Neutrino Mass Ordering from Soliton Topology

Abstract

The neutrino mass ordering — normal ($m_1 < m_2 < m_3$) versus inverted ($m_3 < m_1 < m_2$) — is one of the key open questions in particle physics. The topological soliton framework, developed in Paper IV, predicts normal ordering as a topological necessity: neutrinos are $B = 1$ Skyrmions in $S^3$, organized in a 2+1 structure where the $j = 1/2$ doublet $(\nu_1, \nu_2)$ is the ground state and $\nu_3$ is a Grassmannian singlet excitation. This structure requires the doublet to be lighter than the singlet, enforcing $m_3 > m_2 > m_1$ — normal ordering. The predicted mass sum is $\Sigma m_\nu = 62 \pm 5$ meV, derived from a seesaw relation $m_\nu \sim c \cdot m_e^2/M_W$ with $c = \eta^2$ (the gauge-scalar overlap parameter). We compare this prediction quantitatively with JUNO (reactor neutrino oscillations, mass ordering by $\sim 2028$), DUNE (long-baseline oscillations with matter effects, $\sim 2030$), and cosmological constraints from Planck, DESI BAO, and future CMB-S4. The prediction is falsifiable: if JUNO finds inverted ordering ($m_3 < m_1$), or if cosmological surveys measure $\Sigma m_\nu < 57$ meV or $> 67$ meV at high confidence, the current form of the soliton framework is excluded. This paper establishes the neutrino mass ordering as the most immediate experimental test of the topological soliton programme.

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Key results include:

• The soliton framework predicts normal ordering ($m_1 < m_2 < m_3$) with $\Sigma m_\nu = 62 \pm 5$ meV
• Normal ordering is a topological necessity: the 2+1 Skyrmion structure (doublet + singlet) requires $\Delta m^2_{31} > 0$
• JUNO will determine the mass ordering by $\sim 2028$ at $3$--$4\sigma$ — a near-term falsifiable prediction
• DUNE will independently confirm via matter effects in long-baseline oscillations by $\sim 2030$
• Cosmological constraints (Planck + DESI + CMB-S4) will probe $\Sigma m_\nu$ down to $\sim 20$ meV by $\sim 2030$
• If inverted ordering is found, the soliton framework is falsified in its current form