Abstract
Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations and their consistency with the uncertainty principle are still debated. The goals of the present work are threefold. First, it clarifies the structure of the Liouville term in the presence of mixing. Second, we derive evolution equation for neutrinos propagating in vacuum or matter from the Schrödinger equation and show that in the relativistic limit its form matches the form of the (collisionless part of the) kinetic equation derived by Sigl and Raffelt. Third, by constructing solutions of the evolution equation from the known solutions of the Schrödinger equation, we show that the former also admits solutions consistent with the uncertainty principle and accounts for neutrino wave packet separation. The obtained results speak in favor of a (quantum) kinetic approach to the analysis of neutrino propagation in exploding supernovae where neutrino oscillations and collisions, as well as the effect of wave packet separation, might be equally important.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Davis Jr., D.S. Harmer and K.C. Hoffman, Search for neutrinos from the sun, Phys. Rev. Lett.20 (1968) 1205 [INSPIRE].
V.N. Gribov and B. Pontecorvo, Neutrino astronomy and lepton charge, Phys. Lett.B 28 (1969) 493 [INSPIRE].
V.N. Gavrin and B.T. Cleveland, Radiochemical solar neutrino experiments, Nucl. Phys. Proc. Suppl.221 (2011) 90 [nucl-ex/0703012] [INSPIRE].
A. Strumia and F. Vissani, Neutrino masses and mixings and … , hep-ph/0606054 [I NSPIRE].
Super-Kamiokande collaboration, Solar neutrino measurements in Super-Kamiokand e-I, Phys. Rev.D 73 (2006) 112001 [hep-ex/0508053] [INSPIRE].
E.K. Akhmedov and A.Y. Smirnov, Paradoxes of neutrino oscillations, Phys. Atom. Nucl.72 (2009) 1363 [arXiv:0905.1903] [INSPIRE].
R.S.L. Hansen and A.Y. Smirnov, The Liouville equation for flavour evolution of neutrinos and neutrino wave packets, JCAP12 (2016) 019 [arXiv:1610.00910] [INSPIRE].
E. Akhmedov, J. Kopp and M. Lindner, Collective neutrino oscillations and neutrino wave packets, JCAP09 (2017) 017 [arXiv:1702.08338] [INSPIRE].
G. Sigl and G. Raffelt, General kinetic description of relativistic mixed neutrinos, Nucl. Phys.B 406 (1993) 423 [INSPIRE].
A.D. Dolgov, Neutrinos in the Early Universe, Sov. J. Nucl. Phys.33 (1981) 700 [INSPIRE].
S. Yamada, Boltzmann equations for neutrinos with flavor mixings, Phys. Rev.D 62 (2000) 093026 [astro-ph/0002502] [INSPIRE].
A. Vlasenko, G.M. Fuller and V. Cirigliano, Neutrino Quantum Kinetics, Phys. Rev.D 89 (2014) 105004 [arXiv:1309.2628] [INSPIRE].
V. Cirigliano, G.M. Fuller and A. Vlasenko, A New Spin on Neutrino Quantum Kinetics, Phys. Lett.B 747 (2015) 27 [arXiv:1406.5558] [INSPIRE].
A. Vlasenko, G.M. Fuller and V. Cirigliano, Prospects for Neutrino-Antineutrino Transformation in Astrophysical Environments, arXiv:1406.6724 [INSPIRE].
D.N. Blaschke and V. Cirigliano, Neutrino Quantum Kinetic Equations: The Collision Term, Phys. Rev.D 94 (2016) 033009 [arXiv:1605.09383] [INSPIRE].
S.A. Richers, G.C. McLaughlin, J.P. Kneller and A. Vlasenko, Neutrino Quantum Kinetics in Compact Objects, Phys. Rev.D 99 (2019) 123014 [arXiv:1903. 00022] [INSPIRE].
E.K. Akhmedov and J. Kopp, Neutrino Oscillations: Quantum Mechanics vs. Quantum Field Theory, JHEP04 (2010) 008 [Erratum JHEP10 (2013) 052] [arXiv:1001.4815] [INSPIRE].
G. Cozzella and C. Giunti, Mixed states for mixing neutrinos, Phys. Rev.D 98 (2018) 096010 [arXiv:1804.00184] [INSPIRE].
W. Grimus, Revisiting the quantum field theory of neutrino oscillations in vacuum, arXiv: 1910.13776 [INSPIRE].
W. Grimus, Neutrino physics - Theory, Lect. Notes Phys.629 (2004) 169 [hep-ph/0307149] [INSPIRE].
W. Grimus, P. Stöckinger and S. Mohanty, The Field theoretical approach to coherence in neutrino oscillations, Phys. Rev.D 59 (1999) 013011 [hep-ph/9807442] [INSPIRE].
W. Grimus and P. Stöckinger, Real oscillations of virtual neutrinos, Phys. Rev.D 54 (1996) 3414 [hep-ph/9603430] [INSPIRE].
T. Stirner, G. Sigl and G. Raffelt, Liouville term for neutrinos: Flavor structure and wave interpretation, JCAP05 (2018) 016 [arXiv:1803.04693] [INSPIRE].
M. Sirera and A. Perez, Relativistic Wigner function approach to neutrino propagation in matter, Phys. Rev.D 59 (1999) 125011 [hep-ph/9810347] [INSPIRE].
C.Y. Cardall, Liouville equations for neutrino distribution matrices, Phys. Rev.D 78 (2008) 085017 [arXiv:0712.1188] [INSPIRE].
M. Gamy, A. Kartavtsev and A. Hohenegger, Leptogene sis from first principles in the resonant regime, Annals Phys.328 (2013) 26 [arXiv:1112.6428] [INSPIRE].
A. Kartavtsev, P. Millington and H. Vogel, Lepton asymmetry from mixi ng and oscillations, JHEP06 (2016) 066 [arXiv:1601.03086] [INSPIRE].
M. Herranen, K. Kainulainen and P.M. Rahkila, Kinetic theory for scalar fields with nonlocal quantum coherence, JHEP05 (2009) 119 [arXiv:0812.4029] [INSPIRE].
M. Herranen, K. Kainulainen and P.M. Rahkila, Coherent quantum Bolt zmann equations from cQPA, JHEP12 (2010) 072 [arXiv:1006.1929] [INSPIRE].
M. Herranen, K. Kainulainen and P.M. Rahkila, Flavour-coherent propagators and Feynman rules: Covariant cQPA formulation, JHEP02 (2012) 080 [arXiv:1108.2371] [INSPIRE].
C. Fidler, M. Herranen, K. Kainulainen and P.M. Rahkila, Flavoured quantum Boltzmann equations from cQPA, JHEP02 (2012) 065 [arXiv:1108.2309] [INSPIRE].
M. Blasone, P.A. Henning and G. Vitiello, The Exact formula for neutrino oscillations, Phys. Lett.B 451 (1999) 140 [hep-th/9803157] [INSPIRE].
A.E. Bernardini and S. De Leo, Dirac spinors and flavor oscillations, Eur. Phys. J.C 37 (2004) 471 [hep-ph/0411153] [INSPIRE].
M. Blasone, P. Jizba and L. Smaldone, Flavor Energy uncertainty relations for neutrino oscillations in quantum field theory, Phys. Rev .D 99 (2019) 016014 [arXiv:1810.01648] [INSPIRE].
M. Blasone, L. Smaldone and G. Vitiello, Flavor neutrino states for pedestrians, J. Phys. Conf. Ser.1275 (2019) 012023 [arXiv:1903.01401] [INSPIRE].
A. Kobach, A.V. Manohar and J. McGreevy, Neutrino Oscillation Measurements Computed in Quantum Field Theory, Phys. Lett.B 783 (2018) 59 [arXiv:1711.07491] [INSPIRE].
R. Dickinson, J. Forshaw and P. Millington, Probabilities and signalling in quantum field theory, Phys. Rev .D 93 (2016) 065054 [arXiv:1601.07784] [INSPIRE].
B. Ferretti, Propagation of Signals and Particles, in Old and New Problems in Elementary Particles, Academic Press, New York U.S.A. (1968), pp. 108-119.
E.A. Power and T. Thirunamachandran, Analysis of the causal behavior in energy transfer between atoms, Phys. Rev.A 56 (1997) 3395.
G.G. Raffelt and I. Tamborra, Synchronization versus decohere nce of neutrino oscillations at intermediate densities, Phys. Rev.D 82 (2010) 125004 [arXiv:1006.0002] [INSPIRE].
S. Airen, F. Capozzi, S. Chakraborty, B. Dasgupta, G. Raffelt and T. Stirner, Normal-mod e Analysis for Collective Neutrino Oscillations, JCAP12 (2018) 019 [arXiv:1809.09137] [INSPIRE].
F. Capozzi, B. Dasgupta, A. Mirizzi, M. Sen and G. Sigl, Collisional triggering of fast flavor conversions of supernova neutrinos, Phys. Rev. Lett.122 (2019) 091101 [arXiv:1808.06618] [INSPIRE].
F. Capozzi, G. Raffelt and T. Stirner, Fast Neutrino Flavor Conversion: Collective Motion vs. Decoherence, JCAP09 (2019) 002 [arXiv:1906.08794] [INSPIRE].
S. Abbar, H. Duan, K. Sumiyoshi, T. Takiwaki and M.C. Volpe, Fast Neutrino Flavor Conversion Modes in Multidimensional Core-collapse Supernova Models: the Role of the Asymmetric Neutrino Distributions, arXiv:1911.01983 [INSPIRE].
L. Johns, H. Nagakura, G.M. Fuller and A. Burrows, Neutrino oscillations in supernovae: angular moments and fast instabilities, arXiv:1910.05682 [INSPIRE].
M. Chakraborty and S. Chakraborty, Three flavor neutrino conv ersions in supernovae: Slow & Fast instabilities, arXiv:1909.10420 [INSPIRE].
M.J. Cervia, A.V. Patwardhan, A.B. Balantekin, S.N. Coppersmith and C.W. Johnson, Entanglement and collective flavor oscillations in a dense neutrino gas, Phys. Rev.D 100 (2019) 083001 [arXiv:1908.03511] [INSPIRE].
C. Döring, R.S.L. Hansen and M. Lindner, Stability of three neutrino flavor conversion in supernovae, JCAP08 (2019) 003 [arXiv:1905.03647] [INSPIRE].
S. Shalgar, I. Padilla-Gay and I. Tamborra, Neutrino propagation hinders fast pairwise flavor conversions, arXiv:1911.09110 [INSPIRE].
J. Kersten and A.Y. Smirnov, Decoherence and oscillations of supernova neutrinos, Eur. Phys. J. C 76 (2016) 339 [arXiv:1512.09068] [INSPIRE].
G. Lindblad, On the Generators of Quantum Dynamical Semigroups, Commun. Math. Phys.48 (1976) 119 [INSPIRE].
F. Benatti and R. Floreanini, Open system approach to neutrino oscillations, JHEP02 (2000) 032 [hep-ph/0002221] [INSPIRE].
M.J. Thomson, The Damping of quantum coherence by elastic and inelastic processes, Phys. Rev.A 45 (1992) 2243 [INSPIRE].
S.P. Mikheyev and A.Y. Smirnov, Resonant neutrino oscillations in matter, Frog. Part. Nucl. Phys.23 (1989) 41 [INSPIRE].
M. Maltoni and A.Y. Smirnov, Solar neutrinos and neutrino physics, Eur. Phys. J.A 52 (2016) 87 [arXiv:1507.05287] [INSPIRE].
A. Hohenegger, A. Kartavtsev and M. Lindner, Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space- Time, Phys. Rev.D 78 (2008) 085027 [arXiv:0807.4551] [INSPIRE].
M. Garny, A. Hohenegger, A. Kartavtsev and M. Lindner, Systematic approach to leptogenesis in nonequilibrium QFT: Self-energy contribution to the CP-violating parameter, Phys. Rev.D 81 (2010) 085027 [arXiv:0911.4122] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1404.5626
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Kartavtsev, A. Relating quantum mechanics and kinetics of neutrino oscillations. J. High Energ. Phys. 2020, 138 (2020). https://doi.org/10.1007/JHEP01(2020)138
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)138