On the theory of neutrino mixing and oscillations

Abstract

A brief review of the status of neutrino oscillations is given. The phenomenology of neutrino mixing and the standard seesaw mechanism of neutrino mass generation is discussed. Different approaches to neutrino oscillations are considered and compared. The role of the Heisenberg space-momentum uncertainty relation and the MandelstamTamm time-energy uncertainty relation in neutrino oscillations is discussed in some detail.

Spreading of Wave Packets for Neutrino Oscillations

“…in agreement with the corresponding lengths very well known in the literature [8,[12][13][14][15][16][17][18][19][20][21][22]. To write the expressions (45) and (46), we have used the definition of sin 2 [2θ 12 ] in terms of the parameter Λ given by (3), where θ 12 is the mixing angle in the vacuum between the two mass eigenstates.…”

“…Because in the neutrino oscillation experiments one has L ≃ L osc , then the term exp − L L coh 2 is nearly equal to one [22]. Additionally, it is easy to show that | v 1 − v 2 | L coh ≃ is also nearly equal to one [22]. In this form, the time-integrated oscillation probabilities (45) and (46) can be written as [22]…”

“…In this section, we will obtain the standard time-integrated neutrino oscillation probabilities using the wave packet formalism. To do it, we expand the energy given by (22) up to second order in the power series of ( p − p a ) [16]. This fact is justified taking into account that the width of the wave packets is very narrow around the average momentum.…”

“…If the energy given by (22) is substituted in (20) and (21), keeping up to the second order in the power series of ( p − p a ), we obtain that the neutrino oscillation probabilities are written as…”

“…Now, we take into account the fact that in the atmospheric and reactor neutrino oscillation experiments it is only possible to measure the distance between the neutrino source and the detector L, while the neutrino propagation time T is unknown [8,18,22]. However, in the case of the accelerator neutrino experiments (for instance K2K, MINOS, OPERA) it is possible to measure the neutrino propagation time T [22]. By this reason, if we focus only on the case of atmospheric and reactor neutrino oscillation experiments, then it is necessary the elimination of the time dependence presents in (30) and (31).…”