Neutrino Oscillation

Introduction to Neutrino Oscillation

Neutrino oscillation, now a well-understood phenomenon, indicates that neutrinos have mass, and their flavor eigenstates are different from their mass eigenstates. Neutrino oscillations provide the first evidence of physics be- yond the Standard Model of the elementary particles. Over eight decades, our picture of neutrino physics has been revolutionized, but some fundamental questions still remain unanswered. Neutrino oscillations spring from a quantum mechanical mixing between the mass and flavor eigenstates of neutrinos. Neutrinos, which are observed in the experiments, are created with other fermions through weak nuclear force, which does not change the flavor of the particle. The ν_e, ν_μ and ν_τ are labeled as the flavor eigenstates of neutrinos (generalized as ν_α). The only way flavor eigenstates of neutrinos can be constructed to be invariant under weak nuclear force is a mixture of exactly the right portion of the three flavor-mixed eigenstates ν₁, ν₂ and ν₃. The flavor eigenstates can be derived from the mass eigenstates with a leptonic mixing matrix U_αi, so-called PMNS mixing matrix. The probability of observing a neutrino of flavor β (ν_β) at time t (equivalent to distance L) from a neutrino of original flavor α (ν_α) is then given by:

Oscillation probabilities from ν_μ to ν_e (black), ν_μ (blue) and ν_τ (red). Credit: wikipedia

The above graph is examples of oscillation probability from ν_μ to ν_e (black), ν_μ (blue) and ν_τ (red) an initial muon (flavor) neutrino to other flavors (electron, muon, tau) neutrinos. The oscillation probabilities depend on the baseline (distance btw neutrino production source and neutrino detector) and neutrino energy.

How can we measure neutrino oscillations?

To measure neutrino oscillations, at first we need a source of neutrino in which neutrino flavor components (number of electron neutrinos, muon neutrino, tau neutrinos) are well-understood. It can be from nature (the sun, atmospheric, supernova, etc..) or man-made source (accelerator, accelerator, etc..). In principle, one large detector, which is placed at the location such that the considering oscillation probability is almost maximum, is enough. However, an additional detector placed near the neutrino source (so-called near detector, and the previous one is so-called far detector) is often necessary to understand the neutrino flux before neutrino oscillates.This is so-called two-detector baseline paradigm. In current long-baseline neutrino experiments, T2K and NOvA uses far detector at 295km and 810km away from the neutrino source respectively. These optimal baselines depends mainly on energy of neutrino flux and target of the neutrino physics. There are two conventional ways to measure neutrino oscillation: disappearance and appearance.

Disappearance: to see how much neutrino of original flavor α (ν_α) reduces after traveling a defined distance. For example, you have a beam of ν_μ and you predict that you will see N_{ν_μ} neutrino events of classified ν_μ in detector. However what you observed is M_{ν_μ} events, which is smaller the predicted N_{ν_μ}. In that case, we say, ν_μ is deficit or ν_μ is disappeared.
Appearance: to see a how much neutrino of new flavor β (ν_β) is appeared from a defined neutrino να flux (𝛽≠α). For example, you have a beam of ν_μ and you predict that you will see N_{ν_e} event of ν_e in your detector (can be from intrinsic beam- there is no beam with 100% ν_μ, or from misclassified event) if neutrino oscillation is not existed. However you observe M_{ν_μ} events of classified ν_e event, which is larger the predicted N_{ν_e}. In this case, we say ν_e is appeared.

It is reminded that the neutrino oscillation probability depends on its energy. Thus for precise measurement, it is necessary to reconstruct energy for each neutrino event and present disappearance or appearance as a function of energy. These pattern then is fitted with the oscillation probability formulas to extract the neutrino oscillation parameters.