Tune lightest mass and splittings to explore spectra. See eigenvalues, sums, and effective observables instantly. Use it for lectures, labs, reports, and checks daily.
| Ordering | m0 (eV) | m1 (eV) | m2 (eV) | m3 (eV) | Σm (eV) | mβ (eV) | mββ min (eV) | mββ max (eV) |
|---|---|---|---|---|---|---|---|---|
| Normal | 0.010 | 0.01 | 0.0132 | 0.0512 | 0.0744 | 0.0133 | 0.0018 | 0.0119 |
| Inverted | 0.010 | 0.0512 | 0.0519 | 0.01 | 0.113 | 0.0508 | 0.0192 | 0.0505 |
The calculator starts from the lightest mass m0 and the two independent splittings. Use Δm21² for the solar scale and |Δm3ℓ²| for the atmospheric scale. In normal ordering, m1 is the lightest; in inverted ordering, m3 is the lightest. For small m0, the spectrum is strongly hierarchical; for larger m0, it becomes quasi-degenerate.
With fixed splittings, increasing m0 lifts all three eigenvalues while preserving their squared differences. Normal ordering typically yields m3 separated above m1 and m2. In inverted ordering, m1 and m2 cluster above m3. Comparing the plotted bars helps communicate this signature in lectures and reports.
The sum Σm = m1 + m2 + m3 is a compact diagnostic for cosmological bounds. When m0 is near zero, Σm approaches a minimum set by the splittings. As m0 grows, Σm increases nearly linearly, so sensitivity improves for quasi-degenerate spectra. Exporting CSV is useful for scanning m0 grids.
The effective mass mβ weights each eigenvalue by |Uei|² and uses squared masses. θ12 and θ13 control these electron-flavor weights and therefore shift mβ even at fixed splittings. The plot overlays mβ as a horizontal guide, helping connect oscillation inputs to kinematic searches.
The calculator reports an mββ interval rather than a single value. The maximum occurs when all contributions add coherently. The minimum can be suppressed by destructive interference and may reach zero when triangle conditions are satisfied. This range is a practical way to discuss phase uncertainty without choosing specific Majorana phases.
Start by reproducing your preferred benchmark inputs and verify the derived splittings. Next, sweep m0 over a physically relevant range and compare ordering behavior in the graph. Save several scenarios as PDF summaries for documentation. For publications, keep units explicit and report both ordering assumptions alongside Σm, mβ, and the mββ range.
It refers to whether m1 is lightest (normal ordering) or m3 is lightest (inverted ordering), given the measured mass-squared splittings from oscillations.
By convention, Δm21² = m2² − m1² is defined with m2 above m1, so it is taken as positive when reporting solar-scale oscillation results.
It is the magnitude of the atmospheric-scale splitting between m3 and the lighter pair. The sign depends on ordering, so this tool uses the absolute value as input.
Unknown Majorana phases can make the three contributions add or cancel. The calculator reports the physically allowed minimum and maximum without fixing those phases.
No. It explores consequences of each ordering for a chosen parameter set. Determining ordering requires experimental inputs beyond the parameters entered here.
The lightest mass m0 dominates Σm once it exceeds the scale set by the splittings. The splittings mainly set the minimum Σm when m0 is close to zero.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.