Coherence and Wave Packets in Neutrino Oscillations

2021

Neutrinos are one of the most elusive of the Standard Model particles known to physicists today. Despite the fact that crucial characteristics of these leptons remain largely a mystery, studying them can hold the key to fundamental insights for the field of particle physics and for our understanding of the universe as a whole. In order to learn why there is so much discussion within the physics community about these mysterious particles, its important to start at the beginning and connect one of their most important characteristics that of oscillations between their types with the subject of quantum mechanics. In fact, to engage with the subject of neutrino physics in general, beyond the surface-level qualitative approach, requires the quantum mechanical framework based heavily in linear algebra. Therefore, this paper will give an introduction to neutrino physics, specifically to their oscillations, through connecting the quantum mechanical formalism to current research within this ...

arXiv: High Energy Physics - Phenomenology, 2019

In this work we study the effects of non-standard neutrino matter interactions on the coherence embedded in the system of oscillating neutrinos. The coherence parameter used in this work quantifies the inherent quantumness of the system. The new physics effects on the coherence parameter are incorporated in a model independent way by using the language of effective field theory. We then analyze these non-standard interaction effects on coherence in the context of upcoming DUNE experiment. The recent global analyses [JHEP 1906, 055 (2019)] of neutrino oscillation data show that LMA-LIGHT sector of $\theta_{12}$ with normal mass ordering along with LMA-DARK sector with inverted mass ordering provide a good fit to all data. We find that while the first solution decreases the coherence in the system in comparison to the standard model prediction for all values of neutrino energy $E$ and $CP$ violating phase $\delta$ (except in the narrow region around $E \sim$ 2 GeV), a large enhancemen...

Physical Review D, 2010

In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation and detection, in particular the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled "collapsed" state. The familiar quantum mechanical interpretation and factorization of the detection rate emerges when the quantum state is disentangled on time scales much shorter than the inverse oscillation frequency, in which case the final detection rate factorizes in terms of the usual quantum mechanical transition probability provided the final density of states is insensitive to the neutrino energy difference. We suggest possible corrections for short-baseline experiments. If the charged lepton is unobserved, neutrino oscillations and coherence are described in terms of a reduced density matrix obtained by tracing out an un-observed charged lepton. The diagonal elements in the mass basis describe the production of mass eigenstates whereas the off diagonal ones provide a measure of coherence. It is shown that coherences are of the same order of the diagonal terms on time scales up to the inverse oscillation frequency, beyond which the coherences oscillate as a result of the interference between mass eigenstates.

Physica Scripta, 2003

Using an analogy with the well-known double-slit experiment, we show that the standard phase of neutrino oscillations is correct, refuting recent claims of a factor of two correction. We also improve the wave packet treatment of neutrino oscillations taking into account explicitly the finite coherence time of the detection process.

The State of the Art of Neutrino Physics

The recent wide recognition of the existence of neutrino oscillations concludes the pioneer stage of these studies and poses the problem of how to communicate effectively the basic aspects of this branch of science. In fact, the phenomenon of neutrino oscillations has peculiar features and requires to master some specific idea and some amount of formalism. The main aim of these introductory notes is exactly to cover these aspects, in order to allow the interested students to appreciate the modern developments and possibly to begin to do research in neutrino oscillations. iii Preface The structure of these notes is the following. In the first section, we describe the context of the discussion. Then we will introduce the concept of neutrino mixing and analyze its implications. Next, we will examine the basic formalism of neutrino oscillations, recalling a few interesting applications. Subsequently, we discuss the modifications to neutrino oscillations that occur when these particles propagate in the matter. Finally, we offer a brief summary of the results and outline the perspectives. Several appendices supplement the discussion and collect various technical details. We strive to describe all relevant details of the calculations, in order to allow the Reader to understand thoroughly and to appreciate the physics of neutrino oscillation. Instead, we do not aim to achieve completeness and/or to collect the most recent results. We limit the reference list to a minimum: We cite the seminal papers of this field in the next section, mention some few books and review papers in the last section, and occasionally make reference to certain works that are needed to learn more or on which we relied to some large extent for an aspect or another. These choices are dictated not only by the existence of a huge amount of research work on neutrinos, but also and most simply in view of the introductory character of these notes. We assume that the Reader knows special relativity and quantum mechanics, and some basic aspects of particle physics. As a rule we will adopt the system of "natural units" of particle physics, defined by the choices = c = 1 In the equations, the repeated indices are summed, whenever this is not reason of confusion. Our metric is defined by xp = x µ p µ = x 0 p 0 − x • p where x = (x 0 , x) and p = (p 0 , p) are two quadrivectors. Unless stated otherwise, we will use the Dirac (or non-relativistic) representation of the Dirac matrices; see the appendices for technical details.

Proceedings of 7th Symposium on Prospects in the Physics of Discrete Symmetries, DISCRETE 2020-2021 — PoS(DISCRETE2020-2021), 2022

We investigate quantum correlations in the context of neutrino oscillations, with specific reference to Daya-Bay and MINOS experiments. We compute the non-local advantage of quantum coherence-a valuable quantum resource-for the two experiments, within the wave-packet approach. We find that this kind of non-local correlation may persist at long distances, when oscillations are washed out, depending on the value of the mixing angle.

Springer Proceedings in Physics, 2020

We study the effects of non-standard neutrino matter interactions on the coherence of oscillating neutrino-system in a model independent way in the context of upcoming DUNE experiment. We find that the LMA-LIGHT solution (with normal ordering of mass eigenstates) decreases the coherence in the system in comparison to the standard model prediction for almost all values of neutrino energy E and C P violating phase δ. However, a large enhancement in coherence parameter in the entire (E − δ) plane is possible for the DARK octant of θ 12 for inverted ordering, with a protuberant enhancement at E ∼ 4 GeV, where maximum neutrino flux is expected in the DUNE experiment. Such features make neutrino a promising candidate for carrying out quantum information theoretic tasks.

Nuclear Physics B - Proceedings Supplements, 2011

Description of neutrino oscillation in the case of Non-Standard neutrino Interaction (NSI) is briefly presented. The NSI causes the entanglement between internal degrees of freedom of neutrinos (mass, spin, flavour) and other accompanying particles in the production and detection processes. In such case neutrinos are mostly in the mixed states. Role of the density matrix in description of neutrino oscillation process is shortly explained.

International Journal of Modern Physics A, 2011

The dynamics of neutrino mixing and oscillations are studied directly in finite real time in a model that effectively describes charged current weak interactions. Finite time corrections to the S-matrix result for the appearance and disappearance probabilities are obtained. It is observed that these effects may be of the same order of the S-matrix result in long-baseline appearance experiments. We argue that fundamentally, the S-matrix is ill-suited to describe long-baseline events due to the fact that the neutrino is produced in an entangled state with the charged lepton, which is disentangled by the measurement of the charged lepton near the production site. The appearance and disappearance far-detection process is described from the time evolution of this disentangled "collapsed" state, allowing us to establish the conditions under which factorization of detection rates emerges in long-baseline experiments. Under these conditions the event rate at the far detector factorizes in terms of the quantum mechanical probabilities, but the total number of events factorizes with a different energy dependence of the oscillatory contribution. We also study the time evolution of the reduced density matrix and show explicitly how oscillations are manifest in the off-diagonal terms, i.e., coherences, as a result of a finite time analysis. Lastly, we study a model for the "GSI anomaly" obtaining the time evolution of the population of parent and daughter particles directly in real time. We confirm that the decay rate of parent and growth rate of daughters do not feature oscillatory behavior from interference of mass eigenstates. However, we find an intriguing result that fluctuations in the distribution of daughter particles do show oscillations as a consequence of such interference.

Progress in Particle and Nuclear Physics, 1999

This review is focused on neutrino mixing and neutrino oscillations in the light of the recent experimental developments. After discussing possible types of neutrino mixing for Dirac and Majorana neutrinos and considering in detail the phenomenology of neutrino oscillations in vacuum and matter, we review all existing evidence and indications in favour of neutrino oscillations that have been obtained in the atmospheric, solar and LSND experiments. We present the results of the analyses of the neutrino oscillation data in the framework of mixing of three and four massive neutrinos and investigate possibilities to test the different neutrino mass and mixing schemes obtained in this way. We also discuss briefly future neutrino oscillation experiments. 7 Conclusions 88 A Properties of Majorana neutrinos and fields 92 1 Notice that in the Goldhaber et al. experiment the helicity of the electron neutrino was measured. The helicity of the muon neutrino was measured in several experiments (for the references see the review of V.L. Telegdi [13]). The best accuracy in the measurement of the muon neutrino was achieved in the experiment by Grénacs et al. [14].

Physical Review D, 1993

We discuss neutrino oscillations in the framework of the quantum field theory without introducing the concept of neutrino weak eigenstates. The external particles are described by wave packets and the different mass eigenstate neutrinos propagate between the production and detection interactions, which are macroscopically localized in space-time. The time-averaged cross section, which is the measurable quantity in the usual experimental setting, is calculated. It is shown that only in the extremely relativistic limit the usual quantum mechanical oscillation probability can be factored out of the cross section.

2004

We present a derivation of the flavor neutrino states which describe neutrinos produced or detected in charged-current weak-interaction processes, including those operating in neutrino oscillation experiments. We also present a covariant derivation of the probability of neutrino oscillations which is consistent with the fact that flavor is Lorentz-invariant. Finally, we clarify the negative answers to three commonly asked questions: "Do charged leptons oscillate?"; "Is the standard phase wrong by a factor of 2?" "Are flavor neutrinos described by Fock states?".

Neutrino oscillations are commonly described by the Pontecorvo-Maki-Nakagawa-Sakata matrix. For the existence of intrinsic neutrino masses m k (k = e, µ, τ) it is shown that this matrix cannot exist without flavor-flavor-interactions (FFI). These FFI modify the m k to the masses m i (i = 1, 2, 3) used in this matrix. The FFI are thus the real new physics which depends on the exact behavior of neutrinos in weak interactions. If they produce or detect to 100 percent pure ν k , then only free neutrinos are subject of the FFI. A discussion of these problems is presented from the point of view of atomic physics.

Arxiv preprint arXiv:0810.4132, 2008

We present an expression for the transition probability between Dirac or Majorana neutrino flavors obtained from first principles within quantum field theory. Our derivation is based on a standard quantum mechanical setup and includes the specific mechanism of neutrino production only in as much as it specifies the initial state. Our expression for the transition probability reproduces the usual formula in the plane wave limit and shows the correct non-relativistic and ultra-relativistic behaviors. It also allows a simple understanding of the decoherence of the oscillations and of the question of the arrival times of the different neutrino mass eigenstates. We show numerical examples for the case of two neutrino generations.

2006

I summarize the status of neutrino oscillations that follow from current data, including the status of the small parameters ratio of solar-over-atmospheric splitting and $\sin^2\theta_{13}$ characterizing the strength of CP violation in neutrino oscillations. I briefly discuss the impact of oscillation data on the prospects for probing the absolute scale of neutrino mass in neutrinoless double beta decay. I also comment on the theoretical origin of neutrino mass, mentioning recent attemps to explain current data from first principles.