF) cavities are the backbone of the accelerator and detector systems. But all these low temperature systems depend critically on successful and reliable operation of their supporting technologies, among which the liquid helium cooling system is of the utmost importance. To improve the quality of these systems both in terms of efficiency and reliability, a robust helium cryogenics research and development (R&D) effort is required. The proposed research to be conducted by the FSU cryogenics group aims to produce fundamental knowledge that meets this R&D need. The projects that we have completed over the past grant period at Florida State University consist of experimental research on liquid helium fluid dynamics and heat transfer problems relevant to the development of future superconducting particle physics accelerators. Liquid helium is the coolant used in all such facilities and in many of these facilities He II (the low temperature phase of liquid helium also known as superfluid helium) is preferred due to its outstanding heat transfer characteristics. The work consists of two main experimental studies that probe both fundamental as well as practical aspects of liquid helium cooling. The first is a broad and fundamental study of the heat and mass transfer processes that can occur during a sudden catastrophic loss of vacuum (SCLV) incident in a superconducting accelerator. SCLV refers to the remote but extremely critical accident scenario where atmospheric pressure air is allowed to flood into the insulating vacuum system and impinge on the liquid helium cooled surfaces in the accelerator. Safe performance and recovery from such accidents is essential to the reliable operation of superconducting accelerators. The dynamics of this process is quite complex and so our approach is to conduct a series of well-orchestrated experiments that probe the various physical phenomena that can occur during an SCLV event. The experiments are coupled with analytic and numerical analysis in an effort to develop a general understanding of the process and to assist with future accelerator design and development. The second activity is directed toward fundamental understanding of heat and mass transfer in He II, which is essential to the design of superconducting magnets and radio frequency cavities in accelerators. The work consists of flow visualization of the dynamics of He II using laser assisted techniques. Two complementary techniques are used to study the fundamentals of the turbulent state. The first technique uses neutrally buoyant solid hydrogen particles to probe the flow fields of the superfluid and normal fluid components. The other technique uses laser excited He2* molecules as tracers of the normal fluid motion within the He II. The activities also included an effort to use visualization techniques to locate transient hot spots in radio frequency superconducting cavities. Such work provides valuable information about the heat transfer process in He II and its impact on the performance of superconducting devices. The research effort at Florida State University is not directly in support of a specific high energy physics experiment or facility. Rather, the work is general and coordinated with HEP accelerator laboratories to provide valuable insight that can assist with future accelerator development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Interim report for the International Muon Collider Collaboration (IMCC)

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.

Accelerator Physics (physics.acc-ph)↗
DOE OSTI2025

Measurement of substructure-dependent suppression of large-radius jets with charged particles in Pb+Pb collisions with ATLAS

Measurements of jet substructure in Pb+Pb collisions provide key insights into the mechanism of jet quenching in the hot and dense QCD medium created in these collisions. This Letter presents a measurement of the suppression of large-radius jets with a radius parameter of $R = 1.0$ and its dependence on the jet substructure. The measurement uses 1.72 nb$^{-1}$ of Pb+Pb data and 255 pb$^{-1}$ of $pp$ data, both at $\sqrt{s_{_\mathrm{NN}}} = 5.02$ TeV, recorded with the ATLAS detector at the Large Hadron Collider. Large-radius jets are reconstructed by reclustering $R = 0.2$ calorimetric jets and are measured for transverse momentum above $200$ GeV. Jet substructure is evaluated using charged-particle tracks, and the overall level of jet suppression is quantified using the jet nuclear modification factor ($R_\mathrm{AA}$). The jet $R_\mathrm{AA}$ is measured as a function of jet $p_{\mathrm{T}}$, the charged $k_t$ splitting scale ($\sqrt{d_{12}}$), and the angular separation ($dR_{12}$) of two leading sub-jets. The jet $R_\mathrm{AA}$ gradually decreases with increasing $\sqrt{d_{12}}$, implying significantly stronger suppression of large-radius jets with larger $k_t$ splitting scale. The jet $R_\mathrm{AA}$ gradually decreases for $dR_{12}$ in the range $0.01{-}0.2$ and then remains consistent with a constant for $ΔR_{12} \gtrsim 0.2$. The observed significant dependence of jet suppression on the jet substructure will provide new insights into its role in the quenching process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Precision Measurement of Neutrino Oscillation Parameters with 10 Years of Data from the NOvA Experiment

This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass-splitting, $Δm^2_{32}= 2.431^{+0.036}_{-0.034} (-2.479^{+0.036}_{-0.036}) \times 10^{-3}$~eV$^2$ if the mass ordering is Normal (Inverted). In both orderings, a region close to maximal mixing with $\sin^2θ_{23}=0.55_{+0.06}^{-0.02}$ is preferred. The NOvA data show a mild preference for the Normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the Normal ordering is 2.4 times more probable than the Inverted ordering. When incorporating a 2D $Δm^2_{32}\textrm{--}\sin^2 2θ_{13}$ constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87\%).

FOS: Physical sciences↗