Compact perturbative expressions for oscillations with sterile neutrinos in matter

Parke, Stephen J.; Zhang, Xining

doi:10.1103/physrevd.101.056005

Cited by 9 publications

(14 citation statements)

References 36 publications

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“…which is the same as in Equation (18) with the definitions (19)- (20) for U A and U f . This completes the proof that justifies the use of an average electron density, rather than its large variation around the atomic nuclei.…”

Section: The Connection To the Integration Methodsmentioning

confidence: 99%

“…The neutral current potential is the same for all three active neutrinos, and therefore can be neglected in the analysis of neutrino oscillations (as is the main momentum term in the underlying Dirac equations). However, if the sterile neutrinos are present, the neutral current potential needs to be considered [20]. In Equation (5), the Dirac spinors ψ j = ν j φ j can be viewed as components of some flavor neutrino normalized superposition of mass eigenstates spinors:…”

Section: Neutrino Oscillations In Condensed Mattermentioning

confidence: 99%

“…Previous work on neutrino oscillation probabilities in matter includes perturbative expansions [20,[23][24][25]. The most used approach is to diagonalize the Hamiltonian in matter, and use perturbation theory to identify main contributing terms.…”

Section: The Iterations Algorithmmentioning

confidence: 99%

“…In the case of constant electron density, A(s) in Equation (11) does not depend on the integration variable s, and one can use the diagonalization methods and/or perturbative expansions [20,[23][24][25]. Alternatively, one can directly integrate Equation (11).…”

Section: The Iterations Algorithmmentioning

confidence: 99%

“…Using Equations (17)- (20), one can iteratively find the S-matrix and the associated probabilities of Equation (15). We will call this approach the iterations method.…”

Section: The Iterations Algorithmmentioning

confidence: 99%

See 4 more Smart Citations

Effects of Atomic-Scale Electron Density Profile and a Fast and Efficient Iteration Algorithm for Matter Effect of Neutrino Oscillation

Horoi

Zettel

2020

Universe

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In a recent article, we noticed that the electron density in condensed matter exhibits large spikes close to the atomic nuclei. We showed that the peak magnitude of these spikes in the electron densities, 3–4 orders larger than the average electron plasma density in the Sun’s core, have no effect on the neutrino emission and absorption probabilities or on the neutrinoless double beta decay probability. However, it was not clear if the effect of these spikes is equivalent to that of an average constant electron density in matter. We investigated these effects by a direct integration of the coupled Dirac equations describing the propagation of flavor neutrinos into, through, and out of the matter. We proposed a new iteration-based algorithm for computing the neutrino survival/appearance probability in matter, which we found to be at least 20 times faster than some direct integration algorithms under the same accuracy. With this method, we found little evidence that these spikes affect the standard oscillations probabilities. In addition, we show that the new algorithm can explain the equivalence of using average electron densities instead of the spiked electron densities. The new algorithm is further extended to the case of light sterile neutrinos.

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Section: The Connection To the Integration Methodsmentioning

confidence: 99%

Section: Neutrino Oscillations In Condensed Mattermentioning

confidence: 99%

Section: The Iterations Algorithmmentioning

confidence: 99%

Section: The Iterations Algorithmmentioning

confidence: 99%

“…Using Equations (17)- (20), one can iteratively find the S-matrix and the associated probabilities of Equation (15). We will call this approach the iterations method.…”

Section: The Iterations Algorithmmentioning

confidence: 99%

See 3 more Smart Citations

Effects of Atomic-Scale Electron Density Profile and a Fast and Efficient Iteration Algorithm for Matter Effect of Neutrino Oscillation

Horoi

Zettel

2020

Universe

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Sterile neutrinos: propagation in matter and sensitivity to sterile mass ordering

Chattopadhyay

Devi

Dighe

et al. 2023

J. High Energ. Phys.

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We analytically calculate the neutrino conversion probability Pμe in the presence of sterile neutrinos, with exact dependence on $$ \Delta {m}_{41}^2 $$ ∆ m 41 2 and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles θ24 and θ34 can be separated out, with θ34 dependence only arising due to matter effects. We express Pμe in terms of the quantities of the form sin(x)/x, which helps in elucidating its dependence on matter effects and a wide range of $$ \Delta {m}_{41}^2 $$ ∆ m 41 2 values. Our analytic expressions allow us to predict the effects of the sign of $$ \Delta {m}_{41}^2 $$ ∆ m 41 2 at a long baseline experiment like DUNE. We numerically calculate the sensitivity of DUNE to the sterile mass ordering and find that this sensitivity can be significant in the range $$ \mid \Delta {m}_{41}^2\mid \sim \left({10}^{-4}-{10}^{-2}\right) $$ ∣ Δ m 41 2 ∣ ∼ 10 − 4 − 10 − 2 eV2, for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of $$ \Delta {m}_{41}^2 $$ ∆ m 41 2 for all mass ordering combinations can be explained by investigating the resonance-like terms appearing due to the interplay between the sterile sector and matter effects.

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From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes

Maltoni

2023

J. High Energ. Phys.

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In this note we describe how to complement the neutrino evolution matrix calculated at a given energy and trajectory with additional information which allows to reliably extrapolate it to nearby energies or trajectories without repeating the full computation. Our method works for arbitrary matter density profiles, can be applied to any propagation model described by an Hamiltonian, and exactly guarantees the unitarity of the evolution matrix. As a straightforward application, we show how to enhance the calculation of the theoretical predictions for experimentally measured quantities, so that they remain accurate even in the presence of fast neutrino oscillations. Furthermore, the ability to “move around” a given energy and trajectory opens the door to precise interpolation of the oscillation amplitudes within a grid of tabulated values, with potential benefits for the computation speed of Monte-Carlo codes. We also provide a set of examples to illustrate the most prominent features of our approach.

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Compact perturbative expressions for oscillations with sterile neutrinos in matter

Cited by 9 publications

References 36 publications

Effects of Atomic-Scale Electron Density Profile and a Fast and Efficient Iteration Algorithm for Matter Effect of Neutrino Oscillation

Effects of Atomic-Scale Electron Density Profile and a Fast and Efficient Iteration Algorithm for Matter Effect of Neutrino Oscillation

Sterile neutrinos: propagation in matter and sensitivity to sterile mass ordering

From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes

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