1 Collective Neutrino Oscillations by Basudeb Dasgupta

Neutrino oscillation, the quantum transmutation of one type of neutrino to another, takes on a puzzling new form when the density of neutrinos is very large. This new kind of neutrino oscillation, called collective neutrino oscillation, has presented an interesting challenge for theoretical physicists. Although many aspects remain to be fully understood, its anticipated impact on the explosion of stars and the creation of elements therein promises a new tool for studying supernovae.

Supernovae mark the end of massive stars’ lives, resulting in a powerful explosion. When a massive star depletes its nuclear fuel, its core collapses due to gravity, creating extreme pressure and temperature. This leads to the rapid production of neutrinos through various reactions, mainly electron capture and positron–electron annihilation. These neutrinos play a key role in the explosion by escaping the collapsing core, carrying away a substantial amount of energy, and causing the star to explode as a supernova. Neutrinos are pivotal in this cosmic event.

Neutrinos, elementary particles with three flavors (electron, muon, tau), are unique for their electrically neutral, tiny-mass, and weakly interacting nature, earning them the nickname “ghost particles.” They exhibit a remarkable ability to oscillate between flavors during their journey through space, a concept first theorized in the 1960s by Bruno Pontecorvo, Ziro Maki, Masami Nakagawa, and Shoichi Sakata. The discovery of neutrino oscillations, by experiments like Super-Kamiokande and SNO, revolutionized our understanding of neutrinos and particle physics.

In supernovae, neutrinos can be initially produced in any one of the flavors. As they traverse the star’s outer layers, dense matter can influence their flavor transition. This process is akin to the Mikheyev–Smirnov–Wolfenstein (MSW) effect, proposed in the mid-1980s, that explains the observed deficit of solar neutrinos through partial conversion of the emitted electron neutrinos into other flavors. What is particularly intriguing about neutrino oscillations in supernovae is their dependence on neutrino density in the medium. Unlike neutrinos traveling through empty space or ordinary matter (without a significant contribution from other neutrinos), oscillations within a supernova are also affected by neutrino-neutrino interactions. This self-interaction occurs because neutrinos can scatter off one another through neutral current interactions. The forward-scattering amplitude, where there is no change in the momentum of the neutrino, adds coherently and induces a flavor-dependent effect proportional to the neutrino density.

Theorized by James Pantaleone in a remarkable paper in 1992, this new route for flavor transmutation has been a topic of intense study for the past three decades. Three remarkable features were discovered in mathematical (and computer-based) studies of these collective oscillations: First, collective oscillations can lead to large flavor exchanges, much larger than the small matter-effect suppressed mixing due to the mixing matrix alone. This feature is called an “instability.” Second, these changes take place uniformly among all neutrinos, regardless of their energy or emission direction. This “collective” evolution is rather distinctive and differs from the typical oscillations observed in ordinary neutrinos. Similar collective behavior can be observed in various situations where numerous independent entities end up acting in harmony, such as the coordinated flights of a flock of birds or a school of fish. Even the movements of people in crowded areas exhibit elements of this collective motion, whether it is the Mexican waves in a sports stadium or the synchronized actions of daily commuters in a crowded train station. And third, these changes can occur within remarkably short timeframes (even on the order of nanoseconds), which is, in fact, quicker than any of the neutrinos would have evolved left to themselves. This very unusual feature was compared to a marching band outrunning Usain Bolt! This aspect has often been described as “fast” evolution, to distinguish it from other kinds of collective evolution of neutrinos.

Two primary questions stand out:

  1. What circumstances lead to these collective instabilities? It is critical to ascertain whether these instabilities occur in the dense regions of a star quite generically, or if such unusual oscillations demand highly specific and rare conditions not commonly found in nature.

  2. What happens to neutrinos that have undergone collective oscillations? Oscillations cause a periodic, time-dependent alteration in the flavor makeup of the emitted neutrino flux from the star. Are these changes observable, and what consequences do they carry?

In a series of papers (see refs. [1,2,3,4]) over the last few years, our focus has been on predicting the conditions for instability and ascertaining its ultimate impact. We have identified a fundamental criterion: for instability to occur, the phase space distributions for two flavors need to cross each other at some energies or emission directions. If only one flavor dominates across all energies and angles, no instability arises. As for the ultimate impact of collective oscillations, further investigation is needed, but our findings suggest a partial and irreversible mixing of flavors, known as “depolarization.”

Collective neutrino flavor oscillations may have relevance in a number of ways:

  1. Supernova explosion mechanism: Neutrinos are pivotal in supernova explosions, carrying away crucial energy. Understanding neutrino oscillations is vital for deciphering the explosion process.

  2. Neutrino properties: Supernovae can provide insights into neutrino properties, including the mass ordering.

  3. Supernova neutrino observations: Neutrino detectors like Super-Kamiokande, IceCube, and DUNE aim to observe supernova neutrinos and may find evidence for collective oscillations.

  4. Formation of chemical elements: Collective oscillations may impact the synthesis of heavy elements in supernovae and our understanding of cosmic isotopes. These may be an indirect way to study collective oscillations.

The behavior of collective oscillations in supernovae is intricate and depends on diverse factors, including the neutrino energy spectra, the angular distributions, and the electron and neutrino density profiles within the star. Most of these ingredients are not known. Numerical simulations and theoretical models have been developed to estimate them, but a precise and reliable description remains challenging.

Collective neutrino oscillations in supernovae bridge astrophysics and particle physics, offering insights into cosmic phenomena and fundamental particles. Ongoing research promises to unveil more about these intriguing processes. Several key steps are expected to be undertaken in the coming years: improvements in numerical simulations of the star and neutrinos therein, commissioning of upcoming experiments like DUNE and Hyper-Kamiokande that hold promise for precise supernova neutrino observations, and better understanding of the connections between collective oscillations and nucleosynthesis. This quantum dance of the smallest particles in the backdrop of grandest cosmic explosions, therefore presents a worthy challenge and a rare opportunity.