Neutrino quantum decoherence in supernovae explosions Vasily I. Bokov1, Konstantin L. Stankevich1, Alexander I. Studenikin1,2 1. Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia 2. Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia Correspondence: kl.stankevich@physics.msu.ru; studenik@srd.sinp.msu.ru 1 Introduction We study the inﬂuence of the neutrino quantum decoherence (see [1–4] and references therein) on collective neutrino oscillations. Collective neutrino oscillations is a phenomenon engendered by neutrino-neutrino interaction. It is signiﬁcant in different astro- physical environments where the neutrino density is extremely high. Examples of such environments are the early universe, su- pernovae explosions, binary neutron stars, accretion discs of black holes. The effect of collective neutrino oscillations attracts the growing interest in sight of appearance of multi-messenger astron- omy and constructing of new large-volume neutrino detectors that will be highly efﬁcient for observing neutrino ﬂuxes from super- novae explosions. Previously, it was shown that neutrino quantum decoherence can signiﬁcantly modify the neutrino ﬂuxes from reactors and the sun. Here below we study the inﬂuence of the neutrino quantum de- coherence on supernovae neutrino ﬂuxes. The peculiarity of the supernovae ﬂuxes is that one of the main modes of neutrino oscil- lations in supernovae is engendered by the collective effects. We note, that previous works dedicated to collective neutrino oscilla- tions (see [5] and references therein) accounted only for the kine- matical decoherence. 2 Equations of motion Consider the two-ﬂavor neutrino mixing scenarios, i.e. the mixing between νe and νx states where νx stands for νµ or ντ. Here below we focus on the derivation of the neutrino oscillation probability and highlight the interplay between collective neutrino oscillations and neutrino quantum decoherence. We use the simpliﬁed model of supernova neutrinos that was considered in [6, 7]. In such a model neutrinos are produced and emitted with a single energy and a single emission angle. The neutrino evolution in supernovae environment that accounts for neutrino quantum decoherence is determined by the following equation idρf dt = [H, ρf] + D[ρf] , id¯ρf dt = [ ¯H, ¯ρf] + D[¯ρf], (1) where ρf (¯ρf) is the density matrix for neutrino (antineutrino) in the ﬂavour basis and H ( ¯H) are total neutrino (antineutrino) Hamiltonian. Neutrino quantum decoherence is described by the dissipation term D[ρ] that we deﬁne in the next section. Hamiltonian H contains the three terms H = Hvac + HM + Hνν, (2) where Hvac is the vacuum Hamiltonian, HM and Hνν are Hamil- tonians that describe matter potential and neutrino-neutrino inter- action correspondingly. In the ﬂavour basis they are given by Hvac = δm2 4E −cos(2θ) sin(2θ) sin(2θ) cos(2θ)  , (3) HM = √ 2 2 GFne 1 0 0 −1  , (4) Hνν = √ 2GFnν (1 + β)ρf −α(1 + ¯β)¯ρf  , (5) where β represents the initial asymmetry between the electron and x-type neutrinos, and ¯β the asymmetry between electron and x- type antineutrinos, α is the ratio of electron antineutrinos relative to electron neutrinos, ne and nν describe the electron and neutrino density proﬁles. 3 Neutrino quantum decoherence In our previous studies [1–4] we developed a new theoretical framework that enabled one to consider a concrete process of parti- cles interactions as a source of the decoherence. In particular, in [1] a new mechanism of neutrino quantum decoherence engendered by the neutrino radiative decay. In parallel, another framework was developed [8, 9] for the description of the neutrino quantum decoherence due to the non-forward neutrino scattering processes. Both mechanisms are described by the Lindblad master equation in form [10,11]. In this paper we are are not interested in a speciﬁc mechanism of neutrino quantum decoherence. Therefore, we use the Lindblad master equation for the descr