The CKM Quark Mixing Matrix from Foam Cell Geometry

Key Points

• The aim is to derive certain CKM quark mixing matrix parameters from the geometry of truncated octahedrons.
• Derived two Wolfenstein parameters from truncated octahedron geometry.
• Calculated the Cabibbo angle and parameter A using geometric relationships.
• Established a connection between quark mass ratios and geometric angles.
• Cabibbo angle θ_C calculated as sin(π/14) matched closely with the observed value.
• Parameter A resulted in a value of 0.8128, also close to the observed measurement.
• A new connection related the mass ratio m_d/m_s to sin²(π/14) with high accuracy.