Type-I Seesaw Heavy Neutrino Mass Calculator
Understanding the Type-I Seesaw Mass Scale
This seesaw heavy neutrino mass calculator connects a chosen light neutrino mass and Yukawa coupling to the heavy Majorana scale that would generate them in the simplest type-I seesaw picture. It gives a fast way to see how a tiny observed neutrino mass can arise from a much heavier state rather than from an exceptionally small fundamental mass term.
That relationship is useful because it ties low-energy neutrino data to the scale of new physics. With a coupling of order one, the inferred heavy mass can sit far above collider energies; with a much smaller coupling, the same light mass can be produced by a far lower Majorana scale. The calculator is therefore best read as a bridge between toy-model intuition and more elaborate neutrino model building.
At the level of a one-flavor benchmark, the calculator assumes a Dirac mass term mD = y v and a Majorana mass term for the right-handed neutrino. The matrix below captures the simplest mixing between the active neutrino and a heavy sterile state, which is enough to show how the seesaw suppresses the light eigenvalue.
Diagonalizing this matrix produces one light eigenstate and one heavy eigenstate. In the hierarchy M ≫ mD, the light mass reduces to mν ≈ mD2/M, and the heavy eigenvalue is essentially M. Substituting mD = yv with v ≈ 174 GeV gives the compact relation used by the calculator.
and the heavy mass is essentially M. The smallness of mν thus results from the suppression by the heavy scale. Expressing mD in terms of the Yukawa coupling y and the electroweak Higgs vacuum expectation value v ≈ 174 GeV gives the celebrated relation
Introduction to the Type-I Seesaw Scale
This section explains what the seesaw calculator is estimating and how to read the output. You provide a light neutrino mass in eV and a Yukawa coupling, and the page returns both the corresponding Dirac mass mD = yv and the heavy Majorana mass scale M in GeV.
Because the seesaw relation spans many decades in energy, the same low-energy mass can map to wildly different ultraviolet pictures. A coupling near one tends to imply a very large heavy scale, while a much smaller Yukawa coupling can bring M down by many orders of magnitude. That is why the calculator is handy for comparing benchmark models, checking lecture notes, or sanity-checking an estimate from a paper.
The calculator uses the absolute value of the Yukawa coupling when it computes the masses. In this one-parameter estimate, the sign of y does not change the size of mD, so the result is governed by magnitude rather than phase. Read the output as a simplified seesaw benchmark, not as a full neutrino-flavor reconstruction.
How to Use the Seesaw Neutrino Calculator
Using this seesaw calculator is straightforward: enter a positive light neutrino mass mν in electronvolts and a numeric Yukawa coupling y. The page then computes the Dirac mass in GeV and the heavy Majorana scale implied by the type-I seesaw approximation.
After you click the compute button, the result appears in scientific notation because the heavy scale can be enormous. If the inputs are valid, the copy button becomes available so you can save the output for notes, homework, or model comparisons.
A practical way to think about the seesaw inputs is to treat mν as the low-energy target and y as the knob that sets the Dirac mass mD. Increasing y while holding mν fixed pushes M upward quadratically, while increasing mν with y fixed lowers M.
Keep the units straight when interpreting the result. The input mass is in eV, but the outputs are shown in GeV, and the calculator handles the conversion internally using 1 eV = 10−9 GeV. That conversion matters because the formula combines a tiny neutrino mass with electroweak-scale numbers.
Formula for the Type-I Seesaw Mass
This calculator uses the standard one-flavor type-I seesaw approximation. Start with the Dirac mass relation mD = yv, where v ≈ 174 GeV in the convention used here, and assume the heavy Majorana mass is much larger than mD.
In that limit, the light neutrino mass is approximately mν ≈ mD2/M. Solving this expression for M gives the formula implemented on the page, so the heavy scale grows with the square of the Yukawa coupling and the square of the Higgs vacuum expectation value, and falls as the observed neutrino mass gets larger.
The calculator also reports the Dirac mass because it helps you see which part of the model is doing the work. If y is near one, mD sits near the electroweak scale; if y is tiny, the Dirac mass may be far smaller, and the heavy scale can still remain very large because of the inverse dependence on mν.
The classification labels are only broad guides. Collider-scale, intermediate, and GUT-scale here are descriptive buckets for the inferred Majorana mass, not hard theoretical boundaries or experimental guarantees.
Example: a 0.05 eV Neutrino with y = 1
A benchmark seesaw example makes the scale separation especially clear. If you choose mν = 0.05 eV and y = 1, the Dirac mass becomes about 174 GeV and the heavy scale rises to roughly 6.0 × 1014 GeV, which the calculator labels GUT-scale.
That is the classic seesaw pattern: a neutrino mass that is tiny on laboratory scales can point to a Majorana state far beyond direct experimental reach. It is one reason the seesaw mechanism is often discussed alongside grand unification and other high-scale ideas.
If you keep mν = 0.1 eV but reduce the coupling to y = 10−3, the Dirac mass drops to 0.174 GeV and the heavy scale falls to about 3.0 × 108 GeV. Because M depends on y2, decreasing the coupling by a factor of 1000 reduces the inferred scale by a factor of one million.
The table below shows the same benchmark outputs in the format used by the calculator:
| mν (eV) | y | mD (GeV) | M (GeV) | Classification |
|---|---|---|---|---|
| 0.05 | 1 | 174 | 6.0×1014 | GUT-scale |
| 0.1 | 10−3 | 0.174 | 3.0×108 | Intermediate |
Examples like these help you see how strongly the heavy scale depends on the Yukawa coupling. They also show why different neutrino models can reproduce the same low-energy mass while pointing to very different ultraviolet physics.
Limitations and Assumptions for Seesaw Estimates
This seesaw calculator deliberately uses the simplest possible one-flavor estimate, so it leaves out many ingredients of realistic neutrino physics. Real models usually involve three active flavors, mixing angles, mass splittings, CP-violating phases, and possibly more than one heavy right-handed neutrino, which turns the simple number formula into a matrix problem.
The approximation mν ≈ mD2/M assumes a strong hierarchy with M much larger than mD. If that hierarchy is weak, the shortcut becomes less accurate and a full diagonalization of the mass matrix is needed. The page also does not include renormalization-group running, threshold effects, flavor textures, Casas-Ibarra parameterizations, or model-specific bounds from collider searches, cosmology, or neutrinoless double beta decay.
Another caveat is interpretive. The classification labels are only a rough guide to where the inferred heavy mass sits on an energy map, and they do not tell you whether a particle would actually be observable. A collider-scale label does not guarantee a detectable signal, because production rates and mixing angles matter, and a GUT-scale label does not prove grand unification.
Even with those limits, the calculator remains useful as a transparent benchmark for the seesaw scale. It quickly shows how a tiny neutrino mass can arise from a much larger Majorana mass, which makes it a handy teaching aid and a fast consistency check for toy models.
Physical Interpretation of the Heavy Neutrino Scale
In the seesaw picture, the heavy neutrino mass is the lever that makes the light neutrino small. As the heavy scale rises, the light mass falls, which is why the mechanism is often described as a balancing act between very different energy regimes. In effective field theory language, integrating out the heavy state generates the dimension-five Weinberg operator, and electroweak symmetry breaking turns that operator into a neutrino mass.
That connection is part of what makes the seesaw mechanism so influential in particle physics and cosmology. The same heavy Majorana state can be discussed in the context of lepton-number violation, the matter-antimatter asymmetry of the universe, and the structure of physics beyond the Standard Model. If the heavy neutrinos decay out of equilibrium with CP violation, they can help generate a lepton asymmetry that sphalerons later convert into a baryon asymmetry.
For that reason, the number returned by the calculator is best understood as a scale estimate rather than a discovery claim. It tells you where the heavy state would need to live for the simple seesaw relation to match the light mass you entered, and that makes it a useful starting point for more detailed neutrino studies.