Neutrino Oscillation Probabilities Research Articles

Efficient Neutrino Oscillation Parameter Inference with Gaussian Process

Many experiments have been set-up to measure the parameters governing the neutrino oscillation probabilities accurately, with implications for the fundamental structure of the universe. Very often, this involves inferences from tiny samples of data which have complicated dependencies on multiple oscillation parameters simultaneously. This is typically carried out using the unified approach of Feldman and Cousins which is very computationally expensive, on the order of tens of millions of CPU hours. In this work, we propose an iterative method using Gaussian Process to efficiently find a confidence contour for the oscillation parameters and show that it produces the same results at a fraction of the computation cost.

Neutrino oscillation probabilities through the looking glass

In this paper we review different expansions for neutrino oscillation probabilities in matter in the context of long-baseline neutrino experiments. We examine the accuracy and computational efficiency of different exact and approximate expressions. We find that many of the expressions used in the literature are not precise enough for the next generation of long-baseline experiments, but several of them are while maintaining comparable simplicity. The results of this paper can be used as guidance to both phenomenologists and experimentalists when implementing the various oscillation expressions into their analysis tools.

IceCube flavor ratios with identified astrophysical sources: towards improving new physics testability

Motivated by the discovery of the first high-energy astrophysical neutrino source, the blazar TXS 0506+056, we revisit the IceCube flavor ratio analysis. Assuming large statistics from identified blazars, collected in the forthcoming years by the IceCube detector and its successor IceCube-Gen2, we demonstrate that the constraints on several new physics scenarios in which the baseline dependent terms in neutrino oscillation probabilities are not averaged, can be improved. As a representative case, we consider pseudo-Dirac neutrinos while neutrino decay is also discussed.

Mixed states for mixing neutrinos

Here we discuss the description of flavor neutrinos produced or detected in processes which involve more than one neutrino. We show that in these cases flavor neutrinos cannot be separately described by pure states, but require a density matrix description. We consider explicitly the examples of $\nu_{e}$ and $\bar\nu_{\mu}$ production in $\mu^{+}$ decay and $\nu_{\mu}$ detection through scattering on electrons. We show that the density matrix which describes a flavor neutrino can be approximated with a density matrix of a pure state only when the differences of the neutrino masses are neglected in the interaction process. In this approximation, the pure states are the standard flavor states and one recovers the standard expression for the neutrino oscillation probability. We discuss also the effects of mixing of the three standard light neutrinos with heavy neutrinos which can be either decoupled because their masses are much larger than the maximum neutrino energy in the neutrino production process or because they are produced and detected incoherently. Finally, we discuss the more complicated case of neutrino-electron elastic scattering, in which the initial and final neutrinos do not have determined flavors, but there is a flavor dependence due to the different contributions of charged-current and neutral-current interactions.

Matter effect of light sterile neutrino: an exact analytical approach

The light sterile neutrino, if it exists, will give additional contribution to matter effect when active neutrinos propagate through terrestrial matter. In the simplest 3+1 scheme, three more rotation angles and two more CP-violating phases in lepton mixing matrix make the interaction complicated formally. In this work, the exact analytical expressions for active neutrino oscillation probabilities in terrestrial matter, including sterile neutrino contribution, are derived. It is pointed out that this set of formulas contain information both in matter and in vacuum, and can be easily tuned by choosing related parameters. Based on the generic exact formulas, we present oscillation probabilities of typic medium and long baseline experiments. Taking NOνA experiment as an example, we show that in particular parameter space sterile neutrino gives important contribution to terrestrial matter effect, and Dirac phases play a vital role.

Tomography by neutrino pair beam

We consider tomography of the Earth's interior using the neutrino pair beam which has recently been proposed. The beam produces a large amount of neutrino and antineutrino pairs from the circulating partially stripped ions and provides the possibility to measure precisely the energy spectrum of neutrino oscillation probability together with a sufficiently large detector. It is shown that the pair beam gives a better sensitivity to probe the Earth's crust compared with the neutrino sources at present. In addition we present a method to reconstruct a matter density profile by means of the analytic formula of the oscillation probability in which the matter effect is included perturbatively to the second order.

Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter

We further develop a simple and compact technique for calculating the three flavor neutrino oscillation probabilities in uniform matter density. By performing additional rotations instead of implementing a perturbative expansion we significantly decrease the scale of the perturbing Hamiltonian and therefore improve the accuracy of zeroth order. We explore the relationship between implementing additional rotations and that of performing a perturbative expansion. Based on our analysis, independent of the size of the matter potential, we find that the first order perturbation expansion can be replaced by two additional rotations and a second order perturbative expansion can be replaced by one more rotation. Numerical tests have been applied and all the exceptional features of our analysis have been verified.

Massively parallel computation of atmospheric neutrino oscillations on CUDA-enabled accelerators

The computation of neutrino flavor transition amplitudes through inhomogeneous matter is a time-consuming step and thus could benefit from optimization and parallelization. Next to reliable parameter estimation of intrinsic physical quantities such as neutrino masses and mixing angles, these transition amplitudes are important in hypothesis testing of potential extensions of the standard model of elementary particle physics, such as additional neutrino flavors. Hence, fast yet precise implementations are of high importance to research. In the recent past, massively parallel accelerators such as CUDA-enabled GPUs featuring thousands of compute units have been widely adopted due to their superior memory bandwidth, vast compute capability, and highly competitive compute-to-energy ratio in comparison to traditional multi-core architectures with a few tens of monolithic cores. In this paper, we introduce two scalable multi-GPU extensions of common neutrino oscillation frameworks – namely Prob3++ and νSQuIDS –allowing for the acceleration of oscillation dynamics computation by one to three orders-of-magnitude while preserving numerical accuracy. Our software is licensed under LGPLv3 and can be accessed at https://github.com/fkallen/CUDAProb3 and https://github.com/fkallen/CUDAnuSQuIDS. Program summaryProgram Title: CUDAProb3++ and CUDAνSQuIDSProgram Files doi:http://dx.doi.org/10.17632/j54yymmg5h.1Licensing provisions: LGPLv3Programming language: CUDA, C and C++Nature of problem: Fast computation of neutrino oscillation probabilities in inhomogeneous matter using constant-coefficient or variable-coefficient ODE solvers.Solution method: Solving ordinary differential equations on CUDA-enabled GPUs.

Neutrino oscillations and Lorentz invariance violation in a Finslerian geometrical model

Neutrino oscillations are one of the first evidences of physics beyond the Standard Model (SM). Since Lorentz invariance is a SM fundamental symmetry, recently also neutrino physics has been explored to verify this symmetry eventual modification and its potential magnitude. In this work we study the Lorentz invariance violation (LIV) introduction consequences in the high energy neutrinos propagation and evaluate the impact of this eventual violation on the oscillations predictions. An effective theory explaining these physical effects is introduced via modified dispersion relations. This approach, originally introduced by Coleman and Glashow, corresponds in our model to a special relativity geometry modification. Moreover, this perspective generalization leads to the introduction of a maximum attainable velocity which is specific of the particle. This can be formalized in Finsler geometry, a more general theory of space-time. In the present paper the impact of this kind of LIV on neutrino phenomenology is studied, in particular by analyzing the corrections introduced in neutrino oscillation probabilities for different values of neutrino energies and baselines of experimental interest. The possibility of further improving the present constraints on CPT-even LIV coefficients by means of our analysis is also discussed.

Matter density profile shape effects at DUNE

Quantum mechanical interactions between neutrinos and matter along the path of propagation, the Wolfenstein matter effect, are of particular importance for the upcoming long-baseline neutrino oscillation experiments, specifically the Deep Underground Neutrino Experiment (DUNE). Here, we explore specifically what about the matter density profile can be measured by DUNE, considering both the shape and normalization of the profile between the neutrinos' origin and detection. Additionally, we explore the capability of a perturbative method for calculating neutrino oscillation probabilities and whether this method is suitable for DUNE. We also briefly quantitatively explore the ability of DUNE to measure the Earth's matter density, and the impact of performing this measurement on measuring standard neutrino oscillation parameters.

Effects of Leptonic Nonunitarity on Lepton Flavor Violation, Neutrino Oscillation, Leptogenesis, and Lightest Neutrino Mass

Neutrino physics is a mature branch of science with all the three neutrino mixing angles and two mass squared differences determined with high precision. In spite of several experimental verifications of neutrino oscillations and precise measurements of two mass squared differences and the three mixing angles, the unitarity of the leptonic mixing matrix is not yet established, leaving room for the presence of small nonunitarity effects. Deriving the bounds on these nonunitarity parameters from existing experimental constraints, on cLFV decays such as μ→eγ, μ→τγ, and τ→eγ, we study their effects on the generation of baryon asymmetry through leptogenesis and neutrino oscillation probabilities. We consider a model where see-saw is extended by an additional singlet S which is very light but can give rise to nonunitarity effects without affecting the form on see-saw formula. We do a parameter scan of a minimal see-saw model in a type I see-saw framework satisfying the Planck data on baryon to photon ratio of the Universe, which lies in the interval 5.8×10-10<YB<6.6×10-10(BBN). We predict values of lightest neutrino mass and Dirac and Majorana CP-violating phases δCP, α, and β, for normal hierarchy and inverted hierarchy for one-flavor leptogenesis. It is worth mentioning that all these four quantities are unknown yet, and future experiments will be measuring them.

Revisiting quantum decoherence for neutrino oscillations in matter with constant density

We re-examine the matter neutrino oscillation probabilities considering the decoherence phenomenon as a sub-leading effect. In this paper we point out the relevance of having the correct interpretation of the decoherence matrix in the different quantum bases, within the framework of neutrino oscillation probabilities in matter. Based on this treatment we develop an analytical formula for matter neutrino oscillation probabilities for three generations, with a range of application up to the decoherence parameter $\Gamma \sim 10^{-23}$ GeV. We observe that, due to decoherence, the amplitudes of the neutrino/antineutrino oscillation probabilities increase in an energy independent way. We also find that decoherence can reduce the absolute value of the CP asymmetry, relative to its value at the pure oscillation case. As a side effect we have found a degeneracy between the decoherence parameter $\Gamma$ and the CP violation phase $\delta$.

Fuzzy dark matter and nonstandard neutrino interactions

We discuss novel ways in which neutrino oscillation experiments can probe dark matter. In particular, we focus on interactions between neutrinos and ultra-light ("fuzzy") dark matter particles with masses of order $10^{-22}$ eV. It has been shown previously that such dark matter candidates are phenomenologically successful and might help ameliorate the tension between predicted and observed small scale structures in the Universe. We argue that coherent forward scattering of neutrinos on fuzzy dark matter particles can significantly alter neutrino oscillation probabilities. These effects could be observable in current and future experiments. We set new limits on fuzzy dark matter interacting with neutrinos using T2K and solar neutrino data, and we estimate the sensitivity of reactor neutrino experiments and of future long-baseline accelerator experiments. These results are based on detailed simulations in GLoBES. We allow the dark matter particle to be either a scalar or a vector boson. In the latter case, we find potentially interesting connections to models addressing various $B$ physics anomalies.

Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle and the exchange of first two neutrino masses , if the standard parametrization of lepton flavor mixing matrix is adopted. To maintain this symmetry in perturbative calculations, we present a symmetric formulation of the effective Hamiltonian by introducing an η-gauge neutrino mass-squared difference for , where for , and show that only , or is allowed. Furthermore, we prove that is the best choice to derive more accurate and compact neutrino oscillation probabilities, by implementing the approach of renromalization-group equations. The validity of this approach becomes transparent when an analogy is made between the parameter η herein and the renormalization scale μ in relativistic quantum field theories.

Constraints on large extra dimensions from the MINOS experiment

We report new constraints on the size of large extra dimensions from data collected by the MINOS experiment between 2005 and 2012. Our analysis employs a model in which sterile neutrinos arise as Kaluza-Klein states in large extra dimensions and thus modify the neutrino oscillation probabilities due to mixing between active and sterile neutrino states. Using Fermilab's NuMI beam exposure of $10.56 \times 10^{20}$ protons-on-target, we combine muon neutrino charged current and neutral current data sets from the Near and Far Detectors and observe no evidence for deviations from standard three-flavor neutrino oscillations. The ratios of reconstructed energy spectra in the two detectors constrain the size of large extra dimensions to be smaller than $0.45\,\mu\text{m}$ at 90% C.L. in the limit of a vanishing lightest active neutrino mass. Stronger limits are obtained for non-vanishing masses.

Looking into analytical approximations for three-flavor neutrino oscillation probabilities in matter

Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the $\eta$-gauge neutrino mass-squared difference $\Delta^{}_* \equiv \eta \Delta^{}_{31} + (1-\eta) \Delta^{}_{32}$ is introduced, where $\Delta^{}_{ji} \equiv m^2_j - m^2_i$ for $ji = 21, 31, 32$ are the ordinary neutrino mass-squared differences and $0 \leq \eta \leq 1$ is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of $\alpha \equiv \Delta^{}_{21}/\Delta^{}_*$, we demonstrate that the analytical formulas can be remarkably simplified for $\eta = \cos^2 \theta^{}_{12}$, with $\theta_{12}^{}$ being the solar mixing angle. As a by-product, the mapping from neutrino oscillation parameters in vacuum to their counterparts in matter is obtained at the order of ${\cal O}(\alpha^2)$. Finally, we show that our approximate formulas are not only valid for an arbitrary neutrino energy and any baseline length, but also still maintaining a high level of accuracy.

Studying the physics potential of long-baseline experiments in terms of new sensitivity parameters

We investigate physics opportunities to constraint leptonic CP-violation phase $\delta_{CP}$ through numerical analysis of working neutrino oscillation probability parameters, in the context of long base line experiments. Numerical analysis of two parameters, the transition probability $\delta_{CP}$ phase sensitivity parameter ($A^M$) and CP-violation probability $\delta_{CP}$ phase sensitivity parameter ($A^{CP}$) , as function of beam energy and/or base line has been preferably carried out. It is an elegant technique to broadly analyze different experiments to constraint $\delta_{CP}$ phase and also to investigate mass hierarchy in the leptonic sector. The positive and negative values of parameter $A^{CP}$ corresponding to either of hierarchy in the specific beam energy ranges, could be a very promising way to explore mass hierarchy and $\delta_{CP}$ phase. The keys to more robust bounds on $\delta_{CP}$ phase are improvements of the involved detection techniques to explore bit low energy and relatively long base line regions with better experimental accuracy.

Large extra dimensions at the Deep Underground Neutrino Experiment

We investigate the potential of the long-baseline Deep Underground Neutrino Experiment (DUNE) to study large-extra-dimension (LED) models originally proposed to explain the smallness of neutrino masses by postulating that right-handed neutrinos, unlike all standard model fermion fields, can propagate in the bulk. The massive Kaluza-Klein (KK) modes of the right-handed neutrino fields modify the neutrino oscillation probabilities and can hence affect their propagation. We show that, as far as DUNE is concerned, the LED model is indistinguishable from a $(3 + 3N)$-neutrino framework for modest values of $N$; $N$ = 1 is usually a very good approximation. Nonetheless, there are no new sources of $CP$-invariance violation other than one $CP$-odd phase that can be easily mapped onto the $CP$-odd phase in the standard three-neutrino paradigm. We analyze the sensitivity of DUNE to the LED framework, and explore the capability of DUNE to differentiate the LED model from the three-neutrino scenario and from a generic $(3 + 1)$-neutrino model.

Neutrino experiments: Hierarchy, CP, CPT

We present an overview of our recent investigations regarding the prospects of ongoing neutrino experiments as well as future experiments in determining few of the most important unknowns in the field of neutrino physics, specifically the neutrino mass ordering and leptonic CP-violation phase. The effect of matter oscillations on the neutrino oscillation probabilities has been exploited in resolving the degeneracy between the neutrino mass ordering and the CP violation phase in the leptonic sector. Further, we estimate the extent of extrinsic CP and CPT violation in the experiments with superbeams as well as neutrino factories.

Compact perturbative expressions for neutrino oscillations in matter

We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by neutrino energy plane. This extension also gives the exact oscillation probabilities in vacuum for all values of baseline divided by neutrino energy. The expansion parameter used is related to the ratio of the solar to the atmospheric $\Delta m^2$ scales but with a unique choice of the atmospheric $\Delta m^2$ such that certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using a mixing matrix formulation, this framework has the exceptional feature that the neutrino oscillation probability in matter has the same structure as in vacuum, to all orders in the expansion parameter. It also contains all orders in the matter potential and $\sin\theta_{13}$. It facilitates immediate physical interpretation of the analytic results, and makes the expressions for the neutrino oscillation probabilities extremely compact and very accurate even at zeroth order in our perturbative expansion. The first and second order results are also given which improve the precision by approximately two or more orders of magnitude per perturbative order.