The neutrino sector at eleven parameters: the one mass the compensator writes
Abstract
In the unified theory at eleven parameters every mass is a pure number times the compensator ϕ, the pure-gauge field that sets Newton's constant. Every fermion takes its mass through the Higgs, except one. A right-handed neutrino is a gauge singlet, and a singlet pair has no Yukawa coupling to the Higgs; a bare Majorana mass has Weyl weight +1 and is forbidden; the only Weyl-invariant mass term of dimension four is √ 8π yM ϕ νRνR, of weight zero. The compensator therefore writes exactly one fermion mass, MR = yM MP , and the see-saw becomes a relation between two pure numbers, y 2 D /yM = 2mν MP /v 2 = 2 × 10 4 . This letter gathers what the series says of the sector and adds what it did not say. The Majorana term is allowed by the action. The first-order condition of the spectral geometry, which the theory does not impose, requires it at a value it leaves free. The right-handed neutrino is also the one body that could sit on the gravitational Kerr line, at yM = 1/ √ 2, outside the see-saw. The naturalness of the located hierarchy makes a choice of scale, not a number. Either the two lighter states lie below 10 8 GeV and the asymmetry is made resonantly or by oscillations. Or the see-saw is high, leptogenesis thermal below the reheating temperature of 2 × 10 13 GeV, and the hierarchy tuned in this sector alone. The theory's own suppression, read at dimension one, gives the benchmark MR = √ ζ MP = m h / √ 2 = 88.5 GeV, the Higgs mass parameter. Its see-saw mixing θ 2 = mν /MR = 6 × 10 -13 is far below any foreseen reach. The Dirac Yukawas are located, with a frame. The neutrino mass eigenstates are the tribimaximal frame of the generation space to within nine degrees, and the quark and lepton angles are approximately complementary. The keV state that the theory permits as dark matter stands only with two GeV states beside it to source its asymmetry. The cosmological collider could in principle place one see-saw state, of ten TeV, whose Dirac mass during inflation is the Hubble rate, next to the electron's own. What the instruments can hear is stated with its kind. The scale, the ordering and the phase are located. Neutrinoless double-beta decay establishes yM ̸ = 0 by a detection in either ordering; a null result is informative only in the inverted one. The relativistic species are 3.044 on a condition that nucleosynthesis makes a bound. The cosmological sum, with w = -1 an identity, has no relief from an evolving dark energy, and the present data already press it against the oscillation floor. The sector is twenty-eight bits, sixteen for the angles and the phase and twelve for the mass splittings, and every one of them is the world's.
Related
- Analogue models of gravity at eleven parameters
- The concepts at eleven parameters: the primary, the secondary and the optional, their hierarchy and their graph
- The eleven parameters of a body: the gauged Weyl algebra, its exact identities and the Palatini form of Higgs inflation
- Feynman diagrams of the unified theory at eleven parameters
- A New Probe of Strongly-Interacting Dark Sector using Neutrino Telescopes
BibTeX
@misc{reynaud2026neutrino,
title = {{The neutrino sector at eleven parameters: the one mass the compensator writes}},
author = {Patrick B. Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05765512v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The neutrino sector at eleven parameters: the one mass the compensator writes
AU - Patrick B. Reynaud
PY - 2026
DA - 2026/09/26
PB - HAL
UR - https://hal.science/hal-05765512v2
AB - In the unified theory at eleven parameters every mass is a pure number times the compensator ϕ, the pure-gauge field that sets Newton's constant. Every fermion takes its mass through the Higgs, except one. A right-handed neutrino is a gauge singlet, and a singlet pair has no Yukawa coupling to the Higgs; a bare Majorana mass has Weyl weight +1 and is forbidden; the only Weyl-invariant mass term of dimension four is √ 8π yM ϕ νRνR, of weight zero. The compensator therefore writes exactly one fermion mass, MR = yM MP , and the see-saw becomes a relation between two pure numbers, y 2 D /yM = 2mν MP /v 2 = 2 × 10 4 . This letter gathers what the series says of the sector and adds what it did not say. The Majorana term is allowed by the action. The first-order condition of the spectral geometry, which the theory does not impose, requires it at a value it leaves free. The right-handed neutrino is also the one body that could sit on the gravitational Kerr line, at yM = 1/ √ 2, outside the see-saw. The naturalness of the located hierarchy makes a choice of scale, not a number. Either the two lighter states lie below 10 8 GeV and the asymmetry is made resonantly or by oscillations. Or the see-saw is high, leptogenesis thermal below the reheating temperature of 2 × 10 13 GeV, and the hierarchy tuned in this sector alone. The theory's own suppression, read at dimension one, gives the benchmark MR = √ ζ MP = m h / √ 2 = 88.5 GeV, the Higgs mass parameter. Its see-saw mixing θ 2 = mν /MR = 6 × 10 -13 is far below any foreseen reach. The Dirac Yukawas are located, with a frame. The neutrino mass eigenstates are the tribimaximal frame of the generation space to within nine degrees, and the quark and lepton angles are approximately complementary. The keV state that the theory permits as dark matter stands only with two GeV states beside it to source its asymmetry. The cosmological collider could in principle place one see-saw state, of ten TeV, whose Dirac mass during inflation is the Hubble rate, next to the electron's own. What the instruments can hear is stated with its kind. The scale, the ordering and the phase are located. Neutrinoless double-beta decay establishes yM ̸ = 0 by a detection in either ordering; a null result is informative only in the inverted one. The relativistic species are 3.044 on a condition that nucleosynthesis makes a bound. The cosmological sum, with w = -1 an identity, has no relief from an evolving dark energy, and the present data already press it against the oscillation floor. The sector is twenty-eight bits, sixteen for the angles and the phase and twelve for the mass splittings, and every one of them is the world's.
ER -