The Three Neutrino Flavors

A neutrino’s flavor is the charged lepton it pairs with in a weak-interaction vertex. The Standard Model contains three charged leptons — the electron, muon, and tau — and correspondingly three neutrino flavors: ${\nu }_e$, ${\nu }_{\mu }$, and ${\nu }_{\tau }$. Each flavor, together with its charged partner, forms a weak-isospin doublet:

$\left(\begin{array}{c}{\nu }_e\\ e^{-}\end{array}\right),\left(\begin{array}{c}{\nu }_{\mu }\\ {\mu }^{-}\end{array}\right),\left(\begin{array}{c}{\nu }_{\tau }\\ {\tau }^{-}\end{array}\right)$

How flavor is defined operationally

Flavor is not a label pinned to a neutrino at birth; it is defined by production and detection. A $W^{+}$ boson produced in a charged-current weak interaction can decay to a positron plus electron neutrino, $W^{+}\to e^{+}{\nu }_e$, or to an antimuon plus muon neutrino, $W^{+}\to {\mu }^{+}{\nu }_{\mu }$, or to an antitau plus tau neutrino. The neutrino emitted is given its flavor label by the charged lepton produced with it.

Conversely, when a neutrino undergoes a charged-current interaction on a target, it produces the charged lepton corresponding to its flavor. A ${\nu }_{\mu }$ hitting a nucleon produces a muon in the final state; a ${\nu }_e$ produces an electron. This is the core of how experiments identify neutrino flavor at detection.

Discovery of the three flavors

The first neutrino — the electron neutrino ${\nu }_e$ — was postulated by Pauli in 1930 and detected by Reines and Cowan at the Savannah River reactor in 1956.

The muon neutrino was identified in 1962 at Brookhaven National Laboratory by Leon Lederman, Melvin Schwartz, and Jack Steinberger. They directed a high-energy proton beam at a beryllium target, producing pions that decayed as ${\pi }^{+}\to {\mu }^{+}{\nu }_{\mu }$. A massive steel shield absorbed everything except the resulting neutrinos, which were directed into a spark chamber. The chamber recorded muon tracks from neutrino interactions but no electron tracks — demonstrating that the neutrino paired with the muon is not the same particle as the one paired with the electron. The experiment earned the 1988 Nobel Prize.

The tau neutrino was the last to be observed directly. The tau lepton itself was discovered by Martin Perl at SLAC in 1975, and its partner neutrino was expected by lepton universality. Direct detection came only in 2000, by the DONUT collaboration at Fermilab, which observed the distinct signature of tau leptons produced in neutrino interactions inside nuclear emulsion.

The invisible Z width bound

The number of active, light neutrino flavors is measured independently of oscillation experiments. The $Z$ boson decays to a neutrino–antineutrino pair with a width proportional to the number of kinematically accessible species. Precision measurements of the total $Z$ width at LEP at CERN in the 1990s yielded $N_{\nu }=2.9840\pm 0.0082$ — firmly consistent with three, and excluding any fourth active neutrino with mass below $m_Z/2\approx 45$ GeV.

Production channels by flavor

Accelerator beams can be configured to produce almost pure ${\nu }_{\mu }$ or ${\bar{\nu }}_{\mu }$ beams by selecting the charge of the focused pions. Tau neutrinos are not readily produced at accelerator energies; the DONUT beam used a prompt charm production channel, $D_s\to \tau {\nu }_{\tau }$.

Flavor is not conserved in propagation

Despite the elegance of the lepton-family assignment — electron number, muon number, and tau number were long believed to be separately conserved — the discovery of neutrino oscillations showed that flavor can change during propagation. A ${\nu }_{\mu }$ produced in a pion decay can appear as a ${\nu }_{\tau }$ or ${\nu }_e$ after travelling through vacuum. What is conserved is the total lepton number (or, in some formulations, $B-L$), not the individual family numbers.

This is a direct consequence of neutrino mass and the structure of the PMNS matrix. The charged leptons do not oscillate because they are produced already as mass eigenstates; neutrinos, produced as superpositions of mass eigenstates, accumulate phase differences in flight and thereby change flavor.

Sterile neutrinos

A number of short-baseline experiments have reported anomalies that could be interpreted as oscillations into a fourth, non-interacting flavor — a sterile neutrino with mass $\sim 1$ eV. Such a state would not couple to the $Z$ and is therefore not constrained by the LEP width measurement. Current experimental results remain inconclusive: reactor antineutrino flux measurements, gallium calibration data, and the MiniBooNE electron-like excess have all been cited in favor, while searches at Daya Bay, MINOS+, IceCube, and STEREO have not observed the corresponding disappearance signals expected from the most straightforward sterile models. The situation is tension-filled but not resolved.

Frequently asked

Could there be a fourth, sterile neutrino?

The Standard Model predicts exactly three active flavors, consistent with the invisible Z-boson decay width measured at LEP. Short-baseline oscillation anomalies have motivated searches for an additional 'sterile' neutrino that would not couple to the Z boson, but no definitive evidence has been established.

Are flavor eigenstates the same as mass eigenstates?

No. Flavor eigenstates are defined by weak-interaction production and detection; mass eigenstates are defined by free propagation in vacuum. The two bases are related by the unitary PMNS mixing matrix.