arXiv subjects

Stephen J. Parke

Publications and source records attributed to Stephen J. Parke.

At least 19 recordsLinked to original sources

arXiv2026

NuFast-Earth: Efficient Atmospheric, Solar, and Supernova Neutrino Propagation Through the Earth

Algorithms for computing neutrino oscillation probabilities in sharply varying matter potentials such as the Earth are becoming increasingly important. As the next generation of experiments, DUNE and HyperK as well as the IceCube upgrade and KM3NeT, come online, the computational cost for atmospheric and solar neutrinos will continue to increase. To address these issues, we expand upon our previous algorithm for long-baseline calculations to efficiently handle probabilities through the Earth for atmospheric, nighttime solar, and supernova neutrinos. The algorithm is fast, flexible, and accurate. It can handle arbitrary Earth models with two different schemes for varying density profiles. We also provide a c++ implementation of the code called NuFast-Earth along with a detailed user manual. The code intelligently keeps track of repeated calculations and only recalculates what is needed on each successive call which can also help provide significant speed-ups.

hep-ph↗

arXiv2025

Exploring Quantum Statistics for Dirac and Majorana Neutrinos using Spinor-Helicity techniques

Recently, there has been interest in the applicability of quantum statistics to distinguish Dirac from Majorana neutrinos in multi-neutrino final states. In particular, debate has arisen over the validity of the Dirac-Majorana confusion theorem in these processes, i.e. that any distinction between the Dirac and Majorana processes goes to zero as the neutrino mass goes to zero. Here we approach this problem equipped with spinor-helicity methods generalized for massive Dirac and Majorana fermions. We explicitly calculate all helicity amplitudes for the decay of a light scalar particle to two neutrinos and two oppositely charged leptons. This allows us to pinpoint the crucial steps which could lead to claims of a violation of the confusion theorem. We show that if the correct anti-symmetrization of Dirac to Majorana amplitudes is used, identification of which is clear in this framework, and all relevant contributions are appropriately summed, a scalar decay into two charged leptons and two neutrinos satisfies the Dirac-Majorana confusion theorem.

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arXiv2025

Neutrino Theory in the Precision Era

This document summarises discussions on future directions in theoretical neutrino physics, which are the outcome of a neutrino theory workshop held at CERN in February 2025. The starting point is the realisation that neutrino physics offers unique opportunities to address some of the most fundamental questions in physics. This motivates a vigorous experimental programme which the theory community fully supports. \textbf{A strong effort in theoretical neutrino physics is paramount to optimally take advantage of upcoming neutrino experiments and to explore the synergies with other areas of particle, astroparticle, and nuclear physics, as well as cosmology.} Progress on the theory side has the potential to significantly boost the physics reach of experiments, as well as go well beyond their original scope. Strong collaboration between theory and experiment is essential in the precision era. To foster such collaboration, \textbf{we propose to establish a CERN Neutrino Physics Centre.} Taking inspiration from the highly successful LHC Physics Center at Fermilab, the CERN Neutrino Physics Centre would be the European hub of the neutrino community, covering experimental and theoretical activities.

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arXiv2024

Exploring the Interference between the Atmospheric and Solar Neutrino Oscillation Sub-Amplitudes

The interference between the atmospheric and solar neutrino oscillation sub-amplitudes is said to be responsible for CP violation (CPV) in neutrino appearance channels. More precisely, CPV is generated by the interference between the parts of the neutrino oscillation amplitude which are CP even and CP odd: even or odd when the neutrino mixing matrix is replaced with its complex conjugate. This is the CPV interference term, as it gives a contribution to the oscillation probability, the square of the amplitude, which is opposite in sign for neutrinos and anti-neutrinos and is unique. For this interference to be non-zero, at least two sub-amplitudes are required. There are, however, other interference terms, which are even under the above exchange, these are the CP conserving (CPC) interference terms. In this paper, we explore in detail these CPC interference terms and show that they cannot be uniquely defined, as one can move pieces of the amplitude from the atmospheric sub-amplitude to the solar sub-amplitude and vice versa. This freedom allows one to move the CPC interference terms around, but does not let you eliminate them completely. We also show that there is a reasonable definition of the atmospheric and solar sub-amplitudes for the appearance channels such that in neutrino disappearance probability there is no atmospheric-solar CPC interference term. However, with this choice, there is a CPC interference term within the atmospheric sector.

hep-ph↗

arXiv2024

Fast and Accurate Algorithm for Calculating Long-Baseline Neutrino Oscillation Probabilities with Matter Effects: NuFast

Neutrino oscillation experiments will be entering the precision era in the next decade with the advent of high statistics experiments like DUNE, HK, and JUNO. Correctly estimating the confidence intervals from data for the oscillation parameters requires very large Monte Carlo data sets involving calculating the oscillation probabilities in matter many, many times. In this paper, we leverage past work to present a new, fast, precise technique for calculating neutrino oscillation probabilities in matter optimized for long-baseline neutrino oscillations in the Earth's crust including both accelerator and reactor experiments. For ease of use by theorists and experimentalists, we provide fast c++ and fortran codes.

hep-ph↗

arXiv2024

A Mass Ordering Sum Rule for the Neutrino Disappearance Channels in T2K, NOvA and JUNO

We revisit a method for determining the neutrino mass ordering by using precision measurements of the atmospheric $Δm^2$'s in both electron neutrino and muon neutrino disappearance channels, proposed by the authors in 2005 (hep-ph/0503283). The mass ordering is a very important outstanding question for our understanding of the elusive neutrino and determination of the mass ordering has consequences for other neutrino experiments. The JUNO reactor experiment will start data taking this year, and the precision of the atmospheric $Δm^2$'s from electron anti-neutrino measurements will improve by a factor of three from Daya Bay's 2.4 % to 0.8 % within a year. This measurement, when combined with the atmospheric $Δm^2$'s measurements from T2K and NOvA for muon neutrino disappearance, will contribute substantially to the $Δχ^2$ between the two remaining neutrino mass orderings. In this paper we derive a mass ordering sum rule that can be used to address the possibility that JUNO's atmospheric $Δm^2$'s measurement, when combined with other experiments in particular T2K and NOvA, can determine the neutrino mass ordering at the 3 $σ$ confidence level within one year of operation. For a confidence level of 5 $σ$ in a single experiment we will have to wait until the middle of the next decade when the DUNE experiment is operating.

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arXiv2024

The Smallness of Matter Effects in Long-Baseline Muon Neutrino Disappearance

Current long-baseline accelerator experiments, NOvA and T2K, are making excellent measurements of neutrino oscillations and the next generation of experiments, DUNE and HK, will make measurements at the $\mathcal O(1\%)$ level of precision. These measurements are a combination of the appearance channel which is more challenging experimentally but depends on many oscillation parameters, and the disappearance channel which is somewhat easier and allows for precision measurements of the atmospheric mass splitting and the atmospheric mixing angle. It is widely recognized that the matter effect plays a key role in the appearance probability, yet the effect on the disappearance probability is surprisingly small for these experiments. Here we investigate both exactly how small the effect is and show that it just begins to become relevant in the high statistics regime of DUNE.

hep-ph↗

arXiv2023

Neutrino Oscillations in Matter using the Adjugate of the Hamiltonian

We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix $(λI -H)$, where H is the Hamiltonian, I the identity matrix and $λ$ is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, $(λI -H)$. This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev-LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov-Harrison-Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.

hep-ph↗

arXiv2022

Non-adiabatic Level Crossing in Resonant Neutrino Oscillations

Analytic results are presented for the probability of detecting an electron neutrino after passage through a resonant oscillation region. If the electron neutrino is produced far above the resonance density, this probability is simply given by $\langle \,P_{ν_e} \, \rangle \approx \sin^2 θ_0+ P_\text{x} \cos 2 θ_0$, where $θ_0$ is the vacuum mixing angle. The probability is averaged over the production as well as the detection positions of the neutrino and $P_\text{x} $ is the Landau-Zener transition probability between adiabatic states. Finally, this result is applied to resonance oscillations within the solar interior.

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arXiv2021

Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the $2^7$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an \emph{additional} set of $2^7$ parameter symmetries exist of the matter parameters. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been developed; we show that under certain assumptions, approximate expressions have at most $2^6$ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the LMA-Dark degeneracy that holds under the assumption of CPT invariance; this adds one additional factor of two to all of the above cases. Explicit, non-trivial examples are given of how physical observables in neutrino oscillations, such as the probabilities, CP violation, the position of the solar and atmospheric resonance, and the effective $Δm^2$'s for disappearance probabilities, are invariant under all of the above symmetries. We investigate which of these parameter symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.

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arXiv2021

JUNO's prospects for determining the neutrino mass ordering

The flagship measurement of the JUNO experiment is the determination of the neutrino mass ordering. Here we revisit its prospects to make this determination by 2030, using the current global knowledge of the relevant neutrino parameters as well as current information on the reactor configuration and the critical parameters of the JUNO detector. We pay particular attention to the non-linear detector energy response. Using the measurement of $θ_{13}$ from Daya Bay, but without information from other experiments, we estimate the probability of JUNO determining the neutrino mass ordering at $\ge$ 3$σ$ to be 31% by 2030. As this probability is particularly sensitive to the true values of the oscillation parameters, especially $Δm^2_{21}$, JUNO's improved measurements of $\sin^2 θ_{12}$, $Δm^2_{21}$ and $|Δm^2_{ee}|$, obtained after a couple of years of operation, will allow an updated estimate of the probability that JUNO alone can determine the neutrino mass ordering by the end of the decade. Combining JUNO's measurement of $|Δm^2_{ee}|$ with other experiments in a global fit will most likely lead to an earlier determination of the mass ordering.

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arXiv2021

Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra

If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $λ_1(A),\dots,λ_n(A)$ and $i,j = 1,\dots,n$, then the $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $λ_i(A)$ is related to the eigenvalues $λ_1(M_j),\dots,λ_{n-1}(M_j)$ of the minor $M_j$ of $A$ formed by removing the $j^{\mathrm{th}}$ row and column by the formula $$ |v_{i,j}|^2\prod_{k=1;k\neq i}^{n}\left(λ_i(A)-λ_k(A)\right)=\prod_{k=1}^{n-1}\left(λ_i(A)-λ_k(M_j)\right)\,.$$ We refer to this identity as the \emph{eigenvector-eigenvalue identity} and show how this identity can also be used to extract the relative phases between the components of any given eigenvector. Despite the simple nature of this identity and the extremely mature state of development of linear algebra, this identity was not widely known until very recently. In this survey we describe the many times that this identity, or variants thereof, have been discovered and rediscovered in the literature (with the earliest precursor we know of appearing in 1834). We also provide a number of proofs and generalizations of the identity.

math.RA↗

arXiv2021

Interplay between the factorization of the Jarlskog Invariant and location of the Solar and Atmospheric Resonances for Neutrino Oscillations in Matter

The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact factorization of Jarlskog invariant in matter into the vacuum Jarlskog invariant times two, two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. We compare the location of the minima of the factorizing resonance factors with the location of the solar and atmospheric resonances, precisely defined. They are not identical but the fractional differences are both found to be less than 0.1\%. In addition, we explain why symmetry polynomials of the square of the mass of the neutrino eigenvalues in matter, such as inverse of the square of the Jarlskog invariant in matter, can be given as polynomials in the matter potential.

hep-ph↗

arXiv2021

Back to (Mass-)Square(d) One: The Neutrino Mass Ordering in Light of Recent Data

We inspect recently updated neutrino oscillation data -- specifically coming from the Tokai to Kamioka and NuMI Off-axis $ν_e$ Appearance experiments -- and how they are analyzed to determine whether the neutrino mass ordering is normal ($m_1 < m_2 < m_3$) or inverted ($m_3 < m_1 < m_2$). We show that, despite previous results giving a strong preference for the normal ordering, with the newest data from T2K and NOvA, this preference has all but vanished. Additionally, we highlight the importance of this result for non-oscillation probes of neutrinos, including neutrinoless double beta decay and cosmology. Future experiments, including JUNO, DUNE, and T2HK will provide valuable information and determine the mass ordering at a high confidence level.

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arXiv2020

Fibonacci Fast Convergence for Neutrino Oscillations in Matter

Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exponentially fast wherein the rate of convergence follows the Fibonacci sequence. We find that the convergence rate of this procedure depends very sensitively on the initial choices of the rotations as well as the mechanism of selecting the pivots. We then apply this scheme for neutrino oscillations in matter and discover that the optimal convergence rate is found using the following simple strategy: first apply the vacuum (2-3) rotation and then use the largest off-diagonal element as the pivot for each of the following rotations. The Fibonacci convergence rate presented here may be extendable to systems beyond neutrino oscillations.

hep-ph↗

arXiv2020

Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter

We present a new method of exactly calculating neutrino oscillation probabilities in matter. We leverage the "eigenvector-eigenvalue identity" to show that, given the eigenvalues, all mixing angles in matter follow surprisingly simply. The CP violating phase in matter can then be determined from the Toshev identity. Then, to avoid the cumbersome expressions for the exact eigenvalues, we have applied previously derived perturbative, approximate eigenvalues to this scheme and discovered them to be even more precise than previously realized. We also find that these eigenvalues converge at a rate of five orders of magnitude per perturbative order which is the square of the previously realized expectation. Finally, we provide an updated speed versus accuracy plot for oscillation probabilities in matter, to include the methods of this paper.

hep-ph↗

arXiv2020

Effects of matter density profiles on neutrino oscillations for T2HK and T2HKK

This paper explores the effects of changes in matter density profiles on neutrino oscillation probabilities, and whether these could potentially be seen by the future Hyper-Kamiokande long-baseline oscillation experiment (T2HK). The analysis is extended to include the possibility of having an additional detector in Korea (T2HKK). In both cases, we find that these effects will be immeasurable, as the magnitudes of the changes in the oscillation probabilities induced in all density profile scenarios considered here remain smaller than the estimated experimental sensitivity to the oscillation probabilities of each experiment, for both appearance and disappearance channels. Therefore, we conclude that using a constant density profile is sufficient for both the T2HK and T2HKK experiments.

hep-ph↗

arXiv2020

Why matter effects matter for JUNO

In this paper we focus on the Earth matter effects for the solar parameter determination by a medium baseline reactor experiment such as JUNO. We derive perturbative expansions for the mixing angles $θ_{12}$ and $θ_{13}$ as well as the $Δm^2_{21}$ and $Δm^2_{31}$ in terms of the matter potential relevant for JUNO. These expansions, up to second order in the matter potential, while simple, allow one to calculate the electron antineutrino survival probability to a precision much better than needed for the JUNO experiment. We use these perturbative expansions to semi-analytically explain and confirm the shift caused by the matter effects on the solar neutrino mixing parameters $θ_{12}$ and $Δm^2_{21}$ which were previously obtained by a purely numerical $χ^2$ analysis. Since these shifts do not satisfy the naive expectations and are significant given the precision that can be achieved by the JUNO experiment, a totally independent cross check using a completely different method is of particular importance. We find that these matter effect shifts do not depend on any of the details of the detector characteristics apart from the baseline and earth mass density between reactor(s) and detector, but do depend on the normalized product of reactor neutrino spectrum times the inverse-beta decay cross-section. The results of this manuscript suggests an alternative analysis method for measuring $\sin^2 θ_{12}$ and $Δm^2_{21}$ in JUNO which would be a useful cross check of the standard analysis and for the understanding of the Wolfenstein matter effect. The explanation of these shifts together with a quantitative understanding, using a semi-analytical method, is the principal purpose of this paper.

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