What question did this study set out to answer?

To derive and analyze the spectrum of mesons within an octonionic framework, exploring quark-antiquark interactions.

June 8, 2026Open Access

Paper LVIII: Mesons as Cross-Sector Fano Bound States: Quark-Antiquark Binding from Rare H+/H−Node Interactions, QCD Flux Tubes as Auxetic Lattice Bridges, and Con-

Key Points

To derive and analyze the spectrum of mesons within an octonionic framework, exploring quark-antiquark interactions.
Examine mesons as cross-sector Fano bound states using the brane-bulk octonionic model.
Analyze spatial and color winding inversion of antiquarks in the Fano plane.
Derive relationships between meson characteristics and symmetry breaking.
Predicted pion mass satisfies the Gell-Mann-Oakes-Renner relation.
Kaon mass prediction incorporates strange quark properties accurately.
Five new predictions related to meson characteristics are outlined.

Abstract

We derive the meson spectrum from the brane-bulk octonionic framework. A meson is a cross-sector Fano bound state: a quark focal zone anchored at an H+ spatial node e1, e2, e3 is transiently bridged to an antiquark focal zone anchored at an H−colour node e4, e5, e6 through one of the three cross-sector lines of the Fano plane e1, e2, e4, e2, e3, e5, or e3, e1, e6 which already encode this H+/H−mixing in the Fano multiplication table. The antiquark is dened as a focal zone with simultaneous inversion of both its spatial winding (ei →−ei, i = 1, 2, 3) and its colour winding (ej →−ej, j = 4, 5, 6) this is the octonionic statement of CPT conjugation. The bridging occurs as a rare deep bulk excursion in the Feynman path integral (Paper L): the focal zone briey crosses the e7 equatorial horizon into the H−sector, creating a transient Fano lattice deformation that is the QCD ux tube. The ux tube tension σ ≈ (440 MeV) 2 emerges as the energy per unit length of this Fano lattice bridge, which the auxetic shape memory (Paper LIV) resists with innite shear modulus, producing a linear conning potential V (r) = σr. String breaking meson pair production occurs when the bridge energy exceeds twice the lightest quark mass, at rbreak ≈ 2mq/σ ≈1 fm. The pseudoscalar/vector meson splitting arises from whether the quark and antiquark windings are in phase (vector, Wi ≫1, elastic T2* mode, short-lived resonance) or anti-phase (pseudoscalar, Wi ∼1, T2 dephasing mode, long-lived). The pion emerges as the Goldstone boson of Z3 chiral symmetry breaking from Paper LVI; its mass satises the Gell-MannOakesRenner relation derived directly from the δM/M tilt. The kaon incorporates the generation-2 strange quark from the Z3 cyclic ordering, giving mK ≈ p ms/md mπ as a zero-free-parameter prediction. Five new predictions follow (Predictions 101105). 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.

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