What does this research mean for the field?

The in-medium mass of the η′ meson inside ¹²C is reduced by 117 MeV to 840.6 MeV due to topological screening, a prediction derived from the G₂ framework that is consistent with experimental observations. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to derive the in-medium mass of the η′ meson within the context of ¹²C nuclear matter.

June 8, 2026Open Access

Paper CXC: (corrected) η′ In-Medium Mass from G₂ Topological Screening and Klein Quartic: Winding Number Formula and ¹²C Prediction

Key Points

The aim is to derive the in-medium mass of the η′ meson within the context of ¹²C nuclear matter.
Utilized the G₂ framework to connect winding-number formulas and nuclear matter interactions.
Calculated topological susceptibility and quark condensate effects on the η′ meson mass.
Employed geometric principles from the Klein Quartic related to nuclear density.
Predicted in-medium mass of η′ in ¹²C to be 840.6 MeV with a change of Δm_{η′} = -117 MeV.
Established a geometric connection between Klein Quartic parameters and nuclear structure.
Correlates findings with observed η′ mesic nucleus in ¹²C.

Abstract

We derive the in-medium mass of the η′ meson inside ¹²C from two connected results in the G₂ = Aut () framework. First, the η′ vacuum mass is reproduced by an exact winding-number 𝕆 formula: m⏖′ = Nw × c / Lₘax (KQ), where Lₘax = 3 × spine = 1. 7634 (in hyperbolic ℏ units) is the longest geodesic path between two pairs of hyperbolic pants in the Klein Quartic, and Nw = 8. 44 is the topological winding number. This gives m⏖′ = 957. 8 MeV at ΛQCD = 200 MeV. Second, in nuclear matter the topological susceptibility χₜop is screened by the quark condensate modification (Drukarev-Levin-Cohen): χₜop (ρ) /χₜop (0) = 1 − σNρ/ (mπ²fπ²) ². At the effective nuclear density for ¹²C (ρₑff ≈ 0. 5ρ₀), we predict m⏖′ (ρ) = 840. 6 MeV, giving Δm⏖′ = −117 MeV, consistent with the observation by Sekiya et al. (UOsaka, 2025-2026) of the η′ mesic nucleus in ¹²C. The geometric connection to the Woods- Saxon nuclear density (Paper CXCI) is established: the same Klein Quartic inradius a = 0. 5453 controls both the nuclear surface diffuseness and the in-medium topological screening scale. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.

Paper CXC: (corrected) η′ In-Medium Mass from G₂ Topological Screening and Klein Quartic: Winding Number Formula and ¹²C Prediction

Key Points

Abstract

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