Engineering topics

Parke, Stephen J.

Publications and source records attributed to Parke, Stephen J..

3 records

DOE OSTI2024

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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

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 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. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗