Evolution of the neutrino state inside the Sun

Abstract

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, θ ≪ 1. For large values of θ, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of θ including θ > π/4, are presented. An adiabaticity condition valid for all values of θ is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of ∆m 2 , from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the socalled "quasi-vacuum oscillation regime" are discussed. Finally, it is shown how the known analytical results for the exponential,

Erratum: Supernova neutrino oscillations: A simple analytical approach [Phys. Rev. D65, 073008 (2002)]

“…(13)] was also originally introduced in the context of solar neutrinos [26], typically by calculating r at the point x p = x res defined by the so-called "resonance" condition V (x res ) = ∆m 2 cos 2θ (see, e.g., [33]). Such a choice for x p , although successful at relatively small θ, is clearly not applicable for θ ≥ π/4 [34], and fails to describe correctly nonadiabatic transitions at small k, where P c = 0 at θ ∼ π/4 [22,23]. For large θ, the resonance condition can be misleading, if not meaningless, and it is more appropriate to characterize P c through the point x MVA where maximum violation of adiabaticity (MVA) is attained [22,23,16].…”

“…Such a choice for x p , although successful at relatively small θ, is clearly not applicable for θ ≥ π/4 [34], and fails to describe correctly nonadiabatic transitions at small k, where P c = 0 at θ ∼ π/4 [22,23]. For large θ, the resonance condition can be misleading, if not meaningless, and it is more appropriate to characterize P c through the point x MVA where maximum violation of adiabaticity (MVA) is attained [22,23,16]. Indeed, in the context of solar neutrinos, the prescription x p = x MVA for r(x p ) is more accurate and physically more consistent than x p = x res [23].…”

“…For solar neutrinos, it was shown in [23] that the MVA-inspired recipe for P c [r = r(x MVA )] has to be matched and replaced, at small k, with r = const [31,22]. The constant (limiting) value for r can be elegantly derived, through a perturbative approach [23], in terms of an integral involving V (x) in the convective zone of the Sun, where V (x) experiences a sudden drop.…”

“…In particular, it has been recently realized, first in the context of solar [22,23] and then of supernova [16,17] neutrinos, that the time-honored resonance condition cannot be meaningfully extended at large neutrino mixing. Thus, apart from brute-force numerical calculations of P ee (see, e.g., [24,[18][19][20]), a truly unified approach, valid in the whole three-flavor oscillation parameter space and applicable to generic supernova density profiles, seems still lacking in the literature, as far as we know.…”

“…In this work, we propose a simple, unified analytical approach to the calculation of P ee , based on a double-exponential form for the crossing probability [25,26] and on the condition of maximum violation of adiabaticity [22,23] (replacing the popular resonance condition). In the case of two-flavor transitions (Sec.…”