This white paper provides a comprehensive review of our present understanding of experimental neutrino anomalies that remain unresolved, charting the progress achieved over the last decade at the experimental and phenomenological level, and sets the stage for future programmatic prospects in addressing those anomalies. It is purposed to serve as a guiding and motivational "encyclopedic" reference, with emphasis on needs and options for future exploration that may lead to the ultimate resolution of the anomalies. We see the main experimental, analysis, and theory-driven thrusts that will be essential to achieving this goal being: 1) Cover all anomaly sectors -- given the unresolved nature of all four canonical anomalies, it is imperative to support all pillars of a diverse experimental portfolio, source, reactor, decay-at-rest, decay-in-flight, and other methods/sources, to provide complementary probes of and increased precision for new physics explanations; 2) Pursue diverse signatures -- it is imperative that experiments make design and analysis choices that maximize sensitivity to as broad an array of these potential new physics signatures as possible; 3) Deepen theoretical engagement -- priority in the theory community should be placed on development of standard and beyond standard models relevant to all four short-baseline anomalies and the development of tools for efficient tests of these models with existing and future experimental datasets; 4) Openly share data -- Fluid communication between the experimental and theory communities will be required, which implies that both experimental data releases and theoretical calculations should be publicly available; and 5) Apply robust analysis techniques -- Appropriate statistical treatment is crucial to assess the compatibility of data sets within the context of any given model.

The main goal of the Baikal-GVD deep-sea neutrino telescope is to detect high-energy neutrinos of astrophysical origin by reconstructing muon tracks or showers of particles generated in interactions of neutrino with water. Since 2020, Baikal-GVD has been monitoring IceCube telescope alerts about detecting neutrinos with energies of more than 100 TeV. This work presents results from searching for matches between Baikal-GVD events and IceCube neutrino alerts from September 2020 to April 2022.

Baikal-GVD is a 1 km 3 scale neutrino telescope now under construction in Lake Baikal. The sensitive volume of the detector is currently around 0.5 km 3 . Muons form through the exchange of W-bosons in the interaction between muon- and partial tau-neutrinos near the telescope. The muons then propagate to great distances in the lake’s water. Reconstructing their trajectory allows us to obtain the most accurate estimate of the direction of neutrinos at telescopes of this type. Angular resolution can be as good as 0.5° for fairly long muon tracks. The current state of affairs in analyzing track events at the Baikal-GVD is discussed.

The main goal of the Baikal-GVD deep-sea neutrino telescope is to detect high-energy neutrinos of astrophysical origin by reconstruction of muon tracks or showers of particles generated in interactions of neutrino with water. Since September 2020, Baikal-GVD has been monitoring IceCube telescope alerts about detection of neutrinos with the energy over 100 TeV. When follow-up analysis is carried out in real time, the delay between an IceCube notification and Baikal-GVD analysis does not exceed three minutes. The fast follow-up is complemented by an offline search for coincidences in time intervals of ±1 and ±12 h with refinement of event’s reconstruction. In the absence of a coincidence or in a case of a single coincidence, the value of expected background is calculated and upper limits on the neutrino flux are set.

The current state of the Baksan Large Neutrino Telescope project is reviewed. Selected results are presented from the first stage of the project, a prototype detector with a liquid scintillator weighing 0.5 tons. Results from the second stage of the project, a prototype with a liquid scintillator having a mass of five tons, are described along with prospects for the project.

The status of the Baksan Large Neutrino Telescope project and some selective results of the first stage of the project, namely a prototype detector with a liquid scintillator mass of 0.5 tons are described. The results of the second stage of the project, a prototype with a liquid scintillator mass of 5 tons, and the prospects for the project are discussed.

The article reports on the current status of the Baksan Large Neutrino Telescope project and describes some selective results of the first stage of the project, a detector prototype with a liquid scintillator mass of 0.5 tons. The results of the second stage of the project, a prototype with liquid scintillator mass of 5 tons, and project prospects also presented.

Baikal-GVD is a 1 km3 – scale neutrino telescope being constructed in Lake Baikal. Presently the sensitive volume of the detector constitutes about 0.5 km3. Muons being produced in muon and partly tau-neutrino interactions in the vicinity of the telescope ongoing through the W-boson exchange propagate at large distances in Lake water. Reconstructed muon trajectory provides the most precise probe of the neutrino direction attainable at large-volume neutrino telescopes. Angular resolution can be as good as 0.5° for muon tracks of sufficient length. The status of the data analysis in the muon channel at the Baikal-GVD is discussed.

At the Baksan Neutrino Observatory deployed in the North Caucasus mountains, it is proposed to develop, at a depth corresponding to about 4700 mwe, a large-volume neutrino detector based on a liquid scintillator with a target mass of 10 kt. The main physics goals of the detector are low-energy neutrino physics, astrophysics and geophysics. The highest possible light yield is crucial for such detectors. To improve light yield and energy resolution in large-volume neutrino detectors, light concentrators are often mounted on photomultiplier tubes to increase the detection efficiency of optical photons from scintillation or Cherenkov light induced by charged particles. We present the results of recent R&D work aimed to develop light concentrators for the Baksan large-volume liquid scintillator neutrino detector.

Neutrino telescope Baikal-CVD is a deep-underwater Cherenkov detector of elementary particles of the 1-km3 scale, which has been developed beginning from 2016 in Lake Baikal. The telescope is assembled from separate blocks (clusters of optical modules), which makes it possible to perform scientific research even at early stages of its development. In the 2021 configuration, the detector contains eight clusters with 2304 optical modules in total and is the largest neutrino telescope in the Northern hemisphere. The design and main characteristics of the Baikal-GVD data acquisition system are described, the problems of deep-underwater engineering associated with the development of the detector are considered, and some physical results obtained on the facility are presented

The Baksan Experiment on Sterile Transitions (BEST) probes the gallium anomaly and its possible connections to oscillations between active and sterile neutrinos. Based on the Gallium-Germanium Neutrino Telescope (GGNT) technology of the SAGE experiment, BEST employs two zones of liquid Ga target to explore neutrino oscillations on the meter scale. Oscillations on this short scale could produce deficits in the $^{71}$Ge production rates within the two zones, as well as a possible rate difference between the zones. From July 5th to October 13th 2019, the two-zone target was exposed to a primarily monoenergetic, 3.4-MCi $^{51}$Cr neutrino source 10 times for a total of 20 independent $^{71}$Ge extractions from the two Ga targets. The $^{71}$Ge production rates from the neutrino source were measured from July 2019 to March 2020. At the end of these measurements, the counters were filled with $^{71}$Ge doped gas and calibrated during November 2020. In this paper, results from the BEST sterile neutrino oscillation experiment are presented in details. The ratio of the measured $^{71}$Ge production rates to the predicted rates for the inner and the outer target volumes are calculated from the known neutrino capture cross section. Comparable deficits in the measured ratios relative to predicted values are found for both zones, with the $4 \sigma$ deviations from unity consistent with the previously reported gallium anomaly. If interpreted in the context of neutrino oscillations, the deficits give best fit oscillation parameters of $\Delta m^2=3.3^{+\infty}_{-2.3}$ eV$^2$ and sin$^2 2\theta=0.42^{+0.15}_{-0.17}$, consistent with $\nu_e \rightarrow \nu_s$ oscillations governed by a surprisingly large mixing angle.

The Baksan Experiment on Sterile Transitions (BEST) was designed to investigate the deficit of electron neutrinos ν_{e} observed in previous gallium-based radiochemical measurements with high-intensity neutrino sources, commonly referred to as the "gallium anomaly," which could be interpreted as evidence for oscillations between ν_{e} and sterile neutrino (ν_{s}) states. A 3.414-MCi ^{51}Cr ν_{e} source was placed at the center of two nested Ga volumes and measurements were made of the production of ^{71}Ge through the charged current reaction, ^{71}Ga(ν_{e},e^{-})^{71}Ge, at two average distances. The measured production rates for the inner and the outer targets, respectively, are [54.9_{-2.4}^{+2.5}(stat)±1.4(syst)] and [55.6_{-2.6}^{+2.7}(stat)±1.4(syst)] atoms of ^{71}Ge/d. The ratio (R) of the measured rate of ^{71}Ge production at each distance to the expected rate from the known cross section and experimental efficiencies are R_{in}=0.79±0.05 and R_{out}=0.77±0.05. The ratio of the outer to the inner result is 0.97±0.07, which is consistent with unity within uncertainty. The rates at each distance were found to be similar, but 20%-24% lower than expected, thus reaffirming the anomaly. These results are consistent with ν_{e}→ν_{s} oscillations with a relatively large Δm^{2} (>0.5  eV^{2}) and mixing sin^{2}2θ (≈0.4).

At the Baksan Neutrino Observatory (Institute for Nuclear Research of the Russian Academy of Sciences, Moscow) deployed in the Caucasus mountains, it is proposed to create, at a depth corresponding to about 4700 mwe (meter water equivalent), a large-volume neutrino detector on the basis of a liquid scintillator with a target mass of 10 kt. This article describes the current state of the first stage of the project, namely a prototype detector with a scintillator mass of 0.5 t. The design of the detector, the equipment and methods used are described.

The detectors based on the liquid scintillator (LS) monitored by an array of photo-multiplier tubes (PMT) are often used in low energy experiments such as neutrino oscillation studies and search for dark matter. Detectors of this kind operate in an energy range spanning from hundreds of keV to a few GeV providing a few percent resolution at energies above 1 MeV and allowing to observe fine spectral features. This article gives a brief overview of relevant physical processes and introduces a new universal simulation tool LSMC (Liquid Scintillator Monte Carlo) for simulation of LS-based detectors equipped with PMT arrays. This tool is based on the Geant4 framework and provides supplementing functionality for ease of configuration and comprehensive output. The usage of LSMC is illustrated by modeling and optimization of a compact detector prototype currently being built at Baksan Neutrino Observatory.

A current status of the project of a large volume scintillation telescope at the Baksan neutrino observatory is presented. The main research activities of the BLVST are low-energy neutrino physics, astrophysics and geophysics. To detect geoneutrinos, large-scale new-generation scintillator detectors located at large depths in the regions with a low background level from nuclear reactors are required. The Baksan Neutrino Observatory is geographically located in one of these places. Recently resumed R&D activities are aimed at the creation of new-generation telescope with a target mass of 10 kt at a depth of 4800 m.w.e. A small scale prototype is already under construction.

The activity of the intense artificial neutrino source in the experiment BEST will be determined by measuring of the internal bremsstrahlung (IB) spectrum from 51Cr. The paper describes the measurements of the IB spectrum from unsealed point-like 51Cr source using spectrum recovery method, and the main sources of uncertainties are discussed.

A method of determining the activity of intensive distributed -sources on the measurement of the continuous spectrum of radiation, for example the internal bremsstrahlung, is developed. The recurrent formula for reconstructing of a continuous spectrum, registered in a Ge detector, at distorting it in the detector. The method of precise measurements of the spectrum of 51 Cr internal bremsstrahlung using two point sources of low activity is described.

The activity of the 51 Cr source in the BEST experiment searching for sterile neutrinos is planned to be determined by measuring the spectrum of internal bremsstrahlung. The measurements of activity and the spectrum of internal bremsstrahlung of point low-activity 51 Cr sources with Ge semiconductor detectors are discussed. The accuracy and errors of this measurement method are examined.

The energy deposition spectra of 37Ar and 71Ge in a miniature proportional counter are measured and compared in detail to the model response simulated with Geant4. A certain modification of the Geant4 code, making it possible to trace the deexcitation of atomic shells properly, is suggested. Modified Geant4 is able to reproduce a response of particle detectors in detail in the keV energy range. This feature is very important for the laboratory experiments that search for massive sterile neutrinos as well as for dark matter searches that employ direct detection of recoil nuclei. This work demonstrates the reliability of Geant4 simulation at low energies.

A technique for the measurement of activities of intense β sources by measuring the continuous gamma-radiation (internal bremsstrahlung) spectra is developed. A method for reconstructing the spectrum recorded by a germanium semiconductor detector is described. A method for the absolute measurement of the internal bremsstrahlung spectrum of 51Cr is presented.