# Collective neutrino oscillations accounting for neutrino quantum decoherence

aa r X i v : . [ h e p - ph ] F e b Collective neutrino oscillations accounting for neutrinoquantum decoherence

Konstantin Stankevich π, β and Alexander Studenikin π,π π Faculty of Physics, Lomonosov Moscow State University,Moscow 119991, Russia π Joint Institute for Nuclear Research,Dubna 141980, Moscow Region, Russia

E-mail: [email protected], [email protected]

In our previous studies (see [1] and references therein) we developed a new theoretical frameworkthat enabled one to consider a new mechanism of neutrino quantum decoherence engendered bythe neutrino radiative decay. In parallel, another framework was developed (see [2] and referencestherein) for the description of the neutrino quantum decoherence due to the non-forward neutrinoscattering processes. Both mechanisms are described by the master equations in the Lindbladform.In the present studies we are are not interested in a speciο¬c mechanism of neutrino quantumdecoherence. Therefore, we use the general Lindblad master equation for the description of theneutrino quantum decoherence and do not ο¬x an analytical expressions for the decoherence andrelaxation parameters.We study the inο¬uence of the neutrino quantum decoherence on collective neutrino oscillations.Collective neutrino oscillations is a phenomenon engendered by neutrino-neutrino interaction. Itis signiο¬cant in diο¬erent astrophysical environments where the neutrino density is extremely high.Examples of such environments are the early universe, supernovae explosions, binary neutron stars,accretion discs of black holes. The eο¬ect of collective neutrino oscillations attracts the growinginterest in sight of appearance of multi-messenger astronomy and constructing of new large-volumeneutrino detectors that will be highly eο¬cient for observing neutrino ο¬uxes from supernovaeexplosions. Previously, it was shown that neutrino quantum decoherence can signiο¬cantly modifythe neutrino ο¬uxes from reactors and the sun. Here below we study the inο¬uence of the neutrinoquantum decoherence on supernovae neutrino ο¬uxes. The peculiarity of the supernovae ο¬uxes isthat one of the main modes of neutrino oscillations in supernovae is engendered by the collectiveeο¬ects. Note, in the previous studies dedicated to the collective neutrino oscillations only thekinematical decoherence (see [3] and references therein) was accounted for. β Speaker Β© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ ollective neutrino oscillations accounting for neutrino quantum decoherence

Konstantin StankevichConsider the two-ο¬avor neutrino mixing scenarios, i.e. the mixing between π π and π π₯ stateswhere π π₯ stands for π π or π π . Here below we focus on the derivation of the neutrino oscillationprobability and highlight the interplay between collective neutrino oscillations and neutrino quantumdecoherence. We use the simpliο¬ed model of supernova neutrinos that was considered in [4, 5]. Insuch 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 deco-herence is determined by the following equations π ππ π ππ‘ = [ π», π π ] + π· [ π π ] , π π Β― π π ππ‘ = [ Β― π», Β― π π ] + π· [ Β― π π ] , (1)where π π ( Β― π π ) is the density matrix for neutrino (antineutrino) in the ο¬avour basis and π» ( Β― π» )are total neutrino (antineutrino) Hamiltonian. Neutrino quantum decoherence is described by thedissipation term π· [ π ] that we deο¬ne in the next section.Hamiltonian π» contains the three terms π» = π» π£ππ + π» π + π» ππ , where π» π£ππ is the vacuumHamiltonian, π» π and π» ππ are Hamiltonians that describe matter potential and neutrino-neutrinointeraction correspondingly. The exact expressions one can ο¬nd in [4, 5]. The dissipation term π· [ π ] we write in the Lindblad form π· [ π Λ π ( π‘ )] = Γ π = h π π , π Λ π π β π i + h π π π Λ π , π β π i , (2)where π π are the dissipative operators that arise from interaction between the neutrino system andthe external environment, π Λ π is the neutrino density matrix in the eο¬ective mass basis. Here below,we omit index β Λ π β in order not overload formulas. The operators π π , π π and π» can be expandedover the Pauli matrices π = π π π π , where π π are composed by an identity matrix and the Paulimatrices. In this case eq. (1) can be written in the following form ππ π ( π‘ ) ππ‘ π π = π π ππ π» π π π ( π‘ ) π π + π· ππ π π ( π‘ ) π π , (3)where the matrix π· ππ = β ππππ { Ξ , Ξ , Ξ } and Ξ , Ξ are the parameters that describe two dissipativeeο¬ects: 1) the decoherence eο¬ect and 2) the relaxation eο¬ect, correspondingly. In the case of theenergy conservation in the neutrino system there is an additional requirement on a dissipativeoperators [6] [ π» π , π π ] =

0. In this case the relaxation parameter is equal to zero Ξ =

0. Herebelow, we consider only the case of the energy conservation, i.e. Ξ = πΏπ π around the initial conο¬guration π π and a corresponding variation of the density dependentHamiltonian πΏπ» π around the initial Hamiltonian π» π : π π = π π + πΏπ π where πΏπ π = π β² π π β πππ‘ + π».π. and π» π = π» π + πΏπ» π where πΏπ» π = π» β² π π β πππ‘ + π».π. . Where one can write π» β² π = ππ» π ππ π π β² π + ππ» π π Β― π π Β― π β² π .In the case of high electron density the in-medium eigenstates initially coincide with the ο¬avorstates. Therefore, the initial conditions are given by π» π = (cid:0) , , π» (cid:1) π and π π = (cid:0) , , π (cid:1) π . Putting2 ollective neutrino oscillations accounting for neutrino quantum decoherence Konstantin Stankevicheverything together and considering only the non-diagonal elements ( π = π π₯ + ππ π¦ ) one obtainsthe following equation for eigenvalues (we neglect the higher-order corrections) ( π β π Ξ ) π β² Β― π β² ! = π΄ π΅ Β― π΄ Β― π΅ ! π β² Β― π β² ! , (4)where on the right-hand side of equation is the stability matrix that coincides with one from [4, 7].In case of a single energy and single emission angle it is expressed as π΄ = ( π» β π» ) β ππ» π π ( π β π ) , π΅ = ππ» π Β― π ( π β π ) , Β― π΄ = ( Β― π» β Β― π» ) β π Β― π» π Β― π ( Β― π β Β― π ) , Β― π΅ = π Β― π» π π ( Β― π β Β― π ) . (5)The eigenvalues are given by π = π Ξ + (cid:16) π΄ + Β― π΄ Β± p ( π΄ β Β― π΄ ) + π΅ Β― π΅ (cid:17) . One cansee that if the eigenvalues have an imaginary part, the non-diagonal elements of the neutrino densitymatrix can grow exponentially and thus the system become unstable, that is, if ( ( π΄ β Β― π΄ ) + π΅ Β― π΅ < , I π (cid:0) ( π΄ β Β― π΄ ) + π΅ Β― π΅ (cid:1) > Ξ . (6)The ο¬rst condition is the same as was derived in [4, 7]. The second term is a new one that wasnot considered before. From eq. (6) one can see, that neutrino quantum decoherence prevents asystem from an exponential growth of non-diagonal elements, i.e. neutrino quantum decoherenceleads to the damping of the neutrino collective oscillations.In this paper we considered for the ο¬rst time the eο¬ect of the neutrino quantum decoherencein supernovae ο¬uxes. We derive new conditions of the collective neutrino oscillations accountingfor neutrino quantum decoherence which can appear as a result of the physics beyond the StandardModel. This work was supported by the Russian Foundation for Basic Research under Grant No.20-52-53022-GFEN-a. The work of KS was also supported by the Russian Foundation for BasicResearch under Grant No. 20-32-90107. References [1] K. Stankevich, A. Studenikin,

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