23 Search Results

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 $$(\lambda I -H)$$, where H is the Hamiltonian, I the identity matrix and $$\lambda$$ is a scalar. To calculate the associated eigenvectors we use a method thatmore » is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, $$(\lambda I -H)$$. 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.« less

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 2⁷ 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 additional set of 2⁷ parameter symmetries of the matter parameters exists. 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 mostmore » 2⁶ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the large mixing angle (LMA)-dark degeneracy that holds under the assumption of CPT invariance; this adds one additional factor of 2 to all of the above cases. Explicit, nontrivial 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 Δm²’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.« less

Tmore » he 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 nonlinear detector energy response. Using the measurement of ${\theta }_{13}$ from Daya Bay, but without information from other experiments, we estimate the probability of JUNO determining the neutrino mass ordering at $\ge 3\sigma$ to be 31% by 2030. As this probability is particularly sensitive to the true values of the oscillation parameters, especially $\mathrm{\Delta }{m}_{21}^2$, JUNO’s improved measurements of ${\sin }^2{\theta }_{12}$, $\mathrm{\Delta }{m}_{21}^2$ and $\left|\mathrm{\Delta }{m}_{ee}^2\right|$, 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 $\left|\mathrm{\Delta }{m}_{ee}^2\right|$ with other experiments in a global fit will most likely lead to an earlier determination of the mass ordering.« less

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 the 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 bemore » 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.« less

We inspect recently updated neutrino oscillation data—specifically coming from the Tokai to Kamioka and NuMI Off-axis νe Appearance experiments—and how they are analyzed to determine whether the neutrino mass ordering is normal (m₁₂₃) or inverted (m₃₁₂). 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 nonoscillation 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 orderingmore » at a high confidence level.« less

If $$A$$ is an $$n \times n$$ Hermitian matrix with eigenvalues $$\lambda_1(A),\dots,\lambda_n(A)$$ 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 $$\lambda_i(A)$$ is related to the eigenvalues $$\lambda_1(M_j),\dots,\lambda_{n-1}(M_j)$$ of the minor $$M_j$$ of $$A$$ formed by removing the $$j^{\mathrm{th}}$$ row and column by the formula $$$$ |v_{i,j}|^2\prod_{k=1;k\neq i}^{n}\left(\lambda_i(A)-\lambda_k(A)\right)=\prod_{k=1}^{n-1}\left(\lambda_i(A)-\lambda_k(M_j)\right)\,.$$$$ We refer to this identity as the \emph{eigenvector-eigenvalue identity}. 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 timesmore » that this identity, or variants thereof, have been discovered and rediscovered in the literature (with the earliest precursor we know of appearing in 1934). Further, we provide a number of proofs and generalizations of the identity.« less

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 usingmore » 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.« less

We present a new method of exactly calculating neutrino oscillation probabilities in matter. We show that, given the eigenvalues, all mixing angles follow surprisingly simply and the CP violating phase can also be trivially determined. Then, to avoid the cumbersome expressions for the exact eigenvalues, we have applied previously derived perturbatively approximate eigenvalues to this scheme and found it to be incredibly precise. We also find that these eigenvalues converge at a rate of five orders of magnitude which is the square of the naive expectation.

We extend a simple and compact method for calculating the three flavor neutrino oscillation probabilities in uniform matter density to schemes with sterile neutrinos, with favorable features inherited. The only constraint of the extended method is that the scale of the matter potential is not significantly larger than the atmospheric $$\Delta m^2$$, which is satisfied by all the running and proposed accelerator oscillation experiments. Degeneracy of the zeroth order eigensystem around solar and atmospheric resonances are resolved. Corrections to the zeroth order results are restricted to no larger than the ratio of the solar to the atmospheric $$\Delta m^2$$. Themore » zeroth order expressions are exact in vacuum because all the higher order corrections vanish when the matter potential is set zero. Also because all the corrections are continuous functions of matter potential, the zeroth order precision is much better than $$\Delta m^2_\odot/\Delta m^2_\text{atm}$$ for weak matter effect. Numerical tests are presented to verify the theoretical predictions of the exceptional features. Moreover, possible applications of the method in experiments to check the existence of sterile neutrinos are discussed.« less

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 usingmore » a constant density profile is sufficient for both the T2HK and T2HKK experiments.« less