- Open Access
Interactions of neutrino wave packets
Phys. Rev. D 113, 043010 – Published 5 February, 2026
DOI: https://doi.org/10.1103/r54h-jj1f
Abstract
The low energy effective field theory of interacting neutrinos derived from the Standard Model may be framed as a pointlike interaction and thereby modeled on a lattice of neutrino momenta. We identify a path to take a continuum limit of this lattice problem in the center of momentum frame. In this limit, the weak interaction is found to become trivial between incoming plane waves describing ultrarelativistic particles, unless finite neutrino wave packet sizes are taken into consideration. We follow up with an analytic treatment of interacting neutrino wave packets, demonstrating the importance of the wave packet size for characterizing neutrino-neutrino scattering in dense environments.
Physics Subject Headings (PhySH)
Article Text
References (43)
- Stanislav P. Mikheev and A. Yu. Smirnov, Resonance oscillations of neutrinos in matter, Sov. Phys. Usp. 30, 759 (1987).
- James Pantaleone, Neutrino oscillations at high densities, Phys. Lett. B 287, 128 (1992).
- Stuart Samuel, Neutrino oscillations in dense neutrino gases, Phys. Rev. D 48, 1462 (1993).
- Alexander Friedland and Cecilia Lunardini, Neutrino flavor conversion in a neutrino background: Single- versus multi-particle description, Phys. Rev. D 68, 013007 (2003).
- Alexander Friedland and Cecilia Lunardini, Do many-particle neutrino interactions cause a novel coherent effect?, J. High Energy Phys. 10 (2003) 043.
- C. Lunardini, Neutrino flavor conversion in a neutrino background: Coherent scattering and many body effects, Nucl. Phys. B, Proc. Suppl. 138, 353 (2005).
- Bruce H. J. McKellar and Mark J. Thomson, Oscillating neutrinos in the early universe, Phys. Rev. D 49, 2710 (1994).
- Alexander Friedland, Bruce H. J. McKellar, and Ivona Okuniewicz, Construction and analysis of a simplified many-body neutrino model, Phys. Rev. D 73, 093002 (2006).
- Bruce H. J. McKellar, Ivona Okuniewicz, and James Quach, Non-Boltzmann behavior in models of interacting neutrinos, Phys. Rev. D 80, 013011 (2009).
- Nicole F. Bell, R. F. Sawyer, and Raymond R. Volkas, Entanglement and quantal coherence: Study of two limiting cases of rapid system-bath interactions, Phys. Rev. A 65, 052105 (2002).
- Nicole F. Bell, Andrew A. Rawlinson, and R. F. Sawyer, Speed-up through entanglement—many-body effects in neutrino processes, Phys. Lett. B 573, 86 (2003).
- R. F. Sawyer, Speed-up of neutrino transformations in a supernova environment, Phys. Rev. D 72, 045003 (2005).
- Michael J. Cervia, Amol V. Patwardhan, and A. B. Balantekin, Symmetries of Hamiltonians describing systems with arbitrary spins, Int. J. Mod. Phys. E 28, 1950032 (2019).
- Amol V. Patwardhan, Michael J. Cervia, and A. Baha Balantekin, Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem, Phys. Rev. D 99, 123013 (2019).
- Michael J. Cervia, Amol V. Patwardhan, and A. B. Balantekin, S. N. Coppersmith, and Calvin W. Johnson, Entanglement and collective flavor oscillations in a dense neutrino gas, Phys. Rev. D 100, 083001 (2019).
- Amol V. Patwardhan, Michael J. Cervia, and A. B. Balantekin, Spectral splits and entanglement entropy in collective neutrino oscillations, Phys. Rev. D 104, 123035 (2021).
- Michael J. Cervia, Pooja Siwach, Amol V. Patwardhan, A. B. Balantekin, S. N. Coppersmith, and Calvin W. Johnson, Collective neutrino oscillations with tensor networks using a time-dependent variational principle, Phys. Rev. D 105, 123025 (2022).
- Ermal Rrapaj, Exact solution of multiangle quantum many-body collective neutrino-flavor oscillations, Phys. Rev. C 101, 065805 (2020).
- Alessandro Roggero, Entanglement and many-body effects in collective neutrino oscillations, Phys. Rev. D 104, 103016 (2021).
- Alessandro Roggero, Dynamical phase transitions in models of collective neutrino oscillations, Phys. Rev. D 104, 123023 (2021).
- Zewei Xiong, Many-body effects of collective neutrino oscillations, Phys. Rev. D 105, 103002 (2022).
- Denis Lacroix, A. B. Balantekin, Michael J. Cervia, Amol V. Patwardhan, and Pooja Siwach, Role of non-Gaussian quantum fluctuations in neutrino entanglement, Phys. Rev. D 106, 123006 (2022).
- Denis Lacroix, Angel Bauge, Bulent Yilmaz, Mariane Mangin-Brinet, Alessandro Roggero, and A. Baha Balantekin, Phase-space methods for neutrino oscillations: Extension to multibeams, Phys. Rev. D 110, 103027 (2024).
- Joshua D. Martin, Duff Neill, A. Roggero, Huaiyu Duan, and J. Carlson, Equilibration of quantum many-body fast neutrino flavor oscillations, Phys. Rev. D 108, 123010 (2023).
- Marc Illa and Martin J. Savage, Multi-neutrino entanglement and correlations in dense neutrino systems, Phys. Rev. Lett. 130, 221003 (2023).
- Ivan Chernyshev, Caroline E. P. Robin, and Martin J. Savage, Quantum magic and computational complexity in the neutrino sector, Phys. Rev. Res. 7, 023228 (2025).
- Shashank Shalgar and Irene Tamborra, Do we have enough evidence to invalidate the mean-field approximation adopted to model collective neutrino oscillations?, Phys. Rev. D 107, 123004 (2023).
- Manuel Goimil-García, Shashank Shalgar, and Irene Tamborra, Pauli blocking: Probing beyond-mean-field effects in neutrino flavor evolution, Phys. Rev. D 111, 083054 (2025).
- Vincenzo Cirigliano, Srimoyee Sen, and Yukari Yamauchi, Neutrino many-body flavor evolution: The full Hamiltonian, Phys. Rev. D 110, 123028 (2024).
- Zoha Laraib and Sherwood Richers, Many-body simulations of the fast flavor instability, Phys. Rev. D 112, L101304 (2025).
- Anson Kost, Lucas Johns, and Huaiyu Duan, Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration, Phys. Rev. D 109, 103037 (2024).
- Boris Kayser, On the quantum mechanics of neutrino oscillation, Phys. Rev. D 24, 110 (1981).
- Evgeny Kh. Akhmedov and Alexei Yu. Smirnov, Paradoxes of neutrino oscillations, Phys. At. Nucl. 72, 1363 (2009).
- Evgeny Akhmedov, Joachim Kopp, and Manfred Lindner, Collective neutrino oscillations and neutrino wave packets, J. Cosmol. Astropart. Phys. 09 (2017) 017.
- Ken Kiers, Shmuel Nussinov, and Nathan Weiss, Coherence effects in neutrino oscillations, Phys. Rev. D 53, 537 (1996).
- J. Schechter and J. W. F. Valle, Neutrino masses in SU(2) U(1) theories, Phys. Rev. D 22, 2227 (1980).
- G. Sigl and G. Raffelt, General kinetic description of relativistic mixed neutrinos, Nucl. Phys. B406, 423 (1993).
- James D. Bjorken and Sidney D. Drell, Relativistic Quantum Mechanics, International Series In Pure and Applied Physics (McGraw-Hill, New York, 1965).
- Michael Jason Cervia, Many-body theory of collective neutrino oscillations, Ph.D. thesis, Wisconsin University, Madison, 2021.
- F. Halzen and Alan D. Martin, Quarks and Leptons: An Introductory Course In Modern Particle Physics (John Wiley & Sons, New York, 1984).
- A B Balantekin and Y Pehlivan, Neutrino–neutrino interactions and flavour mixing in dense matter, J. Phys. G 34, 47 (2006).
- Gerald A. Miller, On the impossibility of obtaining time-independent, three-dimensional, spherically-symmetric densities of confined systems of relativistically moving constituents, Phys. Rev. C 112, 045204 (2025).
- Huaiyu Duan, George M. Fuller, and Yong-Zhong Qian, Collective neutrino oscillations, Annu. Rev. Nucl. Part. Sci. 60, 569 (2010).