Neutrino Oscillation Probabilities In Matter Research Articles

Vector leptoquark U_3 and CP violation at T2K, NOvA experiments

In the current epoch of neutrino physics, many experiments are aiming for precision measurements of oscillation parameters. Thus, various new physics scenarios which alter the neutrino oscillation probabilities in matter deserve careful investigation. In this context, we study the effect of a vector leptoquark which induces non-standard neutrino interactions (NSI) that modify the oscillation probabilities of neutrinos in matter. We show that such interactions provide a relatively large value of NSI parameter varepsilon _{e mu }. Considering this NSI parameter, we successfully explain the recent discrepancy between the observed delta _{CP} results of T2K and NOvA.

Neutrino oscillations in matter via eigenvalues

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.

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.

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.

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 $\delta$.

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.

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.

Neutrino oscillation probabilities in matter with direct and indirect unitarity violation in the lepton mixing matrix

In the presence of both direct and indirect unitarity violation in the lepton mixing matrix, we derive a complete set of series expansion formulas for neutrino oscillation probabilities in matter of constant density. Expansions in the mass hierarchy parameter $\alpha \equiv \Delta m_{21}^{2} / \Delta m_{31}^{2}$ and those unitarity violation parameters $s^{2}_{ij}$ (for i = 1, 2, 3 and j = 4, 5, 6) up to the first order are studied in this paper. We analyse the accuracy of the analytical series expansion formulas in different regions of L / E. A detailed numerical analysis is also performed, of which the different effects of the direct and the indirect unitarity violation are particularly emphasized. We also study in this paper the summed $\nu^{}_{\alpha} \rightarrow \nu^{}_{e, \nu, \tau}$ probabilities, whose deviation from the unity provides a definite signal of the unitarity violation.

Simple and compact expressions for neutrino oscillation probabilities in matter

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric $\Delta m^2$ scales. Unlike previous works, we use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. We show that the new framework has an exceptional feature that leads to the neutrino oscillation probability in matter with the same structure as in vacuum to first order in the expansion parameter. It facilitates immediate physical interpretation of the formulas, and makes the expressions for the neutrino oscillation probabilities extremely simple and compact. We find, for example, that the $\nu_e$ disappearance probability at this order is of a simple two-flavor form with an appropriately identified mixing angle and $\Delta m^2$. More generally, all the oscillation probabilities can be written in the universal form with the channel-discrimination coefficient of $0,~\pm1$ or simple functions of $\theta_{23}$. Despite their simple forms they include all order effects of $\theta_{13}$ and all order effects of the matter potential, to first order in our expansion parameter.

Nonadiabatic contributions to the neutrino oscillation probability and the formalism by Kimura, Takamura, and Yokomakura

It is shown that it is possible to obtain the analytical expression for the effective mixing angle in matter using the formalism which was developed by Kimura, Takamura, and Yokomakura for the neutrino oscillation probability in matter with constant density. If we assume that the imaginary part of the integral of the difference of the energy eigenvalues of the two levels at each level crossing is given by the ratio $\ensuremath{\gamma}$ of the difference of the energy eigenvalues of the two levels to the derivative of the effective mixing angle at the level crossing, then the nonadiabatic contribution to the oscillation probability can be expressed analytically by this formalism. We give one example in which the energy eigenvalues cannot be expressed as roots of a quadratic equation and we show that our assumption is correct in the approximation of the small mixing angle.

Analytical approximation of the neutrino oscillation matter effects at large θ 13

We argue that the neutrino oscillation probabilities in matter are best understood by allowing the mixing angles and mass-squared differences in the standard parametrization to `run' with the matter effect parameter $a=2\sqrt{2}G_F N_e E$, where $N_e$ is the electron density in matter and $E$ is the neutrino energy. We present simple analytical approximations to these `running' parameters. We show that for the moderately large value of $\theta_{13}$, as discovered by the reactor experiments, the running of the mixing angle $\theta_{23}$ and the CP violating phase $\delta$ can be neglected. It simplifies the analysis of the resulting expressions for the oscillation probabilities considerably. Approaches which attempt to directly provide approximate analytical expressions for the oscillation probabilities in matter suffer in accuracy due to their reliance on expansion in $\theta_{13}$, or in simplicity when higher order terms in $\theta_{13}$ are included. We demonstrate the accuracy of our method by comparing it to the exact numerical result, as well as the direct approximations of Cervera et al., Akhmedov et al., Asano and Minakata, and Freund. We also discuss the utility of our approach in figuring out the required baseline lengths and neutrino energies for the oscillation probabilities to exhibit certain desirable features.

Series expansions for three-flavor neutrino oscillation probabilities in matter

We present a number of complete sets of series expansion formulas for neutrino oscillation probabilities in matter of constant density for three flavors. In particular, we study expansions in the mass hierarchy parameter $\alpha \equiv \Delta m_{21}^2/\Delta m_{31}^2$ and mixing parameter $s_{13} \equiv \sin \theta_{13}$ up to second order and expansions only in $\alpha$ and only in $s_{13}$ up to first order. For each type of expansion we also present the corresponding formulas for neutrino oscillations in vacuum.We perform a detailed analysis of the accuracy of the different sets of series expansion formulas and investigate which type of expansion is most accurate in different regions of the parameter space spanned by the neutrino energy E, the baseline length L, and the expansion parameters $\alpha$ and $s_{13}$.We also present the formulas for series expansions in $\alpha$ and in $s_{13}$ up to first order for the case of arbitrary matter density profiles. Furthermore, it is shown that in general all the 18 neutrino and antineutrino oscillation probabilities can be expressed through just two independent probabilites.