The Higgs and the Neutrino: A Connection Made Awkward by Mass

In July 2012, ATLAS and CMS at the Large Hadron Collider announced the discovery of a new boson at mass 125 GeV. Within two years, its properties — spin zero, decays consistent with Standard Model predictions, couplings to vector bosons matching theory — had identified it conclusively as the Higgs boson, the long-predicted final piece of the electroweak theory.

The discovery completed a 50-year theoretical journey. Glashow had proposed the SU(2) × U(1) gauge structure in 1961, Salam and Weinberg had grafted the Higgs mechanism onto it in 1967-68, and ‘t Hooft had proven the resulting theory renormalisable in 1971. With the Higgs found, every predicted Standard Model particle had been observed. The Standard Model was, in a strict sense, complete.

For neutrino physics, the discovery posed a question rather than answering one. Every other fermion in the Standard Model — electron, muon, tau, and all six quarks — receives its mass from a Yukawa coupling to the Higgs. The mass is fixed by a parameter, the Yukawa coupling $y_f$, multiplied by the Higgs vacuum expectation value $v=246$ GeV: $m_f=y_f\cdot v/\sqrt{2}$

For the top quark, $y_t\approx 1$ — natural and large. For the electron, $y_e\approx 3\times 10^{-6}$ — very small, but at least non-zero and accessible to measurement.

For the neutrino, if the same mechanism applied, $y_{\nu }\approx 10^{-12}$. Twelve orders of magnitude below the top quark, six below the electron. Why so small?

This is the puzzle. The Higgs gives mass to everything else through a coupling that varies but is always at least within a few orders of magnitude. Neutrinos demand a coupling so small that most physicists find it implausible as a fundamental input. Either the Standard Model has an unnaturally small parameter that we have to accept as a brute fact, or there’s a different mechanism — and the seesaw, with its heavy right-handed Majorana partners, is the most economical alternative.

This post unpacks why the neutrino-Higgs relationship is awkward, what the alternatives are, and how future experiments might distinguish among them.

How the Higgs gives mass to fermions

In the unbroken phase of the Standard Model — temperatures above the electroweak scale, ~100 GeV — all fermions are massless. The gauge symmetry SU(2) × U(1) forbids mass terms.

Below the electroweak scale, the Higgs field acquires a non-zero vacuum expectation value. The Higgs doublet $\varphi$ has a value $⟨\varphi ⟩=(0,v/\sqrt{2})$ in the vacuum. Yukawa interactions, which couple Higgs to fermion bilinears like ${\bar{Q}}_{L}H{t}_R$, become effective mass terms when you replace $H$ with its vev. The result is a fermion mass $m_f=y_{f}v/\sqrt{2}$.

For the down-type quarks and charged leptons, the same machinery works with the conjugate Higgs field $\tilde{\varphi }=i{\sigma }_2{\varphi }^{\ast }$. Same idea, same generation of mass.

This mechanism is elegant. The Higgs vev breaks the electroweak gauge symmetry, gives mass to W and Z bosons, and through Yukawa couplings simultaneously gives mass to fermions. One mechanism, three classes of mass.

Why neutrinos break the pattern

To repeat the trick for neutrinos, you’d need a right-handed neutrino field ${\nu }_R$. In the minimal Standard Model, ${\nu }_R$ doesn’t exist — only the left-handed ${\nu }_L$ that pairs with the charged lepton in the SU(2) doublet. Without ${\nu }_R$, there’s no possible Yukawa coupling for neutrinos, and they remain massless in the original Standard Model.

The discovery of neutrino mass in 1998 made this position untenable. Something has to give the neutrino a non-zero mass. Two options.

Option A: Add right-handed neutrinos and use Higgs Yukawa as usual.

You introduce three new fields, ${\nu }_{R,e}$, ${\nu }_{R,\mu }$, ${\nu }_{R,\tau }$. They are gauge singlets — no SU(2) charge, no U(1) charge, no colour. They couple to the Higgs through Yukawa terms $y_{\nu }\bar{L}\tilde{\varphi }{\nu }_R$ in standard form. After symmetry breaking, this gives the neutrinos a Dirac mass $m_{\nu }=y_{\nu }v/\sqrt{2}$.

For $m_{\nu }\sim 0.1$ eV, the required $y_{\nu }\sim 10^{-12}$. This is the unnatural number.

Option B: Use the seesaw — heavy Majorana right-handed neutrinos.

You still introduce ${\nu }_R$ fields, but you also allow them to have a Majorana mass $M_R$ (since they’re gauge singlets, the gauge symmetry doesn’t forbid it). The Lagrangian then contains both Dirac couplings to the Higgs and a Majorana mass for the right-handed states.

Diagonalising the resulting mass matrix in the limit $M_R\gg v$ produces two eigenstate scales:

• Heavy Majorana states with mass $\sim M_R$
• Light effective neutrinos with mass $m_{\nu }\sim m_D^2/M_R=(y_{\nu }v{)}^2/M_R$

For $y_{\nu }\sim 1$ (natural Yukawa, comparable to the top quark) and $M_R\sim 10^{14}$ GeV, this gives $m_{\nu }\sim 0.1$ eV without fine-tuning. The smallness of the neutrino mass becomes a prediction of the seesaw, not an arbitrary input.

This is the Type-I seesaw mechanism, and it’s why most theorists prefer Majorana neutrinos. Smallness of mass becomes natural rather than fine-tuned.

What the Higgs discovery confirmed

Independently of which neutrino-mass mechanism applies, the Higgs discovery confirmed the underlying framework that makes either option possible.

Spontaneous symmetry breaking is real. The Higgs vev exists, the W and Z get their masses through it, and Yukawa couplings to fermions follow the predicted pattern. The framework is not just theoretical convenience — it describes nature.

The 125-GeV Higgs is consistent with hierarchical Yukawa couplings. Measurements of the Higgs decay rates to $\tau \tau$, $bb$, $WW$, $ZZ$ all match the Standard Model predictions within current precision. The branching fractions to lighter particles (electron, muon) and to heavier (top quark, in production) are also consistent. The Yukawa couplings that the Higgs implements are the ones the Standard Model predicts, scaled by the relevant masses.

No deviation has been observed. Through 12 years of LHC running, the Higgs has matched Standard Model predictions to better than 10% on all measurements. This is a strong constraint on any extension that would modify Higgs-fermion couplings — including extensions that would introduce a different neutrino mass mechanism.

In particular, if neutrinos got Dirac mass through a 10⁻¹² Yukawa coupling, the Higgs would decay invisibly to $\nu \bar{\nu }$ at a tiny but finite rate. Current LHC bounds on invisible Higgs decays sit at roughly 11% branching ratio — far above the predicted 10⁻⁸ from such a coupling. The constraint isn’t useful yet.

Indirect probes of neutrino-Higgs coupling

If we can’t measure $y_{\nu }$ directly, what can we constrain?

Cosmological neutrino mass bound ($\sum m_{\nu }\lesssim 0.12$ eV from Planck + galaxy clustering). This sets the scale: whatever mechanism generates the neutrino mass, the result has to be below this value.

Direct kinematic measurement (KATRIN, Project 8). These measure the absolute mass of ${\nu }_e$ — the value $⟨m_{{\nu }_e}⟩$ that determines what we’d actually call “the neutrino mass”. KATRIN’s current bound is 0.45 eV; Project 8 aims for 0.04 eV.

Neutrinoless double beta decay (KamLAND-Zen, LEGEND, nEXO). Sensitive to the Majorana effective mass $⟨m_{\beta \beta }⟩$. A positive detection would establish neutrinos as Majorana, supporting the seesaw scenario over the Dirac alternative. A null result at meV sensitivity would either rule out Majorana neutrinos or constrain their parameters tightly.

Mass ordering (JUNO, DUNE, Hyper-K, ORCA). Whether $m_3$ is heaviest or lightest affects the value of $⟨m_{\beta \beta }⟩$ and the cosmological mass sum. Already, the data slightly favours normal ordering. JUNO is expected to deliver a 3σ resolution within a few years of operation.

Charged-lepton flavour violation. In some seesaw scenarios, the right-handed neutrinos can mediate $\mu \to e\gamma$, $\mu \to e$ conversion, and other lepton-flavour-violating processes. The current bounds from MEG-II, Mu2e, and similar experiments are consistent with the Standard Model — no positive signal yet.

Heavy neutral leptons (sterile neutrinos at the GeV–TeV scale). If the right-handed neutrinos have masses accessible to colliders, they could be directly produced. Searches at LHCb, CMS, and ATLAS have set bounds, but no positive observation. Some seesaw scenarios with low-scale right-handed neutrinos remain viable.

Combining all these sources, the picture in 2026 is that neutrinos are massive (definitively), with a sum of masses below 0.12 eV (cosmological), with $|U_{ei}|$ values from oscillation, and with no positive signal of Majorana character (yet). Within this empirical landscape, the seesaw mechanism is consistent and theoretically attractive but not yet confirmed.

What would settle the question

A 5σ detection of neutrinoless double beta decay at any of the next-generation experiments would establish neutrinos as Majorana. Combined with mass-ordering determination and a stringent kinematic mass bound from Project 8, this would essentially fix the neutrino-mass mechanism — Type-I seesaw or one of its variants — and constrain the heavy-neutrino mass scale.

A null result at the inverted-ordering meV level (about 15 meV) would constrain the Majorana option severely. The remaining viable scenarios would be either normal-ordering Majorana with very small mass eigenstates, or Dirac neutrinos.

Direct evidence for Dirac character is harder. Kinematic measurements alone don’t distinguish Dirac from Majorana. The only direct test of Dirac character would be observation of non-zero lepton number conservation — for example, $\nu \to \bar{\nu }$ transitions in the early universe constrained by cosmology, or anomalous helicity structure in beta decays.

In practice, the field will progress incrementally. The 2030s will see definitive answers on mass ordering and substantially tighter bounds on $0\nu \beta \beta$. By the 2040s, the absolute mass scale measured kinematically should be at sub-100-meV precision. The neutrino-mass mechanism — Higgs-Yukawa Dirac, seesaw Majorana, or something more exotic — will be settled experimentally.

Until then, the relationship between the Higgs and the neutrino remains the most awkward chapter in the Standard Model. Every other fermion gets its mass from the Higgs; the neutrino does so only with a parameter that requires explanation. The explanation, when it arrives, will likely tell us something fundamental about physics at a much higher energy scale than the LHC can probe.

The 2012 Higgs discovery completed the Standard Model in one direction. It also exposed, more sharply than ever, the open question on the other side.