Why Neutrinos Have Mass — The Oscillation Discovery

For thirty years, the Standard Model of particle physics contained massless neutrinos. The choice was not a matter of principle — it was a matter of economy. Right-handed neutrino fields were not included in the minimal construction, which meant no Dirac mass term was allowed. Observed neutrinos all behaved, within the precision of the day, as if they were light enough to treat as massless. The simpler model was adopted.

Then, in the space of three years around the turn of the millennium, two experiments on opposite sides of the world forced the Standard Model to change.

Super-Kamiokande, June 1998

The first evidence came from a 50-kiloton water Cherenkov detector 1,000 metres underground in central Japan. Super-Kamiokande had been running since 1996, recording interactions from atmospheric neutrinos — the flux of electron and muon neutrinos produced when cosmic rays strike the upper atmosphere and the resulting pions decay.

The expected ratio of muon to electron neutrinos at production is about 2:1, set by the pion-decay chain: ${\pi }^{+}\to {\mu }^{+}+{\nu }_{\mu },{\mu }^{+}\to e^{+}+{\nu }_e+{\bar{\nu }}_{\mu }$ Two muon-flavor neutrinos for every electron-flavor neutrino.

Super-K confirmed the 2:1 ratio for downward-going neutrinos — those produced in the atmosphere directly above the detector. But for upward-going neutrinos — produced on the far side of the Earth and travelling up through the planet before reaching the detector — the muon-to-electron ratio was dramatically suppressed. The upward-going muon neutrinos had gone somewhere.

The Super-K analysis team, led by Takaaki Kajita, tested this against the hypothesis of oscillation: if ${\nu }_{\mu }$ oscillates into ${\nu }_{\tau }$ during flight, the longer the distance travelled (the closer the neutrino to Earth-crossing) the more oscillation should have occurred. The data matched almost exactly, with $\Delta m^2\approx 2\times 10^{-3}$ eV² and near-maximal mixing.

Kajita presented the result at the Neutrino ‘98 conference in Takayama on 5 June 1998. By the end of the week, the physics community had accepted the conclusion: neutrinos oscillate between flavors, and therefore must have mass.

Why oscillation implies mass

The argument is short. A neutrino produced in a pure flavor state — say, ${\nu }_{\mu }$ — is in general a superposition of mass eigenstates: $|{\nu }_{\mu }⟩={\sum }_i{U}_{\mu i}^{\ast }|{\nu }_i⟩$ Each mass eigenstate $|{\nu }_i⟩$ propagates with its own phase, determined by its energy $E_i=\sqrt{p^2+m_i^2}$. If the three masses are all equal, the overall phase factors out and no flavor change occurs. If the masses differ, the relative phases evolve, and the flavor composition oscillates.

The oscillation probability depends on the squared-mass differences $\Delta m_{ij}^2=m_i^2-m_j^2$, not on the individual masses. If the Super-K data required $\Delta m^2\ne 0$, then at least two of the three mass eigenstates must have different, non-zero masses. The Standard Model’s massless-neutrino assumption was dead.

SNO, 2001–2002

The second confirmation came from the Sudbury Neutrino Observatory in Ontario, Canada. SNO used 1 kiloton of heavy water ($D_{2}O$) as its target, allowing three distinct detection channels:

• Charged current: ${\nu }_e+d\to p+p+e^{-}$ — only ${\nu }_e$
• Neutral current: ${\nu }_x+d\to p+n+{\nu }_x$ — all flavors, equal weight
• Elastic scattering: ${\nu }_x+e^{-}\to {\nu }_x+e^{-}$ — heavily weighted toward ${\nu }_e$

By comparing the three rates, SNO could separately measure the total flavor-summed solar neutrino flux and the electron-neutrino fraction. The 2001 and 2002 results were clear: ${\Phi }_{NC}=(5.09\pm 0.44)\times 10^6{\text{ cm}}^{-2}{\text{s}}^{-1}$ ${\Phi }_{CC}=(1.76\pm 0.10)\times 10^6{\text{ cm}}^{-2}{\text{s}}^{-1}$ The neutral-current flux — the total flavor-summed rate — matched the Standard Solar Model prediction exactly. The charged-current flux — the ${\nu }_e$-only rate — was about one third of the total. Two thirds of the solar ${\nu }_e$ had transformed into ${\nu }_{\mu }$ or ${\nu }_{\tau }$ during their eight-minute flight from the Sun.

SNO’s result was the direct demonstration: flavor transformation had occurred, flavor had not simply been lost, and the transformed neutrinos were still there — just in different flavors. Arthur McDonald, SNO’s director, shared the 2015 Nobel Prize with Kajita for this work.

Resolving the Solar Neutrino Problem

The SNO measurement also closed a thirty-year-old puzzle. Ray Davis’s Homestake chlorine experiment had been reporting a solar neutrino deficit — about one-third of the predicted rate — since 1968. Davis’s measurement was sensitive only to ${\nu }_e$, and the deficit had been interpreted variously as a problem with the Standard Solar Model, a systematic error at Homestake, or new neutrino physics.

SNO showed that the Standard Solar Model was fine, Davis’s experiment was fine, and the “missing” neutrinos were real — they had just become other flavors in flight. Davis had been measuring the ${\nu }_e$ survival probability of about 0.35 in the MSW-LMA oscillation regime, though he didn’t know it for thirty years.

The current picture

Since 1998/2001, oscillation has been independently confirmed in many channels and parameter combinations:

• Reactor antineutrinos at KamLAND (2003) confirmed the solar-sector parameters with a terrestrial source
• Reactor antineutrinos at Daya Bay, RENO, and Double Chooz (2012) measured the smallest mixing angle ${\theta }_{13}$
• Accelerator appearance at T2K and NOvA (ongoing) measures the CP-violating phase ${\delta }_{CP}$
• Atmospheric neutrinos at IceCube-DeepCore (ongoing) refine the atmospheric mixing parameters

The three-flavor oscillation framework with a PMNS mixing matrix is now a tested, quantitative theory. Its free parameters — three mixing angles, one Dirac phase, two mass-squared differences, and (if neutrinos are Majorana) two further phases — have nearly all been measured.

What remains

Even with oscillation firmly established, the absolute mass scale is not yet known. Oscillation measures differences, not values. The minimum $\sum m_{\nu }$ consistent with oscillation is about 0.06 eV in normal ordering. The maximum, from cosmology and tritium-endpoint experiments, is about 0.12 eV.

Whether neutrinos are their own antiparticles (Majorana) or distinct from them (Dirac) is also open. Neutrinoless double beta decay searches are the key probe, and no signal has yet been detected.

The 2015 Nobel Prize citation — “for the discovery of neutrino oscillations, which shows that neutrinos have mass” — captured a single fact that took 70 years from Pauli’s postulate to establish. The next 70 years will determine whether neutrinos are Dirac or Majorana, what their absolute mass is, and whether their CP-violating phase contributed to the matter-antimatter asymmetry of the universe. Each of those questions is the subject of at least one active frontier experiment.