The Neutrino in the Standard Model

The Standard Model organizes elementary fermions into three generations, each with two quarks and two leptons:

Each neutrino shares a weak-isospin doublet with its charged lepton. In the minimal Standard Model, only left-handed neutrinos exist; right-handed neutrinos, if present, would be sterile (singlets under all gauge groups).

Gauge interactions

Neutrinos participate in weak interactions through both charged-current and neutral-current vertices.

Charged current — a neutrino absorbs or emits a $W^{\pm }$ boson, converting to its charged-lepton partner: ${\nu }_{\ell }+n\to {\ell }^{-}+p$ This is the process by which flavor is identified at detectors such as Super-Kamiokande and DUNE.

Neutral current — a neutrino scatters off a target via $Z^0$ exchange without changing flavor: $\nu +X\to \nu +X$ Neutral-current scattering is flavor-blind and was the pivotal measurement used by SNO to resolve the solar neutrino problem: the total neutrino flux (all flavors, from neutral-current data) matched the Standard Solar Model while the electron-neutrino flux (from charged-current data) was deficient by two-thirds.

The mass problem

In the minimal Standard Model a Dirac mass term $m{\bar{\psi }}_L{\psi }_R+\text{h.c.}$ requires both chiralities to exist. Since right-handed neutrinos are absent from the minimal model, the neutrino cannot acquire mass in the same way the charged leptons do. The original formulation simply set $m_{\nu }=0$.

The 1998 Super-Kamiokande observation of atmospheric oscillations and the 2001–2002 SNO confirmation with solar neutrinos made clear that this cannot be correct. At least two neutrino mass eigenstates are non-zero and non-degenerate. The Standard Model must therefore be extended.

Extension 1: add right-handed neutrinos (Dirac mass)

The simplest extension introduces three right-handed neutrino fields ${\nu }_R$, sterile under $SU(2{)}_L\times U(1{)}_Y$. A Dirac mass then arises through Yukawa coupling to the Higgs: ${\mathcal{L}}_Y\supset -y_{\nu }\bar{L}\tilde{H}{\nu }_R+\text{h.c.}⟹m_{\nu }=y_{\nu }v/\sqrt{2}$ For $m_{\nu }\sim 0.1$ eV and the Higgs VEV $v=246$ GeV, the required Yukawa is $y_{\nu }\sim 10^{-12}$, twelve orders of magnitude below the top Yukawa. This is theoretically unsatisfying but not inconsistent.

Extension 2: Majorana mass via the Weinberg operator

A second possibility is the unique dimension-five operator compatible with Standard Model symmetries, introduced by Steven Weinberg in 1979: ${\mathcal{L}}_{\text{Weinberg}}=-\frac{c_{\alpha \beta }}{\Lambda }({\bar{L}}_{\alpha }\tilde{H})({\tilde{H}}^{†}{L}_{\beta })+\text{h.c.}$ After electroweak symmetry breaking this yields a Majorana mass $m_{\nu }\sim \frac{c{v}^2}{\Lambda }$ For $m_{\nu }\sim 0.1$ eV and $c\sim 1$, the new-physics scale is $\Lambda \sim 10^{14}$ GeV — close to the grand-unification scale. This is a much more appealing framework theoretically: small neutrino masses arise naturally from physics at a very high scale.

The seesaw mechanism realizes this operator by introducing heavy right-handed neutrinos with large Majorana masses $M\gg v$; integrating them out reproduces the Weinberg operator with $c/\Lambda \sim y_{\nu }^2/M$.

What is known, what is not

The Standard Model framework plus the minimal mass extension accommodates the oscillation data. But several fundamental questions remain open:

1. Dirac or Majorana? — Whether neutrinos are distinct from antineutrinos is unresolved. Neutrinoless double beta decay is the key experimental probe.
2. Absolute mass scale — Oscillation measures squared differences only. KATRIN and cosmological data provide bounds but not values.
3. Mass ordering — Whether $m_3$ is the largest or smallest mass eigenstate.
4. CP violation — The PMNS phase ${\delta }_{CP}$ is beginning to be measured by T2K, NOvA, and DUNE; its value may shed light on the matter-antimatter asymmetry of the Universe.
5. Number of flavors — LEP fixes three active species, but additional sterile states remain possible.

The neutrino sector is, in many ways, the most open frontier within the otherwise well-tested Standard Model.

Frequently asked

Are neutrinos part of the Standard Model?

Yes, as the neutral members of the three lepton generations. However, neutrino mass is not accommodated in the minimal Standard Model, which had neutrinos as massless. Accommodating mass requires an extension — either right-handed neutrino fields (Dirac) or a higher-dimension Weinberg operator (Majorana).