Dark matter glueball candidate from a G(2)--E6--E7 exceptional grand unified theory: G-parity, spin, mass and stability
Abstract
We determine the gauge-invariant identity, mass scale and ultraviolet stability of the dark matter candidate arising from G(2)→ SU(3)C in the exceptional G(2) − E6 − E7 construction. The broken G(2) sector contains odd 1+− and 0−− channels, whereas the scalar 0++∼ XX̅ state is even and unprotected. For mX≃5.7×1013 GeV, weak-binding reference masses are M2X≃1.14×1014 GeV and M3X≃1.71×1014 GeV, while the exact pole masses remain nonperturbative. Gauge-invariant Fröhlich--Morchio--Strocchi (FMS) operators, Hall--Post bounds, Y-junction arguments and the pure-SU(3) glue spectrum favor 1+− in their controlled regimes without excluding a deeply bound 0−− state. We then test whether this dark grading survives the full chiral exceptional embedding. An on-shell analysis finds no independent purely dark odd operator through dimension seven: the first nonvanishing basis appears at dimension nine. So the minimal one-copy exceptional embedding does not provide an exact ultraviolet dark G-parity. Moving the dark Higgs from the common 1463H parent to a separated 1539H removes the scalar-parent obstruction and the relevant dimension-nine exceptional parents vanish on the selected pure-dark component in the undressed limit. A genuinely gauged or geometric ℤ2,D would therefore leave a bosonic parity after dark Higgsing. Its extension to the mirror-free theory nevertheless fails because the required G(2) conjugation also conjugates color, 3C↔3̅C. The remaining obstruction to exact dark matter stability is therefore ultraviolet and chiral, rather than low-energy or purely scalar.
Related
- Decipher the nature of glueball candidate X(2370)
- Unified Spectral, Dynamical, and Correlation Signatures of an Exceptional Point in Cavity Optomechanics
- Unified light-matter metric of molecular and nanophotonic chirality
- Unified description of longitudinal and transverse parton dynamics in cold nuclear matter
- Single Dirac Fermions on a Lattice: A Unified View of Chiral and Parity Anomalies in Condensed Matter
BibTeX
@misc{masi2026dark,
title = {{Dark matter glueball candidate from a $G(2)$--$E_6$--$E_7$ exceptional grand unified theory: $G$-parity, spin, mass and stability}},
author = {Nicolo' Masi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04296},
eprint = {2609.04296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04296},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dark matter glueball candidate from a G(2)--E_6--E_7 exceptional grand unified theory: G-parity, spin, mass and stability
AU - Nicolo' Masi
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04296
UR - https://arxiv.org/abs/2609.04296
AB - We determine the gauge-invariant identity, mass scale and ultraviolet stability of the dark matter candidate arising from G(2)→ SU(3)_C in the exceptional G(2) − E_6 − E_7 construction. The broken G(2) sector contains odd 1^+− and 0^−− channels, whereas the scalar 0^++∼ XX̅ state is even and unprotected. For m_X≃5.7×10^13 GeV, weak-binding reference masses are M_2X≃1.14×10^14 GeV and M_3X≃1.71×10^14 GeV, while the exact pole masses remain nonperturbative. Gauge-invariant Fröhlich--Morchio--Strocchi (FMS) operators, Hall--Post bounds, Y-junction arguments and the pure-SU(3) glue spectrum favor 1^+− in their controlled regimes without excluding a deeply bound 0^−− state. We then test whether this dark grading survives the full chiral exceptional embedding. An on-shell analysis finds no independent purely dark odd operator through dimension seven: the first nonvanishing basis appears at dimension nine. So the minimal one-copy exceptional embedding does not provide an exact ultraviolet dark G-parity. Moving the dark Higgs from the common 1463_H parent to a separated 1539_H removes the scalar-parent obstruction and the relevant dimension-nine exceptional parents vanish on the selected pure-dark component in the undressed limit. A genuinely gauged or geometric ℤ_2,D would therefore leave a bosonic parity after dark Higgsing. Its extension to the mirror-free theory nevertheless fails because the required G(2) conjugation also conjugates color, 3_C↔3̅_C. The remaining obstruction to exact dark matter stability is therefore ultraviolet and chiral, rather than low-energy or purely scalar.
ER -